#### Sample records for non-linear dynamics analysis

1. Employment of CB models for non-linear dynamic analysis

NASA Technical Reports Server (NTRS)

Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

1990-01-01

The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

2. Non-linear dynamic analysis of beams with variable stiffness

Katsikadelis, J. T.; Tsiatas, G. C.

2004-03-01

In this paper the analog equation method (AEM), a BEM-based method, is employed to the non-linear dynamic analysis of a Bernoulli-Euler beam with variable stiffness undergoing large deflections, under general boundary conditions which maybe non-linear. As the cross-sectional properties of the beam vary along its axis, the coefficients of the differential equations governing the dynamic equilibrium of the beam are variable. The formulation is in terms of the displacements. The governing equations are derived in both deformed and undeformed configuration and the deviations of the two approaches are studied. Using the concept of the analog equation, the two coupled non-linear hyperbolic differential equations with variable coefficients are replaced by two uncoupled linear ones pertaining to the axial and transverse deformation of a substitute beam with unit axial and bending stiffness, respectively, under fictitious time-dependent load distributions. A significant advantage of this method is that the time history of the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. Beams with constant and varying stiffness are analyzed under various boundary conditions and loadings to illustrate the merits of the method as well as its applicability, efficiency and accuracy.

3. DYNAMIC NON LINEAR IMPACT ANALYSIS OF FUEL CASK CONTAINMENT VESSELS

SciTech Connect

Leduc, D

2008-06-10

4. Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

5. Ammonia quantitative analysis model based on miniaturized Al ionization gas sensor and non-linear bistable dynamic model

PubMed Central

Ma, Rongfei

2015-01-01

In this paper, ammonia quantitative analysis based on miniaturized Al ionization gas sensor and non-linear bistable dynamic model was proposed. Al plate anodic gas-ionization sensor was used to obtain the current-voltage (I-V) data. Measurement data was processed by non-linear bistable dynamics model. Results showed that the proposed method quantitatively determined ammonia concentrations. PMID:25975362

6. Non-linear dynamic analysis of a flexible rotor supported on porous oil journal bearings

Laha, S. K.; Kakoty, S. K.

2011-03-01

In the present paper, the non-linear dynamic analysis of a flexible rotor with a rigid disk under unbalance excitation mounted on porous oil journal bearings at the two ends is carried out. The system equation of motion is obtained by finite element formulation of Timoshenko beam and the disk. The non-linear oil-film forces are calculated from the solution of the modified Reynolds equation simultaneously with Darcy's equation. The system equation of motion is then solved by the Wilson- θ method. Bifurcation diagrams, Poincaré maps, time response, journal trajectories, FFT-spectrum, etc. are obtained to study the non-linear dynamics of the rotor-bearing system. The effect of various non-dimensional rotor-bearing parameters on the bifurcation characteristics of the system is studied. It is shown that the system undergoes Hopf bifurcation as the speed increases. Further, slenderness ratio, material properties of the rotor, ratio of disk mass to shaft mass and permeability of the porous bush are shown to have profound effect on the bifurcation characteristics of the rotor-bearing system.

7. Non-Linear Dynamics Tools for the Motion Analysis and Condition Monitoring of Robot Joints

Trendafilova, I.; van Brussel, H.

2001-11-01

Time series from non-damaged and three types of damaged robot joints are considered and analysed from the viewpoint of non-linear dynamics. The embedding spaces for the four types of signals are recovered. The application of surrogate data tests is used to prove the presence of non-linearities in the joints. The results suggest a rise in unstable behaviour due to the introduction of backlash in robot joints. The chaotic behaviour gets stronger with the increase of the backlash extent. This is confirmed by the increase of the embedding dimension as well as by the increase of the Lyapunov exponents and the correlation dimension with the backlash increase. A straightforward method for condition monitoring using non-linear dynamics characteristics, based on a classification procedure, is suggested.

8. Dynamic analysis of space-related linear and non-linear structures

NASA Technical Reports Server (NTRS)

Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.

1990-01-01

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

9. Dynamic analysis of space-related linear and non-linear structures

NASA Technical Reports Server (NTRS)

Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.

1990-01-01

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic control system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

10. A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

Özgüven, H. N.

1991-03-01

A six-degree-of-freedom non-linear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the non-linear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the "static transmission error method" developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.

11. Study on Brain Dynamics by Non Linear Analysis of Music Induced EEG Signals

Banerjee, Archi; Sanyal, Shankha; Patranabis, Anirban; Banerjee, Kaushik; Guhathakurta, Tarit; Sengupta, Ranjan; Ghosh, Dipak; Ghose, Partha

2016-02-01

Music has been proven to be a valuable tool for the understanding of human cognition, human emotion, and their underlying brain mechanisms. The objective of this study is to analyze the effect of Hindustani music on brain activity during normal relaxing conditions using electroencephalography (EEG). Ten male healthy subjects without special musical education participated in the study. EEG signals were acquired at the frontal (F3/F4) lobes of the brain while listening to music at three experimental conditions (rest, with music and without music). Frequency analysis was done for the alpha, theta and gamma brain rhythms. The finding shows that arousal based activities were enhanced while listening to Hindustani music of contrasting emotions (romantic/sorrow) for all the subjects in case of alpha frequency bands while no significant changes were observed in gamma and theta frequency ranges. It has been observed that when the music stimulus is removed, arousal activities as evident from alpha brain rhythms remain for some time, showing residual arousal. This is analogous to the conventional 'Hysteresis' loop where the system retains some 'memory' of the former state. This is corroborated in the non linear analysis (Detrended Fluctuation Analysis) of the alpha rhythms as manifested in values of fractal dimension. After an input of music conveying contrast emotions, withdrawal of music shows more retention as evidenced by the values of fractal dimension.

12. Non-Linear Analysis Indicates Chaotic Dynamics and Reduced Resilience in Model-Based Daphnia Populations Exposed to Environmental Stress

PubMed Central

Ottermanns, Richard; Szonn, Kerstin; Preuß, Thomas G.; Roß-Nickoll, Martina

2014-01-01

In this study we present evidence that anthropogenic stressors can reduce the resilience of age-structured populations. Enhancement of disturbance in a model-based Daphnia population lead to a repression of chaotic population dynamics at the same time increasing the degree of synchrony between the population's age classes. Based on the theory of chaos-mediated survival an increased risk of extinction was revealed for this population exposed to high concentrations of a chemical stressor. The Lyapunov coefficient was supposed to be a useful indicator to detect disturbance thresholds leading to alterations in population dynamics. One possible explanation could be a discrete change in attractor orientation due to external disturbance. The statistical analysis of Lyapunov coefficient distribution is proposed as a methodology to test for significant non-linear effects of general disturbance on populations. Although many new questions arose, this study forms a theoretical basis for a dynamical definition of population recovery. PMID:24809537

13. An edge-based smoothed triangle element for non-linear explicit dynamic analysis of shells

Zheng, Gang; Cui, Xiangyang; Li, Guangyao; Wu, Suzhen

2011-07-01

The paper presents an edge-based smoothed triangular element (EST) for nonlinear analysis of shell structures using an explicit dynamic formulation. In order to improve the accuracy and the convergence of the shell element without additional parameters, the gradient smoothing operation is performed to the strain rates in the smoothing domains associated with the edges of triangular elements. An edge coordinate system is defined local on the edges of the triangular element for the strain smoothing operation. The material nonlinearities for the dynamic solution are treated by using the updated Lagrangian description and an elastic-plastic constitutive law. The shear strains in the element formulation are approximated using the discrete shear gap method to mitigate the shear locking, and this element can be applicable for both thin shells and thick shells. Numerical results for elastic and elastic-plastic problems show the effectiveness and efficiency of the proposed shell element.

14. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

SciTech Connect

Speck, Thomas; Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut

2015-06-14

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.

15. Non-Linear Dynamics of Saturn's Rings

Esposito, L. W.

2015-10-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Results of driven N-body systems by Stuart Robbins: Even unforced rings show large variations; Forcing triggers aggregation; Some limit cycles and phase lags seen, but not always as predicted by predator-prey model. Summary of Halo Results: A predatorprey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw'. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon

16. Non-Linear Dynamics of Saturn's Rings

Esposito, Larry W.

2015-04-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible Results of driven N-body systems by Stuart Robbins: Even unforced rings show large variations; Forcing triggers aggregation; Some limit cycles and phase lags seen, but not always as predicted by predator-prey model. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw'. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon

17. Non-linear dynamic analysis of geared systems. Final Report Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

Under driving conditions, a typical geared system may be subjected to large dynamic loads. Also, the vibration level of the geared system is directly related to the noise radiated from the gear box. The steady state dynamic behavior of the system is examined in order to design reliable and quiet transmissions. The scope is limited to a system containing a spur gear pair with backlash and periodically time varying mesh stiffness, and rolling element bearings with clearance type nonlinearities. The internal static transmission error at the gear mesh, which is of importance from high frequency noise and vibration control view point, is considered in the formulation in sinusoidal or periodic form. A dynamic finite element model of the linear time invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and forced vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solutions with the finite element model results. Using the reduced order formulations, a three degree of freedom dynamic model is developed which includes nonlinearities associated with radical clearances in the radial rolling element bearings, backlash between a spur gear pair and periodically varying gear mesh stiffness. As a limiting case, a single degree of freedom model of the spur gear pair with backlash is considered and mathematical conditions for tooth separation and back collision are defined. Both digital simulation technique and analytical models such as method of harmonic balance and the method of multiple scales were used to develop the steady state frequency response characteristics for various nonlinear and/or time varying cases.

18. Non-linear dynamic compensation system

NASA Technical Reports Server (NTRS)

Lin, Yu-Hwan (Inventor); Lurie, Boris J. (Inventor)

1992-01-01

A non-linear dynamic compensation subsystem is added in the feedback loop of a high precision optical mirror positioning control system to smoothly alter the control system response bandwidth from a relatively wide response bandwidth optimized for speed of control system response to a bandwidth sufficiently narrow to reduce position errors resulting from the quantization noise inherent in the inductosyn used to measure mirror position. The non-linear dynamic compensation system includes a limiter for limiting the error signal within preselected limits, a compensator for modifying the limiter output to achieve the reduced bandwidth response, and an adder for combining the modified error signal with the difference between the limited and unlimited error signals. The adder output is applied to control system motor so that the system response is optimized for accuracy when the error signal is within the preselected limits, optimized for speed of response when the error signal is substantially beyond the preselected limits and smoothly varied therebetween as the error signal approaches the preselected limits.

19. Non-linear dynamics in parkinsonism.

PubMed

Darbin, Olivier; Adams, Elizabeth; Martino, Anthony; Naritoku, Leslie; Dees, Daniel; Naritoku, Dean

2013-12-25

Over the last 30 years, the functions (and dysfunctions) of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the "rate hypothesis" and the "oscillatory hypothesis." In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively. More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e., parkinsonism, dyskinesia, healthy control) and are responsive to treatments (i.e., l-DOPA, deep brain stimulation). A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series) is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG), muscular activities (EMG), or kinetic of motor symptoms (tremor, gait) of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity, and hypokinesia.

20. Non-Linear Dynamics of Saturn's Rings

Esposito, L. W.

2015-12-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from

1. Perspective - Open problems in earth surface dynamics require innovative new methodologies from graph theory and non-linear analysis

Foufoula-Georgiou, Efi; Schwenk, Jon; Tejedor, Alejandro

2015-04-01

Are the dynamics of meandering rivers non-linear? What information does the shape of an oxbow lake carry about its forming process? How to characterize self-dissimilar landscapes carrying the signature of larger-scale geologic or tectonic controls? Do we have proper frameworks for quantifying the topology and dynamics of deltaic systems? What can the structural complexity of river networks (erosional and depositional) reveal about their vulnerability and response to change? Can the structure and dynamics of river networks reveal potential hotspots of geomorphic change? All of the above problems are at the heart of understanding landscape evolution, relating process to structure and form, and developing methodologies for inferring how a system might respond to future changes. We argue that a new surge of rigorous methodologies is needed to address these problems. The innovations introduced herein are: (1) gradual wavelet reconstruction for depicting threshold nonlinearity (due to cutoffs) versus inherent nonlinearity (due to underlying dynamics) in river meandering, (2) graph theory for studying the topology and dynamics of deltaic river networks and their response to change, and (3) Lagrangian approaches combined with topology and non-linear dynamics for inferring sediment-driven hotspots of geomorphic change.

2. Determining Stochasticity and Causality of Vegetation Dynamics in the Southwestern Amazon: Non-linear Time Series Analysis and Dynamic Factor Analysis of EVI2 Data

Klarenberg, G.

2015-12-01

Infrastructure projects such as road paving have proven to bring a variety of (mainly) socio-economic advantages to countries and populations. However, many studies have also highlighted the negative socio-economic and biophysical effects that these developments have at local, regional and even larger scales. The "MAP" area (Madre de Dios in Peru, Acre in Brazil, and Pando in Bolivia) is a biodiversity hotspot in the southwestern Amazon where sections of South America's Inter-Oceanic Highway were paved between 2006 and 2010. We are interested in vegetation dynamics in the area since it plays an important role in ecosystem functions and ecosystem services in socio-ecological systems: it provides information on productivity and structure of the forest. In preparation of more complex and mechanistic simulation of vegetation, non-linear time series analysis and Dynamic Factor Analysis (DFA) was conducted on Enhanced Vegetation Index (EVI) time series - which is a remote sensing product and provides information on vegetation dynamics as it detects chlorophyll (productivity) and structural change. Time series of 30 years for EVI2 (from MODIS and AVHRR) were obtained for 100 communities in the area. Through specific time series cluster analysis of the vegetation data, communities were clustered to facilitate data analysis and pattern recognition. The clustering is spatially consistent, and appears to be driven by median road paving progress - which is different for each cluster. Non-linear time series analysis (multivariate singular spectrum analysis, MSSA) separates common signals (or low-dimensional attractors) across clusters. Despite the presence of this deterministic structure though, time series behavior is mostly stochastic. Granger causality analysis between EVI2 and possible response variables indicates which variables (and with what lags) are to be included in DFA, resulting in unique Dynamic Factor Models for each cluster.

3. A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

NASA Technical Reports Server (NTRS)

Ozguven, H. Nevzat

1991-01-01

A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.

4. Characterising dynamic non-linearity in floating wind turbines

Lupton, R. C.

2014-12-01

Fully coupled aero-hydro-control-elastic codes are being developed to cope with the new modelling challenges presented by floating wind turbines, but there is also a place for more efficient methods of analysis. One option is linearisation and analysis in the frequency domain. For this to be an effective method, the non-linearities in the system must be well understood. The present study focusses on understanding the dynamic response of the rotor to the overall platform motion, as would arise from wave loading, by using a simple model of a floating wind turbine with a rigid tower and flexible rotor (represented by hinged rigid blades). First, an equation of motion of the blade is derived and an approximate solution for the blade response is found using the perturbation method. Secondly, the full non-linear solution is found by time- domain simulation. The response is found to be linear at lower platform pitching frequencies, becoming non-linear at higher frequencies, with the approximate solution giving good results for weakly non-linear behaviour. Higher rotor speeds have a stabilising effect on the response. In the context of typical floating turbine parameters, it is concluded that the blade flapwise response is likely to be linear.

5. Sensitivity analysis of the non-linear dynamic viscoplastic response of 2-d structures with respect to material parameters

NASA Technical Reports Server (NTRS)

Kulkarni, Makarand; Noor, Ahmed K.

1995-01-01

A computational procedure is presented for evaluating the sensitivity coefficients of the viscoplastic response of structures subjected to dynamic loading. A state of plane stress is assumed to exist in the structure, a velocity strain-Cauchy stress formulation is used, and the geometric non-linearities arising from large strains are incorporated. The Jaumann rate is used as a frame indifferent stress rate. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. The equations of motion emanating from a finite element semi-discretization are integrated using an explicit central difference scheme with an implicit stress update. The sensitivity coefficients are evaluated using a direct differentiation approach. Since the domain of integration is the current configuration, the sensitivity coefficients of the spatial derivatives of the shape functions must be included. Numerical results are presented for a thin plate with a central cutout subjected to an in-plane compressive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients, and spatial distributions at selected times are presented.

6. The analysis of non-linear dynamic behavior (including snap-through) of postbuckled plates by simple analytical solution

NASA Technical Reports Server (NTRS)

Ng, C. F.

1988-01-01

Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.

7. Linear Algebraic Method for Non-Linear Map Analysis

SciTech Connect

Yu,L.; Nash, B.

2009-05-04

We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.

8. Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

9. Size-dependent dynamic pull-in analysis of geometric non-linear micro-plates based on the modified couple stress theory

2017-02-01

This paper focuses on the size-dependent dynamic pull-in instability in rectangular micro-plates actuated by step-input DC voltage. The present model accounts for the effects of in-plane displacements and their non-classical higher-order boundary conditions, von Kármán geometric non-linearity, non-classical couple stress components and the inherent non-linearity of distributed electrostatic pressure on the micro-plate motion. The governing equations of motion, which are clearly derived using Hamilton's principle, are solved through a novel computationally very efficient Galerkin-based reduced order model (ROM) in which all higher-order non-classical boundary conditions are completely satisfied. The present findings are compared and successfully validated by available results in the literature as well as those obtained by three-dimensional finite element simulations carried out using COMSOL Multyphysics. A detailed parametric study is also conducted to illustrate the effects of in-plane displacements, plate aspect ratio, couple stress components and geometric non-linearity on the dynamic instability threshold of the system.

10. Non-Linear Dynamics of Saturn’s Rings

Esposito, Larry W.

2015-11-01

Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects

11. Real-Time Monitoring of Non-linear Suicidal Dynamics: Methodology and a Demonstrative Case Report

PubMed Central

Fartacek, Clemens; Schiepek, Günter; Kunrath, Sabine; Fartacek, Reinhold; Plöderl, Martin

2016-01-01

In recent years, a number of different authors have stressed the usefulness of non-linear dynamic systems approach in suicide research and suicide prevention. This approach applies specific methods of time series analysis and, consequently, it requires a continuous and fine-meshed assessment of the processes under consideration. The technical means for this kind of process assessment and process analysis are now available. This paper outlines how suicidal dynamics can be monitored in high-risk patients by an Internet-based application for continuous self-assessment with integrated tools of non-linear time series analysis: the Synergetic Navigation System. This procedure is illustrated by data from a patient who attempted suicide at the end of a 90-day monitoring period. Additionally, future research topics and clinical applications of a non-linear dynamic systems approach in suicidology are discussed. PMID:26913016

12. Left-Right Non-Linear Dynamical Higgs

Shu, Jing; Yepes, Juan

2016-12-01

All the possible CP-conserving non-linear operators up to the p4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically, from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)L × SU(2)R × U(1)B-L. Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV-2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators. J. Y. also acknowledges KITPC financial support during the completion of this work

13. Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: sub-harmonic motions

Al-shyyab, A.; Kahraman, A.

2005-01-01

In this study, a non-linear time-varying dynamic model is used to investigate sub-harmonic and chaotic motions exhibited by a typical multi-mesh gear train. The purely torsional system is formed by three rigid shafts connected to each other by two spur gear pairs. The lumped parameter dynamic model includes both gear backlash clearances and parametric gear mesh stiffness fluctuations. Steady state period-one motions of the same system were studied in another by using a multi-term harmonic balance method in conjunction with discrete Fourier transforms. This study expands the same solution technique for an investigation of sub-harmonic resonances of the forced response. The accuracy of the predictions is demonstrated by comparing them to the direct numerical integration results. Effect of several system parameters such as alternating mesh stiffness amplitudes, gear mesh damping and static torque transmitted on sub-harmonic motions are described. It is shown that stable sub-harmonic motions mostly in the form of softening type resonances dictate the frequency ranges in which the period-one motions are unstable due to parametric excitations. Other non-linear phenomena including long sub-harmonic motions and period-doubling bifurcations leading to chaotic behavior are also predicted.

14. Non-linear analysis of moderately thick sector plates

Nath, Y.; Sharda, H. B.; Sharma, Ashish

2005-10-01

Non-linear static analysis of moderately thick sector plates under uniformly distributed loading is presented. Using the first-order shear deformation theory and Von Karman type non-linearity, the governing equations of equilibrium are developed and expressed in terms of displacement components. The Chebyshev polynomial is used for spatial discretization of the differential equations. An iterative incremental approach based on Newton-Raphson method is used for the solution. Convergence study is carried out. Effects of annularity, thickness ratio, sector angle and boundary conditions are investigated. Results are compared with those available from the literature.

15. Structural Dynamic Analyses And Test Predictions For Spacecraft Structures With Non-Linearities

Vergniaud, Jean-Baptiste; Soula, Laurent; Newerla, Alfred

2012-07-01

The overall objective of the mechanical development and verification process is to ensure that the spacecraft structure is able to sustain the mechanical environments encountered during launch. In general the spacecraft structures are a-priori assumed to behave linear, i.e. the responses to a static load or dynamic excitation, respectively, will increase or decrease proportionally to the amplitude of the load or excitation induced. However, past experiences have shown that various non-linearities might exist in spacecraft structures and the consequences of their dynamic effects can significantly affect the development and verification process. Current processes are mainly adapted to linear spacecraft structure behaviour. No clear rules exist for dealing with major structure non-linearities. They are handled outside the process by individual analysis and margin policy, and analyses after tests to justify the CLA coverage. Non-linearities can primarily affect the current spacecraft development and verification process on two aspects. Prediction of flights loads by launcher/satellite coupled loads analyses (CLA): only linear satellite models are delivered for performing CLA and no well-established rules exist how to properly linearize a model when non- linearities are present. The potential impact of the linearization on the results of the CLA has not yet been properly analyzed. There are thus difficulties to assess that CLA results will cover actual flight levels. Management of satellite verification tests: the CLA results generated with a linear satellite FEM are assumed flight representative. If the internal non- linearities are present in the tested satellite then there might be difficulties to determine which input level must be passed to cover satellite internal loads. The non-linear behaviour can also disturb the shaker control, putting the satellite at risk by potentially imposing too high levels. This paper presents the results of a test campaign performed in

16. Non-linear dynamics of a spur gear pair

Kahraman, A.; Singh, R.

1990-10-01

Non-linear frequency response characteristics of a spur gear pair with backlash are examined in this paper for both external and internal excitations. The internal excitation is of importance from the high frequency noise and vibration control viewpoint and it represents the overall kinematic or static transmission error. Such problems may be significantly different from the rattle problems associated with external, low frequency torque excitation. Two solution methods, namely the digital simulation technique and the method of harmonic balance, have been used to develop the steady state solutions for the internal sinusoidal excitation. Difficulties associated with the determination of the multiple solutions at a given frequency in the digital simulation technique have been resolved, as one must search the entire initial conditions map. Such solutions and the transition frequencies for various impact situations are easily found by the method of harmonic balance. Further, the principle of superposition can be employed to analyze the periodic transmission error excitation and/or combined excitation problems provided that the excitation frequencies are sufficiently apart from each other. Our analytical predictions match satisfactorily with the limited experimental data available in the literature. Using the digital simulation, we have also observed that the chaotic and subharmonic resonances may exist in a gear pair depending upon the mean or design load, mean to alternating force ratio, damping and backlash. Specifically, the mean load determines the conditions for no impacts, single-sided impacts and double-sided impacts. Our results are different from the frequency response characteristics of the conventional, single-degree-of-freedom, clearance type non-linear system. Our formulation should form the basis of further analytical and experimental work in the geared rotor dynamics area.

17. Passive dynamic controllers for non-linear mechanical systems

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.

1991-01-01

A methodology for model-independent controller design for controlling large angular motion of multi-body dynamic systems is outlined.The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system, and at the same time suppress the vibrations due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameters, even if the controlled system is non-linear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach applied to a flexible six-degree-of-freedom manipulator.

18. Non-linear controls influence functions in an aircraft dynamics simulator

Guerreiro, Nelson M.; Hubbard, James E., Jr.; Motter, Mark A.

2006-03-01

In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft's control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland's continuing study of active wing load control.

19. Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: period-one motions

Al-shyyab, A.; Kahraman, A.

2005-06-01

A non-linear time-varying dynamic model of a typical multi-mesh gear train is proposed in this study. The physical system includes three rigid shafts coupled by two gear pairs. The lumped parameter dynamic model includes the gear backlash in the form of clearance-type displacement functions and parametric variation of gear mesh stiffness values dictated by the gear contact ratios. The system is reduced to a two-degree-of-freedom definite model by using the relative gear mesh displacements as the coordinates. Dimensionless equations of motion are solved for the steady-state period-1 response by using a multi-term Harmonic Balance Method (HBM) in conjunction with discrete Fourier Transforms and a Parametric Continuation scheme. The accuracy of the HBM solutions is demonstrated by comparing them to direct numerical integration solutions. Floquet theory is applied to determine the stability of the steady-state harmonic balance solutions. An example gear train is used to investigate the influence of key system parameters including alternating mesh stiffness amplitudes, gear mesh damping, static torque transmitted, and the gear mesh frequency ratio.

20. Non-linear analysis of EEG signals at various sleep stages.

PubMed

Acharya U, Rajendra; Faust, Oliver; Kannathal, N; Chua, TjiLeng; Laxminarayan, Swamy

2005-10-01

Application of non-linear dynamics methods to the physiological sciences demonstrated that non-linear models are useful for understanding complex physiological phenomena such as abrupt transitions and chaotic behavior. Sleep stages and sustained fluctuations of autonomic functions such as temperature, blood pressure, electroencephalogram (EEG), etc., can be described as a chaotic process. The EEG signals are highly subjective and the information about the various states may appear at random in the time scale. Therefore, EEG signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. The sleep data analysis is carried out using non-linear parameters: correlation dimension, fractal dimension, largest Lyapunov entropy, approximate entropy, Hurst exponent, phase space plot and recurrence plots. These non-linear parameters quantify the cortical function at different sleep stages and the results are tabulated.

1. Non-linear controls influence functions in an aircraft dynamics simulator

NASA Technical Reports Server (NTRS)

Guerreiro, Nelson M.; Hubbard, James E., Jr.; Motter, Mark A.

2006-01-01

In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft s control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland s continuing study of active wing load control.

2. NOLB : Non-linear rigid block normal mode analysis method.

PubMed

Hoffmann, Alexandre; Grudinin, Sergei

2017-04-05

We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.

3. State-variable analysis of non-linear circuits with a desk computer

NASA Technical Reports Server (NTRS)

Cohen, E.

1981-01-01

State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.

4. Non-linear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability

PubMed Central

Terrier, Philippe; Dériaz, Olivier

2013-01-01

It has been observed that times series of gait parameters [stride length (SL), stride time (ST), and stride speed (SS)], exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another non-linear method estimates the degree of resilience of gait control to small perturbations, i.e., the local dynamic stability (LDS). The method makes use of the maximal Lyapunov exponent, which estimates how fast a non-linear system embedded in a reconstructed state space (attractor) diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST, and SS from which the statistical persistence among consecutive strides can be assessed), and the trajectory of the center of pressure (from which the LDS can be estimated). In 20 healthy participants, the response to rhythmic auditory cueing (RAC) of LDS and of statistical persistence [assessed with detrended fluctuation analysis (DFA)] was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor) was strongly enhanced (relative change +73%). That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step) was smaller (+3%). DFA results (scaling exponents) confirmed an anti-persistent pattern in ST, SL, and SS. Long-term LDS (but not short-term LDS) and scaling exponents exhibited a significant correlation between them (r = 0.7). Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders. PMID

5. a Frequency Domain Based NUMERIC-ANALYTICAL Method for Non-Linear Dynamical Systems

Narayanan, S.; Sekar, P.

1998-04-01

In this paper a multiharmonic balancing technique is used to develop certain algorithms to determine periodic orbits of non-liner dynamical systems with external, parametric and self excitations. Essentially, in this method the non-linear differential equations are transformed into a set of non-linear algebraic equations in terms of the Fourier coefficients of the periodic solutions which are solved by using the Newton-Raphson technique. The method is developed such that both fast Fourier transform and discrete Fourier transform algorithms can be used. It is capable of treating all types of non-linearities and higher dimensional systems. The stability of periodic orbits is investigated by obtaining the monodromy matrix. A path following algorithm based on the predictor-corrector method is also presented to enable the bifurcation analysis. The prediction is done with a cubic extrapolation technique with an arc length incrementation while the correction is done with the use of the least square minimisation technique. The under determined system of equations is solved by singular value decomposition. The suitability of the method is demonstrated by obtaining the bifurcational behaviour of rolling contact vibrations modelled by Hertz contact law.

6. Non-Linear Dynamic Response of a Spur Gear Pair: Modelling and Experimental Comparisons

PARKER, R. G.; VIJAYAKAR, S. M.; IMAJO, T.

2000-10-01

The dynamic response of a spur gear pair is investigated using a finite element/contact mechanics model that offers significant advantages for dynamic gear analyses. The gear pair is analyzed across a wide range of operating speeds and torques. Comparisons are made to other researchers' published experiments that reveal complex non-linear phenomena. The non-linearity source is contact loss of the meshing teeth, which, in contrast to the prevailing understanding, occurs even for large torques despite the use of high-precision gears. A primary feature of the modelling is that dynamic mesh forces are calculated using a detailed contact analysis at each time step as the gears roll through the mesh; there is no need to externally specify the excitation in the form of time-varying mesh stiffness, static transmission error input, or the like. A semi-analytical model near the tooth surface is matched to a finite element solution away from the tooth surface, and the computational efficiency that results permits dynamic analysis. Two-single-degree-of-freedom models are also studied. While one gives encouragingly good results, the other, which appears to have better mesh stiffness modelling, gives poor comparisons with experiments. The results indicate the sensitivity of such models to the Fourier spectrum of the changing mesh stiffness.

7. Passive dynamic controllers for non-linear mechanical systems

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.

1992-01-01

The objective is to develop active model-independent controllers for slewing and vibration control of nonlinear multibody flexible systems, including flexible robots. The topics are presented in viewgraph form and include: passive stabilization; work-energy rate principle; Liapunov theory; displacement feedback; dynamic controller; displacement and acceleration feedback; velocity feedback; displacement feedback; physical interaction; a 6-DOF robot; and simulation results.

8. Non-linear and unstable flux vortex dynamics.

SciTech Connect

Kunchur, M. N.; Liang, M.; Hua, J.; Xiao, Z.

2011-01-01

Vortex dynamics in molybdenum-germanium superconducting films were found to well approximate the ideal unpinned free limit even at low driving forces. This provided a first opportunity to confirm the predictions of time-dependent Ginzburg Landau (TDGL) mean-field theory. At high driving forces the flux flow enters the classic Larkin-Ovchinnikov (LO) regime and the nonlinear current-voltage response can be well fitted to a hybrid TDGL-LO model.

9. Derivative pricing with non-linear Fokker-Planck dynamics

Michael, Fredrick; Johnson, M. D.

2003-06-01

We examine how the Black-Scholes derivative pricing formula is modified when the underlying security obeys non-extensive statistics and Fokker-Planck dynamics. An unusual feature of such securities is that the volatility in the underlying Ito-Langevin equation depends implicitly on the actual market rate of return. This complicates most approaches to valuation. Here we show that progress is possible using variations of the Cox-Ross valuation technique.

10. Non-linear optical studies of adsorbates: Spectroscopy and dynamics

SciTech Connect

Zhu, Xiangdong.

1989-08-01

In the first part of this thesis, we have established a systematic procedure to apply the surface optical second-harmonic generation (SHG) technique to study surface dynamics of adsorbates. In particular, we have developed a novel technique for studies of molecular surface diffusions. In this technique, the laser-induced desorption with two interfering laser beams is used to produce a monolayer grating of adsorbates. The monolayer grating is detected with diffractions of optical SHG. By monitoring the first-order second-harmonic diffraction, we can follow the time evolution of the grating modulation from which we are able to deduce the diffusion constant of the adsorbates on the surface. We have successfully applied this technique to investigate the surface diffusion of CO on Ni(111). The unique advantages of this novel technique will enable us to readily study anisotropy of a surface diffusion with variable grating orientation, and to investigate diffusion processes of a large dynamic range with variable grating spacings. In the second part of this work, we demonstrate that optical infrared-visible sum-frequency generation (SFG) from surfaces can be used as a viable surface vibrational spectroscopic technique. We have successfully recorded the first vibrational spectrum of a monolayer of adsorbates using optical infrared-visible SFG. The qualitative and quantitative correlation of optical SFG with infrared absorption and Raman scattering spectroscopies are examined and experimentally demonstrated. We have further investigated the possibility to use transient infrared-visible SFG to probe vibrational transients and ultrafast relaxations on surfaces. 146 refs.

11. Non linear dynamics of flame cusps: from experiments to modeling

Almarcha, Christophe; Radisson, Basile; Al-Sarraf, Elias; Quinard, Joel; Villermaux, Emmanuel; Denet, Bruno; Joulin, Guy

2016-11-01

The propagation of premixed flames in a medium initially at rest exhibits the appearance and competition of elementary local singularities called cusps. We investigate this problem both experimentally and numerically. An analytical solution of the two-dimensional Michelson Sivashinsky equation is obtained as a composition of pole solutions, which is compared with experimental flames fronts propagating between glass plates separated by a thin gap width. We demonstrate that the front dynamics can be reproduced numerically with a good accuracy, from the linear stages of destabilization to its late time evolution, using this model-equation. In particular, the model accounts for the experimentally observed steady distribution of distances between cusps, which is well-described by a one-parameter Gamma distribution, reflecting the aggregation type of interaction between the cusps. A modification of the Michelson Sivashinsky equation taking into account gravity allows to reproduce some other special features of these fronts. Aix-Marseille Univ., IRPHE, UMR 7342 CNRS, Centrale Marseille, Technopole de Château Gombert, 49 rue F. Joliot Curie, 13384 Marseille Cedex 13, France.

12. Non-linear modal analysis of structural components subjected to unilateral constraints

Attar, M.; Karrech, A.; Regenauer-Lieb, K.

2017-02-01

In this paper, we present a detailed numerical study of the non-linear dynamics in structural components under unilateral contact constraints. Here, the unilateral term characterises the constitutive law of the restoring force in the constraints as they only sustain elastic reactions in one direction, either compressive or tensile. Thus, the non-differentiability of the contact law at the discontinuity point is the only source of non-linearity. In our approach, the discrete lattice method (DLM) is used to treat the continuous system as a piecewise linear model. Thus, the trajectory of each node in the discrete model would be a sequence of smooth solutions with the switching times between them. The application of the one-step integration scheme allows us to detect the occurrence of contact (i.e. the instants that the lattice nodes cross the discontinuity boundary) and consequently update the active constraints. We also consider embedding the bisection algorithm into the time integration procedure to localise the instants at which the nodes cross the boundary and minimise the accumulative error. Subsequently, the resulting unconditionally stable integration scheme is utilised as the modelling tool in combination with the shooting technique to perform a novel non-smooth modal analysis. In analogy with the smooth non-linear systems, the evolution of non-smooth periodic motions is presented in the frequency-stiffness plots. We apply our method to obtain non-linear normal modes (NNMs) for a number of representative problems, including a bar-obstacle system, a beam-substrate system and a granular chain with tensionless interactions. These numerical examples demonstrate the efficiency of the solution procedure to trace the family of energy-independent non-linear modes across the range of contact stiffnesses. Moreover, the stability analysis of the modes on the plot backbone reveal that they may become unstable due to the interaction with the higher modes or bifurcation of

13. Enhanced studies on a composite time integration scheme in linear and non-linear dynamics

Klarmann, S.; Wagner, W.

2015-03-01

In Bathe and Baig (Comput Struct 83:2513-2524, 2005), Bathe (Comput Struct 85:437-445, 2007), Bathe and Noh (Comput Struct 98-99:1-6, 2012) Bathe et al. have proposed a composite implicit time integration scheme for non-linear dynamic problems. This paper is aimed at the further investigation of the scheme's behaviour for use in case of linear and non-linear problems. Therefore, the examination of the amplification matrix of the scheme will be extended in order to get in addition the properties for linear calculations. Besides, it will be demonstrated that the integration scheme also has an impact on some of these properties when used for non-linear calculations. In conclusion, a recommendation for the only selectable parameter of the scheme will be given for application in case of geometrically non-linear calculations.

14. Characterization of memory load in an arithmetic task using non-linear analysis of EEG signals.

PubMed

Zarjam, Pega; Epps, Julien; Lovell, Nigel H; Chen, Fang

2012-01-01

In this paper, we investigate non-linear analysis of electroencephalogram (EEG) signals to examine changes in working memory load during the performance of a cognitive task with varying difficulty levels. EEG signals were recorded during an arithmetic task while the induced load was varying in seven levels from very easy to extremely difficult. The EEG signals were analyzed using three different non-linear/dynamic measures; namely: correlation dimension, Hurst exponent and approximate entropy. Experimental results show that the values of the measures extracted from the delta frequency band of signals acquired from the frontal and occipital lobes of the brain vary in accordance with the task difficulty level induced. The values of the correlation dimension increased as the task difficulty increased, showing a rise in complexity of the EEG signals, while the values of the Hurst exponent and approximate entropy decreased as task difficulty increased, indicating more regularity and predictability in the signals.

15. Exciton dynamics and non-linearities in two-dimensional hybrid organic perovskites

Abdel-Baki, K.; Boitier, F.; Diab, H.; Lanty, G.; Jemli, K.; Lédée, F.; Garrot, D.; Deleporte, E.; Lauret, J. S.

2016-02-01

Due to their high potentiality for photovoltaic applications or coherent light sources, a renewed interest in hybrid organic perovskites has emerged for few years. When they are arranged in two dimensions, these materials can be considered as hybrid quantum wells. One consequence of the unique structure of 2D hybrid organic perovskites is a huge exciton binding energy that can be tailored through chemical engineering. We present experimental investigations of the exciton non-linearities by means of femtosecond pump-probe spectroscopy. The exciton dynamics is fitted with a bi-exponential decay with a free exciton life-time of ˜100 ps. Moreover, an ultrafast intraband relaxation (<150 fs) is also reported. Finally, the transient modification of the excitonic line is analyzed through the moment analysis and described in terms of reduction of the oscillator strength and linewidth broadening. We show that excitonic non-linearities in 2D hybrid organic perovskites share some behaviours of inorganic semiconductors despite their high exciton binding energy.

16. Exciton dynamics and non-linearities in two-dimensional hybrid organic perovskites

SciTech Connect

Abdel-Baki, K.; Boitier, F.; Diab, H.; Lanty, G.; Jemli, K.; Lédée, F.; Deleporte, E.; Lauret, J. S.; Garrot, D.

2016-02-14

Due to their high potentiality for photovoltaic applications or coherent light sources, a renewed interest in hybrid organic perovskites has emerged for few years. When they are arranged in two dimensions, these materials can be considered as hybrid quantum wells. One consequence of the unique structure of 2D hybrid organic perovskites is a huge exciton binding energy that can be tailored through chemical engineering. We present experimental investigations of the exciton non-linearities by means of femtosecond pump-probe spectroscopy. The exciton dynamics is fitted with a bi-exponential decay with a free exciton life-time of ∼100 ps. Moreover, an ultrafast intraband relaxation (<150 fs) is also reported. Finally, the transient modification of the excitonic line is analyzed through the moment analysis and described in terms of reduction of the oscillator strength and linewidth broadening. We show that excitonic non-linearities in 2D hybrid organic perovskites share some behaviours of inorganic semiconductors despite their high exciton binding energy.

17. Non linear approach to study the dynamics of neurodegenerative diseases by Multifractal Detrended Cross-correlation Analysis-A quantitative assessment on gait disease

Dutta, Srimonti; Ghosh, Dipak; Samanta, Shukla

2016-04-01

This paper studies the human gait pattern of normal people and patients suffering from Parkinson's disease using the MFDXA (Multifractal Detrended Cross-correlation Analysis) methodology. The auto correlation and cross correlation of the time series of the total force under the left foot and right foot were studied. The study reveals that the degree of multifractality (W) and degree of correlation (γ) are generally more for normal patients than the diseased set. It is also observed that the values of W and γ are nearly same for left foot and right. It is also observed that the study of autocorrelation alone is not sufficient, cross correlations should also be studied to get a better concept of neurodegenerative diseases.

18. The Creative Chaos: Speculations on the Connection Between Non-Linear Dynamics and the Creative Process

Zausner, Tobi

Chaos theory may provide models for creativity and for the personality of the artist. A collection of speculative hypotheses examines the connection between art and such fundamentals of non-linear dynamics as iteration, dissipative processes, open systems, entropy, sensitivity to stimuli, autocatalysis, subsystems, bifurcations, randomness, unpredictability, irreversibility, increasing levels of organization, far-from-equilibrium conditions, strange attractors, period doubling, intermittency and self-similar fractal organization. Non-linear dynamics may also explain why certain individuals suffer mental disorders while others remain intact during a lifetime of sustained creative output.

19. Biomagnetic activity and non linear analysis in obstetrics and gynecology in a Greek population.

PubMed

2016-01-01

This article reports the application of non-linear analysis to biomagnetic signals recorded from fetal growth restriction, fetal brain activity, ovarian lesions, breast lesions, umbilical arteries, uterine myomas, and uterine arteries in a Greek population. The results were correlated with clinical findings. The biomagnetic measurements and the application of non-linear analysis are promising procedures in Obstetrics and Gynecology.

20. Black hole hair removal: non-linear analysis

Jatkar, Dileep P.; Sen, Ashoke; Srivastava, Yogesh K.

2010-02-01

BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, — degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.

1. Optimal design of linear and non-linear dynamic vibration absorbers

Jordanov, I. N.; Cheshankov, B. I.

1988-05-01

An efficient numerical method is applied to obtain optimal parameters for both linear and non-linear damped dynamic vibration absorbers. The minimization of the vibration response has been carried out for damped as well as undamped force excited primary systems with linear and non-linear spring characteristics. Comparison is made with the optimum absorber parameters that are determined by using Den Hartog's classical results in the linear case. Six optimization criteria by which the response is minimized over narrow and broad frequency bands are examined. Pareto optimal solutions of the multi-objective decision making problem are obtained.

2. Non-linear dynamics of a geared rotor-bearing system with multiple clearances

Kahraman, A.; Singh, R.

1991-02-01

Non-linear frequency response characteristics of a geared rotor-bearing system are examined in this paper. A three-degree-of-freedom dynamic model is developed which includes non-linearities associated with radial clearances in the radial rolling element bearings and backlash between a spur gear pair; linear time-invariant gear meshing stiffness is assumed. The corresponding linear system problem is also solved, and predicted natural frequencies and modes match with finite element method results. The bearing non-linear stiffness function is approximated for the sake of convenience by a simple model which is identical to that used for the gear mesh. This approximate bearing model has been verified by comparing steady state frequency spectra. Applicability of both analytical and numerical solution techniques to the multi-degree-of-freedom non-linear problem is investigated. Satisfactory agreement has been found between our theory and available experimental data. Several key issues such as non-linear modal interactions and differences between internal static transmission error excitation and external torque excitation are discussed. Additionally, parametric studies are performed to understand the effect of system parameters such as bearing stiffness to gear mesh stiffness ratio, alternating to mean force ratio and radial bearing preload to mean force ratio on the non-linear dynamic behavior. A criterion used to classify the steady state solutions is presented, and the conditions for chaotic, quasi-periodic and subharmonic steady state solutions are determined. Two typical routes to chaos observed in this geared system are also identified.

3. Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid. Part i: Stability

AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.

1999-08-01

The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.

4. Non-linear dynamics of operant behavior: a new approach via the extended return map.

PubMed

Li, Jay-Shake; Huston, Joseph P

2002-01-01

Previous efforts to apply non-linear dynamic tools to the analysis of operant behavior revealed some promise for this kind of approach, but also some doubts, since the complexity of animal behavior seemed to be beyond the analyzing ability of the available tools. We here outline a series of studies based on a novel approach. We modified the so-called 'return map' and developed a new method, the 'extended return map' (ERM) to extract information from the highly irregular time series data, the inter-response time (IRT) generated by Skinner-box experiments. We applied the ERM to operant lever pressing data from rats using the four fundamental reinforcement schedules: fixed interval (FI), fixed ratio (FR), variable interval (VI) and variable ratio (VR). Our results revealed interesting patterns in all experiment groups. In particular, the FI and VI groups exhibited well-organized clusters of data points. We calculated the fractal dimension out of these patterns and compared experimental data with surrogate data sets, that were generated by randomly shuffling the sequential order of original IRTs. This comparison supported the finding that patterns in ERM reflect the dynamics of the operant behaviors under study. We then built two models to simulate the functional mechanisms of the FI schedule. Both models can produce similar distributions of IRTs and the stereotypical 'scalloped' curve characteristic of FI responding. However, they differ in one important feature in their formulation: while one model uses a continuous function to describe the probability of occurrence of an operant behavior, the other one employs an abrupt switch of behavioral state. Comparison of ERMs showed that only the latter was able to produce patterns similar to the experimental results, indicative of the operation of an abrupt switch from one behavioral state to another over the course of the inter-reinforcement period. This example demonstrated the ERM to be a useful tool for the analysis of

5. Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

NASA Technical Reports Server (NTRS)

Pai, P. F.; Lee, S.-Y.

2003-01-01

This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \\ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

6. Using Linear and Non-Linear Methods to Study Precipitation-Vegetation Dynamics at Global Scales

Lotsch, A.; Friedl, M. A.

2002-12-01

Large areas of the Earth's land surface experience significant spatio-temporal variability in precipitation regimes. This variability can result in important perturbations to ecosystem processes. In recent years remote sensing observations have been used to examine large-scale dynamics in ecosystem response to climate. However, because of the complexity of both the processes and data sets involved, analysis of coupled spatio-temporal variability in remote sensing and other earth science data poses a challenging problem. In this paper, linear and non-linear statistical learning techniques are used to perform automated feature extraction and unsupervised data analysis of precipitation and remotely sensed vegetation index data sets at global and inter-annual scales. To examine the joint variability of precipitation and vegetation, canonical correlation analysis (CCA) and maximum covariance analysis (MCA) are used. These techniques are designed to isolate coupled modes of different variables in both space and time. Unfortunately, MCA and CCA require fairly strict assumptions concerning the statistical distribution of the input variables. When such assumptions are not met, non-linear techniques can provide additional information that cannot be retrieved using linear techniques. In particular, independent component analysis (ICA) has recently emerged as a novel technique to isolate non-Gaussian signals from multivariate data. While many linear techniques rely on the variance/covariance information contained in a dataset, ICA uses higher order statistical moments to isolate patterns. ICA is particularly powerful for identifying spatial and temporal artifacts that are commonly contained in Earth science data sets and for isolating anomalous events that arise from perturbations in the atmosphere-biosphere system such as droughts and floods associated with El-Niño (and other) events. In this paper, ICA is used to extract information related to the spatial and temporal

7. Analysis of some bivariate non-linear interpolatory subdivision schemes

2008-07-01

This paper is devoted to the convergence analysis of a class of bivariate subdivision schemes that can be defined as a specific perturbation of a linear subdivision scheme. We study successively the univariate and bivariate case and apply the analysis to the so called Powerp scheme (Serna and Marquina, J Comput Phys 194:632-658, 2004).

8. On psychoanalysis and non-linear dynamics: the paradigm of bifurcation.

PubMed

Priel, B; Schreiber, G

1994-09-01

Some of Freud's main theoretical conceptualizations drew on metaphors from 19th century physics. However, though the physics of Freud's era was based on deterministic Newtonian mechanics and equilibrium thermodynamics, his descriptions of the dynamics of instincts, therapeutic change, and even transference, were far beyond this model. Freud's dynamic description of psychic development evokes contemporary theories of irreversible, far-from-equilibrium thermodynamics and non-linear dynamics. The present paper focuses on bifurcation theory, which offers a paradigm for the investigation of unpredictable but deterministic phenomena; this paradigm sheds a retroactive light on the classical psychoanalytical conceptualizations of complemental series, repetition compulsion, transference and cure.

9. Non-linear analysis in Light Water Reactor design

SciTech Connect

Rashid, Y.R.; Sharabi, M.N.; Nickell, R.E.; Esztergar, E.P.; Jones, J.W.

1980-03-01

The results obtained from a scoping study sponsored by the US Department of Energy (DOE) under the Light Water Reactor (LWR) Safety Technology Program at Sandia National Laboratories are presented. Basically, this project calls for the examination of the hypothesis that the use of nonlinear analysis methods in the design of LWR systems and components of interest include such items as: the reactor vessel, vessel internals, nozzles and penetrations, component support structures, and containment structures. Piping systems are excluded because they are being addressed by a separate study. Essentially, the findings were that nonlinear analysis methods are beneficial to LWR design from a technical point of view. However, the costs needed to implement these methods are the roadblock to readily adopting them. In this sense, a cost-benefit type of analysis must be made on the various topics identified by these studies and priorities must be established. This document is the complete report by ANATECH International Corporation.

10. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-02-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.

11. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

SciTech Connect

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-02-28

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.

12. Denoising and robust non-linear wavelet analysis

Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.

1994-04-01

In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistance wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transforms, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the S+Wavelets object-oriented toolkit for wavelet analysis.

13. Non-linear analysis of vibrations of irregular plates

NASA Technical Reports Server (NTRS)

Lobitz, D. W.; Nayfeh, A. H.; Mook, D. T.

1977-01-01

A numerical perturbation method is used to investigate the forced vibrations of irregular plates. Nonlinear terms associated with the midplane stretching are retained in the analysis. The numerical part of the method involves the use of linear, finite element techniques to determine the free oscillation mode shapes and frequencies and to obtain the linear midplane stress resultants caused by the midplane stretching. Representing the solution as an expansion in terms of these linear mode shapes, these modes and the resultants are used to determine the equations governing the time-dependent coefficients of this expansion. These equations are solved by using the method of multiple scales. Specific solutions are given for the main-resonant vibrations of an elliptical plate in the presence of internal resonances. The results indicate that modes other than the driven mode can be drawn into the steady state response. Though the excitation is composed of a single harmonic, the response may not be periodic. Moreover, the particular types of responses that can occur are highly dependent on the mode being excited and are sensitive to small geometrical changes.

14. Application of non-linear dynamics to the characterization of cardiac electrical instability

NASA Technical Reports Server (NTRS)

Kaplan, D. T.; Cohen, R. J.

1987-01-01

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

15. Non-Linear Dynamical Classification of Short Time Series of the Rössler System in High Noise Regimes

PubMed Central

Lainscsek, Claudia; Weyhenmeyer, Jonathan; Hernandez, Manuel E.; Poizner, Howard; Sejnowski, Terrence J.

2013-01-01

Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson’s disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to −30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A′ under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data. PMID

16. Dynamics of atom-field probability amplitudes in a coupled cavity system with Kerr non-linearity

SciTech Connect

Priyesh, K. V.; Thayyullathil, Ramesh Babu

2014-01-28

We have investigated the dynamics of two cavities coupled together via photon hopping, filled with Kerr non-linear medium and each containing a two level atom in it. The evolution of various atom (field) state probabilities of the coupled cavity system in two excitation sub space are obtained numerically. Detailed analysis has been done by taking different initial conditions of the system, with various coupling strengths and by varying the susceptibility of the medium. The role of susceptibility factor, on the dynamics atom field probability has been examined. In a coupled cavity system with strong photon hopping it is found that the susceptibility factor modifies the behaviour of probability amplitudes.

17. Dynamics of heavy impurities in non-linear MHD simulations of sawtoothing tokamak plasmas

Ahn, Jae-H.; Garbet, X.; Lütjens, H.; Guirlet, R.

2016-12-01

The effect of sawteeth on impurity dynamics is studied with the XTOR-2F code. Non-linear full 3D MHD simulations including appropriate fluid equations for impurities in the high collisional regime show that the presence of regular sawtooth crashes affects the impurity behaviour. A spatial non-uniformity of 5 % in post-crash impurity density profiles persists due to 2D structures of impurity density which appear during sawtooth crashes. They are shown to be mainly driven by the \\mathbf{E}× \\mathbf{B} velocity, and are responsible for the sudden impurity transport in the core plasmas.

18. A process fault estimation strategy for non-linear dynamic systems

Pazera, Marcin; Korbicz, Józef

2017-01-01

The paper deals with the problem of simultaneous state and process fault estimation for non-linear dynamic systems. Instead of estimating the fault directly, its product with state and the state itself are estimated. To derive the fault from the product, a simple algebraic approach is proposed. The estimation strategy is based on the quadratic boundedness approach. The final part of the paper presents an illustrative example concerning a laboratory multi-tank system. The real data experiments clearly exhibit the performance of the proposed approach.

19. Intelligent control of non-linear dynamical system based on the adaptive neurocontroller

Engel, E.; Kovalev, I. V.; Kobezhicov, V.

2015-10-01

This paper presents an adaptive neuro-controller for intelligent control of non-linear dynamical system. The formed as the fuzzy selective neural net the adaptive neuro-controller on the base of system's state, creates the effective control signal under random perturbations. The validity and advantages of the proposed adaptive neuro-controller are demonstrated by numerical simulations. The simulation results show that the proposed controller scheme achieves real-time control speed and the competitive performance, as compared to PID, fuzzy logic controllers.

20. Analysis of structural seismic behaviour: from non stationary to non linear effects

Carlo Ponzo, Felice; Ditommaso, Rocco; Monaco, Lisa

2014-05-01

The change in fundamental frequency of a building is considered the simplest way to detect the onset of damage. Several authors in the past proposed that the difference in periods that can be observed among ambient noise, earthquake weak-motion measurements can be attributed to transient non-linearity due to reversible modification of the building characteristic (e.g. the degree of coupling between frame and infill in reinforced concrete buildings). The necessity of effective and efficient seismic protection of vast and aging structures and infrastructure has increased markedly the interest in the development of structural monitoring techniques. Damage to any structure alters its dynamic properties and for that dynamic monitoring techniques enable the identification of damage by comparing pre and post seismic excitation characteristic. The principle parameters usually monitored are: fundamental period, damping factors and modal shapes. Several damage identification and localization techniques are based on variations in these parameters (see, e.g Ponzo et al. 2010 and reference therein). Non Destructive Evaluation (NDE) methods can be rank on four different levels with the higher levels requiring increased quality and quantity of available information. The most common methods are therefore related to Level 1, due to their simplified and economic implementation. These methods are based mainly upon the variation of vibration frequencies and/or variations in Equivalent Viscous Damping associated with these vibration modes. It is important to underline however that although the presence of damage will lead to alterations in vibration modes the opposite does not necessarily hold true. Two types of frequency variation can be distinguished; long time period variations (due to variations in temperature, foundation soil moisture content etc.) and short period variations (for example due to a seismic event). For short period variations, changes in frequency can be attributed

1. Analysis of linear and non-linear genotype × environment interaction.

PubMed

Yang, Rong-Cai

2014-01-01

The usual analysis of genotype × environment interaction (G × E) is based on the linear regression of genotypic performance on environmental changes (e.g., classic stability analysis). This linear model may often lead to lumping together of the non-linear responses to the whole range of environmental changes from suboptimal and super optimal conditions, thereby lowering the power of detecting G × E variation. On the other hand, the G × E is present when the magnitude of the genetic effect differs across the range of environmental conditions regardless of whether the response to environmental changes is linear or non-linear. The objectives of this study are: (i) explore the use of four commonly used non-linear functions (logistic, parabola, normal and Cauchy functions) for modeling non-linear genotypic responses to environmental changes and (ii) to investigate the difference in the magnitude of estimated genetic effects under different environmental conditions. The use of non-linear functions was illustrated through the analysis of one data set taken from barley cultivar trials in Alberta, Canada (Data A) and the examination of change in effect sizes is through the analysis another data set taken from the North America Barley Genome Mapping Project (Data B). The analysis of Data A showed that the Cauchy function captured an average of >40% of total G × E variation whereas the logistic function captured less G × E variation than the linear function. The analysis of Data B showed that genotypic responses were largely linear and that strong QTL × environment interaction existed as the positions, sizes and directions of QTL detected differed in poor vs. good environments. We conclude that (i) the non-linear functions should be considered when analyzing multi-environmental trials with a wide range of environmental variation and (ii) QTL × environment interaction can arise from the difference in effect sizes across environments.

2. Analysis of linear and non-linear genotype × environment interaction

PubMed Central

Yang, Rong-Cai

2014-01-01

The usual analysis of genotype × environment interaction (G × E) is based on the linear regression of genotypic performance on environmental changes (e.g., classic stability analysis). This linear model may often lead to lumping together of the non-linear responses to the whole range of environmental changes from suboptimal and super optimal conditions, thereby lowering the power of detecting G × E variation. On the other hand, the G × E is present when the magnitude of the genetic effect differs across the range of environmental conditions regardless of whether the response to environmental changes is linear or non-linear. The objectives of this study are: (i) explore the use of four commonly used non-linear functions (logistic, parabola, normal and Cauchy functions) for modeling non-linear genotypic responses to environmental changes and (ii) to investigate the difference in the magnitude of estimated genetic effects under different environmental conditions. The use of non-linear functions was illustrated through the analysis of one data set taken from barley cultivar trials in Alberta, Canada (Data A) and the examination of change in effect sizes is through the analysis another data set taken from the North America Barley Genome Mapping Project (Data B). The analysis of Data A showed that the Cauchy function captured an average of >40% of total G × E variation whereas the logistic function captured less G × E variation than the linear function. The analysis of Data B showed that genotypic responses were largely linear and that strong QTL × environment interaction existed as the positions, sizes and directions of QTL detected differed in poor vs. good environments. We conclude that (i) the non-linear functions should be considered when analyzing multi-environmental trials with a wide range of environmental variation and (ii) QTL × environment interaction can arise from the difference in effect sizes across environments. PMID:25101112

3. A Signal Transmission Technique for Stability Analysis of Multivariable Non-Linear Control Systems

NASA Technical Reports Server (NTRS)

Jackson, Mark; Zimpfer, Doug; Adams, Neil; Lindsey, K. L. (Technical Monitor)

2000-01-01

Among the difficulties associated with multivariable, non-linear control systems is the problem of assessing closed-loop stability. Of particular interest is the class of non-linear systems controlled with on/off actuators, such as spacecraft thrusters or electrical relays. With such systems, standard describing function techniques are typically too conservative, and time-domain simulation analysis is prohibitively extensive, This paper presents an open-loop analysis technique for this class of non-linear systems. The technique is centered around an innovative use of multivariable signal transmission theory to quantify the plant response to worst case control commands. The technique has been applied to assess stability of thruster controlled flexible space structures. Examples are provided for Space Shuttle attitude control with attached flexible payloads.

4. Non-Linear Dynamics Approach to Assessing Woody-Encroachment in Grasslands

Brunsell, N. A.; Nippert, J. B.; Van Vleck, E.

2015-12-01

Woody species are encroaching on grasslands globally. Here, we investigate the spatial and temporal dynamics of this encroachment in relation to climate and fire regimes in the central U.S. A low-dimensional model is used to assess stability of species composition. Sixe years of eddy covariance data at a paired grassland and woody encroachment site at the Konza Prairie LTER site are used to verify carbon and water dynamics. Historical aerial photography and remote sensing data are used to quantify the spatial diffusion of woody tree fraction into grasslands. Non-linear dynamics approaches are used to quantify the stability of vegetation and the presence of tipping points in relation to woody fraction, fire frequency and precipitation and temperature variability. Understanding the roles of multiple confounding forcing factors operating at disparate timescales is essential for predicting future woody encroachment and the water and climate implications of land cover transitions.

5. Controlling the non-linear intracavity dynamics of large He-Ne laser gyroscopes

Cuccato, D.; Beghi, A.; Belfi, J.; Beverini, N.; Ortolan, A.; Di Virgilio, A.

2014-02-01

A model based on Lamb's theory of gas lasers is applied to a He-Ne ring laser (RL) gyroscope to estimate and remove the laser dynamics contribution from the rotation measurements. The intensities of the counter-propagating laser beams exiting one cavity mirror are continuously observed together with a monitor of the laser population inversion. These observables, once properly calibrated with a dedicated procedure, allow us to estimate cold cavity and active medium parameters driving the main part of the non-linearities of the system. The quantitative estimation of intrinsic non-reciprocal effects due to cavity and active medium non-linear coupling plays a key role in testing fundamental symmetries of space-time with RLs. The parameter identification and noise subtraction procedure has been verified by means of a Monte Carlo study of the system, and experimentally tested on the G-PISA RL oriented with the normal to the ring plane almost parallel to the Earth's rotation axis. In this configuration the Earth's rotation rate provides the maximum Sagnac effect while the contribution of the orientation error is reduced to a minimum. After the subtraction of laser dynamics by a Kalman filter, the relative systematic errors of G-PISA reduce from 50 to 5 parts in 103 and can be attributed to the residual uncertainties on geometrical scale factor and orientation of the ring.

6. Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities

Tokluoglu, Erinc K.

Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged

7. Non-linear dynamics and instability of a rotating shaft-disk system

Chang, C. O.; Cheng, J. W.

1993-01-01

The instability and non-linear dynamics of a slender rotating shaft with a rigid disk at the mid-span are analyzed. The shaft is simply supported at both ends and is made of a viscoelastic material. The stability criteria are determined from the linear equations of motion based on the small strain assumption. The bifurcation of the double zero eigenvalue point on the stability boundaries in the parametric space is analyzed by using center manifold theory on the non-linear equations of motion, for which a large transverse displacement of the shaft is assumed. Analytical expressions for the radius of synchronous whirling and the radius and precession rate of non-synchronous whirling near the double zero eigenvalue point are obtained explicitly. The behaviors of the parametric points away from the stability boundaries are analyzed numerically. The general effects on the precession rate for these points are somewhat different from those for the parametric points in the vicinity of the double zero eigenvalue.

8. Non-linear dynamics of viscoelastic liquid trilayers subjected to an electric field

Karapetsas, George; Bontozoglou, Vasilis

2014-11-01

The scope of this work is to investigate the non-linear dynamics of the electro-hydrodynamic instability of a trilayer of immiscible liquids. We consider the case of a polymer film which is separated from the top electrode by two viscous fluids. We develop a computational model and carry out 2D numerical simulations fully accounting for the flow and electric field in all phases. For the numerical solution of the governing equations we employ the mixed finite element method combined with a quasi-elliptic mesh generation scheme which is capable of following the large deformations of the liquid-liquid interface. We model the viscoelastic behavior using the Phan-Thien and Tanner (PTT) constitutive equation taking fully into account the non-linear elastic effects as well as a varying shear and extensional viscosity. We perform a thorough parametric study and investigate the influence of the electric properties of fluids, applied voltage and various rheological parameters. The authors acknowledge the support by the General Secretariat of Research and Technology of Greece under the action Supporting Postdoctoral Researchers'' (Grant Number PE8/906), co-funded by the European Social Fund and National Resources.

9. Design curves for non-linear analysis of simply-supported, uniformly-loaded rectangular plates

NASA Technical Reports Server (NTRS)

Moore, D.

1979-01-01

Design curves for the non-linear analysis of simply-supported rectangular plates subjected to uniform normal pressure loads have been developed. These curves yield the center deflection, center stress and corner stress in non-dimensionalized form plotted against a dimensionless parameter describing the load intensity. The results presented are based on extensive non-linear finite element analysis employing the ARGUS structural analysis program. Plates with length to width ratios of 1, 1.5, 2, 3 and 4 are included. The load range considered extends to 1000 times the load at which the behavior of the plate becomes significantly non-linear. Over the load range considered, the analysis shows that the ratio of center deflection to plate thickness for a square plate is less than 16 to 1, whereas linear theory would predict a center deflection 400 times the plate thickness. Likewise, the stress is markedly lower than would be predicted by linear theory. The present results are shown to be in excellent agreement with the classical linear theory up to a central deflection to plate thickness ratio of about one-half. In the non-linear regime the present results for deflection and stress are in very good agreement with the analytical and experimental work of other investigators.

10. Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials.

PubMed

Verotta, Davide; Schaedeli, Franziska

2002-04-01

Human immunodeficiency virus (HIV) dynamics represent a complicated variant of the text-book case of non-linear dynamics: predator-prey interaction. The interaction can be described as naturally reproducing T-cells (prey) hunted and killed by virus (predator). Virus reproduce and increase in number as a consequence of successful predation; this is countered by the production of T-cells and the reaction of the immune system. Multi-drug anti-HIV therapy attempts to alter the natural dynamics of the predator-prey interaction by decreasing the reproductive capability of the virus and hence predation. These dynamics are further complicated by varying compliance to treatment and insurgence of resistance to treatment. When following the temporal progression of viral load in plasma during therapy one observes a short-term (1-12 weeks) decrease in viral load. In the long-term (more than 12 weeks from the beginning of therapy) the reduction in viral load is either sustained, or it is followed by a rebound, oscillations and a new (generally lower than at the beginning of therapy) viral load level. Biomathematicians have investigated these dynamics by means of simulations. However the estimation of the parameters associated with the dynamics from real data has been mostly limited to the case of simplified, in particular linearized, models. Linearized model can only describe the short-term changes of viral load during therapy and can only predict (apparent) suppression. In this paper we put forward relatively simple models to characterize long-term virus dynamics which can incorporate different factors associated with resurgence: (Fl) the intrinsic non-linear HIV-1 dynamics, (F2) drug exposure and in particular compliance to treatment, and (F3) insurgence of resistant HIV-1 strains. The main goal is to obtain models which are mathematically identifiable given only measurements of viral load, while retaining the most crucial features of HIV dynamics. For the purpose of

11. Does the Cerebral Cortex Exploit High-Dimensional, Non-linear Dynamics for Information Processing?

PubMed Central

Singer, Wolf; Lazar, Andreea

2016-01-01

The discovery of stimulus induced synchronization in the visual cortex suggested the possibility that the relations among low-level stimulus features are encoded by the temporal relationship between neuronal discharges. In this framework, temporal coherence is considered a signature of perceptual grouping. This insight triggered a large number of experimental studies which sought to investigate the relationship between temporal coordination and cognitive functions. While some core predictions derived from the initial hypothesis were confirmed, these studies, also revealed a rich dynamical landscape beyond simple coherence whose role in signal processing is still poorly understood. In this paper, a framework is presented which establishes links between the various manifestations of cortical dynamics by assigning specific coding functions to low-dimensional dynamic features such as synchronized oscillations and phase shifts on the one hand and high-dimensional non-linear, non-stationary dynamics on the other. The data serving as basis for this synthetic approach have been obtained with chronic multisite recordings from the visual cortex of anesthetized cats and from monkeys trained to solve cognitive tasks. It is proposed that the low-dimensional dynamics characterized by synchronized oscillations and large-scale correlations are substates that represent the results of computations performed in the high-dimensional state-space provided by recurrently coupled networks. PMID:27713697

12. Alteration of the P-wave non-linear dynamics near the onset of paroxysmal atrial fibrillation.

PubMed

Martínez, Arturo; Abásolo, Daniel; Alcaraz, Raúl; Rieta, José J

2015-07-01

The analysis of P-wave variability from the electrocardiogram (ECG) has been suggested as an early predictor of the onset of paroxysmal atrial fibrillation (PAF). Hence, a preventive treatment could be used to avoid the loss of normal sinus rhythm, thus minimising health risks and improving the patient's quality of life. In these previous studies the variability of different temporal and morphological P-wave features has been only analysed in a linear fashion. However, the electrophysiological alteration occurring in the atria before the onset of PAF has to be considered as an inherently complex, chaotic and non-stationary process. This work analyses the presence of non-linear dynamics in the P-wave progression before the onset of PAF through the application of the central tendency measure (CTM), which is a non-linear metric summarising the degree of variability in a time series. Two hour-length ECG intervals just before the arrhythmia onset belonging to 46 different PAF patients were analysed. In agreement with the invasively observed inhomogeneous atrial conduction preceding the onset of PAF, CTM for all the considered P-wave features showed higher variability when the arrhythmia was closer to its onset. A diagnostic accuracy around 80% to discern between ECG segments far from PAF and close to PAF was obtained with the CTM of the metrics considered. This result was similar to previous P-wave variability methods based on linear approaches. However, the combination of linear and non-linear methods with a decision tree improved considerably their discriminant ability up to 90%, thus suggesting that both dynamics could coexist at the same time in the fragmented depolarisation of the atria preceding the arrhythmia.

13. Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

SciTech Connect

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin E-mail: izumi@phys.ntu.edu.tw

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.

14. The amazing evolutionary dynamics of non-linear optical systems with feedback

Yaroslavsky, Leonid

2013-09-01

Optical systems with feedback are, generally, non-linear dynamic systems. As such, they exhibit evolutionary behavior. In the paper we present results of experimental investigation of evolutionary dynamics of several models of such systems. The models are modifications of the famous mathematical "Game of Life". The modifications are two-fold: "Game of Life" rules are made stochastic and mutual influence of cells is made spatially non-uniform. A number of new phenomena in the evolutionary dynamics of the models are revealed: - "Ordering of chaos". Formation, from seed patterns, of stable maze-like patterns with chaotic "dislocations" that resemble natural patterns, such as skin patterns of some animals and fishes, see shell, fingerprints, magnetic domain patterns and alike, which one can frequently find in the nature. These patterns and their fragments exhibit a remarkable capability of unlimited growth. - "Self-controlled growth" of chaotic "live" formations into "communities" bounded, depending on the model, by a square, hexagon or octagon, until they reach a certain critical size, after which the growth stops. - "Eternal life in a bounded space" of "communities" after reaching a certain size and shape. - "Coherent shrinkage" of "mature", after reaching a certain size, "communities" into one of stable or oscillating patterns preserving in this process isomorphism of their bounding shapes until the very end.

15. Hippotherapy acute impact on heart rate variability non-linear dynamics in neurological disorders.

PubMed

Cabiddu, Ramona; Borghi-Silva, Audrey; Trimer, Renata; Trimer, Vitor; Ricci, Paula Angélica; Italiano Monteiro, Clara; Camargo Magalhães Maniglia, Marcela; Silva Pereira, Ana Maria; Rodrigues das Chagas, Gustavo; Carvalho, Eliane Maria

2016-05-15

Neurological disorders are associated with autonomic dysfunction. Hippotherapy (HT) is a therapy treatment strategy that utilizes a horse in an interdisciplinary approach for the physical and mental rehabilitation of people with physical, mental and/or psychological disabilities. However, no studies have been carried out which evaluated the effects of HT on the autonomic control in these patients. Therefore, the objective of the present study was to investigate the effects of a single HT session on cardiovascular autonomic control by time domain and non-linear analysis of heart rate variability (HRV). The HRV signal was recorded continuously in twelve children affected by neurological disorders during a HT session, consisting in a 10-minute sitting position rest (P1), a 15-minute preparatory phase sitting on the horse (P2), a 15-minute HT session (P3) and a final 10-minute sitting position recovery (P4). Time domain and non-linear HRV indices, including Sample Entropy (SampEn), Lempel-Ziv Complexity (LZC) and Detrended Fluctuation Analysis (DFA), were calculated for each treatment phase. We observed that SampEn increased during P3 (SampEn=0.56±0.10) with respect to P1 (SampEn=0.40±0.14, p<0.05), while DFA decreased during P3 (DFA=1.10±0.10) with respect to P1 (DFA=1.26±0.14, p<0.05). A significant SDRR increase (p<0.05) was observed during the recovery period P4 (SDRR=50±30ms) with respect to the HT session period P3 (SDRR=30±10ms). Our results suggest that HT might benefit children with disabilities attributable to neurological disorders by eliciting an acute autonomic response during the therapy and during the recovery period.

16. Automatic Assessment and Reduction of Noise using Edge Pattern Analysis in Non-Linear Image Enhancement

NASA Technical Reports Server (NTRS)

Jobson, Daniel J.; Rahman, Zia-Ur; Woodell, Glenn A.; Hines, Glenn D.

2004-01-01

Noise is the primary visibility limit in the process of non-linear image enhancement, and is no longer a statistically stable additive noise in the post-enhancement image. Therefore novel approaches are needed to both assess and reduce spatially variable noise at this stage in overall image processing. Here we will examine the use of edge pattern analysis both for automatic assessment of spatially variable noise and as a foundation for new noise reduction methods.

17. Wavelet shrinkage of a noisy dynamical system with non-linear noise impact

Garcin, Matthieu; Guégan, Dominique

2016-06-01

By filtering wavelet coefficients, it is possible to construct a good estimate of a pure signal from noisy data. Especially, for a simple linear noise influence, Donoho and Johnstone (1994) have already defined an optimal filter design in the sense of a minimization of the error made when estimating the pure signal. We set here a different framework where the influence of the noise is non-linear. In particular, we propose a method to filter the wavelet coefficients of a discrete dynamical system disrupted by a weak noise, in order to construct good estimates of the pure signal, including Bayes' estimate, minimax estimate, oracular estimate or thresholding estimate. We present the example of a logistic and a Lorenz chaotic dynamical system as well as an adaptation of our technique in order to show empirically the robustness of the thresholding method in presence of leptokurtic noise. Moreover, we test both the hard and the soft thresholding and also another kind of smoother thresholding which seems to have almost the same reconstruction power as the hard thresholding. Finally, besides the tests on an estimated dataset, the method is tested on financial data: oil prices and NOK/USD exchange rate.

18. Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam

Rizov, V.

2016-03-01

Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.

19. Non-linear analysis and calculation of the performance of a shelving protection system by FEM

García Nieto, P. J.; del Coz Díaz, J. J.; Vilán Vilán, J. A.; Suárez Sierra, J. L.

2012-12-01

The aim of this paper consists on the study, analysis and calculation of the efficiency of a shelving protection system by means of the finite element method (FEM). These shelving protection systems are intended to prevent the eventual damage due to the impacts of transport elements in motion, such as: forklifts, dumpers, hand pallet trucks, and so on. The impact loads may threaten the structural integrity of the shelving system. The present structural problem is highly non-linear, due to the simultaneous presence of the following nonlinearities: material non-linearity (plasticity in this case), geometrical non-linearity (large displacements) and contact-type boundary conditions (between the rigid body and the protection system). A total of forty eight different FEM models are built varying the thickness of the steel plate (4, 5 and 6 mm), the impact height (0.1, 0.2, 0.3 and 0.4 meters) and the impact direction (head-on collision and side impact). Once the models are solved, the stress distribution, the overall displacements and the absorbed impact energy were calculated. In order to determine the best shelving protection's candidate, some constraints must be taken into account: the maximum allowable stress (235 MPa), the maximum displacement (0.05 m) and the absorbed impact energy (400 J according to the European Standard Rule PREN-15512). Finally, the most important results are shown and conclusions of this study are exposed.

20. Non-linear dynamics of human periodic breathing and implications for sleep apnea therapy.

PubMed

Yamashiro, S M

2007-04-01

A mathematical model of non-obstructive human periodic breathing (Cheyne-Stokes respiration) or central sleep apnea (CSA) is described which focused on explaining recently reported non-linear behavior. Evidence was presented that CHF (chronic heart failure)-CSA and ICSA (idiopathic central sleep apnea) both involved limit cycle oscillations. The validity of applying linear control theory for stabilization must then be re-examined. Critical threshold values and ranges of parameters were predicted which caused a change (bifurcation) from limit cycle periodic breathing to stable breathing. Changes in lung volume were predicted to form a bifurcation during CHF-CSA where stability and instability can involve a lung volume change as small as 0.1 l. CSA therapy based on reducing control loop gain was predicted to be relatively ineffective during stable limit cycle oscillation. The relative ratios of durations of ventilation to apnea (T(v)/T(a)) during periodic breathing were primarily determined by peripheral chemoreceptor dynamics during crescendo, de-crescendo, and apnea phases of CSA.

1. How does non-linear dynamics affect the baryon acoustic oscillation?

SciTech Connect

Sugiyama, Naonori S.; Spergel, David N. E-mail: dns@astro.princeton.edu

2014-02-01

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-k solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-k solutions, some of the recently proposed improved perturbation theories do not guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-k regions. We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at z = 0.35 as ∼ 7.7Mpc/h and describes the small non-linear shift in the peak position due to the galaxy random motions.

2. A non-linear dynamical approach to belief revision in cognitive behavioral therapy

PubMed Central

Kronemyer, David; Bystritsky, Alexander

2014-01-01

Belief revision is the key change mechanism underlying the psychological intervention known as cognitive behavioral therapy (CBT). It both motivates and reinforces new behavior. In this review we analyze and apply a novel approach to this process based on AGM theory of belief revision, named after its proponents, Carlos Alchourrón, Peter Gärdenfors and David Makinson. AGM is a set-theoretical model. We reconceptualize it as describing a non-linear, dynamical system that occurs within a semantic space, which can be represented as a phase plane comprising all of the brain's attentional, cognitive, affective and physiological resources. Triggering events, such as anxiety-producing or depressing situations in the real world, or their imaginal equivalents, mobilize these assets so they converge on an equilibrium point. A preference function then evaluates and integrates evidentiary data associated with individual beliefs, selecting some of them and comprising them into a belief set, which is a metastable state. Belief sets evolve in time from one metastable state to another. In the phase space, this evolution creates a heteroclinic channel. AGM regulates this process and characterizes the outcome at each equilibrium point. Its objective is to define the necessary and sufficient conditions for belief revision by simultaneously minimizing the set of new beliefs that have to be adopted, and the set of old beliefs that have to be discarded or reformulated. Using AGM, belief revision can be modeled using three (and only three) fundamental syntactical operations performed on belief sets, which are expansion; revision; and contraction. Expansion is like adding a new belief without changing any old ones. Revision is like adding a new belief and changing old, inconsistent ones. Contraction is like changing an old belief without adding any new ones. We provide operationalized examples of this process in action. PMID:24860491

3. Analysis of non linear partially standing waves from 3D velocity measurements

Drevard, D.; Rey, V.; Svendsen, Ib; Fraunie, P.

2003-04-01

Surface gravity waves in the ocean exhibit an energy spectrum distributed in both frequency and direction of propagation. Wave data collection is of great importance in coastal zones for engineering and scientific studies. In particular, partially standing waves measurements near coastal structures and steep or barred beaches may be a requirement, for instance for morphodynamic studies. The aim of the present study is the analysis of partially standing surface waves icluding non-linear effects. According to 1st order Stokes theory, synchronous measurements of horizontal and vertical velocity components allow calculation of rate of standing waves (Drevard et al, 2003). In the present study, it is demonstrated that for deep water conditions, partially standing 2nd order Stokes waves induced velocity field is still represented by the 1st order solution for the velocity potential contrary to the surface elevation which exhibits harmonic components. For intermediate water depth, harmonic components appear not only in the surface elevation but also in the velocity fields, but their weight remains much smaller, because of the vertical decreasing wave induced motion. For irregular waves, the influence of the spectrum width on the non-linear effects in the analysis is discussed. Keywords: Wave measurements ; reflection ; non-linear effects Acknowledgements: This work was initiated during the stay of Prof. Ib Svendsen, as invited Professor, at LSEET in autumn 2002. This study is carried out in the framework of the Scientific French National Programmes PNEC ART7 and PATOM. Their financial supports are acknowledged References: Drevard, D., Meuret, A., Rey, V. Piazzola, J. And Dolle, A.. (2002). "Partially reflected waves measurements using Acoustic Doppler Velocimeter (ADV)", Submitted to ISOPE 03, Honolulu, Hawaii, May 2003.

4. Comments on "arithmetic coding as a non-linear dynamical system"

Pande, Amit; Zambreno, Joseph; Mohapatra, Prasant

2012-12-01

Nagaraj et al. [1,2] present a skewed-non-linear generalized Luroth Series (s-nGLS) framework. S-nGLS uses non-linear maps for GLS to introduce a security parameter a which is used to build a keyspace for image or data encryption. The map introduces non-linearity to the system to add an "encryption key parameter". The skew is added to achieve optimal compression efficiency. s-nGLS used as such for joint encryption and compression is a weak candidate, as explained in this communication. First, we show how the framework is vulnerable to known plaintext based attacks and that a key of size 256 bits can be broken within 1000 trials. Next, we demonstrate that the proposed non-linearity exponentially increases the hardware complexity of design. We also discover that s-nGlS cannot be implemented as such for large bitstreams. Finally, we demonstrate how correlation of key parameter with compression performance leads to further key vulnerabilities.

5. Non-linear analysis and the design of Pumpkin Balloons: stress, stability and viscoelasticity

Rand, J. L.; Wakefield, D. S.

Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures Founded upon their inTENS finite element analysis suite these activities have broadened to encompass lighter than air structures such as aerostats hybrid air-vehicles and stratospheric balloons Winzen Engineering couple many years of practical balloon design and fabrication experience with both academic and practical knowledge of the characterisation of the non-linear viscoelastic response of the polymeric films typically used for high-altitude scientific balloons Both companies have provided consulting services to the NASA Ultra Long Duration Balloon ULDB Program Early implementations of pumpkin balloons have shown problems of geometric instability characterised by improper deployment and these difficulties have been reproduced numerically using inTENS The solution lies in both the shapes of the membrane lobes and also the need to generate a biaxial stress field in order to mobilise in-plane shear stiffness Balloons undergo significant temperature and pressure variations in flight The different thermal characteristics between tendons and film can lead to significant meridional stress Fabrication tolerances can lead to significant local hoop stress concentrations particularly adjacent to the base and apex end fittings The non-linear viscoelastic response of the envelope film acts positively to help dissipate stress concentrations However creep over time may produce lobe geometry variations that may

6. Non-linear dynamic analyses of 3D masonry structures by means of a homogenized rigid body and spring model (HRBSM)

Bertolesi, Elisa; Milani, Gabriele; Casolo, Siro

2016-12-01

A simple homogenized rigid body and spring model (HRBSM) is presented and applied for the non-linear dynamic analysis of 3D masonry structures. The approach, previously developed by the authors for the modeling of in-plane loaded walls is herein extended to real 3D buildings subjected to in- and out-of-plane deformation modes. The elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. At a structural level, the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM) by means of which both in and out of plane mechanisms are allowed. All the simulations here presented are performed using the commercial software Abaqus. In order to validate the proposed model for the analyses of full scale structures subjected to seismic actions, two different examples are critically discussed, namely a church façade and an in-scale masonry building, both subjected to dynamic excitation. The results obtained are compared with experimental or numerical results available in literature.

7. Litchi freshness rapid non-destructive evaluating method using electronic nose and non-linear dynamics stochastic resonance model.

PubMed

Ying, Xiaoguo; Liu, Wei; Hui, Guohua

2015-01-01

In this paper, litchi freshness rapid non-destructive evaluating method using electronic nose (e-nose) and non-linear stochastic resonance (SR) was proposed. EN responses to litchi samples were continuously detected for 6 d Principal component analysis (PCA) and non-linear stochastic resonance (SR) methods were utilized to analyze EN detection data. PCA method could not totally discriminate litchi samples, while SR signal-to-noise ratio (SNR) eigen spectrum successfully discriminated all litchi samples. Litchi freshness predictive model developed using SNR eigen values shows high predictive accuracy with regression coefficients R(2) = 0 .99396.

8. Non-linear canonical correlation for joint analysis of MEG signals from two subjects.

PubMed

Campi, Cristina; Parkkonen, Lauri; Hari, Riitta; Hyvärinen, Aapo

2013-01-01

Traditional stimulus-based analysis methods of magnetoencephalography (MEG) data are often dissatisfactory when applied to naturalistic experiments where two or more subjects are measured either simultaneously or sequentially. To uncover the commonalities in the brain activity of the two subjects, we propose a method that searches for linear transformations that output maximally correlated signals between the two brains. Our method is based on canonical correlation analysis (CCA), which provides linear transformations, one for each subject, such that the temporal correlation between the transformed MEG signals is maximized. Here, we present a non-linear version of CCA which measures the correlation of energies and allows for a variable delay between the time series to accommodate, e.g., leader-follower changes. We test the method with simulations and with MEG data from subjects who received the same naturalistic stimulus sequence. The method may help analyse future experiments where the two subjects are measured simultaneously while engaged in social interaction.

9. Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

SciTech Connect

Zhu, Z. W.; Zhang, W. D. Xu, J.

2014-03-15

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

10. Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

11. Three dimensional, non-linear, finite element analysis of compactable soil interaction with a hyperelastic wheel

Chiroux, Robert Charles

The objective of this research was to produce a three dimensional, non-linear, dynamic simulation of the interaction between a hyperelastic wheel rolling over compactable soil. The finite element models developed to produce the simulation utilized the ABAQUS/Explicit computer code. Within the simulation two separate bodies were modeled, the hyperelastic wheel and a compactable soil-bed. Interaction between the bodies was achieved by allowing them to come in contact but not to penetrate the contact surface. The simulation included dynamic loading of a hyperelastic, rubber tire in contact with compactable soil with an applied constant angular velocity or torque, including a tow load, applied to the wheel hub. The constraints on the wheel model produced a straight and curved path. In addition the simulation included a shear limit between the tire and soil allowing for the introduction of slip. Soil properties were simulated using the Drucker-Prager, Cap Plasticity model available within the ABAQUS/Explicit program. Numerical results obtained from the three dimensional model were compared with related experimental data and showed good correlation for similar conditions. Numerical and experimental data compared well for both stress and wheel rut formation depth under a weight of 5.8 kN and a constant angular velocity applied to the wheel hub. The simulation results provided a demonstration of the benefit of three-dimensional simulation in comparison to previous two-dimensional, plane strain simulations.

12. Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

PubMed Central

2011-01-01

Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520

13. Non-linear Dynamics Of Toroidicity-induced Alfven Eigenmodes On The National Spherical Torus Experiment

SciTech Connect

Podesta, M; Crocker, N A; Fredrickson, E D; Gorelenkov, N N; Heidbrink, W W; Kubota, S; LeBlanc, B P

2011-04-26

The National Spherical Torus Experiment (NSTX, [M. Ono et al., Nucl. Fusion 40, 557 (2000)]) routinely operates with neutral beam injection as the primary system for heating and current drive. The resulting fast ion population is super-Alfv enic, with velocities 1 < vfast=vAlfven < 5. This provides a strong drive for toroidicity-induced Alfv en eigenmodes (TAEs). As the discharge evolves, the fast ion population builds up and TAEs exhibit increasing bursts in amplitude and down-chirps in frequency, which eventually lead to a so-called TAE avalanche. Avalanches cause large (≤ 30%) fast ion losses over ~ 1 ms, as inferred from the neutron rate. The increased fast ion losses correlate with a stronger activity in the TAE band. In addition, it is shown that a n = 1 mode with frequency well below the TAE gap appears in the Fourier spectrum of magnetic fluctuations as a result of non-linear mode coupling between TAEs during avalanche events. The non-linear coupling between modes, which leads to enhanced fast ion transport during avalanches, is investigated.

14. Helical waves and non-linear dynamics of fluid/structure interactions in a tube row

SciTech Connect

1997-12-31

The goal of this study has been to investigate low-dimensional models for fluid-structure dynamics of flow across a row of cylindrical tubes. Four principle results of this experimental-theoretical study are discussed. (i) Experimental evidence has shown that the dynamic instability of the tube row is a subcritical Hopf bifurcation. (ii) The critical flow velocity decreases as the number of flexible cylinders increases. (iii) The linear model exhibits coupled helical wave solutions in the tube dynamics. (iv) A nonlinear model of the tube motions shows a complex subcritical Hopf bifurcation with a secondary bifurcation to a torus or quasi-periodic oscillation. In this analysis the tools of center manifolds, normal forms and numerical simulation are used.

15. Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

16. Numerical insight into the seismic behavior of eight masonry towers in Northern Italy: FE pushover vs non-linear dynamic analyses

Milani, Gabriele; Valente, Marco

2015-12-01

This study presents some FE results regarding the behavior under horizontal loads of eight existing masonry towers located in the North-East of Italy. The towers, albeit unique for geometric and architectural features, show some affinities which justify a comparative analysis, as for instance the location and the similar masonry material. Their structural behavior under horizontal loads is therefore influenced by geometrical issues, such as slenderness, walls thickness, perforations, irregularities, presence of internal vaults, etc., all features which may be responsible for a peculiar output. The geometry of the towers is deduced from both existing available documentation and in-situ surveys. On the basis of such geometrical data, a detailed 3D realistic mesh is conceived, with a point by point characterization of each single geometric element. The FE models are analysed under seismic loads acting along geometric axes of the plan section, both under non-linear static (pushover) and non-linear dynamic excitation assumptions. A damage-plasticity material model exhibiting softening in both tension and compression, already available in the commercial code Abaqus, is used for masonry. Pushover analyses are performed with both G1 and G2 horizontal loads distribution, according to Italian code requirements, along X+/- and Y+/- directions. Non-linear dynamic analyses are performed along both X and Y directions with a real accelerogram scaled to different peak ground accelerations. Some few results are presented in this paper. It is found that the results obtained with pushover analyses reasonably well fit expensive non-linear dynamic simulations, with a slightly less conservative trend.

17. Numerical insight into the seismic behavior of eight masonry towers in Northern Italy: FE pushover vs non-linear dynamic analyses

SciTech Connect

Milani, Gabriele E-mail: gabriele.milani@polimi.it; Valente, Marco

2015-12-31

This study presents some FE results regarding the behavior under horizontal loads of eight existing masonry towers located in the North-East of Italy. The towers, albeit unique for geometric and architectural features, show some affinities which justify a comparative analysis, as for instance the location and the similar masonry material. Their structural behavior under horizontal loads is therefore influenced by geometrical issues, such as slenderness, walls thickness, perforations, irregularities, presence of internal vaults, etc., all features which may be responsible for a peculiar output. The geometry of the towers is deduced from both existing available documentation and in-situ surveys. On the basis of such geometrical data, a detailed 3D realistic mesh is conceived, with a point by point characterization of each single geometric element. The FE models are analysed under seismic loads acting along geometric axes of the plan section, both under non-linear static (pushover) and non-linear dynamic excitation assumptions. A damage-plasticity material model exhibiting softening in both tension and compression, already available in the commercial code Abaqus, is used for masonry. Pushover analyses are performed with both G1 and G2 horizontal loads distribution, according to Italian code requirements, along X+/− and Y+/− directions. Non-linear dynamic analyses are performed along both X and Y directions with a real accelerogram scaled to different peak ground accelerations. Some few results are presented in this paper. It is found that the results obtained with pushover analyses reasonably well fit expensive non-linear dynamic simulations, with a slightly less conservative trend.

18. Dynamics of glass-forming liquids. XX. Third harmonic experiments of non-linear dielectric effects versus a phenomenological model

Kim, Pyeongeun; Young-Gonzales, Amanda R.; Richert, Ranko

2016-08-01

We have re-measured the third harmonic non-linear dielectric response of supercooled glycerol using zero-bias sinusoidal electric fields, with the aim of comparing the resulting susceptibilities with a phenomenological model of non-linear dielectric responses. In the absence of known chemical effects in this liquid, the present model accounts for three sources of non-linear behavior: dielectric saturation, field induced entropy reduction, and energy absorption from the time dependent field. Using parameters obtained from static high field results, the present model reproduces the characteristic features observed in the third harmonic susceptibility spectra: a low frequency plateau originating from dielectric saturation and a peak positioned below the loss peak frequency whose amplitude increases with decreasing temperature. Semi-quantitative agreement is achieved between experiment and the present model, which does not involve spatial scales or dynamical correlations explicitly. By calculating the three contributions separately, the model reveals that the entropy effect is the main source of the "hump" feature of this third harmonic response.

19. Applying non-linear dynamics to atrial appendage flow data to understand and characterize atrial arrhythmia

SciTech Connect

Chandra, S.; Grimm, R.A.; Katz, R.; Thomas, J.D.

1996-06-01

The aim of this study was to better understand and characterize left atrial appendage flow in atrial fibrillation. Atrial fibrillation and flutter are the most common cardiac arrhythmias affecting 15% of the older population. The pulsed Doppler velocity profile data was recorded from the left atrial appendage of patients using transesophageal echocardiography. The data was analyzed using Fourier analysis and nonlinear dynamical tools. Fourier analysis showed that appendage mechanical frequency ({ital f{sub f}}) for patients in sinus rhythm was always lower (around1 Hz) than that in atrial fibrillation (5-8 Hz). Among patients with atrial fibrillation spectral power below {ital f{sub f}} was significantly different suggesting variability within this group of patients. Results that suggested the presence of nonlinear dynamics were: a) the existence of two arbitrary peak frequencies {ital f{sub 1}, f{sub 2}}, and other peak frequencies as linear combinations thereof ({ital mf{sub 1}{+-}nf{sub 2}}), and b) the similarity between the spectrum of patient data and that obtained using the Lorenz equation. Nonlinear analysis tools, including Phase plots and differential radial plots, were also generated from the velocity data using a delay of 10. In the phase plots, some patients displayed a torus-like structure, while others had a more random-like pattern. In the differential radial plots, the first set of patients (with torus-like phase plots) showed fewer values crossing an arbitrary threshold of 10 than did the second set (8 vs. 27 in one typical example). The outcome of cardioversion was different for these two set of patients. Fourier analysis helped to: differentiate between sinus rhythm and atrial fibrillation, understand the characteristics of the wide range of atrial fibrillation patients, and provide hints that atrial fibrillation could be a nonlinear process. Nonlinear dynamical tools helped to further characterize and sub-classify atrial fibrillation.

20. The behaviour of PM10 and ozone in Malaysia through non-linear dynamical systems

Sapini, Muhamad Luqman; Rahim, Nurul Zahirah binti Abd; Noorani, Mohd Salmi Md.

2015-10-01

Prediction of ozone (O3) and PM10 is very important as both these air pollutants affect human health, human activities and more. Short-term forecasting of air quality is needed as preventive measures and effective action can be taken. Therefore, if it is detected that the ozone data is of a chaotic dynamical systems, a model using the nonlinear dynamic from chaos theory data can be made and thus forecasts for the short term would be more accurate. This study uses two methods, namely the 0-1 Test and Lyapunov Exponent. In addition, the effect of noise reduction on the analysis of time series data will be seen by using two smoothing methods: Rectangular methods and Triangle methods. At the end of the study, recommendations were made to get better results in the future.

1. The behaviour of PM10 and ozone in Malaysia through non-linear dynamical systems

SciTech Connect

Sapini, Muhamad Luqman; Rahim, Nurul Zahirah binti Abd; Noorani, Mohd Salmi Md.

2015-10-22

Prediction of ozone (O3) and PM10 is very important as both these air pollutants affect human health, human activities and more. Short-term forecasting of air quality is needed as preventive measures and effective action can be taken. Therefore, if it is detected that the ozone data is of a chaotic dynamical systems, a model using the nonlinear dynamic from chaos theory data can be made and thus forecasts for the short term would be more accurate. This study uses two methods, namely the 0-1 Test and Lyapunov Exponent. In addition, the effect of noise reduction on the analysis of time series data will be seen by using two smoothing methods: Rectangular methods and Triangle methods. At the end of the study, recommendations were made to get better results in the future.

2. Analysis of non linear land subsidence in Mexico city lacustrine plain

López-Quiroz, P.; Doin, M.; Carreon-Freyre, D.; Cerca, M.

2012-12-01

Mexico city, one of the biggest cities in the world, faces a subsidence problem mostly caused by heavy groundwater extraction from its aquifer. To monitor subsidence, from 2002 to 2007, we developed time series using InSAR and the Small Baseline interferograms (SBAS) approach. Results showed that subsidence rates can reach up to 40 cm/yr and that most of the subsidence in Mexico city's plain can be explained almost perfectly using a linear model. In fact, most of the previous studies focus mainly on linear subsidence processes. However, we detected some areas distributed on the plain showing two clear patterns of non-linear behavior: acceleration and deceleration. The spatial and temporal distribution of these areas can be related with geological features and rates of groundwater withdrawal taking place in the surrounding areas. In this work, results are presented over an area of the most populated district of the city where subsidence velocity appears to be increasing rapidly. The phenomenon is analyzed through the integration of InSAR results with different field monitoring techniques including Ground Penetrating Radar and geomechanical analysis in selected points.

3. Influence of shear in the non-linear analysis of RC members

SciTech Connect

Diotallevi, Pier Paolo; Landi, Luca; Cardinetti, Filippo

2008-07-08

The purpose of this study is to develop an analytical model characterized by a beam-column finite element which is able to reproduce the non-linear flexural-shear behavior of RC structures. The paper shows a brief description of the finite element formulation, the theory used for modeling the constitutive relationship and the scheme of the algorithm, transformed in a computer program, which was developed for implementing the theoretical model. Finally it illustrates a comparison with available experimental results for the calibration and validation of the model and a study on the influence of the non-linear shear response.

4. Discriminative analysis of non-linear brain connectivity for leukoaraiosis with resting-state fMRI

Lai, Youzhi; Xu, Lele; Yao, Li; Wu, Xia

2015-03-01

Leukoaraiosis (LA) describes diffuse white matter abnormalities on CT or MR brain scans, often seen in the normal elderly and in association with vascular risk factors such as hypertension, or in the context of cognitive impairment. The mechanism of cognitive dysfunction is still unclear. The recent clinical studies have revealed that the severity of LA was not corresponding to the cognitive level, and functional connectivity analysis is an appropriate method to detect the relation between LA and cognitive decline. However, existing functional connectivity analyses of LA have been mostly limited to linear associations. In this investigation, a novel measure utilizing the extended maximal information coefficient (eMIC) was applied to construct non-linear functional connectivity in 44 LA subjects (9 dementia, 25 mild cognitive impairment (MCI) and 10 cognitively normal (CN)). The strength of non-linear functional connections for the first 1% of discriminative power increased in MCI compared with CN and dementia, which was opposed to its linear counterpart. Further functional network analysis revealed that the changes of the non-linear and linear connectivity have similar but not completely the same spatial distribution in human brain. In the multivariate pattern analysis with multiple classifiers, the non-linear functional connectivity mostly identified dementia, MCI and CN from LA with a relatively higher accuracy rate than the linear measure. Our findings revealed the non-linear functional connectivity provided useful discriminative power in classification of LA, and the spatial distributed changes between the non-linear and linear measure may indicate the underlying mechanism of cognitive dysfunction in LA.

5. Transonic and Low-Supersonic Aeroelastic Analysis of a Two-Degree Airfoil with a Freeplay Non-Linearity

KIM, DONG-HYUN; LEE, IN

2000-07-01

A two-degree-of-freedom airfoil with a freeplay non-linearity in the pitch and plunge directions has been analyzed in the transonic and low-supersonic flow region, where aerodynamic non-linearities also exist. The primary purpose of this study is to show aeroelastic characteristics due to freeplay structural non-linearity in the transonic and low-supersonic regions. The unsteady aerodynamic forces on the airfoil were evaluated using two-dimensional unsteady Euler code, and the resulting aeroelastic equations are numerically integrated to obtain the aeroelastic time responses of the airfoil motions and to investigate the dynamic instability. The present model has been considered as a simple aeroelastic model, which is equivalent to the folding fin of an advanced generic missile. From the results of the present study, characteristics of important vibration responses and aeroelastic instabilities can be observed in the transonic and supersonic regions, especially considering the effect of structural non-linearity in the pitch and plunge directions. The regions of limit-cycle oscillation are shown at much lower velocities, especially in the supersonic flow region, than the divergent flutter velocities of the linear structure model. It is also shown that even small freeplay angles can lead to severe dynamic instabilities and dangerous fatigue conditions for the flight vehicle wings and control fins.

6. Cold gas in cluster cores: global stability analysis and non-linear simulations of thermal instability

Choudhury, Prakriti Pal; Sharma, Prateek

2016-04-01

We perform global linear stability analysis and idealized numerical simulations in global thermal balance to understand the condensation of cold gas from hot/virial atmospheres (coronae), in particular the intracluster medium (ICM). We pay particular attention to geometry (e.g. spherical versus plane-parallel) and the nature of the gravitational potential. Global linear analysis gives a similar value for the fastest growing thermal instability modes in spherical and Cartesian geometries. Simulations and observations suggest that cooling in haloes critically depends on the ratio of the cooling time to the free-fall time (tcool/tff). Extended cold gas condenses out of the ICM only if this ratio is smaller than a threshold value close to 10. Previous works highlighted the difference between the nature of cold gas condensation in spherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier in spherical atmospheres. This apparent difference due to geometry arises because the previous plane-parallel simulations focused on in situ condensation of multiphase gas but spherical simulations studied condensation anywhere in the box. Unlike previous claims, our non-linear simulations show that there are only minor differences in cold gas condensation, either in situ or anywhere, for different geometries. The amount of cold gas depends on the shape of tcool/tff; gas has more time to condense if gravitational acceleration decreases towards the centre. In our idealized plane-parallel simulations with heating balancing cooling in each layer, there can be significant mass/energy/momentum transfer across layers that can trigger condensation and drive tcool/tff far beyond the critical value close to 10.

7. Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

8. Transverse beam dynamics in non-linear Fixed Field Alternating Gradient accelerators

SciTech Connect

Haj, Tahar M.; Meot, F.

2016-03-02

In this paper, we present some aspects of the transverse beam dynamics in Fixed Field Ring Accelerators (FFRA): we start from the basic principles in order to derive the linearized transverse particle equations of motion for FFRA, essentially FFAGs and cyclotrons are considered here. This is a simple extension of a previous work valid for linear lattices that we generalized by including the bending terms to ensure its correctness for FFAG lattice. The space charge term (contribution of the internal coulombian forces of the beam) is contained as well, although it is not discussed here. The emphasis is on the scaling FFAG type: a collaboration work is undertaken in view of better understanding the properties of the 150 MeV scaling FFAG at KURRI in Japan, and progress towards high intensity operation. Some results of the benchmarking work between different codes are presented. Analysis of certain type of field imperfections revealed some interesting features about this machine that explain some of the experimental results and generalize the concept of a scaling FFAG to a non-scaling one for which the tune variations obey a well-defined law.

9. Analysis and Evaluation of Technical Data on the Photochromic and Non-Linear Optical Properties of Materials

DTIC Science & Technology

1990-06-25

t ,, A FILE C’D AD-A2 23 855 Sixth Quarterly Technical Report Analysis and Evaluation of Technical Data on the Photochromic and Non-Linear Optical...the back surface of a transparent support and place an absorbing beam dump behind and at an angle to that of the reflective coating . In this

10. Storage Dynamics and Non-Linear Connectivity between Landscape Units Control Runoff Generation and Stream Water Age Distributions

Soulsby, C.; Birkel, C.; Geris, J.; Tetzlaff, D.

2015-12-01

We assess the influence of storage dynamics and non-linearities in hydrological connectivity on runoff generation and stream water ages, using a long-term record of daily isotopes in precipitation and stream flow. These were used to test a parsimonious tracer-aided runoff model for a Scottish catchment. The model tracks tracers and the ages of water fluxes through and between conceptual stores representing steeper hillslopes, dynamically saturated riparian peatlands and deeper groundwater (i.e. the main landscape units involved in runoff generation). Storage is largest in groundwater and on the steep hillslopes, though most dynamic mixing occurs in smaller stores in the riparian peat. The model also couples the ecohydrological effects of different vegetation communities in contrasting landscape units, by estimating evaporation, resulting moisture deficits and the ages of evaporated waters, which also affect the generation and age of runoff. Both stream flow and isotope variations are well-captured by the model, and the simulated storage and tracer dynamics in the main landscape units are consistent with independent measurements. The model predicts the mean age of runoff as ~1.8 years. On a daily basis, this varies from ~1 month in storm events, when younger waters draining the riparian peatland dominate, to around 4 years in dry periods, when groundwater sustains flow. Hydrological connectivity between the units varies non-linearly with storage which depends upon antecedent conditions and event characteristics. This, in turn, determines the spatial distribution of flow paths and the integration of their contrasting non-stationary ages. Improving the representation of storage dynamics and quantifying the ages of water fluxes in such models gives a more complete conceptualisation of the importance of the soil water fluxes in critical zone processes and a framework for tracking diffuse pollutants in water quality assessment.

11. Exact Adjustment of Dynamic Forces in Presence of Non-Linear Feedback and SINGULARITY—THEORY and Algorithm

Bucher, I.

1998-11-01

This paper describes the theory and algorithm allowing one to tune a multi-exciter system in order to obtain specified temporal and spatial structural response properties. Considerable effort is being put upon the desire to overcome practical difficulties and limitations as found in real-world systems. The main application that was envisaged for this algorithm is the creation of travelling vibration waves in structures. Such waves may be useful in testing and diagnostic applications or in ultrasonic motors for generating motion. The proposed method adaptively modifies a set of perturbations applied to the model so that an increasing amount of information is extracted from the system. The algorithm strives to overcome the following difficulties: (a) singular model inversion, (b) poor signal to noise ratio, (c) feedback, and (d) certain types of non-linear behaviour. High response levels, exciter-structure coupling and the inherent feedback existing in electro-mechanical systems are demonstrated to cause singularity, poor signal to noise levels and, to some extent, non linear behaviour. These phenomena pose some difficulties under operating conditions commonly encountered during dynamic testing of structures. The tuning of the multi-shaker system is approached in this work, as a non-linear optimisation problem where insight into the physical behaviour is emphasised in choosing the algorithmic strategy. The system's unknown model is inverted in an implicit manner using an automatic orthogonal and adaptive search direction. This adaptation uses the measured responses and forces at each step in order to determine the direction of progression during the tuning process. The non-linear behaviour of the exciters is compensated, in this work, by identification of the high-order (Volterra-like) transfer functions. This high-order model is than inverted allowing one to create a signal that cancels the unwanted harmonics. The proposed approach is analytically shown to converge

12. First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics

Bagarello, F.; Haven, E.

2016-02-01

We discuss a non linear extension of a model of alliances in politics, recently proposed by one of us. The model is constructed in terms of operators, describing the interest of three parties to form, or not, some political alliance with the other parties. The time evolution of what we call the decision functions is deduced by introducing a suitable Hamiltonian, which describes the main effects of the interactions of the parties amongst themselves and with their environments, which are generated by their electors and by people who still have no clear idea for which party to vote (or even if to vote). The Hamiltonian contains some non-linear effects, which takes into account the role of a party in the decision process of the other two parties. Moreover, we show how the same Hamiltonian can also be used to construct a formal structure which can describe the dynamics of buying and selling financial assets (without however implying a specific price setting mechanism).

13. Linear to non linear analysis for positron acceleration in plasma hollow channel wakefields

Amorim, Ligia Diana; An, Weiming; Mori, Warren B.; Vieira, Jorge

2016-10-01

Plasma wakefield accelerators are promising candidates for future generation compact accelerators. The standard regime of operation, non-linear or blowout regime, is reached when a particle bunch space charge or laser pulse ponderomotive force radially expels plasma electrons forming a bucket of ions that defocus positron bunches, thus preventing their acceleration. To avoid defocusing, hollow plasma channels have been considered. The corresponding wakefields have been examined in the linear and non-linear excitation regimes for electrons. It is therefore important to extend the theory for positron acceleration, particularly in the nonlinear regime where the wakefields strongly differ. In this work we explore the wakefield structure, examine the differences between the electron and positron beam cases, and explore positron acceleration in nonlinear regimes. We support our findings with multi-dimensional particle-in-cell simulations performed with OSIRIS and quasi-3D and QuickPIC.

14. Finite element analysis of the non-linear vibrations of moderately thick unsymmetrically laminated composite plates

Singh, Gajbir; Venkateswara Rao, G.; Iyengar, N. G. R.

1995-03-01

The influence of finite amplitudes on the free flexural vibration response of moderately thick laminated plates is investigated. For this purpose, a simple higher order theory involving only four unknowns and satisfying the stress free conditions at the top and bottom surface of the composite plate is proposed. The proposed theory eliminates the use of shear correction factors which are otherwise required in Mindlin's plate theory. A rectangular four-node[formula]continuous finite element is developed based on this theory. The non-linear finite element equations are reduced to two non-linear ordinary differential equations governing the response of positive and negative deflection cycles. Direct numerical integration method is then employed to obtain the periods or non-linear frequencies. The finite element developed and the direct numerical integration method employed are validated for the case of isotropic rectangular plates. It is found that unsymmetrically laminated rectangular plates with hinged-hinged edge conditions oscillate with different amplitudes in the positive and negative deflection cycles. Furthermore, such plates would oscillate with a frequency less than the fundamental frequency for finite small amplitudes of oscillation. It is shown that this behaviour is strongly influenced by the boundary conditions. Results are presented for many configurations of composite plates.

15. Reservoir computing and extreme learning machines for non-linear time-series data analysis.

PubMed

Butcher, J B; Verstraeten, D; Schrauwen, B; Day, C R; Haycock, P W

2013-02-01

Random projection architectures such as Echo state networks (ESNs) and Extreme Learning Machines (ELMs) use a network containing a randomly connected hidden layer and train only the output weights, overcoming the problems associated with the complex and computationally demanding training algorithms traditionally used to train neural networks, particularly recurrent neural networks. In this study an ESN is shown to contain an antagonistic trade-off between the amount of non-linear mapping and short-term memory it can exhibit when applied to time-series data which are highly non-linear. To overcome this trade-off a new architecture, Reservoir with Random Static Projections (R(2)SP) is investigated, that is shown to offer a significant improvement in performance. A similar approach using an ELM whose input is presented through a time delay (TD-ELM) is shown to further enhance performance where it significantly outperformed the ESN and R(2)SP as well other architectures when applied to a novel task which allows the short-term memory and non-linearity to be varied. The hard-limiting memory of the TD-ELM appears to be best suited for the data investigated in this study, although ESN-based approaches may offer improved performance when processing data which require a longer fading memory.

16. Dynamic Range Enhancement of High-Speed Electrical Signal Data via Non-Linear Compression

NASA Technical Reports Server (NTRS)

Laun, Matthew C. (Inventor)

2016-01-01

Systems and methods for high-speed compression of dynamic electrical signal waveforms to extend the measuring capabilities of conventional measuring devices such as oscilloscopes and high-speed data acquisition systems are discussed. Transfer function components and algorithmic transfer functions can be used to accurately measure signals that are within the frequency bandwidth but beyond the voltage range and voltage resolution capabilities of the measuring device.

17. Dynamic characteristics of a jacket type offshore structure considering non-linear behavior of pile foundations

SciTech Connect

Aaghaakouchak, A.A.; Asgarian, B.

1996-12-31

Dynamic characteristics of a typical six legged jacket type platform in Persian Gulf have been studied. An equivalent linearized pile stub has been used to model the pile-soil system. The properties of pile stub have been calculated for different levels of the pile-head deformations resulting from the action of different waves. Natural frequencies and mode shapes of resulting linear models have been determined and compared to each other.

18. Non-linear dynamics of viscous bilayers subjected to an electric field: 3D phase field simulations

Dritselis, Christos; Karapetsas, George; Bontozoglou, Vasilis

2014-11-01

The scope of this work is to investigate the non-linear dynamics of the electro-hydrodynamic instability of a bilayer of immiscible liquids. We consider the case of two viscous films which is separated from the top electrode by air. We assume that the liquids are perfect dielectrics and consider the case of both flat and patterned electrodes. We develop a computational model using the diffuse interface method and carry out 3D numerical simulations fully accounting for the flow and electric field in all phases. We perform a parametric study and investigate the influence of the electric properties of fluids, applied voltage and various geometrical characteristics of the mask. The authors acknowledge the support by the General Secretariat of Research and Technology of Greece under the action Supporting Postdoctoral Researchers'' (Grant Number PE8/906), co-funded by the European Social Fund and National Resources.

19. Prediction of Dynamic Stall Characteristics Using Advanced Non-Linear Panel Methods.

DTIC Science & Technology

1984-04-04

three- dimensional method , incorporating the techniques that are being examined in the two-dimensional pilot code. r.• - t... . .. -..-. .°.- S °"°"° I...RD-Ai48 453 PREDICTION OF DYNAMIC STRLL CHARACTERISTICS USING 1/1 RDVRNCED NON-LINERR PAN..(U) ANALYTICAL METHODS INC REDMOND WA B MRSKEW ET AL. 84...1 2.0 micROCOPY RESOLUTION TEST CHART hAyl0#dM. @UAU M STAUIOAPOI A VOSR-TR 84.0 97 5 Analytical methods Report 8406 FINAL REPORT Tw. ’ PREDICITON OF

20. Dynamics of glass-forming liquids. XIX. Rise and decay of field induced anisotropy in the non-linear regime

Young-Gonzales, Amanda R.; Samanta, Subarna; Richert, Ranko

2015-09-01

For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility.

1. Dynamics of glass-forming liquids. XIX. Rise and decay of field induced anisotropy in the non-linear regime.

PubMed

Young-Gonzales, Amanda R; Samanta, Subarna; Richert, Ranko

2015-09-14

For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility.

2. Non-linearity dynamics in ecosystem response to climate change: Case studies and policy implications

USGS Publications Warehouse

Burkett, V.R.; Wilcox, D.A.; Stottlemyer, R.; Barrow, W.; Fagre, D.; Baron, J.; Nielsen, J.L.; Allen, C.D.; Peterson, D.L.; Ruggerone, G.; Doyle, T.

2005-01-01

Many biological, hydrological, and geological processes are interactively linked in ecosystems. These ecological phenomena normally vary within bounded ranges, but rapid, nonlinear changes to markedly different conditions can be triggered by even small differences if threshold values are exceeded. Intrinsic and extrinsic ecological thresholds can lead to effects that cascade among systems, precluding accurate modeling and prediction of system response to climate change. Ten case studies from North America illustrate how changes in climate cna lead to rapid, threshold-type responses within ecological communities; the case studies also highlight the role of human activities that alter the rate or direction of system response to climate change. Understanding and anticipating nonlinear dynamics are important aspects of adaptation planning since responses of biological resources to changes in the physical climate system are not necessarily proportional and sometimes, as in the case of complex ecological systems, inherently nonlinear.

3. Non-linear QCD dynamics and exclusive production in ep collisions

Gonçalves, V. P.; Machado, M. V. T.; Meneses, A. R.

2010-07-01

The exclusive processes in electron-proton ( ep) interactions are an important tool to investigate the QCD dynamics at high energies as they are in general driven by the gluon content of proton which is strongly subject to parton saturation effects. In this paper we compute the cross sections for the exclusive vector meson production as well as the deeply virtual Compton scattering (DVCS) relying on the color dipole approach and considering the numerical solution of the Balitsky-Kovchegov equation including running coupling corrections. We show that the small- x evolution given by this evolution equation is able to describe the DESY-HERA data and is relevant for the physics of the exclusive observables in future electron-proton colliders and in photoproduction processes to be measured in coherent interactions at the LHC.

4. Extreme responses of non-linear dynamic systems using constrained simulations

SciTech Connect

Harland, L.A.; Vugts, J.H.; Jonathan, P.; Taylor, P.H.

1996-12-31

The dynamic behavior of structures in the offshore environment is complex, especially in extreme storm conditions. The most accurate methods for estimating structural behavior are based on extensive random time domain simulations of the ocean surface to obtain statistics of the extreme response in (typically) a 3 hour period of a severe storm. However, random time domain simulation is time-consuming and expensive for both the computer and the engineer. In this work the authors use a method to determine the distribution of the extreme structural response in a robust, faster and cheaper way than with full random simulations. This method, which is based on constrained random simulations, has been successfully developed using a grossly simplified model of a jack-up. The aim of this study is now to include more realistic modelling parameters in order to demonstrate that the method can be successfully applied to real problems and that accurate results can be obtained with relatively little effort.

5. Assessing the performance of linear and non-linear soil carbon dynamics models using the Multi-Objective Evolutionary Algorithm Borg-MOEA

Ramcharan, A. M.; Kemanian, A.; Richard, T.

2013-12-01

The largest terrestrial carbon pool is soil, storing more carbon than present in above ground biomass (Jobbagy and Jackson, 2000). In this context, soil organic carbon has gained attention as a managed sink for atmospheric CO2 emissions. The variety of models that describe soil carbon cycling reflects the relentless effort to characterize the complex nature of soil and the carbon within it. Previous works have laid out the range of mathematical approaches to soil carbon cycling but few have compared model structure performance in diverse agricultural scenarios. As interest in increasing the temporal and spatial scale of models grows, assessing the performance of different model structures is essential to drawing reasonable conclusions from model outputs. This research will address this challenge using the Evolutionary Algorithm Borg-MOEA to optimize the functionality of carbon models in a multi-objective approach to parameter estimation. Model structure performance will be assessed through analysis of multi-objective trade-offs using experimental data from twenty long-term carbon experiments across the globe. Preliminary results show a successful test of this proof of concept using a non-linear soil carbon model structure. Soil carbon dynamics were based on the amount of carbon inputs to the soil and the degree of organic matter saturation of the soil. The degree of organic matter saturation of the soil was correlated with the soil clay content. Six parameters of the non-linear soil organic carbon model were successfully optimized to steady-state conditions using Borg-MOEA and datasets from five agricultural locations in the United States. Given that more than 50% of models rely on linear soil carbon decomposition dynamics, a linear model structure was also optimized and compared to the non-linear case. Results indicate linear dynamics had a significantly lower optimization performance. Results show promise in using the Evolutionary Algorithm Borg-MOEA to assess

6. Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism

PubMed Central

Scarneciu, Camelia C.; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D.; Varciu, Mihai S.; Andreescu, Oana; Scarneciu, Ioan

2017-01-01

Objectives: This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. Methods: The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). Results: From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. Conclusions: The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is

7. Non-linear dynamics in recurrently connected neural circuits implement Bayesian inference by sampling

Ticchi, Alessandro; Faisal, Aldo A.; Brain; Behaviour Lab Team

2015-03-01

Experimental evidence at the behavioural-level shows that the brains are able to make Bayes-optimal inference and decisions (Kording and Wolpert 2004, Nature; Ernst and Banks, 2002, Nature), yet at the circuit level little is known about how neural circuits may implement Bayesian learning and inference (but see (Ma et al. 2006, Nat Neurosci)). Molecular sources of noise are clearly established to be powerful enough to pose limits to neural function and structure in the brain (Faisal et al. 2008, Nat Rev Neurosci; Faisal et al. 2005, Curr Biol). We propose a spking neuron model where we exploit molecular noise as a useful resource to implement close-to-optimal inference by sampling. Specifically, we derive a synaptic plasticity rule which, coupled with integrate-and-fire neural dynamics and recurrent inhibitory connections, enables a neural population to learn the statistical properties of the received sensory input (prior). Moreover, the proposed model allows to combine prior knowledge with additional sources of information (likelihood) from another neural population, and to implement in spiking neurons a Markov Chain Monte Carlo algorithm which generates samples from the inferred posterior distribution.

8. Non-linear QCD dynamics in two-photon interactions at high energies

Gonçalves, V. P.; Kugeratski, M. S.; Cazaroto, E. R.; Carvalho, F.; Navarra, F. S.

2011-10-01

Perturbative QCD predicts that the growth of the gluon density at high energies should saturate, forming a Color Glass Condensate (CGC), which is described in mean field approximation by the Balitsky-Kovchegov (BK) equation. In this paper we study the γγ interactions at high energies and estimate the main observables which will be probed at future linear colliders using the color dipole picture. We discuss in detail the dipole-dipole cross section and propose a new relation between this quantity and the dipole scattering amplitude. The total γγ, γ ∗ γ ∗ cross sections and the real photon structure function F2^{γ }(x,Q2) are calculated using the recent solution of the BK equation with running coupling constant and the predictions are compared with those obtained using phenomenological models for the dipole-dipole cross section and scattering amplitude. We demonstrate that these models are able to describe the LEP data at high energies, but predict a very different behavior for the observables at higher energies. Therefore we conclude that the study of γγ interactions can be useful to constrain the QCD dynamics.

9. Non-linear hydrotectonic phenomena: Part I - fluid flow in open fractures under dynamical stress loading

SciTech Connect

Archambeau, C.B.

1994-01-01

A fractured solid under stress loading (or unloading) can be viewed as behaving macroscopically as a medium with internal, hidden, degrees of freedom, wherein changes in fracture geometry (i.e. opening, closing and extension) and flow of fluid and gas within fractures will produce major changes in stresses and strains within the solid. Likewise, the flow process within fractures will be strongly coupled to deformation within the solid through boundary conditions on the fracture surfaces. The effects in the solid can, in part, be phenomenologically represented as inelastic or plastic processes in the macroscopic view. However, there are clearly phenomena associated with fracture growth and open fracture fluid flows that produce effects that can not be described using ordinary inelastic phenomenology. This is evident from the fact that a variety of energy release phenomena can occur, including seismic emissions of previously stored strain energy due to fracture growth, release of disolved gas from fluids in the fractures resulting in enhanced buoyancy and subsequent energetic flows of gas and fluids through the fracture system which can produce raid extension of old fractures and the creation of new ones. Additionally, the flows will be modulated by the opening and closing of fractures due to deformation in the solid, so that the flow process is strongly coupled to dynamical processes in the surrounding solid matrix, some of which are induced by the flow itself.

10. Stability of cool flux tubes in the solar chromosphere. II - Non-linear dynamical behaviour

Hassan, S. S.; Kneer, F.

1990-06-01

A single vertical cool flux tube in the solar chromosphere is focused upon for stability studies. The analysis of a previous study by Hasan and Kneer (1986) is extended to the nonlinear regime with a view to examining the consequences of having self-exciting mechanisms of oscillations above the photosphere. In particular, the possibility of whether the motions driven by the convective instability caused by the presence of CO could extract sufficient energy from the radiation field near the Tmin region of empirical models and deposit it in higher layers to produce chromospheric heating is investigated. The time evolution of this instability is followed by solving the MHD equations in the thin flux tube approximation. The analysis includes energy exchange with the radiation field. The simulations of a flux tube with a transmitting upper boundary show that the average energy flux in the oscillations is inadequate for chromospheric heating.

11. A multi-step transversal linearization (MTL) method in non-linear structural dynamics

Roy, D.; Kumar, Rajesh

2005-10-01

An implicit family of multi-step transversal linearization (MTL) methods is proposed for efficient and numerically stable integration of nonlinear oscillators of interest in structural dynamics. The presently developed method is a multi-step extension and further generalization of the locally transversal linearization (LTL) method proposed earlier by Roy (Proceedings of the Academy of the Royal Society (London) 457 (2001) 539-566), Roy and Ramachandra (Journal of Sound and Vibration 41 (2001a) 653-679, International Journal for Numerical Methods in Engineering 51 (2001b) 203-224) and Roy (International Journal of Numerical Methods in Engineering 61 (2004) 764). The MTL-based linearization is achieved through a non-unique replacement of the nonlinear part of the vector field by a conditionally linear interpolating expansion of known accuracy, whose coefficients contain the discretized state variables defined at a set of grid points. In the process, the nonlinear part of the vector field becomes a conditionally determinable equivalent forcing function. The MTL-based linearized differential equations thus become explicitly integrable. Based on the linearized solution, a set of algebraic, constraint equations are so formed that transversal intersections of the linearized and nonlinearized solution manifolds occur at the multiple grid points. The discretized state vectors are thus found as the zeros of the constraint equations. Simple error estimates for the displacement and velocity vectors are provided and, in particular, it is shown that the formal accuracy of the MTL methods as a function of the time step-size depends only on the error of replacement of the nonlinear part of the vector field. Presently, only two different polynomial-based interpolation schemes are employed for transversal linearization, viz. the Taylor-like interpolation and the Lagrangian interpolation. While the Taylor-like interpolation leads to numerical ill-conditioning as the order of

12. Higher-order sinusoidal input describing functions for the analysis of non-linear systems with harmonic responses

Nuij, P. W. J. M.; Bosgra, O. H.; Steinbuch, M.

2006-11-01

For high-precision motion systems, modelling and control design specifically oriented at friction effects is instrumental. The sinusoidal input describing function theory represents an approximative mathematical framework for analysing non-linear system behaviour. This theory, however, limits the description of the non-linear system behaviour to a quasi-linear amplitude-dependent relation between sinusoidal excitation and sinusoidal response. In this paper, an extension to higher-order describing functions is realised by introducing the concept of the harmonics generator. The resulting higher-order sinusoidal input describing functions (HOSIDFs) relate the magnitude and phase of the higher harmonics of the periodic response of the system to the magnitude and phase of a sinusoidal excitation. Based on this extension two techniques to measure HOSIDFs are presented. The first technique is FFT based. The second technique is based on IQ (in-phase/quadrature-phase) demodulation. In a simulation, the measurement techniques have been tested by comparing the simulation results to analytically derived results from a known (backlash) non-linearity. In a subsequent practical case study both techniques are used to measure the changes in dynamic behaviour as a function of drive level due to friction in an electric motor. Both methods prove successful for measuring HOSIDFs.

13. Exciton Dynamics and Many Body Interactions in Layered Semiconducting Materials Revealed with Non-linear Coherent Spectroscopy

Dey, Prasenjit

understanding the basic unexplored science as well as creating technological developments. The dephasing dynamics in semiconductors typically occur in the picosecond to femtosecond timescale, thus the use of ultrafast laser spectroscopy is a potential route to probe such excitonic responses. The focus of this dissertation is two-fold: firstly, to develop the necessary instrumentation to accurately probe the aforementioned parameters and secondly, to explore the quantum dynamics and the underlying many-body interactions in different layered semiconducting materials. A custom-built multidimensional optical non-linear spectrometer was developed in order to perform two-dimensional spectroscopic (2DFT) measurements. The advantages of this technique are multifaceted compared to regular one-dimensional and non-linear incoherent techniques. 2DFT technique is based on an enhanced version of Four wave mixing experiments. This powerful tool is capable of identifying the resonant coupling, probing the coherent pathways, unambiguously extracting the homogeneous linewidth in the presence of inhomogeneity and decomposing a complex spectra into real and imaginary parts. It is not possible to uncover such crucial features by employing one dimensional non-linear technique. Monolayers as well as bulk TMDs and group III-VI bulk layered materials are explored in this dissertation. The exciton quantum dynamics is explored with three pulse four-wave mixing whereas the phase sensitive measurements are obtained by employing two-dimensional Fourier transform spectroscopy. Temperature and excitation density dependent 2DFT experiments unfold the information associated with the many-body interactions in the layered semiconducting samples.

14. Non-linear visco-elastic analysis and the design of super-pressure balloons : stress, strain and stability

Wakefield, David

Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures. Founded upon their inTENS finite element analysis suite, these activities have broadened to encompass ‘lighter than air' structures such as aerostats, hybrid air-vehicles and stratospheric balloons. Since 2004 Tensys have acted as consultants to the NASA Ultra Long Duration Balloon (ULDB) Program. Early implementations of the super-pressure balloon design chosen for ULDB have shown problems of geometric instability, characterised by improper deployment and the potential for overall geometric instability once deployed. The latter has been reproduced numerically using inTENS, and the former are better understood following a series of large-scale hangar tests simulating launch and ascent. In both cases the solution lies in minimising the film lobing between the tendons. These tendons, which span between base and apex end fittings, cause the characteristic pumpkin shape of the balloons and also provide valuable constraint against excessive film deformation. There is also the requirement to generate a biaxial stress field in order to mobilise in-plane shear stiffness. A consequence of reduced lobing between tendons is the development of higher stresses in the balloon film under pressure. The different thermal characteristics between tendons and film lead to further significant meridional stress under low temperature flight conditions. The non-linear viscoelastic response of the envelope film acts positively to help dissipate excessive stress and local concentrations. However, creep over time may produce lobe geometry variations sufficient to compromise the geometric stability of the balloon. The design of a balloon requires an analysis approach that addresses the questions of stress and stability over the duration of a flight by time stepping analyses using an appropriate material model. This paper summarises the Dynamic Relaxation

15. A limit analysis approach to derive a thermodynamic damage potential for non-linear geomaterials

Karrech, A.; Poulet, T.; Regenauer-Lieb, K.

2012-10-01

This paper introduces a mathematical model which describes the continuum damage of non-linear geo-materials. The model accounts for full thermo-mechanical coupling as well as irreversible failure and its effect on shear heating. It involves multi-mechanisms creep to describe the material rheology depending on time, temperature, pressure and water content. This coupled thermo-mechanical model combined with the upper bound theory is used to formulate a potential capable of predicting the damage evolution. The model is implemented and applied to a cross-sectional geological layer subjected to extension. It reveals that damage accelerates the creation of faults and accentuates the localization of shear zones, thereby competing with the increase in material rigidity due to rate dependency, especially at high temperature.

16. Methods for accurate analysis of galaxy clustering on non-linear scales

2017-01-01

Measurements of galaxy clustering with the low-redshift galaxy surveys provide sensitive probe of cosmology and growth of structure. Parameter inference with galaxy clustering relies on computation of likelihood functions which requires estimation of the covariance matrix of the observables used in our analyses. Therefore, accurate estimation of the covariance matrices serves as one of the key ingredients in precise cosmological parameter inference. This requires generation of a large number of independent galaxy mock catalogs that accurately describe the statistical distribution of galaxies in a wide range of physical scales. We present a fast method based on low-resolution N-body simulations and approximate galaxy biasing technique for generating mock catalogs. Using a reference catalog that was created using the high resolution Big-MultiDark N-body simulation, we show that our method is able to produce catalogs that describe galaxy clustering at a percentage-level accuracy down to highly non-linear scales in both real-space and redshift-space.In most large-scale structure analyses, modeling of galaxy bias on non-linear scales is performed assuming a halo model. Clustering of dark matter halos has been shown to depend on halo properties beyond mass such as halo concentration, a phenomenon referred to as assembly bias. Standard large-scale structure studies assume that halo mass alone is sufficient in characterizing the connection between galaxies and halos. However, modeling of galaxy bias can face systematic effects if the number of galaxies are correlated with other halo properties. Using the Small MultiDark-Planck high resolution N-body simulation and the clustering measurements of Sloan Digital Sky Survey DR7 main galaxy sample, we investigate the extent to which the dependence of galaxy bias on halo concentration can improve our modeling of galaxy clustering.

17. Non-linear analysis of body responses to functional electrical stimulation on hemiplegic subjects.

PubMed

Yu, W W; Acharya, U R; Lim, T C; Low, H W

2009-08-01

Functional electrical stimulation (FES) is a method of applying low-level electrical currents to restore or improve body functions lost through nervous system impairment. FES is applied to peripheral nerves that control specific muscles or muscle groups. Application of advanced signal computing techniques to the medical field has helped to achieve practical solutions to the health care problems accurately. The physiological signals are essentially non-stationary and may contain indicators of current disease, or even warnings about impending diseases. These indicators may be present at all times or may occur at random on the timescale. However, to study and pinpoint these subtle changes in the voluminous data collected over several hours is tedious. These signals, e.g. walking-related accelerometer signals, are not simply linear and involve non-linear contributions. Hence, non-linear signal-processing methods may be useful to extract the hidden complexities of the signal and to aid physicians in their diagnosis. In this work, a young female subject with major neuromuscular dysfunction of the left lower limb, which resulted in an asymmetric hemiplegic gait, participated in a series of FES-assisted walking experiments. Two three-axis accelerometers were attached to her left and right ankles and their corresponding signals were recorded during FES-assisted walking. The accelerometer signals were studied in three directions using the Hurst exponent H, the fractal dimension (FD), the phase space plot, and recurrence plots (RPs). The results showed that the H and FD values increase with increasing FES, indicating more synchronized variability due to FES for the left leg (paralysed leg). However, the variation in the normal right leg is more chaotic on FES.

18. Beading instability in soft cylindrical gels with capillary energy: Weakly non-linear analysis and numerical simulations

Taffetani, M.; Ciarletta, P.

2015-08-01

Soft cylindrical gels can develop a long-wavelength peristaltic pattern driven by a competition between surface tension and bulk elastic energy. In contrast to the Rayleigh-Plateau instability for viscous fluids, the macroscopic shape in soft solids evolves toward a stable beading, which strongly differs from the buckling arising in compressed elastic cylinders. This work proposes a novel theoretical and numerical approach for studying the onset and the non-linear development of the elasto-capillary beading in soft cylinders, made of neo-Hookean hyperelastic material with capillary energy at the free surface, subjected to axial stretch. Both a theoretical study, deriving the linear and the weakly non-linear stability analyses for the problem, and numerical simulations, investigating the fully non-linear evolution of the beaded morphology, are performed. The theoretical results prove that an axial elongation can not only favour the onset of beading, but also determine the nature of the elastic bifurcation. The fully non-linear phase diagrams of the beading are also derived from finite element numerical simulations, showing two peculiar morphological transitions when varying either the axial stretch or the material properties of the gel. Since the bifurcation is found to be subcritical for very slender cylinders, an imperfection sensitivity analysis is finally performed. In this case, it is shown that a surface sinusoidal imperfection can resonate with the corresponding marginally stable solution, thus selecting the emerging beading wavelength. In conclusion, the results of this study provide novel guidelines for controlling the beaded morphology in different experimental conditions, with important applications in micro-fabrication techniques, such as electrospun fibres.

19. Non-linear finite element analysis for prediction of seismic response of buildings considering soil-structure interaction

Çelebi, E.; Göktepe, F.; Karahan, N.

2012-11-01

The objective of this paper focuses primarily on the numerical approach based on two-dimensional (2-D) finite element method for analysis of the seismic response of infinite soil-structure interaction (SSI) system. This study is performed by a series of different scenarios that involved comprehensive parametric analyses including the effects of realistic material properties of the underlying soil on the structural response quantities. Viscous artificial boundaries, simulating the process of wave transmission along the truncated interface of the semi-infinite space, are adopted in the non-linear finite element formulation in the time domain along with Newmark's integration. The slenderness ratio of the superstructure and the local soil conditions as well as the characteristics of input excitations are important parameters for the numerical simulation in this research. The mechanical behavior of the underlying soil medium considered in this prediction model is simulated by an undrained elasto-plastic Mohr-Coulomb model under plane-strain conditions. To emphasize the important findings of this type of problems to civil engineers, systematic calculations with different controlling parameters are accomplished to evaluate directly the structural response of the vibrating soil-structure system. When the underlying soil becomes stiffer, the frequency content of the seismic motion has a major role in altering the seismic response. The sudden increase of the dynamic response is more pronounced for resonance case, when the frequency content of the seismic ground motion is close to that of the SSI system. The SSI effects under different seismic inputs are different for all considered soil conditions and structural types.

20. A non linear analysis of human gait time series based on multifractal analysis and cross correlations

2005-01-01

We analyzed databases with gait time series of adults and persons with Parkinson, Huntington and amyotrophic lateral sclerosis (ALS) diseases. We obtained the staircase graphs of accumulated events that can be bounded by a straight line whose slope can be used to distinguish between gait time series from healthy and ill persons. The global Hurst exponent of these series do not show tendencies, we intend that this is because some gait time series have monofractal behavior and others have multifractal behavior so they cannot be characterized with a single Hurst exponent. We calculated the multifractal spectra, obtained the spectra width and found that the spectra of the healthy young persons are almost monofractal. The spectra of ill persons are wider than the spectra of healthy persons. In opposition to the interbeat time series where the pathology implies loss of multifractality, in the gait time series the multifractal behavior emerges with the pathology. Data were collected from healthy and ill subjects as they walked in a roughly circular path and they have sensors in both feet, so we have one time series for the left foot and other for the right foot. First, we analyzed these time series separately, and then we compared both results, with direct comparison and with a cross correlation analysis. We tried to find differences in both time series that can be used as indicators of equilibrium problems.

1. A new non-linear parameter Q from FT-Rheology under nonlinear dynamic oscillatory shear for polymer melts system

Hyun, Kyu; Kim, Wonho

2011-12-01

Large Amplitude Oscillatory Shear (LAOS) is a test method for the characterization of complex fluids. Varying independently both strain amplitude (γ0) and frequency (ω) allows covering a broad spectrum of rheological responses with respect to time scales and involved non-linearity. Moreover, it is experimentally relatively simple to generate LAOS flow, because dynamic oscillatory shear does not involve any sudden jump in either strain or strain rate. There are several methods to analyze the resulting torque data received from the LAOS test protocol: (1) the G' and G″ as a function of strain amplitude (2) Stress shape (stress vs. time) or Lissajous pattern (stress vs. strain or stress vs. strain rate) (3) Fourier transform (4) generalized "storage" and "loss" modulus when decomposing the nonlinear stress data (5) Chebyschev polynomials using decomposing stress data and further development of Chebyschev polynomials. The Fourier Transform (FT)-Rheology is perhaps the most sensitive method of those discussed above. A new nonlinear parameter Q established from FT-Rheolgy under LAOS flow, i.e. Q( ω,γ 0) ≡ I 3/1/ γ {0/2}, as well as the zero-strain nonlinearity or intrinsic nonlinearity Q_0 ( ω ) equiv lim _{γ _0 to 0} Q( {ω ,γ _0 } ) by Hyun and Wilhelm (2009). In this study, therefore recent experiment and simulation results of nonlinear parameter Q from FT-Rheology for polymer melt and polymer composite systemsare reviewed.

2. A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

PubMed

Brown, A M

2001-06-01

The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.

3. A continuum three-dimensional, fully coupled, dynamic, non-linear finite element formulation for magnetostrictive materials

Pérez-Aparicio, José L.; Sosa, Horacio

2004-06-01

Magnetostriction is a phenomenon observed in all ferromagnetic materials. It couples elastic, electric, magnetic and in some situations also thermal fields and is of great industrial interest for use in sensors, actuators, adaptive or functional structures, robotics, transducers and MEMS. In this work, the governing equations of the three-field problem (i.e., the interactions of elastic, electric and magnetic effects) are formulated in three dimensions, accounting for non-linear (through magnetic body forces represented by the Maxwell tensor) and dynamic effects, and with constitutive equations resembling those of piezoelectricity. Through manipulation of Maxwell equations it is possible to find suitable expressions for developing the numerical weak, Galerkin and matrix forms in a natural way, including seven residuals (one for each nodal degree of freedom) and non-symmetric tangent, 'capacity' and mass consistent matrices. Simple backward Euler and central difference schemes can be used for the time domain integration. The only assumption made in this work for simplification is that the time variation of electric induction is negligible. This is justified by the relatively low frequencies ({\\ll }1 GHz) under which magnetostrictive materials usually work. The principal feature of the equations is the use of a magnetic potential (without much physical meaning) that allows a complete 'displacement' finite element formulation: all elastic, electric and magnetic nodal unknowns are zero derivatives. This allows the algorithm to be treated in a standard way, and important effects such as eddy currents can be obtained naturally. The formulation is implemented in the research finite element code FEAP. Although seven degrees of freedom per node is computer expensive to solve (especially for 3D problems), the current trend in the performance of computers, even personal ones, makes it worthwhile to build complete finite elements following the well-established (in mechanics

4. Some Considerations on Simple Non-Linear Magnetic Analysis-Based Optimum Design of Multi-Pole Permanent Magnet Machines

Kano, Yoshiaki; Kosaka, Takashi; Matsui, Nobuyuki

This paper presents a simple non-linear magnetic analysis-based optimum design of a multi-pole permanent magnet machine as an assistant design tool of 3D-FEM. The proposed analysis is based on the equivalent magnetic circuit and the air gap permeance model between the stator and rotor teeth of the motor, taking into account the local magnetic saturation in the pointed end of teeth. The availability of the proposed analysis is verified by comparing with 3D-FEM analysis from the standpoints of the torque calculation accuracy for the variations of design free parameter and the computation time. After verification, the proposed analysis-based optimum design of the dimensions of permanent magnet is examined, by which the minimization of magnet volume is realized while keeping torque/current ratio at the specified value.

5. Surprisal analysis of rotational-translational energy transfer - Non-linear versus linear rotors

NASA Technical Reports Server (NTRS)

Green, S.

1979-01-01

Surprisal versus energy gap analyses of state-to-state cross sections are presented for a number of linear rigid rotors excited by collisions with atoms for H2-H, H2-He, HCl-He, HCl-Ar, CO-He, CS-H2 (j=0) OCS-H2 (j=0) and HN2(+)-He, where (j=0) indicates that the hydrogen molecule was constrained to remain in its lowest level. Different systems exhibit wide variations in the slope of the surprisal plot and in certain cases, enough to indicate that the energy gap may not be the static dynamical constraint. Similar analyses are presented for nonlinear rotors excited by atoms for H2CO-He and H2O-He. For these, the data show a great deal of scatter, indicating that the reduced energy gap is probably not the appropriate independent variable.

6. Linear and Non-linear Analysis of Fibre Reinforced Plastic Bridge Deck due to Vehicle Loads

Ray, Chaitali; Mandal, Bibekananda

2015-06-01

The present work deals with linear and nonlinear static analysis of fibre reinforced plastics composite bridge deck structures using the finite element method. The nonlinear static analysis has been carried out considering geometric nonlinearity. The analysis of bridge deck has been carried out under vehicle load as specified by IRC Class B wheel load classification. The formulation has been carried out using the finite element software package ANSYS 14.0 and the SHELL281 element is used to model the bridge deck. The bridge deck has also been modeled as a plate stiffened with closely spaced hollow box sections and a computer code is developed based on this formulation. The results obtained from the present formulation are compared with those available in the published literature. A parametric study on the stiffened bridge deck has also been carried out with varying dimensions of the stiffeners under vehicle loads.

7. Asymptotic Analysis of Non-Linear Elliptic and Parabolic Singular Perturbations.

DTIC Science & Technology

1985-09-01

SINGULAR PERTURBATIONS, ASYMPTOTICS, VARIATIONAL CALCULUS , KINETIC THEORY, MEMBRANES WITH ENZYMOTIC ACTIVITY, MICHAELIS COEFFICIENT. 20. ASSTRACr (C ,th.o...Operators, Singular Perturbations, Asymptotics, Variational Calculus , Kinetic theory, membranes with enzymotic activity, Michaelis coefficient. TABLE OF...information concerning variational inequalities, maximal monotone operators, variational calculus and bonvex analysis, free boundary problems and

8. Non-linear buffeting response analysis of long-span suspension bridges with central buckle

Wang, Hao; Li, Aiqun; Zhao, Gengwen; Li, Jian

2010-06-01

The rigid central buckle employed in the Runyang Suspension Bridge (RSB) was the first time it was used in a suspension bridge in China. By using a spectral representation method and FFT technique combined with measured data, a 3D fluctuating wind field considering the tower wind effect is simulated. A novel FE model for buffeting analysis is then presented, in which a specific user-defined Matrix27 element in ANSYS is employed to simulate the aeroelastic forces and its stiffness or damping matrices are parameterized by wind velocity and vibration frequency. A nonlinear time history analysis is carried out to study the influence of the rigid central buckle on the wind-induced buffeting response of a long-span suspension bridge. The results can be used as a reference for wind resistance design of long-span suspension bridges with a rigid central buckle in the future.

9. Analysis of linear elasticity and non-linearity due to plasticity and material damage in woven and biaxial braided composites

Goyal, Deepak

Textile composites have a wide variety of applications in the aerospace, sports, automobile, marine and medical industries. Due to the availability of a variety of textile architectures and numerous parameters associated with each, optimal design through extensive experimental testing is not practical. Predictive tools are needed to perform virtual experiments of various options. The focus of this research is to develop a better understanding of linear elastic response, plasticity and material damage induced nonlinear behavior and mechanics of load flow in textile composites. Textile composites exhibit multiple scales of complexity. The various textile behaviors are analyzed using a two-scale finite element modeling. A framework to allow use of a wide variety of damage initiation and growth models is proposed. Plasticity induced non-linear behavior of 2x2 braided composites is investigated using a modeling approach based on Hill's yield function for orthotropic materials. The mechanics of load flow in textile composites is demonstrated using special non-standard postprocessing techniques that not only highlight the important details, but also transform the extensive amount of output data into comprehensible modes of behavior. The investigations show that the damage models differ from each other in terms of amount of degradation as well as the properties to be degraded under a particular failure mode. When compared with experimental data, predictions of some models match well for glass/epoxy composite whereas other's match well for carbon/epoxy composites. However, all the models predicted very similar response when damage factors were made similar, which shows that the magnitude of damage factors are very important. Full 3D as well as equivalent tape laminate predictions lie within the range of the experimental data for a wide variety of braided composites with different material systems, which validated the plasticity analysis. Conclusions about the effect of

10. Input-Output Stability Analysis with Magnetic Hysteresis Non-Linearity - A Class of Multipliers,

DTIC Science & Technology

1984-06-08

Circuit Theory, Vol. CT-17. that the same properties hold for yl(t). i.e.. p. 564. Nov. 1970. YI(t)ELa, is continuous, and go to zero as t--. [12] Desoer ...inductor (trans- former), but from circuit analysis point of view. zero as t . the input and output of the model replaced for N U as shown in Fig. (2...output [I. I],"Lumped- Circuit Models for Non-linearcof Industors Exhibiting Hysteresis Loop.’therefore, eEL., and el(t)- 0 as t- . imply IEEE Trans. on

11. Label-Free Analysis of Cellular Lipid Droplet Formation by Non-Linear Microscopy

Schie, Iwan W.

Cellular lipid droplets (LD) are cellular organelles that can be found in every cell type. Recent research indicates that cellular LD are involved in a large number of cellular metabolic functions, such as lipid metabolism, protection from lipotoxicity, protein storage and degradation, and many more. LD formation is frequently associated with adverse health effects, i.e. alcoholic and non-alcoholic fatty liver disease, diabetes type-2, as well as many cardiovascular disorders. Despite their wide presence, LDs are the least studied and most poorly understood cellular organelles. Typically, LDs are investigated using fluorescence-based techniques that require staining with exogenous fluorophores. Other techniques, e.g. biochemical assays, require the destruction of cells that prohibit the analysis of living cells. Therefore, in my thesis research I developed a novel compound fast-scanning nonlinear optical microscope equipped with the ability to also acquire Raman spectra at specific image locations. This system allows us to image label-free cellular LD formation in living cells and analyze the composition of single cellular LDs. Images can be acquired at near video-rate (˜16 frames/s). Furthermore, the system has the ability to acquire very large images of tissue of up to 7.5x15 cm2 total area by stitching together scans with dimensions of 1x1 mm2 in less than 1 minute. The system also enables the user to acquire Raman spectra from points of interest in the multiphoton images and provides chemically-specific data from sample volumes as small as 1 femtoliter. In my thesis I used this setup to determine the effects of VLDL lipolysis products on primary rat hepatocytes. By analyzing the Raman spectra and comparing the peak ratios for saturated and unsaturated fatty acid it was determined that the small cellular LD are highly saturated, while large cellular LDs contain mostly unsaturated lipids. Furthermore, I established a method to determine the specific contribution

12. Trace analysis of acids and bases by conductometric titration with multiparametric non-linear regression.

PubMed

Coelho, Lúcia H G; Gutz, Ivano G R

2006-03-15

A chemometric method for analysis of conductometric titration data was introduced to extend its applicability to lower concentrations and more complex acid-base systems. Auxiliary pH measurements were made during the titration to assist the calculation of the distribution of protonable species on base of known or guessed equilibrium constants. Conductivity values of each ionized or ionizable species possibly present in the sample were introduced in a general equation where the only unknown parameters were the total concentrations of (conjugated) bases and of strong electrolytes not involved in acid-base equilibria. All these concentrations were adjusted by a multiparametric nonlinear regression (NLR) method, based on the Levenberg-Marquardt algorithm. This first conductometric titration method with NLR analysis (CT-NLR) was successfully applied to simulated conductometric titration data and to synthetic samples with multiple components at concentrations as low as those found in rainwater (approximately 10 micromol L(-1)). It was possible to resolve and quantify mixtures containing a strong acid, formic acid, acetic acid, ammonium ion, bicarbonate and inert electrolyte with accuracy of 5% or better.

13. Non-linear numerical analysis of the Iosipescu specimen for composite materials

NASA Technical Reports Server (NTRS)

Ho, Henjen; Morton, John; Farley, Gary L.

1994-01-01

A nonlinear elastic finite element analysis is presented of the Iosipescu shear specimen tested in the modified Wyoming fixture for unidirectional graphite/epoxy composites. It is shown that the nonlinear effects due to specimen-to-fixture contact interactions and specimen geometry on the overall shear response are negligible. It is proposed that the tangential shear modulus should be used to characterize the shear resistance of composite materials with highly nonlinear shear response. The correction factors, which are needed to compensate for the nonuniformity of the shear stress or strain distribution in the specimen test section for shear modulus measurement, have to be defined carefully. Strain contours in the nonlinear response ranges are presented and the initiation of failure in the notch regions is investigated.

14. Non-Linear Time Series Analysis of Dissolved Oxygen in Five Diverse Aquatic Environments

Simpson, K. E.; Barton, C. C.; Smigelski, J. R.; Tebbens, S. F.

2008-12-01

Temporal variations in the concentration of Dissolved oxygen (DO) can create catastrophic conditions for organisms that rely on aerobic metabolic processes for survival. Dissolved oxygen (DO) is an aquatic parameter whose concentration is controlled by physical, biological, and chemical processes. The concentration of DO in an aquatic system is important to organisms that rely on aerobic metabolic processes for survival. A power-spectral-density analysis of time series of DO concentration is used to quantify persistence (the degree of internal correlation) over durations of 3 months to 19 years. The interval between data points was either 15 minutes or one hour. The data are from ten different water bodies throughout the United States. Four of these sites are large, slow moving bodies of water including three estuaries: Chesapeake Bay (Virginia), Winyah Bay (North Carolina) and Elkhorn Slough (California); and one reservoir: the Cheney Reservoir in Kansas. The other six sites are small, fast moving water bodies. They included four rivers: Christina River (Delaware), St. Croix River (Maine), Ramapo River (New Jersey), and Passaic River, New Jersey; one stream: Green Pond Brook (New Jersey); and one man-made channel: Reynolds Channel (New York). The analysis quantifies persistence as the power scaling exponent (β), which for all ten water bodies β ranges between 1.2 and 1.6 meaning that the signal is persistent and non-stationary. Rivers and streams, exhibit higher β-values of 1.5 < β<1.6 (greater persistence) than estuaries and lakes, which have β-values of 1.2< β <1.4t.

15. Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

Rahman, M. A.; Ahmed, U.; Uddin, M. S.

2013-08-01

A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

16. Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid. Part Iv: Large-Amplitude Vibrations with Flow

AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.

2000-11-01

The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. The theoretical model has already been presented in Part I of the present study. Non-linearities due to moderately large-amplitude shell motion are considered by using Donnell's non-linear shallow-shell theory. Linear potential flow theory is applied to describe the fluid-structure interaction by using the model proposed by Paı̈doussis and Denise. For different amplitudes and frequencies of the excitation and for different flow velocities, the following are investigated numerically: (1) periodic response of the system; (2) unsteady and stochastic motion; (3) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the non-linear periodic response of the system has also been investigated. Poincaré maps and bifurcation diagrams are used to study the unsteady and stochastic dynamics of the system. Amplitude modulated motions, multi-periodic solutions, chaotic responses, cascades of bifurcations as the route to chaos and the so-called “blue sky catastrophe” phenomenon have all been observed for different values of the system parameters; the latter two have been predicted here probably for the first time for the dynamics of circular cylindrical shells.

17. Monte Carlo simulation of parameter confidence intervals for non-linear regression analysis of biological data using Microsoft Excel.

PubMed

Lambert, Ronald J W; Mytilinaios, Ioannis; Maitland, Luke; Brown, Angus M

2012-08-01

This study describes a method to obtain parameter confidence intervals from the fitting of non-linear functions to experimental data, using the SOLVER and Analysis ToolPaK Add-In of the Microsoft Excel spreadsheet. Previously we have shown that Excel can fit complex multiple functions to biological data, obtaining values equivalent to those returned by more specialized statistical or mathematical software. However, a disadvantage of using the Excel method was the inability to return confidence intervals for the computed parameters or the correlations between them. Using a simple Monte-Carlo procedure within the Excel spreadsheet (without recourse to programming), SOLVER can provide parameter estimates (up to 200 at a time) for multiple 'virtual' data sets, from which the required confidence intervals and correlation coefficients can be obtained. The general utility of the method is exemplified by applying it to the analysis of the growth of Listeria monocytogenes, the growth inhibition of Pseudomonas aeruginosa by chlorhexidine and the further analysis of the electrophysiological data from the compound action potential of the rodent optic nerve.

18. booc.io: An Education System with Hierarchical Concept Maps and Dynamic Non-linear Learning Plans.

PubMed

Schwab, Michail; Strobelt, Hendrik; Tompkin, James; Fredericks, Colin; Huff, Connor; Higgins, Dana; Strezhnev, Anton; Komisarchik, Mayya; King, Gary; Pfister, Hanspeter

2017-01-01

Information hierarchies are difficult to express when real-world space or time constraints force traversing the hierarchy in linear presentations, such as in educational books and classroom courses. We present booc.io, which allows linear and non-linear presentation and navigation of educational concepts and material. To support a breadth of material for each concept, booc.io is Web based, which allows adding material such as lecture slides, book chapters, videos, and LTIs. A visual interface assists the creation of the needed hierarchical structures. The goals of our system were formed in expert interviews, and we explain how our design meets these goals. We adapt a real-world course into booc.io, and perform introductory qualitative evaluation with students.

19. Detection of epileptiform activity in EEG signals based on time-frequency and non-linear analysis.

PubMed

Gajic, Dragoljub; Djurovic, Zeljko; Gligorijevic, Jovan; Di Gennaro, Stefano; Savic-Gajic, Ivana

2015-01-01

We present a new technique for detection of epileptiform activity in EEG signals. After preprocessing of EEG signals we extract representative features in time, frequency and time-frequency domain as well as using non-linear analysis. The features are extracted in a few frequency sub-bands of clinical interest since these sub-bands showed much better discriminatory characteristics compared with the whole frequency band. Then we optimally reduce the dimension of feature space to two using scatter matrices. A decision about the presence of epileptiform activity in EEG signals is made by quadratic classifiers designed in the reduced two-dimensional feature space. The accuracy of the technique was tested on three sets of electroencephalographic (EEG) signals recorded at the University Hospital Bonn: surface EEG signals from healthy volunteers, intracranial EEG signals from the epilepsy patients during the seizure free interval from within the seizure focus and intracranial EEG signals of epileptic seizures also from within the seizure focus. An overall detection accuracy of 98.7% was achieved.

20. [Non linear principal component analysis and clues for a differential approach of five groups experiencing social precariousness].

PubMed

Meyer, C

2008-01-01

We wished to develop an original way of taking care of people experiencing great social precariousness. Our purpose was to develop communication and relational skills, to stimulate expression of emotions and feelings, to bring out personal resources, to increase well-being, motivation and self-esteem, and thus favour rehabilitation. Our sample is composed of long-term unemployed people, of people benefiting from measures of integration into the working process, of people living in community homes, of drug addicts, and of drug-addicted female prisoners. Our research is based on an integrated quantitative and qualitative methodology, with rating scales for the artistic production and observational frames for items of verbal and non-verbal behaviour completing the psychometric questionnaires. It is an action research; we use art therapy, which is a common practice in the health sector, especially with subjects having problems expressing there feelings through words. We have carried out a non linear principal component analysis (PRINCALS) on the data of the projective test (Rotter), as well as a between groups comparison of the responses to the questionnaire on life satisfaction (FLZ), with the help of the Mann-Whitney test. It is from these comparisons that we are able to draw out a few clues for differential treating strategies, depending on the inclusion into the five sub-groups that we have followed.

1. A Study of Care Work in Welfare Facilities for the Elderly, Using Non Linear Analysis of Finger Plethysmograms

Hirohashi, Yoko; Oyama-Higa, Mayumi; Lee, Sangjae

2011-06-01

The fingertip pulse waves of a number of staff working in a daycare center for the elderly and a special nursing home for the elderly were measured several times throughout the day for a period of one or two days, and the chaotic information gained was analyzed using a non linear analysis method. As a result, a relation between the staff's length of career and the change of Largest Lyapunov Exponent (LLE) of the fingertip pulse waves that synchronized with the mental revitalization degrees and the tension of the sympathetic nerve was evident. The LLE of the staff with short careers dramatically changed and also took a long time to settle down again. In addition, staff LLE changed greatly after sessions of bathing assistance and watching residents with dementia. LLE measurements showed drops in some staff after a period of rest, but this was not the case for other staff. It can be concluded that the LLE is related to the length of the staff member's career and what is actually done during working hours and rest periods. A high level of sympathetic nerve was seen in almost all of the care workers. On this basis, the authors propose that improvements are needed in the content of the care work.

2. Application of correlation dimension and pointwise dimension for non-linear topographical analysis of focal onset seizures.

PubMed

Feucht, M; Möller, U; Witte, H; Benninger, F; Asenbaum, S; Prayer, D; Friedrich, M H

1999-03-01

For many patients who are candidates for epilepsy surgery, non-invasive evaluation fails to provide sufficient information to permit surgical treatment. Since there are also definite risks and considerable costs associated with invasive procedures, new (non-invasive) techniques are required. This study provides empirical evidence that a non-linear approach applied to ictal surface electroencephalograms (EEGs) can help to delineate the area of seizure onset and may prove useful in complementing visual analysis of the EEG. Multichannel EEGs, recorded from eight patients with different drug-resistant localisation-related epilepsies, were analysed using the concept of correlation dimension and two extensions based on the pointwise dimension. The latter also provided results in cases where assessment of the correlation dimension was not feasible. Comparative values between 2 and 6 were accepted as the result of the algorithms, mostly 3-4 for the EEG channels strongly reflecting epileptic activity, and 4-6 for the other signals. The proportion of accepted pointwise values was usually 200-800% for strong epileptic EEG activity compared to the other data. The approach permitted the characterisation of the scalp area reflecting epileptic activity. The results obtained were in perfect concordance with those obtained during pre-surgical work-up and confirmed by the post-operative outcome.

3. Multi-disease analysis of maternal antibody decay using non-linear mixed models accounting for censoring.

PubMed

Goeyvaerts, Nele; Leuridan, Elke; Faes, Christel; Van Damme, Pierre; Hens, Niel

2015-09-10

Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter-subject heterogeneity. Even though it is common for biological processes to entail non-linear relationships, examples of multivariate non-linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non-linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non-linear longitudinal profiles subject to censoring, by combining multivariate random effects, non-linear growth and Tobit regression. We explore the hypothesis of a common infant-specific mechanism underlying maternal immunity using a pairwise correlated random-effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4 months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs.

4. Integrating real-time and manual monitored data to predict hillslope soil moisture dynamics with high spatio-temporal resolution using linear and non-linear models

Zhu, Qing; Zhou, Zhiwen; Duncan, Emily W.; Lv, Ligang; Liao, Kaihua; Feng, Huihui

2017-02-01

Spatio-temporal variability of soil moisture (θ) is a challenge that remains to be better understood. A trade-off exists between spatial coverage and temporal resolution when using the manual and real-time θ monitoring methods. This restricted the comprehensive and intensive examination of θ dynamics. In this study, we integrated the manual and real-time monitored data to depict the hillslope θ dynamics with good spatial coverage and temporal resolution. Linear (stepwise multiple linear regression-SMLR) and non-linear (support vector machines-SVM) models were used to predict θ at 39 manual sites (collected 1-2 times per month) with θ collected at three real-time monitoring sites (collected every 5 mins). By comparing the accuracies of SMLR and SVM for each depth and manual site, an optimal prediction model was then determined at this depth of this site. Results showed that θ at the 39 manual sites can be reliably predicted (root mean square errors <0.028 m3 m-3) using both SMLR and SVM. The linear or non-linear relationship between θ at each manual site and at the three real-time monitoring sites was the main reason for choosing SMLR or SVM as the optimal prediction model. The subsurface flow dynamics was an important factor that determined whether the relationship was linear or non-linear. Depth to bedrock, elevation, topographic wetness index, profile curvature, and θ temporal stability influenced the selection of prediction model since they were related to the subsurface soil water distribution and movement. Using this approach, hillslope θ spatial distributions at un-sampled times and dates can be predicted. Missing information of hillslope θ dynamics can be acquired successfully.

5. Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

SciTech Connect

Minati, Ludovico E-mail: ludovico.minati@unitn.it

2015-03-15

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

6. Synchronization, non-linear dynamics and low-frequency fluctuations: analogy between spontaneous brain activity and networked single-transistor chaotic oscillators.

PubMed

Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; D'Incerti, Ludovico; Jovicich, Jorge

2015-03-01

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

7. Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; D'Incerti, Ludovico; Jovicich, Jorge

2015-03-01

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

8. How to include the nonlinear Cox-Voinov law into sloshing dynamics? A weakly non linear approach

Viola, Francesco; Brun, Pierre-Thomas; Gallaire, Francois

2015-11-01

Fluid sloshing in a glass is a common example of damped oscillator, with the frequency derived in the potential flow limit. The damping rate is then evaluated considering the viscous dissipation at the wall, in the bulk and at the free surface, respectively. This classical theoretical result however differs from what is often seen in the laboratory when the attenuation of gravity waves happens in a small basin. In particular, the damping rate is found to increase as the sloshing amplitude decreases. Here we show that this enhanced damping is due to capillary forces at the contact line between the liquid and the container. The angle θd made by the liquid interface with the container walls (contact angle) is modeled as a non-linear function of the interface speed U, (Cox-Voinov law θd3 α U). We propose a multiple scale expansion scheme to consistently derive an amplitude equation using the Cox-Voinov law as boundary condition at the moving interface. The zero order problem reduces to the classical static meniscus problem, while the first order problem yields an eigenvalue problem defining the viscous sloshing modes. At an higher order, a compatibility condition has to be enforced, yielding an amplitude equation. Solving the later, we recover the expected increase of the damping rate as the sloshing amplitude decreases, an effect thus attributed to capillary effects.

9. On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh Nagumo (FN) mathematical model

Chavarette, Fábio Roberto; Balthazar, José Manoel; Peruzzi, Nelson José; Rafikov, Marat

2009-03-01

The Fitzhugh-Nagumo (FH) mathematical model is considered a simplification of the Hodgkin-Huxley (HH) model. This paper analyzes the non-linear dynamics of the Fitzhugh-Nagumo (FN) mathematical model, and still presents some modifications in the governing equations of the system in order to transform it into a non-ideal one (taking into account that an energy source has limited power supply). We also developed an optimal linear control design and used Sinhas's theory for the membrane's action potential in order to stabilize the variation of this potential.

10. Non-Linear finite element analysis of cone penetration in layered sandy loam soil-considering precompression stress state

Technology Transfer Automated Retrieval System (TEKTRAN)

Axisymmetric finite element (FE) method was developed using a commercial computer program to simulate cone penetration process in layered granular soil. Soil was considered as a non-linear elastic plastic material which was modeled using variable elastic parameters of Young’s Modulus and Poisson’s r...

11. The linear and non-linear characterization of dust ion acoustic mode in complex plasma in presence of dynamical charging of dust

SciTech Connect

Bhattacharjee, Saurav Das, Nilakshi

2015-10-15

A systematic theoretical investigation has been carried out on the role of dust charging dynamics on the nature and stability of DIA (Dust Ion Acoustic) mode in complex plasma. The study has been made for both linear and non-linear scale regime of DIA mode. The observed results have been characterized in terms of background plasma responses towards dust surface responsible for dust charge fluctuation, invoking important dusty plasma parameters, especially the ion flow speed and dust size. The linear analyses confirm the nature of instability in DIA mode in presence of dust charge fluctuation. The instability shows a damping of DIA mode in subsonic flow regime followed by a gradual growth in instability in supersonic limit of ion flow. The strength of non-linearity and their existence domain is found to be driven by different dusty plasma parameters. As dust is ubiquitous in interstellar medium with plasma background, the study also addresses the possible effect of dust charging dynamics in gravito-electrostatic characterization and the stability of dust molecular clouds especially in proto-planetary disc. The observations are influential and interesting towards the understanding of dust settling mechanism and formation of dust environments in different regions in space.

12. Hydro-climatic Changes: Potential Non-linear Responses of Phosphorus Dynamic in Aquatic/Semi-aquatic Systems

Pant, H. K.

2007-12-01

Depending on resilience, threshold and lag times, hydro-climatic changes can cause nonlinear and/or irreversible changes in phosphorus (P) dynamic, and instigate P enrichment in aquatic/semi-aquatic systems. Thus, studying direct/indirect effects of expected global climate change on bioavailability of organic P in aquatic systems are in critical need, to help manage or increase the resilience of the ecosystem. The central hypothesis of this study is that P dynamic in aquatic, especially freshwater, ecosystem is likely to behave nonlinearly due to expected changes in sediment and water acidity, redox status, etc., because of potential hydro-climatic changes in the decades to come, thus, could face irreversible adverse changes. Devising possible biological and chemical treatments for the removal of P from eutrophic lakes, estuaries, etc, as well as helping in predicting the movement and fate of P under changing hydro-climatic conditions would be crucial to manage aquatic ecosystem in the near future. The critical question is not how much P is stored in any given aquatic/semi-aquatic system, but how the resilience and nonlinearity relate to the stability of stored P are affected due to the levels of environmental stressors, which are expected to fluctuate due to global change in the decades to come. Studies related to 31P Nuclear Magnetic Resonance Spectroscopy analysis, and multiple hydraulic retention cycles showed that, in general, frequent drying and reflooding of a semi-aquatic system such as wetland could significantly increase the bioavailability of P due to degradation of relatively less stable organic P, e.g., glycerophosphate and nucleoside monophosphate. Moreover, nutrients flux from sediments to the water column depended on the concentration gradients of the sediment-water interface and redox status. Shift in equilibrium P concentration of the water column as the water level rises, may cause release of adsorbed P from the sediments. Restoration of a

13. Development of a Probabilistic Technique for On-line Parameter and State Estimation in Non-linear Dynamic Systems

SciTech Connect

Tunc Aldemir; Don W. Miller; Brian k. Hajek; Peng Wang

2002-04-01

The DSD (Dynamic System Doctor) is a system-independent, interactive software under development for on-line state/parameter estimation in dynamic systems (1), partially supported through a Nuclear Engineering Education (NEER) grant during 1998-2001. This paper summarizes the recent accomplishments in improving the user-friendliness and computational capability of DSD

14. A comparative study of linear and non-linear regression analysis for ammonium exchange by clinoptilolite zeolite.

PubMed

Karadag, Dogan; Koc, Yunus; Turan, Mustafa; Ozturk, Mustafa

2007-06-01

Ammonium ion exchange from aqueous solution using clinoptilolite zeolite was investigated at laboratory scale. Batch experimental studies were conducted to evaluate the effect of various parameters such as pH, zeolite dosage, contact time, initial ammonium concentration and temperature. Freundlich and Langmuir isotherm models and pseudo-second-order model were fitted to experimental data. Linear and non-linear regression methods were compared to determine the best fitting of isotherm and kinetic model to experimental data. The rate limiting mechanism of ammonium uptake by zeolite was determined as chemical exchange. Non-linear regression has better performance for analyzing experimental data and Freundlich model was better than Langmuir to represent equilibrium data.

SciTech Connect

Newman, Gregory A.; Commer, Michael

2006-11-17

Software that simulates and inverts electromagnetic field data for subsurface electrical properties (electrical conductivity) of geological media. The software treats data produced by a time harmonic source field excitation arising from the following antenna geometery: loops and grounded bipoles, as well as point electric and magnetic dioples. The inversion process is carried out using a non-linear conjugate gradient optimization scheme, which minimizes the misfit between field data and model data using a least squares criteria. The software is an upgrade from the code NLCGCS_MP ver 1.0. The upgrade includes the following components: Incorporation of new 1 D field sourcing routines to more accurately simulate the 3D electromagnetic field for arbitrary geologic& media, treatment for generalized finite length transmitting antenna geometry (antennas with vertical and horizontal component directions). In addition, the software has been upgraded to treat transverse anisotropy in electrical conductivity.

16. Non-linear dynamics of stable carbon and hydrogen isotope signatures based on a biological kinetic model of aerobic enzymatic methane oxidation.

PubMed

Vavilin, Vasily A; Rytov, Sergey V; Shim, Natalia; Vogt, Carsten

2016-06-01

The non-linear dynamics of stable carbon and hydrogen isotope signatures during methane oxidation by the methanotrophic bacteria Methylosinus sporium strain 5 (NCIMB 11126) and Methylocaldum gracile strain 14 L (NCIMB 11912) under copper-rich (8.9 µM Cu(2+)), copper-limited (0.3 µM Cu(2+)) or copper-regular (1.1 µM Cu(2+)) conditions has been described mathematically. The model was calibrated by experimental data of methane quantities and carbon and hydrogen isotope signatures of methane measured previously in laboratory microcosms reported by Feisthauer et al. [ 1 ] M. gracile initially oxidizes methane by a particulate methane monooxygenase and assimilates formaldehyde via the ribulose monophosphate pathway, whereas M. sporium expresses a soluble methane monooxygenase under copper-limited conditions and uses the serine pathway for carbon assimilation. The model shows that during methane solubilization dominant carbon and hydrogen isotope fractionation occurs. An increase of biomass due to growth of methanotrophs causes an increase of particulate or soluble monooxygenase that, in turn, decreases soluble methane concentration intensifying methane solubilization. The specific maximum rate of methane oxidation υm was proved to be equal to 4.0 and 1.3 mM mM(-1) h(-1) for M. sporium under copper-rich and copper-limited conditions, respectively, and 0.5 mM mM(-1) h(-1) for M. gracile. The model shows that methane oxidation cannot be described by traditional first-order kinetics. The kinetic isotope fractionation ceases when methane concentrations decrease close to the threshold value. Applicability of the non-linear model was confirmed by dynamics of carbon isotope signature for carbon dioxide that was depleted and later enriched in (13)C. Contrasting to the common Rayleigh linear graph, the dynamic curves allow identifying inappropriate isotope data due to inaccurate substrate concentration analyses. The non-linear model pretty adequately described experimental

17. A wavelet-based non-linear autoregressive with exogenous inputs (WNARX) dynamic neural network model for real-time flood forecasting using satellite-based rainfall products

Nanda, Trushnamayee; Sahoo, Bhabagrahi; Beria, Harsh; Chatterjee, Chandranath

2016-08-01

18. Dynamic topology and flux rope evolution during non-linear tearing of 3D null point current sheets

SciTech Connect

Wyper, P. F. Pontin, D. I.

2014-10-15

In this work, the dynamic magnetic field within a tearing-unstable three-dimensional current sheet about a magnetic null point is described in detail. We focus on the evolution of the magnetic null points and flux ropes that are formed during the tearing process. Generally, we find that both magnetic structures are created prolifically within the layer and are non-trivially related. We examine how nulls are created and annihilated during bifurcation processes, and describe how they evolve within the current layer. The type of null bifurcation first observed is associated with the formation of pairs of flux ropes within the current layer. We also find that new nulls form within these flux ropes, both following internal reconnection and as adjacent flux ropes interact. The flux ropes exhibit a complex evolution, driven by a combination of ideal kinking and their interaction with the outflow jets from the main layer. The finite size of the unstable layer also allows us to consider the wider effects of flux rope generation. We find that the unstable current layer acts as a source of torsional magnetohydrodynamic waves and dynamic braiding of magnetic fields. The implications of these results to several areas of heliophysics are discussed.

19. Analog implementation of radix-2, 16-FFT processor for OFDM receivers: non-linearity behaviours and system performance analysis

Mokhtarian, N.; Hodtani, G. A.

2015-12-01

Analog implementations of decoders have been widely studied by considering circuit complexity, as well as power and speed, and their integration with other analog blocks is an extension of analog decoding research. In the front-end blocks of orthogonal frequency-division multiplexing (OFDM) systems, combination of an analog fast Fourier transform (FFT) with an analog decoder is suitable. In this article, the implementation of a 16-symbol FFT processor based on analog complementary metal-oxide-semiconductor current mirrors within circuit and system levels is presented, and the FFT is implemented using a butterfly diagram, where each node is implemented using analog circuits. Implementation details include consideration of effects of transistor mismatch and inherent noises and effects of circuit non-linearity in OFDM system performance. It is shown that not only can transistor inherent noises be measured but also transistor mismatch can be applied as an input-referred noise source that can be used in system- and circuit-level studies. Simulations of a radix-2, 16-symbol FFT show that proposed circuits consume very low power, and impacts of noise, mismatch and non-linearity for each node of this processor are very small.

20. On the complex non-linear interaction between bacteria and redox dynamics in sediments and its effects on water quality

Sanchez-Vila, X.; Rubol, S.; Fernandez-Garcia, D.

2011-12-01

Despite the fact that the prognoses on the availability of resources related to different climate scenarios have been already formulated, the complex hydrological and biogeochemical reactions taking place in different compartments in natural environmental media are poorly understood, especially regarding the interactions between water bodies, and the reactions taking place at soil-water interfaces. Amongst them, the inter-relationship between hydrology, chemistry and biology has important implications in natural (rivers, lakes) and man-made water facilities (lagoons, artificial recharge pounds, reservoirs, slow infiltration systems, etc). The consequences involve environment, economic, social and health-risk aspects. At the current stage, only limited explanations are available to understand the implications of these relationships on ecosystem services, water quality and water quantity. Therefore, there is an urgent need to seek a full understanding of these physical-biogeochemical processes in water-bodies, sediments and biota and its implications in ecological and health risk. We present a soil column experiment and a mathematical model which aim to study the mutual interplay between water and bacteria activity in porous media, the corresponding dynamics and the feedback on nutrient cycling by using a multidisciplinary approach.

1. A mathematical model of psychotherapy: an investigation using dynamic non-linear equations to model the therapeutic relationship.

PubMed

Peluso, Paul R; Liebovitch, Larry S; Gottman, John M; Norman, Michael D; Su, Jessica

2012-01-01

Mathematical models, such as the one developed by Gottman et al. (1998, 2000, 2002) to understand the interaction between husbands and wives, can provide novel insights into the dynamics of the therapeutic relationship. A set of nonlinear equations were used to model the changing emotional state of a therapist and client. The results suggest: (1) The person that is most responsive to the other achieves the most positive state, (2) the emotional state of the client oscillates before reaching its final state, (3) therapy is least successful when the therapist starts from a negative state, and (4) there is an inverse relationship between models that change only the influence parameter and models that change only the inertia parameter, creating a series of four basic models to work with. These theoretical models require further, empirical investigation to test the derived parameters. If validated, or revised based on observations of therapist-client relationships in development, they could provide specific direction in creating successful therapeutic relationships for training clinicians and those already in practice.

2. The impact of geometric non-linearities on the fatigue analysis of trailing edge bond lines in wind turbine rotor blades

Noever Castelos, Pablo; Balzani, Claudio

2016-09-01

3. State-resolved molecular photoionization dynamics of polyatomic systems: Effects of non-linear changes in molecular geometry

Miller, James Scott

An important topic in the absorption of vacuum ultraviolet photons by molecules is the correlation between electronic and nuclear degrees of freedom during photoionization. However, no previous investigations have probed the correlation between bending excitation and photoejection dynamics over a wide spectral range. We present the first such studies by reporting the influence of bending excitation following CO2 3σu -1 and N2O 7σ-1 photoionization over the photon energy range (15 eV < hvexc < 200 eV). Using dispersed fluorescence spectroscopy in conjunction with synchrotron radiation, we determine the vibrational branching ratio v+ = (0,1,0)( 0,0,0) for the CO2+ (B 2Σu+) and N2O+ (A 2Σ+) electronic states. The relative rate of production of the υ2 = 1 upper vibrational state varies over a broad ionization energy range, and in ways that are largely unanticipated. These branching ratios exhibit a strong thermal dependence, and we are able to separate out effects due to hot-band excitation from those that are due to vibronic coupling. The data indicate that the continuum electron is responsible for the observed energy dependence in CO2 3σ u-1 photoionization. This is a previously unobserved result. Additional studies examine the influence of simultaneous excitation in the bending and symmetric stretching modes in N2O+ [A 2Σ+, v + = (1,1,0)] to determine the effect of changing the energy separation of vibronically coupled potential surfaces. Finally, the CF4 + [D 2A1, v+ = (1,0,0,0)/(0,0,0,0)] branching ratio is studied, which provides the first experimental observation of a predicted low-energy shape resonance in this photoionization pathway.

4. Complementary use of partial least-squares and artificial neural networks for the non-linear spectrophotometric analysis of pharmaceutical samples.

PubMed

Goicoechea, Héctor C; Collado, María S; Satuf, María L; Olivieri, Alejandro C

2002-10-01

The complementary use of partial least-squares (PLS) multivariate calibration and artificial neural networks (ANNs) for the simultaneous spectrophotometric determination of three active components in a pharmaceutical formulation has been explored. The presence of non-linearities caused by chemical interactions was confirmed by a recently discussed methodology based on Mallows augmented partial residual plots. Ternary mixtures of chlorpheniramine, naphazoline and dexamethasone in a matrix of excipients have been resolved by using PLS for the two major analytes (chlorpheniramine and naphazoline) and ANNs for the minor one (dexamethasone). Notwithstanding the large number of constituents, their high degree of spectral overlap and the occurrence of non-linearities, rapid and simultaneous analysis has been achieved, with reasonably good accuracy and precision. No extraction procedures using non-aqueous solvents are required.

5. Error-rate estimation in discriminant analysis of non-linear longitudinal data: A comparison of resampling methods.

PubMed

de la Cruz, Rolando; Fuentes, Claudio; Meza, Cristian; Núñez-Antón, Vicente

2016-07-08

Consider longitudinal observations across different subjects such that the underlying distribution is determined by a non-linear mixed-effects model. In this context, we look at the misclassification error rate for allocating future subjects using cross-validation, bootstrap algorithms (parametric bootstrap, leave-one-out, .632 and [Formula: see text]), and bootstrap cross-validation (which combines the first two approaches), and conduct a numerical study to compare the performance of the different methods. The simulation and comparisons in this study are motivated by real observations from a pregnancy study in which one of the main objectives is to predict normal versus abnormal pregnancy outcomes based on information gathered at early stages. Since in this type of studies it is not uncommon to have insufficient data to simultaneously solve the classification problem and estimate the misclassification error rate, we put special attention to situations when only a small sample size is available. We discuss how the misclassification error rate estimates may be affected by the sample size in terms of variability and bias, and examine conditions under which the misclassification error rate estimates perform reasonably well.

6. Performance analysis of an all-optical OFDM system in presence of non-linear phase noise.

PubMed

Hmood, Jassim K; Harun, Sulaiman W; Emami, Siamak D; Khodaei, Amin; Noordin, Kamarul A; Ahmad, Harith; Shalaby, Hossam M H

2015-02-23

The potential for higher spectral efficiency has increased the interest in all-optical orthogonal frequency division multiplexing (OFDM) systems. However, the sensitivity of all-optical OFDM to fiber non-linearity, which causes nonlinear phase noise, is still a major concern. In this paper, an analytical model for estimating the phase noise due to self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in an all-optical OFDM system is presented. The phase noise versus power, distance, and number of subcarriers is evaluated by implementing the mathematical model using Matlab. In order to verify the results, an all-optical OFDM system, that uses coupler-based inverse fast Fourier transform/fast Fourier transform without any nonlinear compensation, is demonstrated by numerical simulation. The system employs 29 subcarriers; each subcarrier is modulated by a 4-QAM or 16-QAM format with a symbol rate of 25 Gsymbol/s. The results indicate that the phase variance due to FWM is dominant over those induced by either SPM or XPM. It is also shown that the minimum phase noise occurs at -3 dBm and -1 dBm for 4-QAM and 16-QAM, respectively. Finally, the error vector magnitude (EVM) versus subcarrier power and symbol rate is quantified using both simulation and the analytical model. It turns out that both EVM results are in good agreement with each other.

7. High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

NASA Technical Reports Server (NTRS)

Carlson, John R.

1996-01-01

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

8. The biopsychology-nonlinear analysis toolbox: a free, open-source Matlab-toolbox for the non-linear analysis of time series data.

PubMed

Beste, Christian; Otto, Tobias; Hoffmann, Sven

2010-10-01

We provide a free, open-source toolbox for non-linear time series analyses. The major goal of this project was to provide a toolbox for nonlinear time series analyses that is easily accessible to a wide range of neuroscientists. The toolbox offers modular, powerful and flexible algorithms embedded in an easy to handle graphical user interface (GUI). The toolbox can be run within the Matlab environment, but also as stand-alone solution without reference to a programming environment that is also usable for different PC operating systems (Windows and Linux). The Biopsychology--Nonlinear Analysis Toolbox and documentation are available freely and open-source from http://biopsynltoolbox.sourceforge.net.

9. Direct forecasting of subsurface flow response from non-linear dynamic data by linear least-squares in canonical functional principal component space

2015-03-01

Inverse modeling is widely used to assist with forecasting problems in the subsurface. However, full inverse modeling can be time-consuming requiring iteration over a high dimensional parameter space with computationally expensive forward models and complex spatial priors. In this paper, we investigate a prediction-focused approach (PFA) that aims at building a statistical relationship between data variables and forecast variables, avoiding the inversion of model parameters altogether. The statistical relationship is built by first applying the forward model related to the data variables and the forward model related to the prediction variables on a limited set of spatial prior models realizations, typically generated through geostatistical methods. The relationship observed between data and prediction is highly non-linear for many forecasting problems in the subsurface. In this paper we propose a Canonical Functional Component Analysis (CFCA) to map the data and forecast variables into a low-dimensional space where, if successful, the relationship is linear. CFCA consists of (1) functional principal component analysis (FPCA) for dimension reduction of time-series data and (2) canonical correlation analysis (CCA); the latter aiming to establish a linear relationship between data and forecast components. If such mapping is successful, then we illustrate with several cases that (1) simple regression techniques with a multi-Gaussian framework can be used to directly quantify uncertainty on the forecast without any model inversion and that (2) such uncertainty is a good approximation of uncertainty obtained from full posterior sampling with rejection sampling.

10. Stability of non-linear integrable accelerator

SciTech Connect

Batalov, I.; Valishev, A.; /Fermilab

2011-09-01

The stability of non-linear Integrable Optics Test Accelerator (IOTA) model developed in [1] was tested. The area of the stable region in transverse coordinates and the maximum attainable tune spread were found as a function of non-linear lens strength. Particle loss as a function of turn number was analyzed to determine whether a dynamic aperture limitation present in the system. The system was also tested with sextupoles included in the machine for chromaticity compensation. A method of evaluation of the beam size in the linear part of the accelerator was proposed.

11. Social complexity, modernity and suicide: an assessment of Durkheim's suicide from the perspective of a non-linear analysis of complex social systems.

PubMed

Condorelli, Rosalia

2016-01-01

Can we share even today the same vision of modernity which Durkheim left us by its suicide analysis? or can society 'surprise us'? The answer to these questions can be inspired by several studies which found that beginning the second half of the twentieth century suicides in western countries more industrialized and modernized do not increase in a constant, linear way as modernization and social fragmentation process increases, as well as Durkheim's theory seems to lead us to predict. Despite continued modernizing process, they found stabilizing or falling overall suicide rate trends. Therefore, a gradual process of adaptation to the stress of modernization associated to low social integration levels seems to be activated in modern society. Assuming this perspective, the paper highlights as this tendency may be understood in the light of the new concept of social systems as complex adaptive systems, systems which are able to adapt to environmental perturbations and generate as a whole surprising, emergent effects due to nonlinear interactions among their components. So, in the frame of Nonlinear Dynamical System Modeling, we formalize the logic of suicide decision-making process responsible for changes at aggregate level in suicide growth rates by a nonlinear differential equation structured in a logistic way, and in so doing we attempt to capture the mechanism underlying the change process in suicide growth rate and to test the hypothesis that system's dynamics exhibits a restrained increase process as expression of an adaptation process to the liquidity of social ties in modern society. In particular, a Nonlinear Logistic Map is applied to suicide data in a modern society such as the Italian one from 1875 to 2010. The analytic results, seeming to confirm the idea of the activation of an adaptation process to the liquidity of social ties, constitutes an opportunity for a more general reflection on the current configuration of modern society, by relating the

12. Non-linear aeroelastic prediction for aircraft applications

de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.

2007-05-01

Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. To evaluate the methodologies on real aircraft problems. To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research

13. Non Linear Step By Step Seismic Response and the Push Over Analysis Comparison of a Reinforced Concrete of Ductile Frames 25 Level Building

SciTech Connect

Avila, Jorge A.; Martinez, Eduardo

2008-07-08

Based on a ductile frames 25 level building, a non-linear analysis with increased monotonically lateral loads (Push-Over) was made in order to determine its collapse and its principal responses were compared against the time-history seismic responses determined with the SCT-EW-85 record. The seismic-resistance design and faced to gravitational loads was made according to the Complementary Technical Norms of Concrete Structures Design (NTC-Concrete) and the NTC-Seismic of the Mexico City Code (RDF-04), satisfying the limit service states (relative lateral displacement between story height maximum relations, story drifts {<=}0.012) and failure (seismic behavior factor, Q = 3). The compressible (soft) seismic zone III{sub b} and the office use type (group B) were considered. The non-lineal responses were determined with nominal and over-resistance effects. The comparison were made with base shear force-roof lateral displacement relations, global distribution of plastic hinges, failure mechanics tendency, lateral displacements and story drift and its distribution along the height of the building, local and global ductility demands, etc. For the non-linear static analysis with increased monotonically lateral loads, was important to select the type of lateral forces distribution.

14. Determination of tartrazine in beverage samples by stopped-flow analysis and three-way multivariate calibration of non-linear kinetic-spectrophotometric data.

PubMed

Schenone, Agustina V; Culzoni, María J; Marsili, Nilda R; Goicoechea, Héctor C

2013-06-01

The performance of MCR-ALS was studied in the modeling of non-linear kinetic-spectrophotometric data acquired by a stopped-flow system for the quantitation of tartrazine in the presence of brilliant blue and sunset yellow FCF as possible interferents. In the present work, MCR-ALS and U-PCA/RBL were firstly applied to remove the contribution of unexpected components not included in the calibration set. Secondly, a polynomial function was used to model the non-linear data obtained by the implementation of the algorithms. MCR-ALS was the only strategy that allowed the determination of tartrazine in test samples accurately. Therefore, it was applied for the analysis of tartrazine in beverage samples with minimum sample preparation and short analysis time. The proposed method was validated by comparison with a chromatographic procedure published in the literature. Mean recovery values between 98% and 100% and relative errors of prediction values between 4% and 9% were indicative of the good performance of the method.

15. nonlinMIP contribution to CMIP6: model intercomparison project for non-linear mechanisms: physical basis, experimental design and analysis principles (v1.0)

Good, Peter; Andrews, Timothy; Chadwick, Robin; Dufresne, Jean-Louis; Gregory, Jonathan M.; Lowe, Jason A.; Schaller, Nathalie; Shiogama, Hideo

2016-11-01

nonlinMIP provides experiments that account for state-dependent regional and global climate responses. The experiments have two main applications: (1) to focus understanding of responses to CO2 forcing on states relevant to specific policy or scientific questions (e.g. change under low-forcing scenarios, the benefits of mitigation, or from past cold climates to the present day), or (2) to understand the state dependence (non-linearity) of climate change - i.e. why doubling the forcing may not double the response. State dependence (non-linearity) of responses can be large at regional scales, with important implications for understanding mechanisms and for general circulation model (GCM) emulation techniques (e.g. energy balance models and pattern-scaling methods). However, these processes are hard to explore using traditional experiments, which explains why they have had so little attention in previous studies. Some single model studies have established novel analysis principles and some physical mechanisms. There is now a need to explore robustness and uncertainty in such mechanisms across a range of models (point 2 above), and, more broadly, to focus work on understanding the response to CO2 on climate states relevant to specific policy/science questions (point 1). nonlinMIP addresses this using a simple, small set of CO2-forced experiments that are able to separate linear and non-linear mechanisms cleanly, with a good signal-to-noise ratio - while being demonstrably traceable to realistic transient scenarios. The design builds on the CMIP5 (Coupled Model Intercomparison Project Phase 5) and CMIP6 DECK (Diagnostic, Evaluation and Characterization of Klima) protocols, and is centred around a suite of instantaneous atmospheric CO2 change experiments, with a ramp-up-ramp-down experiment to test traceability to gradual forcing scenarios. In all cases the models are intended to be used with CO2 concentrations rather than CO2 emissions as the input. The understanding

16. Non-linear waveform analysis for water-layer response and its application to high-frequency receiver function analysis using OBS array

Akuhara, Takeshi; Mochizuki, Kimihiro; Kawakatsu, Hitoshi; Takeuchi, Nozomu

2016-09-01

Determination of a response of the sea water column to teleseismic plane wave is important to suppress adverse effects of water reverberations in calculating receiver functions (RFs) using ocean-bottom seismometer (OBS) records. We present a novel non-linear waveform analysis method using the simulated annealing algorithm to determine such a water-layer response recorded by an OBS array. We then demonstrate its usefulness for the RF estimation through its application to synthetic and observed data. Synthetic experiments suggest that the water-layer response constrained in this way has a potential to improve RFs of OBS records drastically even in the high-frequency range (to 4 Hz). By applying it to data observed by the OBS array around the Kii Peninsula, southwestern Japan, we identified a low-velocity zone at the top of the subducting Philippine Sea plate. This zone may represent the incoming fluid-rich sediment layer that has been reported by active-source seismic survey.

17. USE OF WEIBULL FUNCTION FOR NON-LINEAR ANALYSIS OF EFFECTS OF LOW LEVELS OF SIMULATED HERBICIDE DRIFT ON PLANTS

EPA Science Inventory

We compared two regression models, which are based on the Weibull and probit functions, for the analysis of pesticide toxicity data from laboratory studies on Illinois crop and native plant species. Both mathematical models are continuous, differentiable, strictly positive, and...

18. A Bayesian Hierarchical Non-Linear Regression Model in Receiver Operating Characteristic Analysis of Clustered Continuous Diagnostic Data

PubMed Central

Zou, Kelly H.; O’Malley, A. James

2005-01-01

Receiver operating characteristic (ROC) analysis is a useful evaluative method of diagnostic accuracy. A Bayesian hierarchical nonlinear regression model for ROC analysis was developed. A validation analysis of diagnostic accuracy was conducted using prospective multi-center clinical trial prostate cancer biopsy data collected from three participating centers. The gold standard was based on radical prostatectomy to determine local and advanced disease. To evaluate the diagnostic performance of PSA level at fixed levels of Gleason score, a normality transformation was applied to the outcome data. A hierarchical regression analysis incorporating the effects of cluster (clinical center) and cancer risk (low, intermediate, and high) was performed, and the area under the ROC curve (AUC) was estimated. PMID:16161801

19. A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere

PubMed Central

Rossi, Sergio; Anfodillo, Tommaso; Čufar, Katarina; Cuny, Henri E.; Deslauriers, Annie; Fonti, Patrick; Frank, David; Gričar, Jožica; Gruber, Andreas; King, Gregory M.; Krause, Cornelia; Morin, Hubert; Oberhuber, Walter; Prislan, Peter; Rathgeber, Cyrille B. K.

2013-01-01

Background and Aims Ongoing global warming has been implicated in shifting phenological patterns such as the timing and duration of the growing season across a wide variety of ecosystems. Linear models are routinely used to extrapolate these observed shifts in phenology into the future and to estimate changes in associated ecosystem properties such as net primary productivity. Yet, in nature, linear relationships may be special cases. Biological processes frequently follow more complex, non-linear patterns according to limiting factors that generate shifts and discontinuities, or contain thresholds beyond which responses change abruptly. This study investigates to what extent cambium phenology is associated with xylem growth and differentiation across conifer species of the northern hemisphere. Methods Xylem cell production is compared with the periods of cambial activity and cell differentiation assessed on a weekly time scale on histological sections of cambium and wood tissue collected from the stems of nine species in Canada and Europe over 1–9 years per site from 1998 to 2011. Key Results The dynamics of xylogenesis were surprisingly homogeneous among conifer species, although dispersions from the average were obviously observed. Within the range analysed, the relationships between the phenological timings were linear, with several slopes showing values close to or not statistically different from 1. The relationships between the phenological timings and cell production were distinctly non-linear, and involved an exponential pattern Conclusions The trees adjust their phenological timings according to linear patterns. Thus, shifts of one phenological phase are associated with synchronous and comparable shifts of the successive phases. However, small increases in the duration of xylogenesis could correspond to a substantial increase in cell production. The findings suggest that the length of the growing season and the resulting amount of growth could respond

20. NEW REACTOR DESIGN AND ANALYSIS OF NON LINEAR VIBRATIONS OF DOUBLY CURVED SHALLOW SHELL UNDER A THERMAL GRADIENT

SciTech Connect

Chanda, S.

2004-10-06

The present study concerns with the effects of material orthotropy,curvature, shear ratio and circumferential modulus under the influence of a temperature distribution throughout the shell structure. Here analysis is restricted to the study of nonlinear vibration of a doubly curved shell structure considering the periodic response of a simple bending mode due to curtailment of pages. Solutions of the problems with suitable illustrations are also presented.

1. Finite-time H∞ filtering for non-linear stochastic systems

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

2. White noise analysis of pace-maker-response interactions and non-linearities in slowly adapting crayfish stretch receptor.

PubMed Central

Buño, W; Bustamante, J; Fuentes, J

1984-01-01

Input-output relations were investigated in the slowly adapting stretch receptor organ of crayfish using a Gaussian white noise length input with a 0.03-12.5 Hz band width and the resulting action potential output. The noise input was presented to the de-efferented receptor in situ, at three mean elongations and at four different amplitudes. The three mean elongations were set within the normal range in vivo, two at the extremes close to the minimum and maximum physiological lengths and the other in the mid-range. With white noise inputs there is a finite probability that the system will be tested in all possible conditions within the chosen band width because white noise has the advantage that it contains, with a finite probability, all possible stimulus wave forms at random. The analysis indicated similarities between the effects of the input variables, namely white noise amplitude and mean elongation. With low input variables the activity was periodic. With larger inputs, impulse rates were higher and irregular. The average length trajectories leading to a spike (i.e. the average stimulus) were either biphasic with high inputs or multiphasic and periodic with lower input variables. The frequency of periodicity increased with mean elongation. Although for a given length and noise amplitude a variety of individual length trajectories preceded spikes, the final biphasic shortening-lengthening average stimulus sequence before a spike was similar in all cases irrespective of the input variables. The number of possible trajectories decreased with increments in the input variables. The standard deviation of length values for each average stimulus was computed and displayed as a function of time relative to the spike. It was first constant, and decreased gradually to a minimum value at the spike reference. Standard deviation values were lower for higher white noise amplitudes and mean elongation. Simple, short-lasting stimulus wave forms in the white noise were isolated

3. Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains

Wang, Gang; Wang, Chaoli; Du, Qinghui; Cai, Xuan

2016-10-01

In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.

4. Quantitative methods for stochastic high frequency spatio-temporal and non-linear analysis: Assessing health effects of exposure to extreme ambient temperature

Liss, Alexander

Extreme weather events, such as heat waves and cold spells, cause substantial excess mortality and morbidity in the vulnerable elderly population, and cost billions of dollars. The accurate and reliable assessment of adverse effects of extreme weather events on human health is crucial for environmental scientists, economists, and public health officials to ensure proper protection of vulnerable populations and efficient allocation of scarce resources. However, the methodology for the analysis of large national databases is yet to be developed. The overarching objective of this dissertation is to examine the effect of extreme weather on the elderly population of the Conterminous US (ConUS) with respect to seasonality in temperature in different climatic regions by utilizing heterogeneous high frequency and spatio-temporal resolution data. To achieve these goals the author: 1) incorporated dissimilar stochastic high frequency big data streams and distinct data types into the integrated data base for use in analytical and decision support frameworks; 2) created an automated climate regionalization system based on remote sensing and machine learning to define climate regions for the Conterminous US; 3) systematically surveyed the current state of the art and identified existing gaps in the scientific knowledge; 4) assessed the dose-response relationship of exposure to temperature extremes on human health in relatively homogeneous climate regions using different statistical models, such as parametric and non-parametric, contemporaneous and asynchronous, applied to the same data; 5) assessed seasonal peak timing and synchronization delay of the exposure and the disease within the framework of contemporaneous high frequency harmonic time series analysis and modification of the effect by the regional climate; 6) modeled using hyperbolic functional form non-linear properties of the effect of exposure to extreme temperature on human health. The proposed climate

5. Strain modelling of extensional fault-propagation folds based on an improved non-linear trishear model: A numerical simulation analysis

Zhao, Haonan; Guo, Zhaojie; Yu, Xiangjiang

2017-02-01

This paper focuses on the strain modelling of extensional fault-propagation folds to reveal the effects of key factors on the strain accumulation and the relationship between the geometry and strain distribution of fault-related folds. A velocity-geometry-strain method is proposed for the analysis of the total strain and its accumulation process within the trishear zone of an extensional fault-propagation fold. This paper improves the non-linear trishear model proposed by Jin and Groshong (2006). Based on the improved model, the distribution of the strain rate within the trishear zone and the total strain are obtained. The numerical simulations of different parameters performed in this study indicate that the shape factor R, the total apical angle, and the P/S ratio control the final geometry and strain distribution of extensional fault-propagation folds. A small P/S ratio, a small apical angle, and an R value far greater or far smaller than 1 produce an asymmetric, narrow, and strongly deformed trishear zone. The velocity-geometry-strain analysis method is applied to two natural examples from Big Brushy Canyon in Texas and the northwestern Red Sea in Egypt. The strain distribution within the trishear zone is closely related to the geometry of the folds.

6. Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid. Part Iii: Truncation Effect Without Flow and Experiments

AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.

2000-11-01

The response of simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of one of the lowest natural frequencies is investigated by using improved mode expansions with respect to those assumed in Parts I and II of the present study. Two cases are studied: (1) shells in vacuo; and (2) shells filled with stagnant water. The improved expansions allow checking the accuracy of the solutions previously obtained and giving definitive results within the limits of Donnell's non-linear shallow-shell theory. The improved mode expansions include: (1) harmonics of the circumferential mode number n under consideration, and (2) only the principal n, but with harmonics of the longitudinal mode included. The effect of additional longitudinal modes is absolutely insignificant in both the driven and companion mode responses. The effect of modes with 2 n circumferential waves is very limited on the trend of non-linearity, but is significant in the response with companion mode participation in the case of lightly damped shells (empty shells). In particular, the travelling wave response appears for much lower vibration amplitudes and presents a frequency range without stable responses, corresponding to a beating phenomenon. A liquid (water) contained in the shell generates a much stronger softening behaviour of the system. Experiments with a water-filled circular cylindrical shell made of steel are in very good agreement with the present theory.

7. Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid, Part II: Large-Amplitude Vibrations Without Flow

AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.

1999-12-01

The non-linear response of empty and fluid-filled circular cylindrical shells to harmonic excitations is investigated. Both modal and point excitations have been considered. The model is suitable to study simply supported shells with and without axial constraints. Donnell's non-linear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The radial deflection of the shell is expanded by using a basis of seven linear modes. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The equations of motion, obtained in Part I of this study, are studied by using a code based on the collocation method. The validation of the present model is obtained by comparison with other authoritative results. The effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated, clarifying questions open for a long time. The results show the occurrence of travelling wave response in the proximity of the resonance frequency, the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half-wave, and limit cycle responses. Modes with two longitudinal half-waves are also investigated.

8. Short-term population-based non-linear concentration-response associations between fine particulate matter and respiratory diseases in Taipei (Taiwan): a spatiotemporal analysis.

PubMed

Yu, Hwa-Lung; Chien, Lung-Chang

2016-01-01

Fine particulate matter <2.5 μm (PM2.5) has been associated with human health issues; however, findings regarding the influence of PM2.5 on respiratory disease remain inconsistent. The short-term, population-based association between the respiratory clinic visits of children and PM2.5 exposure levels were investigated by considering both the spatiotemporal distributions of ambient pollution and clinic visit data. We applied a spatiotemporal structured additive regression model to examine the concentration-response (C-R) association between children's respiratory clinic visits and PM2.5 concentrations. This analysis was separately performed on three respiratory disease categories that were selected from the Taiwanese National Health Insurance database, which includes 41 districts in the Taipei area of Taiwan from 2005 to 2007. The findings reveal a non-linear C-R pattern of PM2.5, particularly in acute respiratory infections. However, a PM2.5 increase at relatively lower levels can elevate the same-day respiratory health risks of both preschool children (<6 years old) and schoolchildren (6-14 years old). In preschool children, same-day health risks rise when concentrations increase from 0.76 to 7.44 μg/m(3), and in schoolchildren, same-day health risks rise when concentrations increase from 0.76 to 7.52 μg/m(3). Changes in PM2.5 levels generally exhibited no significant association with same-day respiratory risks, except in instances where PM2.5 levels are extremely high, and these occurrences do exhibit a significant positive influence on respiratory health that is especially notable in schoolchildren. A significant high relative rate of respiratory clinic visits are concentrated in highly populated areas. We highlight the non-linearity of the respiratory health effects of PM2.5 on children to investigate this population-based association. The C-R relationship in this study can provide a highly valuable alternative for assessing the effects of ambient air

9. Quantitative analysis of Fe and Co in Co-substituted magnetite using XPS: The application of non-linear least squares fitting (NLLSF)

Liu, Hongmei; Wei, Gaoling; Xu, Zhen; Liu, Peng; Li, Ying

2016-12-01

Quantitative analysis of Co and Fe using X-ray photoelectron spectroscopy (XPS) is of important for the evaluation of the catalytic ability of Co-substituted magnetite. However, the overlap of XPS peaks and Auger peaks for Co and Fe complicate quantification. In this study, non-linear least squares fitting (NLLSF) was used to calculate the relative Co and Fe contents of a series of synthesized Co-substituted magnetite samples with different Co doping levels. NLLSF separated the XPS peaks of Co 2p and Fe 2p from the Auger peaks of Fe and Co, respectively. Compared with a control group without fitting, the accuracy of quantification of Co and Fe was greatly improved after elimination by NLLSF of the disturbance of Auger peaks. A catalysis study confirmed that the catalytic activity of magnetite was enhanced with the increase of Co substitution. This study confirms the effectiveness and accuracy of the NLLSF method in XPS quantitative calculation of Fe and Co coexisting in a material.

10. Bispectrum Analysis of Non-linear wave-wave Interaction between VLF Transmitter signal and ELF emission on the Basis of DEMETER satellite observations

Sondhiya, Deepak Kumar; Gwal, Ashok Kumar; Kasde, Satish Kumar

2016-07-01

Symmetric sidebands are observed in the ionosphere by the DEMETER (Detection of Electromagnetic Radiation Transmitted through Earthquake Region) satellite, when it passes above the Indian VLF transmitter, named VTX (18.2 kHz), located near Kanyakumari, India. The spectral boarding phenomena may be divided into two types: (1) spectrally broadened components occurring without any association with ELF/VLF emissions under disturbed ionospheric condition, (2) Spectrally broadened components with predominant side band structure in association with ELF emission. Generally spectral analysis at second order (Power spectrum) is used to analyze the frequency component of signal, but it losses the phase information among the different Fourier components. To retain this information the bispectrum (third order) and/or the bicoherence (normalized bispectrum) are used. Results suggest a non-linear mode coupling between the transmitter signal and ELF emission which produces sidebands that are quasi-electrostatic in nature. However, faint spectral broadened components in both types 1 and 2 may be connected with Doppler shift of quasi-electrostatic, whistler mode waves with a broad spectrum near resonance cone, due to scattering of the transmitter signals from ionospheric irregularities in the F-region. Keywords: spectral boarding, wave-wave Interaction, whistler mode waves and Doppler shift

11. Strain Transient Detection Techniques: A Comparison of Source Parameter Inversions of Signals Isolated through Principal Component Analysis (PCA), Non-Linear PCA, and Rotated PCA

Lipovsky, B.; Funning, G. J.

2009-12-01

We compare several techniques for the analysis of geodetic time series with the ultimate aim to characterize the physical processes which are represented therein. We compare three methods for the analysis of these data: Principal Component Analysis (PCA), Non-Linear PCA (NLPCA), and Rotated PCA (RPCA). We evaluate each method by its ability to isolate signals which may be any combination of low amplitude (near noise level), temporally transient, unaccompanied by seismic emissions, and small scale with respect to the spatial domain. PCA is a powerful tool for extracting structure from large datasets which is traditionally realized through either the solution of an eigenvalue problem or through iterative methods. PCA is an transformation of the coordinate system of our data such that the new "principal" data axes retain maximal variance and minimal reconstruction error (Pearson, 1901; Hotelling, 1933). RPCA is achieved by an orthogonal transformation of the principal axes determined in PCA. In the analysis of meteorological data sets, RPCA has been seen to overcome domain shape dependencies, correct for sampling errors, and to determine principal axes which more closely represent physical processes (e.g., Richman, 1986). NLPCA generalizes PCA such that principal axes are replaced by principal curves (e.g., Hsieh 2004). We achieve NLPCA through an auto-associative feed-forward neural network (Scholz, 2005). We show the geophysical relevance of these techniques by application of each to a synthetic data set. Results are compared by inverting principal axes to determine deformation source parameters. Temporal variability in source parameters, estimated by each method, are also compared.

12. A novel stress-accurate FE technology for highly non-linear analysis with incompressibility constraint. Application to the numerical simulation of the FSW process

Chiumenti, M.; Cervera, M.; Agelet de Saracibar, C.; Dialami, N.

2013-05-01

In this work a novel finite element technology based on a three-field mixed formulation is presented. The Variational Multi Scale (VMS) method is used to circumvent the LBB stability condition allowing the use of linear piece-wise interpolations for displacement, stress and pressure fields, respectively. The result is an enhanced stress field approximation which enables for stress-accurate results in nonlinear computational mechanics. The use of an independent nodal variable for the pressure field allows for an adhoc treatment of the incompressibility constraint. This is a mandatory requirement due to the isochoric nature of the plastic strain in metal forming processes. The highly non-linear stress field typically encountered in the Friction Stir Welding (FSW) process is used as an example to show the performance of this new FE technology. The numerical simulation of the FSW process is tackled by means of an Arbitrary-Lagrangian-Eulerian (ALE) formulation. The computational domain is split into three different zones: the work.piece (defined by a rigid visco-plastic behaviour in the Eulerian framework), the pin (within the Lagrangian framework) and finally the stirzone (ALE formulation). A fully coupled thermo-mechanical analysis is introduced showing the heat fluxes generated by the plastic dissipation in the stir-zone (Sheppard rigid-viscoplastic constitutive model) as well as the frictional dissipation at the contact interface (Norton frictional contact model). Finally, tracers have been implemented to show the material flow around the pin allowing a better understanding of the welding mechanism. Numerical results are compared with experimental evidence.

13. Testing procedures for non-stationarity and non-linearity in physiological signals.

PubMed

Popivanov, D; Mineva, A

1999-03-15

Most of the physiological signals (EEG, ECG, blood flow, human gait, etc.) characterize by complex dynamics including both non-stationarities and non-linearities. These time series resemble red noise with long-range correlation and 1/(f beta) power spectrum. A question arises as to how to distinguish the characteristics of the process underlying the signal dynamics from the properties of the observed time series. The classical methods to determine possible non-linear (chaotic) dynamics (e.g. correlation dimension) often fail in such signals because of relatively short data records containing stochastic components and non-stationarities. We report an application of several approaches, aimed at (1) determining of the non-stationarities in the signals and (2) testing whether non-linear dynamics exists. Assessment of the intrinsic correlation properties of the dynamic process and distinguishing the same from external trends was performed using singular spectra and detrended fluctuation analysis. The existence of non-linear dynamics was tested by correlation dimension (modified algorithm of re-embedding) and by correlation integrals of real and surrogate data. The correlation integrals of real signal and surrogate data sets were statistically compared using Kolmogorov-Smirnov (K-S) test. The procedures were tested on EEG and laser-Doppler (LD) blood flow. Our suggestion is that no one approach taken alone is the best for our aims. Instead, a battery of methods should be used.

14. NICMOS non-linearity tests

de Jong, Roelof

2005-07-01

This program incorporates a number of tests to analyse the count rate dependent non-linearity seen in NICMOS spectro-photometric observations. In visit 1 we will observe a few fields with stars of a range in luminosity in NGC1850 with NICMOS in NIC1 in F090M, F110W and F160W and NIC2 F110W, F160W, and F180W. We will repeat the observations with flatfield lamp on, creating artificially high count-rates, allowing tests of NICMOS linearity as function of count rate. To access the effect of charge trapping and persistence, we first take darks {so there is not too much charge already trapped}, than take exposures with the lamp off, exposures with the lamp on, and repeat at the end with lamp off. Finally, we continue with taking darks during occultation. In visit 2 we will observe spectro-photometric standard P041C using the G096 and G141 grisms in NIC3, and repeat the lamp off/on/off test to artificially create a high background. In visits 3&4 we repeat photometry measurements of faint standard stars SNAP-2 and WD1657+343, on which the NICMOS non-linearity was originally discovered using grism observations. These measurements are repeated, because previous photometry was obtained with too short exposure times, hence substantially affected by charge trapping non-linearity. Measurements will be made with NIC1: Visit 5 forms the persistence test of the program. The bright star GL-390 {used in a previous persistence test} will iluminate the 3 NICMOS detectors in turn for a fixed time, saturating the center many times, after which a series of darks will be taken to measure the persistence {i.e. trapped electrons and the decay time of the traps}. To determine the wavelength dependence of the trap chance, exposures of the bright star in different filters will be taken, as well as one in the G096 grism with NIC3. Most exposures will be 128s long, but two exposures in the 3rd orbit will be 3x longer, to seperate the effects of count rate versus total counts of the trap

15. Polarised Raman and infrared spectral analysis of L-alanine oxalate (C5H9NO6)--a non-linear optical single crystal.

PubMed

Krishnakumar, V; Nagalakshmi, R

2006-06-01

L-alanine oxalate (C5H9NO6), a promising material for effective frequency conversion, was grown by standard slow evaporation technique. Solubility studies were carried out at different temperatures. Unambiguous assignments of fundamental modes of various molecular groups were made from the recorded infrared and polarised Raman spectra. The non-linear optical property has been confirmed from the optical transmission and fluorescence spectra.

16. The Association between Ambient Temperature and Childhood Hand, Foot, and Mouth Disease in Chengdu, China: A Distributed Lag Non-linear Analysis

PubMed Central

Yin, Fei; Zhang, Tao; Liu, Lei; Lv, Qiang; Li, Xiaosong

2016-01-01

Hand, foot and mouth disease (HFMD) has recently been recognized as a critical challenge to disease control and public health response in China. This study aimed to quantify the association between temperature and HFMD in Chengdu. Daily HFMD cases and meteorological variables in Chengdu between January 2010 and December 2013 were obtained to construct the time series. A distributed lag non-linear model was performed to investigate the temporal lagged association of daily temperature with age- and gender-specific HFMD. A total of 76,403 HFMD cases aged 0–14 years were reported in Chengdu during the study period, and a bimodal seasonal pattern was observed. The temperature-HFMD relationships were non-linear in all age and gender groups, with the first peak at 14.0–14.1 °C and the second peak at 23.1–23.2 °C. The high temperatures had acute and short-term effects and declined quickly over time, while the effects in low temperature ranges were persistent over longer lag periods. Males and children aged <1 year were more vulnerable to temperature variations. Temperature played an important role in HFMD incidence with non-linear and delayed effects. The success of HFMD intervention strategies could benefit from giving more consideration to local climatic conditions. PMID:27248051

17. Asymptotic Stability of Interconnected Passive Non-Linear Systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Joshi, S. M.; Kelkar, A. G.

1999-01-01

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

18. Hybrid fusion of linear, non-linear and spectral models for the dynamic modeling of sEMG and skeletal muscle force: an application to upper extremity amputation.

PubMed

Potluri, Chandrasekhar; Anugolu, Madhavi; Schoen, Marco P; Subbaram Naidu, D; Urfer, Alex; Chiu, Steve

2013-11-01

Estimating skeletal muscle (finger) forces using surface Electromyography (sEMG) signals poses many challenges. In general, the sEMG measurements are based on single sensor data. In this paper, two novel hybrid fusion techniques for estimating the skeletal muscle force from the sEMG array sensors are proposed. The sEMG signals are pre-processed using five different filters: Butterworth, Chebychev Type II, Exponential, Half-Gaussian and Wavelet transforms. Dynamic models are extracted from the acquired data using Nonlinear Wiener Hammerstein (NLWH) models and Spectral Analysis Frequency Dependent Resolution (SPAFDR) models based system identification techniques. A detailed comparison is provided for the proposed filters and models using 18 healthy subjects. Wavelet transforms give higher mean correlation of 72.6 ± 1.7 (mean ± SD) and 70.4 ± 1.5 (mean ± SD) for NLWH and SPAFDR models, respectively, when compared to the other filters used in this work. Experimental verification of the fusion based hybrid models with wavelet transform shows a 96% mean correlation and 3.9% mean relative error with a standard deviation of ± 1.3 and ± 0.9 respectively between the overall hybrid fusion algorithm estimated and the actual force for 18 test subjects' k-fold cross validation data.

19. Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

PubMed

Kumar, K Vasanth; Porkodi, K; Rocha, F

2008-01-15

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

20. Controllability of non-linear biochemical systems.

PubMed

2005-07-01

Mathematical methods of biochemical pathway analysis are rapidly maturing to a point where it is possible to provide objective rationale for the natural design of metabolic systems and where it is becoming feasible to manipulate these systems based on model predictions, for instance, with the goal of optimizing the yield of a desired microbial product. So far, theory-based metabolic optimization techniques have mostly been applied to steady-state conditions or the minimization of transition time, using either linear stoichiometric models or fully kinetic models within biochemical systems theory (BST). This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system, within a given time period, from an initial state to some target state, which may or may not be a steady state. For this purpose, BST models in S-system form are transformed into affine non-linear control systems, which are subjected to an exact feedback linearization that permits controllability through independent variables. The method is exemplified with a small glycolytic-glycogenolytic pathway that had been analyzed previously by several other authors in different contexts.

1. Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: comparison of various error functions.

PubMed

Kumar, K Vasanth; Porkodi, K; Rocha, F

2008-03-01

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r2 was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r2), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K2 was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

2. Integrating real-time and manual monitored data to predict hillslope soil moisture dynamics with high spatio-temporal resolution using linear and non-linear models

Technology Transfer Automated Retrieval System (TEKTRAN)

Spatio-temporal variability of soil moisture (') is a challenge that remains to be better understood. A trade-off exists between spatial coverage and temporal resolution when using the manual and real-time ' monitoring methods. This restricted the comprehensive and intensive examination of ' dynamic...

3. Investigation of Non-Linear Dynamics of the Rock Massive,Using Seismological Catalogue data and Induction Electromagnetic Monitoring Data in a Rock Burst Mine.

Hachay, O. A.; Khachay, O. Y.; Klimko, V. K.; Shipeev, O. V.

2012-04-01

Geological medium is an open dynamical system, which is influenced on different scales by natural and man-made impacts, which change the medium state and lead as a result to a complicated many ranked hierarchic evolution. That is the subject of geo synergetics. Paradigm of physical mesomechanics, which was advanced by academician Panin V.E. and his scientific school, which includes the synergetic approach is a constructive method for research and changing the state of heterogenic materials [1]. That result had been obtained on specimens of different materials. In our results of research of no stationary geological medium in a frame of natural experiments in real rock massifs, which are under high man-made influence it was shown, that the state dynamics can be revealed with use synergetics in hierarchic medium. Active and passive geophysical monitoring plays a very important role for research of the state of dynamical geological systems. It can be achieved by use electromagnetic and seismic fields. Our experience of that research showed the changing of the system state reveals on the space scales and times in the parameters, which are linked with the peculiarities of the medium of the second or higher ranks [2-5]. Results of seismological and electromagnetic information showed the mutual additional information on different space-time levels of rock massive state, which are energetic influenced by explosions, used in mining technology. It is revealed a change of nonlinearity degree in time of the massive state by active influence on it. The description of massive movement in a frame of linear dynamical system does not satisfy the practical situation. The received results are of great significance because for the first time we could find the coincidences with the mathematical theory of open systems and experimental natural results with very complicated structure. On that base we developed a new processing method for the seismological information which can be used in

4. Detector noise statistics in the non-linear regime

NASA Technical Reports Server (NTRS)

Shopbell, P. L.; Bland-Hawthorn, J.

1992-01-01

The statistical behavior of an idealized linear detector in the presence of threshold and saturation levels is examined. It is assumed that the noise is governed by the statistical fluctuations in the number of photons emitted by the source during an exposure. Since physical detectors cannot have infinite dynamic range, our model illustrates that all devices have non-linear regimes, particularly at high count rates. The primary effect is a decrease in the statistical variance about the mean signal due to a portion of the expected noise distribution being removed via clipping. Higher order statistical moments are also examined, in particular, skewness and kurtosis. In principle, the expected distortion in the detector noise characteristics can be calibrated using flatfield observations with count rates matched to the observations. For this purpose, some basic statistical methods that utilize Fourier analysis techniques are described.

5. Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Helbing, D.; Moussaid, M.

2009-06-01

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerically in the past. Here, we present an analytical study for the optimal velocity model with a stepwise specification of the optimal velocity function and a simple kind of perturbation. Despite various approximations, the analytical results are shown to reproduce numerical results very well.

6. Non-linear dynamics and pattern selection at the crystal-melt interface. Final report, September 1, 1984--February 28, 1998

SciTech Connect

Cummins, H.Z.

1998-07-01

Pattern formation at the solidifying crystal-melt interface was investigated with a model binary alloy system of the molecular crystal succinonitrile doped with the laser dye Coumarin 152. Videomicroscopy and computerized digital image analysis provided detailed data for quantitative comparison with theoretical predictions. Application of a single localized laser pulse or a row of UV spots to the interface during solidification allowed for direct measurements of pattern stability. These thermal perturbations also resulted in dramatic modifications of the observed solidification patterns, suggesting that the controlled thermal perturbation approach may allow the microstructure of metallic alloys to be controlled during solidification.

7. Non-linear Flood Risk Assessment

Mazzarella, A.

The genesis of floodings is very complex depending on hydrologic, meteorological and evapo-transpirative factors that are linked among themselves in a non linear way with numerous feedback processes. The Cantor dust and the rank-ordering statistics supply a proper framework for identifying a kind of a non linear order in the time succession of the floodings and so provide a basis for their prediction. When a catalogue is analysed, it is necessary to test its completeness with respect to the size of the recorded events and results obtained from analysis of catalogues that do not take into account such a test are suspect and possibly wrong, or, at least, unreliable. Floodings have no instrumentally determined magnitude scale, like that conventionally used for earthquakes, and this is why they are generally described in qualitative terms. For this reason, a semi-quantitative index, called ASI (Alluvial Strength Index) has been here developed that combines attributes of alluvial triggering mechanisms and effects on the territorial and hydraulic system.The historical succession of alluvial events occurred at high valley of Po river (Northern Italy), mean valley of Calore river (Southern Italy) and at Sarno, near Naples, have been accurately reconstructed on the basis of old documents and classified according to their ASI. The catalogues have been verified to be complete only for events classified at least as moderate and this probably because many of the lowest energetic events, especially in the past, escaped the detection. The identification of scale-invariances in the time clustering of alluvial events, both on short and long time scales, even if indicative of the complexity of their genesis, might be very helpful for the assessment and reduction of the hazard of future disasters. For example, on the basis of the results of the rank-ordering statistics, the most probable occurrence of an alluvial event at Sarno, classified at least as strong, is predicted to occur

8. A two dimensional interface element for coupling of independently modeled three dimensional finite element meshes and extensions to dynamic and non-linear regimes

NASA Technical Reports Server (NTRS)

1995-01-01

The work reported here pertains only to the first year of research for a three year proposal period. As a prelude to this two dimensional interface element, the one dimensional element was tested and errors were discovered in the code for built-up structures and curved interfaces. These errors were corrected and the benchmark Boeing composite crown panel was analyzed successfully. A study of various splines led to the conclusion that cubic B-splines best suit this interface element application. A least squares approach combined with cubic B-splines was constructed to make a smooth function from the noisy data obtained with random error in the coordinate data points of the Boeing crown panel analysis. Preliminary investigations for the formulation of discontinuous 2-D shell and 3-D solid elements were conducted.

9. Non-linearity in clinical practice.

PubMed

Petros, Peter

2003-05-01

The whole spectrum of medicine consists of complex non-linear systems that are balanced and interact with each other. How non-linearity confers stability on a system and explains variation and uncertainty in clinical medicine is discussed. A major theme is that a small alteration in initial conditions may have a major effect on the end result. In the context of non-linearity, it is argued that 'evidence-based medicine' (EBM) as it exists today can only ever be relevant to a small fraction of the domain of medicine, that the 'art of medicine' consists of an intuitive 'tuning in' to these complex systems and as such is not so much an art as an expression of non-linear science. The main cause of iatrogenic disease is interpreted as a failure to understand the complexity of the systems being treated. Case study examples are given and analysed in non-linear terms. It is concluded that good medicine concerns individualized treatment of an individual patient whose body functions are governed by non-linear processes. EBM as it exists today paints with a broad and limited brush, but it does promise a fresh new direction. In this context, we need to expand the spectrum of scientific medicine to include non-linearity, and to look upon the 'art of medicine' as a historical (but unstated) legacy in this domain.

10. Using non-linear analogue of Nyquist diagrams for analysis of the equation describing the hemodynamics in blood vessels near pathologies

Cherevko, A. A.; Bord, E. E.; Khe, A. K.; Panarin, V. A.; Orlov, K. J.; Chupakhin, A. P.

2016-06-01

This article considers method of describing the behaviour of hemodynamic parameters near vascular pathologies. We study the influence of arterial aneurysms and arteriovenous malformations on the vascular system. The proposed method involves using generalized model of Van der Pol-Duffing to find out the characteristic behaviour of blood flow parameters. These parameters are blood velocity and pressure in the vessel. The velocity and pressure are obtained during the neurosurgery measurements. It is noted that substituting velocity on the right side of the equation gives good pressure approximation. Thus, the model reproduces clinical data well enough. In regard to the right side of the equation, it means external impact on the system. The harmonic functions with various frequencies and amplitudes are substituted on the right side of the equation to investigate its properties. Besides, variation of the right side parameters provides additional information about pressure. Non-linear analogue of Nyquist diagrams is used to find out how the properties of solution depend on the parameter values. We have analysed 60 cases with aneurysms and 14 cases with arteriovenous malformations. It is shown that the diagrams are divided into classes. Also, the classes are replaced by another one in the definite order with increasing of the right side amplitude.

11. Linear and non-linear optics of nano-scale 2‧,7‧dichloro-fluorescein/FTO optical system: Bandgap and dielectric analysis

Iqbal, Javed; Yahia, I. S.; Zahran, H. Y.; AlFaify, S.; AlBassam, A. M.; El-Naggar, A. M.

2016-12-01

2‧,7‧ dichloro-Fluorescein (DCF) is a promising organic semiconductor material in different technological aspects such as solar cell, photodiode, Schottky diode. DCF thin film/conductive glass (FTO glass) was prepared by a low-cost spin coating technique. The spectrophotometric data such as the absorbance, reflectance and transmittance were cogitated in the 350-2500 nm wavelength range, at the normal incidence. The absorption (n) and linear refractive indices (k) were computed using the Fresnel's equations. The optical band gap was evaluated and it was found that there is two band gap described as follows: (1) It is related to the band gap of FTO/glass which is equal 3.4 eV and (2) the second one is related to the absorption edge of DCF equals 2.25 eV. The non-linear parameters such as the refractive index (n2) and optical susceptibility χ(3) were evaluated by the spectroscopic method based on the refractive index. Both (n2) and χ(3) increased rapidly on increasing the wavelength with redshift absorption. Our work represents a new idea about using FTO glass for a new generation of the optical device and technology.

12. Non-linear dynamics in photochemistry

Pimienta, V.; Lévy, G.; Lavabre, D.; Laplante, J. P.; Micheau, J. C.

1992-09-01

The rate law of an elementary photochemical reaction: A → B ( hv), contains 4 independent factors: the quantum yield, the photon flux, the concentration of the photosensitive substrate and the photokinetic factor. This type of reaction will always slow down. However, by increasing one of these 4 factors artificially, the reaction can be made to speed up. Using kinetic models comprising one or more photochemical reactions, we show that appropriate coupling between two or more elementary processes gives rise to a cooperative effect. This effect increases one or more of these 4 factors, and makes the coupled photochemical model bistable in a CSTR. The values of the parameters for which one observes bistability are experimentally realistic. One of these models provides a simplified simulation of the stages underlying the bistable photochemical behavior of the TPID/CHCl 3, system.

13. Characterizing the relationship between temperature and mortality in tropical and subtropical cities: a distributed lag non-linear model analysis in Hue, Viet Nam, 2009-2013.

PubMed

Dang, Tran Ngoc; Seposo, Xerxes T; Duc, Nguyen Huu Chau; Thang, Tran Binh; An, Do Dang; Hang, Lai Thi Minh; Long, Tran Thanh; Loan, Bui Thi Hong; Honda, Yasushi

2016-01-01

Background The relationship between temperature and mortality has been found to be U-, V-, or J-shaped in developed temperate countries; however, in developing tropical/subtropical cities, it remains unclear. Objectives Our goal was to investigate the relationship between temperature and mortality in Hue, a subtropical city in Viet Nam. Design We collected daily mortality data from the Vietnamese A6 mortality reporting system for 6,214 deceased persons between 2009 and 2013. A distributed lag non-linear model was used to examine the temperature effects on all-cause and cause-specific mortality by assuming negative binomial distribution for count data. We developed an objective-oriented model selection with four steps following the Akaike information criterion (AIC) rule (i.e. a smaller AIC value indicates a better model). Results High temperature-related mortality was more strongly associated with short lags, whereas low temperature-related mortality was more strongly associated with long lags. The low temperatures increased risk in all-category mortality compared to high temperatures. We observed elevated temperature-mortality risk in vulnerable groups: elderly people (high temperature effect, relative risk [RR]=1.42, 95% confidence interval [CI]=1.11-1.83; low temperature effect, RR=2.0, 95% CI=1.13-3.52), females (low temperature effect, RR=2.19, 95% CI=1.14-4.21), people with respiratory disease (high temperature effect, RR=2.45, 95% CI=0.91-6.63), and those with cardiovascular disease (high temperature effect, RR=1.6, 95% CI=1.15-2.22; low temperature effect, RR=1.99, 95% CI=0.92-4.28). Conclusions In Hue, the temperature significantly increased the risk of mortality, especially in vulnerable groups (i.e. elderly, female, people with respiratory and cardiovascular diseases). These findings may provide a foundation for developing adequate policies to address the effects of temperature on health in Hue City.

14. Characterizing the relationship between temperature and mortality in tropical and subtropical cities: a distributed lag non-linear model analysis in Hue, Viet Nam, 2009–2013

PubMed Central

Dang, Tran Ngoc; Seposo, Xerxes T.; Duc, Nguyen Huu Chau; Thang, Tran Binh; An, Do Dang; Hang, Lai Thi Minh; Long, Tran Thanh; Loan, Bui Thi Hong; Honda, Yasushi

2016-01-01

Background The relationship between temperature and mortality has been found to be U-, V-, or J-shaped in developed temperate countries; however, in developing tropical/subtropical cities, it remains unclear. Objectives Our goal was to investigate the relationship between temperature and mortality in Hue, a subtropical city in Viet Nam. Design We collected daily mortality data from the Vietnamese A6 mortality reporting system for 6,214 deceased persons between 2009 and 2013. A distributed lag non-linear model was used to examine the temperature effects on all-cause and cause-specific mortality by assuming negative binomial distribution for count data. We developed an objective-oriented model selection with four steps following the Akaike information criterion (AIC) rule (i.e. a smaller AIC value indicates a better model). Results High temperature-related mortality was more strongly associated with short lags, whereas low temperature-related mortality was more strongly associated with long lags. The low temperatures increased risk in all-category mortality compared to high temperatures. We observed elevated temperature-mortality risk in vulnerable groups: elderly people (high temperature effect, relative risk [RR]=1.42, 95% confidence interval [CI]=1.11–1.83; low temperature effect, RR=2.0, 95% CI=1.13–3.52), females (low temperature effect, RR=2.19, 95% CI=1.14–4.21), people with respiratory disease (high temperature effect, RR=2.45, 95% CI=0.91–6.63), and those with cardiovascular disease (high temperature effect, RR=1.6, 95% CI=1.15–2.22; low temperature effect, RR=1.99, 95% CI=0.92–4.28). Conclusions In Hue, the temperature significantly increased the risk of mortality, especially in vulnerable groups (i.e. elderly, female, people with respiratory and cardiovascular diseases). These findings may provide a foundation for developing adequate policies to address the effects of temperature on health in Hue City. PMID:26781954

15. Proceedings of the Non-Linear Aero Prediction Requirements Workshop

NASA Technical Reports Server (NTRS)

Logan, Michael J. (Editor)

1994-01-01

The purpose of the Non-Linear Aero Prediction Requirements Workshop, held at NASA Langley Research Center on 8-9 Dec. 1993, was to identify and articulate requirements for non-linear aero prediction capabilities during conceptual/preliminary design. The attendees included engineers from industry, government, and academia in a variety of aerospace disciplines, such as advanced design, aerodynamic performance analysis, aero methods development, flight controls, and experimental and theoretical aerodynamics. Presentations by industry and government organizations were followed by panel discussions. This report contains copies of the presentations and the results of the panel discussions.

16. Using Non-Linear Statistical Methods with Laboratory Kinetic Data

NASA Technical Reports Server (NTRS)

Anicich, Vincent

1997-01-01

This paper will demonstrate the usefulness of standard non-linear statistical analysis on ICR and SIFT kinetic data. The specific systems used in the demonstration are the isotopic and change transfer reactions in the system of H2O+/D2O, H30+/D2O, and other permutations.

17. Non-linear Post Processing Image Enhancement

NASA Technical Reports Server (NTRS)

Hunt, Shawn; Lopez, Alex; Torres, Angel

1997-01-01

A non-linear filter for image post processing based on the feedforward Neural Network topology is presented. This study was undertaken to investigate the usefulness of "smart" filters in image post processing. The filter has shown to be useful in recovering high frequencies, such as those lost during the JPEG compression-decompression process. The filtered images have a higher signal to noise ratio, and a higher perceived image quality. Simulation studies comparing the proposed filter with the optimum mean square non-linear filter, showing examples of the high frequency recovery, and the statistical properties of the filter are given,

18. Global search of non-linear systems periodic solutions: A rotordynamics application

Sarrouy, E.; Thouverez, F.

2010-08-01

Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions—where T is known—of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.

19. A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

20. Dynamic analysis of process reactors

SciTech Connect

Shadle, L.J.; Lawson, L.O.; Noel, S.D.

1995-06-01

The approach and methodology of conducting a dynamic analysis is presented in this poster session in order to describe how this type of analysis can be used to evaluate the operation and control of process reactors. Dynamic analysis of the PyGas{trademark} gasification process is used to illustrate the utility of this approach. PyGas{trademark} is the gasifier being developed for the Gasification Product Improvement Facility (GPIF) by Jacobs-Siffine Engineering and Riley Stoker. In the first step of the analysis, process models are used to calculate the steady-state conditions and associated sensitivities for the process. For the PyGas{trademark} gasifier, the process models are non-linear mechanistic models of the jetting fluidized-bed pyrolyzer and the fixed-bed gasifier. These process sensitivities are key input, in the form of gain parameters or transfer functions, to the dynamic engineering models.

1. Non-linear cord-rubber composites

NASA Technical Reports Server (NTRS)

Clark, S. K.; Dodge, R. N.

1989-01-01

A method is presented for calculating the stress-strain relations in a multi-layer composite made up of materials whose individual stress-strain characteristics are non-linear and possibly different. The method is applied to the case of asymmetric tubes in tension, and comparisons with experimentally measured data are given.

2. Possibilities Of Optically Non Linear Thin Films

De Micheli, Marc; Zyss, Joseph; Azema, Alain

1983-11-01

Efficient integrated frequency doubling devices transparent in the visible and near I.R. are demanded by a number of applications. The optimization of both wave interaction configurations and material intrinsic nonlinear susceptibility are successively discussed within this scope. Basic features such as power confinement, interaction length dependence, phase matching techniques, underlying the second harmonic generation conversion rate in bulk and waveguided structures are compared. Undoped Ga As film epitaxied over n+ doped Ga As substrate and TIPE Lithium Lobate waveguides exemplify the possibilities of non linear thin films. The higher non linear susceptibility of certain organic molecular single crys-tals should help raise the efficiency of doubling devices. We report the definition and bulk performances of two non linear organic crystals, namely POM (3-methyl-4 nitropyridine-1-oxyde) and MAP (methyl-(2,4-dinitropheny1)-aminopropanoate) with a figure of merit up to one order of magnitude above that of Li Nb 03. The combination of organic materials and waveguided configuration should lead to a new generation of non linear devices.

3. Statistical analysis of Amenamevir (ASP2151) between pharmacokinetics and clinical efficacies with non-linear effect model for the treatment of genital herpes.

PubMed

Takada, Akitsugu; Katashima, Masataka; Kaibara, Atsunori; Sawamoto, Taiji; Zhang, Wenhui; Keirns, James

2014-09-01

Amenamevir is the international non-proprietary name for ASP2151 synthesized by Astellas Pharma, Inc. It is a structurally novel class of helicase-primase inhibitor and demonstrated more potency in vitro anti-viral activity with low cytotoxicity against varicella-zoster virus (VZV), herpes simplex virus type 1 (HSV-1), and herpes simplex virus type 2 (HSV-2) than acyclovir (ACV). Phase II randomized trial assessed the safety and efficacy of ASP2151 for episodic therapy of recurrent genital herpes was conducted. Participants self-initiated with ASP2151 (100, 200, or 400 mg daily for 3 days), ASP2151 (1,200 mg as a single dose), placebo for 3 days, or Valacyclovir (500 mg twice daily for 3 days). We present a first population pharmacokinetic (PPK) modeling analysis of Amenamevir for genital herpes patients. The final model retained the effect of Weight and Albumin on CL. Statistical analysis between pharmacokinetics and clinical efficacies was done by using the time above 200 ng/mL (T200 ). T200 derived from the final PPK model to consider the correlation with Time to lesion healing and viral shedding. This finding suggested that it could be necessary to maintain the Amenamevir concentration above the threshold level to prevent the virus replication.

4. Pharmaceutical applications of non-linear imaging.

PubMed

Strachan, Clare J; Windbergs, Maike; Offerhaus, Herman L

2011-09-30

Non-linear optics encompasses a range of optical phenomena, including two- and three-photon fluorescence, second harmonic generation (SHG), sum frequency generation (SFG), difference frequency generation (DFG), third harmonic generation (THG), coherent anti-Stokes Raman scattering (CARS), and stimulated Raman scattering (SRS). The combined advantages of using these phenomena for imaging complex pharmaceutical systems include chemical and structural specificities, high optical spatial and temporal resolutions, no requirement for labels, and the ability to image in an aqueous environment. These features make such imaging well suited for a wide range of pharmaceutical and biopharmaceutical investigations, including material and dosage form characterisation, dosage form digestion and drug release, and drug and nanoparticle distribution in tissues and within live cells. In this review, non-linear optical phenomena used in imaging will be introduced, together with their advantages and disadvantages in the pharmaceutical context. Research on pharmaceutical and biopharmaceutical applications is discussed, and potential future applications of the technology are considered.

5. Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

NASA Technical Reports Server (NTRS)

Bielawa, R. L.

1976-01-01

The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

6. The use of non-linear regression analysis and the F test for model discrimination with dose-response curves and ligand binding data.

PubMed

Bardsley, W G; McGinlay, P B

1987-05-21

Computer fitting of binding data is discussed and it is concluded that the main problem is the choice of starting estimates and internal scaling parameters, not the optimization software. Solving linear overdetermined systems of equations for starting estimates is investigated. A function, Q, is introduced to study model discrimination with binding isotherms and the behaviour of Q as a function of model parameters is calculated for the case of 2 and 3 sites. The power function of the F test is estimated for models with 2 to 5 binding sites and necessary constraints on parameters for correct model discrimination are given. The sampling distribution of F test statistics is compared to an exact F distribution using the Chi-squared and Kolmogorov-Smirnov tests. For low order modes (n less than 3) the F test statistics are approximately F distributed but for higher order models the test statistics are skewed to the left of the F distribution. The parameter covariance matrix obtained by inverting the Hessian matrix of the objective function is shown to be a good approximation to the estimate obtained by Monte Carlo sampling for low order models (n less than 3). It is concluded that analysis of up to 2 or 3 binding sites presents few problems and linear, normal statistical results are valid. To identify correctly 4 sites is much more difficult, requiring very precise data and extreme parameter values. Discrimination of 5 from 4 sites is an upper limit to the usefulness of the F test.

7. Radiation damping of near-shore oscillations created by sudden wind set-down: a new approach with non-linear analysis of run-up and run-down

Ozeren, M. S.; Postacioglu, N.; Canli, U.

2012-12-01

In this study we are developing an analytical approach to the radiation damping of the oscillations created due to sudden cessation of the wind blowing from the coast towards the open ocean . For the shoreline slope we follow Carrier-Greenspan approach to treat the non-linear problem. This approach is based on a particular hodograph transformation of the shallow water equations using two auxiliary variables, both function of time and space. This analysis is valid over a constant slope in one-dimensional propagation. In the far-field, the wave equation is linearized. A matching between the linear solution off-shore and the non-linear solution near the shore is performed at the point of bathymetric discontinuity where the constant-slope part of the bathymetry reaches its deepest point. Our aim is to quantify the radiation damping, namely the energy loss of the system due to the waves propagating towards open-ocean as a function of the magnitude of bathymetric discontinuity. We calculate the response to a wind forcing that is logarithmic in space and periodic in time using Green's functions. A sudden cessation of the forcing is a linear combination of these type of excitations. The radiation condition off-shore renders the natural frequencies of oscillations of the system complex. Accordingly, the integration over the continuous frequency spectrum becomes a series of complex residues. We calculate these residues numerically. Solutions indicate that the radiation damping can be significant if the bathymetric discontinuity is negligible. However when the non-dimensional discontinuity is 20 (all depths are normalized using the deepest point at the end of the constant-slope part) the amplitude of the oscillations is reduced about 20% over one period of oscillation.

8. The Prognostic Value of Non-Linear Analysis of Heart Rate Variability in Patients with Congestive Heart Failure—A Pilot Study of Multiscale Entropy

PubMed Central

Ho, Yi-Lwun; Lin, Chen; Lin, Yen-Hung; Lo, Men-Tzung

2011-01-01

Aims The influences of nonstationarity and nonlinearity on heart rate time series can be mathematically qualified or quantified by multiscale entropy (MSE). The aim of this study is to investigate the prognostic value of parameters derived from MSE in the patients with systolic heart failure. Methods and Results Patients with systolic heart failure were enrolled in this study. One month after clinical condition being stable, 24-hour Holter electrocardiogram was recording. MSE as well as other standard parameters of heart rate variability (HRV) and detrended fluctuation analysis (DFA) were assessed. A total of 40 heart failure patients with a mea age of 56±16 years were enrolled and followed-up for 684±441 days. There were 25 patients receiving β-blockers treatment. During follow-up period, 6 patients died or received urgent heart transplantation. The short-term exponent of DFA and the slope of MSE between scale 1 to 5 were significantly different between patients with or without β-blockers (p = 0.014 and p = 0.028). Only the area under the MSE curve for scale 6 to 20 (Area6–20) showed the strongest predictive power between survival (n = 34) and mortality (n = 6) groups among all the parameters. The value of Area6–2021.2 served as a significant predictor of mortality or heart transplant (p = 0.0014). Conclusion The area under the MSE curve for scale 6 to 20 is not relevant to β-blockers and could further warrant independent risk stratification for the prognosis of CHF patients. PMID:21533258

9. Localization of non-linearly modeled autonomous mobile robots using out-of-sequence measurements.

PubMed

Besada-Portas, Eva; Lopez-Orozco, Jose A; Lanillos, Pablo; de la Cruz, Jesus M

2012-01-01

This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS) measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors) and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost.

10. Localization of Non-Linearly Modeled Autonomous Mobile Robots Using Out-of-Sequence Measurements

PubMed Central

Besada-Portas, Eva; Lopez-Orozco, Jose A.; Lanillos, Pablo; de la Cruz, Jesus M.

2012-01-01

This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS) measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors) and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost. PMID:22736962

11. Non-linear memristor switching model

Chernov, A. A.; Islamov, D. R.; Pik'nik, A. A.

2016-10-01

We introduce a thermodynamical model of filament growing when a current pulse via memristor flows. The model is the boundary value problem, which includes nonstationary heat conduction equation with non-linear Joule heat source, Poisson equation, and Shockley- Read-Hall equations taking into account strong electron-phonon interactions in trap ionization and charge transport processes. The charge current, which defines the heating in the model, depends on the rate of the oxygen vacancy generation. The latter depends on the local temperature. The solution of the introduced problem allows one to describe the kinetics of the switch process and the final filament morphology.

DTIC Science & Technology

1986-05-01

interesting possibilities for future study . These seem at the moment to fall into 3 categories: 1) Do we need the step that works on ends of abutting swooshes...Unear’smoothers to00 31. Recent work at Stanford 100 32. Coments an ocaly-lnear ttu.ng 101 .’ .. 33. Qevelnd’s i.ow 102 34. smelting 103 APPENDIX C: A...limited degree, with "Benchmarks’. We are, in most subareas, early in our study of non-linear smoothers. As as consequence, we often have to emphasize

13. Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

SciTech Connect

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.

14. Study of the effect of static/dynamic Coulomb friction variation at the tape-head interface of a spacecraft tape recorder by non-linear time response simulation

NASA Technical Reports Server (NTRS)

1978-01-01

A description is presented of six simulation cases investigating the effect of the variation of static-dynamic Coulomb friction on servo system stability/performance. The upper and lower levels of dynamic Coulomb friction which allowed operation within requirements were determined roughly to be three times and 50% respectively of nominal values considered in a table. A useful application for the nonlinear time response simulation is the sensitivity analysis of final hardware design with respect to such system parameters as cannot be varied realistically or easily in the actual hardware. Parameters of the static/dynamic Coulomb friction fall in this category.

15. A survey on non-linear oscillations

Atherton, D. P.; Dorrah, H. T.

1980-06-01

This survey paper presents a comprehensive review of work in the field of non-linear oscillations. A brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems. Multivariable systems are then covered from an analogous viewpoint which allows the reader to clearly identify both how single variable methods have been extended and the possibilities for further research. Particular emphasis is placed on describing function methods since it is believed that, where exact solutions are not possible, the approach may not only give approximate solutions but provides good insight for further computational or simulation studies. The coverage is essentially restricted to continuous lumped parameter systems and includes both free and forced oscillations. Several applications of the theories in various fields of engineering and science are discussed and indicate the broad interest in non-linear oscillatory phenomena. Finally, a detailed bibliography on the subject is provided.

16. Simulation of magnetisation switching by non-linear resonance

Thirion, C.; Wernsdorfer, W.

2004-05-01

The sub-nanosecond dynamics have recently been probed via non-linear resonance on single magnetic nanoparticles using the micro-SQUID technique. In the presence of a magnetic field considerably smaller than the switching field, the magnetisation of a nanoparticle can be reversed by the application of a small RF field. The experimental determination of the most effective frequency is a direct probe of the small oscillations of the magnetisation in the metastable energy well. We present here a simulation of this experiment using the Landau-Lifschitz-Gilbert equation.

17. Travelling and standing envelope solitons in discrete non-linear cyclic structures

Grolet, Aurelien; Hoffmann, Norbert; Thouverez, Fabrice; Schwingshackl, Christoph

2016-12-01

Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.

18. Non-linearities in Holocene floodplain sediment storage

Notebaert, Bastiaan; Nils, Broothaerts; Jean-François, Berger; Gert, Verstraeten

2013-04-01

that a strong multifractality is present in the scaling relationship between sediment storage and catchment area, depending on geomorphic landscape properties. Extrapolation of data from one spatial scale to another inevitably leads to large errors: when only the data of the upper floodplains are considered, a regression analysis results in an overestimation of total floodplain deposition for the entire catchment of circa 115%. This example demonstrates multifractality and related non-linearity in scaling relationships, which influences extrapolations beyond the initial range of measurements. These different examples indicate how traditional extrapolation techniques and assumptions in sediment budget studies can be challenged by field data, further complicating our understanding of these systems. Although simplifications are often necessary when working on large spatial scale, such non-linearities may form challenges for a better understanding of system behavior.

19. Non-linear sequencing and cognizant failure

Gat, Erann

1999-01-01

Spacecraft are traditionally commanded using linear sequences of time-based commands. Linear sequences work fairly well, but they are difficult and expensive to generate, and are usually not capable of responding to contingencies. Any anomalous behavior while executing a linear sequence generally results in the spacecraft entering a safe mode. Critical sequences like orbit insertions which must be able to respond to faults without going into safe mode are particularly difficult to design and verify. The effort needed to generate command sequences can be reduced by extending the vocabulary of sequences to include more sophisticated control constructs. The simplest extensions are conditionals and loops. Adding these constructs would make a sequencing language look more or less like a traditional programming language or scripting language, and would come with all the difficulties associated with such a language. In particular, verifying the correctness of a sequence would be tantamount to verifying the correctness of a program, which is undecidable in general. We describe an extended vocabulary for non-linear sequencing based on the architectural notion of cognizant failure. A cognizant failure architecture is divided into components whose contract is to either achieve (or maintain) a certain condition, or report that they have failed to do so. Cognizant failure is an easier condition to verify than correctness, but it can provide high confidence in the safety of the spacecraft. Because cognizant failure inherently implies some kind of representation of the intent of an action, the system can respond to contingencies in more robust and general ways. We will describe an implemented non-linear sequencing system that is being flown on the NASA New Millennium Deep Space 1 Mission as part of the Remote Agent Experiment.

20. Computational models of signalling networks for non-linear control.

PubMed

Fuente, Luis A; Lones, Michael A; Turner, Alexander P; Stepney, Susan; Caves, Leo S; Tyrrell, Andy M

2013-05-01

Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.

1. Optimal control of a satellite-robot system using direct collocation with non-linear programming

Coverstone-Carroll, V. L.; Wilkey, N. M.

1995-08-01

The non-holonomic behavior of a satellite-robot system is used to develop the system's equations of motion. The resulting non-linear differential equations are transformed into a non-linear programming problem using direct collocation. The link rates of the robot are minimized along optimal reorientations. Optimal solutions to several maneuvers are obtained and the results are interpreted to gain an understanding of the satellite-robot dynamics.

2. Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes

DTIC Science & Technology

2016-04-20

AFRL-RV-PS- AFRL-RV-PS- TR-2015-0182 TR-2015-0182 CHARACTERIZATION OF NON-LINEARIZED SPACECRAFT RELATIVE MOTION USING NONLINEAR NORMAL MODES Eric...Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62601F...public release; distribution is unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT Characterize the nonlinear dynamics for large amplitude relative motion

3. Optimization of Passive and Active Non-Linear Vibration Mounting Systems Based on Vibratory Power Transmission

Royston, T. J.; Singh, R.

1996-07-01

While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.

4. Non-linear structure in modified action theories of gravity

Lima, Marcos V.

We study the effects and carry out a suite of cosmological simulations of modified action f(R) models where cosmic acceleration arises from an alteration of gravity instead of dark energy. These models introduce an extra scalar degree of freedom which enhances the force of gravity below the Compton scale of the scalar. The simulations exhibit the so-called chameleon mechanism, necessary for satisfying local constraints on gravity, where this scale depends on environment, in particular the depth of the local gravitational potential. We find that the chameleon mechanism can substantially suppress the enhancement of power spectrum in the non-linear regime if the background field value is comparable to or smaller than the depth of the gravitational potentials of typical structures. Nonetheless power spectrum enhancements at intermediate scales remain at a measurable level even when the expansion history is indistinguishable from a cosmological constant, cold dark matter model. We also investigate the effects of the modified dynamics on halo properties such as their abundance and clustering. We find that the f(R) effects on the halo mass- function and bias depend mostly on the linear power spectrum modifications, but that the chameleon mechanism suppresses the modifications at high-mass halos with deep potential wells. The f(R) modifications also affect the threshold density for collapse, or similarly the overdensity for virialization and therefore can change halo definitions from those of ACDM. As a result, simple scaling relations that take the linear matter power spectrum into a non-linear spectrum fail to capture the modifications of f(R) due to the change in collapsed structures, the chameleon mechanism, and the time evolution of the modifications. A quantification of these effects, including modifications on halo profiles, is necessary to accurately describe halo properties and potentially construct a halo model of the non-linear power spectrum.

5. A study of passive and adaptive hydraulic engine mount systems with emphasis on non-linear characteristics

Kim, G.; Singh, R.

1995-01-01

Passive hydraulic mounts exhibit excitation frequency variant and deflection amplitude sensitive stiffness and damping properties. Such non-linear dynamic characteristics are examined by using analytical and experimental methods, both at the device level and within the context of a simplified vehicle model. A new lumped parameter non-linear mathematical model of the hydraulic mount is developed by simulating its decoupler switching mechanism and inertia track dynamics. The low frequency performance features and limitations of several passive mounts are made clear through the non-linear vehicle model simulation and comparable laboratory vibration tests. The high frequency performance problems of the passive hydraulic mount are identified by applying the quasi-linear analysis method. Based on these results, a new adaptive mount system is developed which exhibits broad bandwidth performance features up to 250 Hz. It implements an on-off damping control mode by using engine intake manifold vacuum and a microprocessor based solenoid valve controller. A laboratory bench set-up has already demonstrated its operational feasibility. Through analytical methods, it is observed that our adaptive mount provides superior dynamic performance to passive engine mounts and comparable performance to a small scale active mount over a wide frequency range, given the engine mounting resonance control, shock absorption and vibration isolation performance requirements. Although technical prospects of the proposed adaptive system appear promising, the in situperformance needs to be evaluated.

6. Non-linear modelling and control of semi-active suspensions with variable damping

Chen, Huang; Long, Chen; Yuan, Chao-Chun; Jiang, Hao-Bin

2013-10-01

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f-v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief-desire-intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.

7. Non-Linear Electrohydrodynamics in Microfluidic Devices

PubMed Central

Zeng, Jun

2011-01-01

Since the inception of microfluidics, the electric force has been exploited as one of the leading mechanisms for driving and controlling the movement of the operating fluid and the charged suspensions. Electric force has an intrinsic advantage in miniaturized devices. Because the electrodes are placed over a small distance, from sub-millimeter to a few microns, a very high electric field is easy to obtain. The electric force can be highly localized as its strength rapidly decays away from the peak. This makes the electric force an ideal candidate for precise spatial control. The geometry and placement of the electrodes can be used to design electric fields of varying distributions, which can be readily realized by Micro-Electro-Mechanical Systems (MEMS) fabrication methods. In this paper, we examine several electrically driven liquid handling operations. The emphasis is given to non-linear electrohydrodynamic effects. We discuss the theoretical treatment and related numerical methods. Modeling and simulations are used to unveil the associated electrohydrodynamic phenomena. The modeling based investigation is interwoven with examples of microfluidic devices to illustrate the applications. PMID:21673912

8. In situ characterisation of non linear capacitors

Laudebat, L.; Bley, V.; Lebey, T.; Schneider, H.; Tounsi, P.

2001-05-01

Multilayers ceramic capacitors (MLCC) presenting non linear behaviours of their C(V) characteristics may have interesting applications in power electronics. Most of them have already been described. Nevertheless, the choice of a particular type instead of another one is all the more so difficult since, on one hand the physical mechanisms able to explain this behaviour is far from being understood. On the other hand, C(V) characteristics are in general obtained for low voltage values different from the ones they are going to be involved in. In this paper, direct in situ characterisations of different BaTiO3 based capacitors commercially available are achieved. The role of the capacitors' type (X7R,Z5U), of the temperature and of the voltage waveform (and more particularly its polarity) is demonstrated. Temperature values up to 200 oC are measured during normal operations in a RCD dissipative snubber without any alterations of the C(V) characteristics. All these results are discussed as regards the main physical properties of the constitutive materials in order to reach an optimisation of their use through an appropriate dimensioning.

9. The Linear-Non-Linear Frontier for the Goldstone Higgs

SciTech Connect

Gavela, M. B.; Kanshin, K.; Machado, P. A.N.; Saa, S.

2016-10-25

The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.

10. The linear-non-linear frontier for the Goldstone Higgs

Gavela, M. B.; Kanshin, K.; Machado, P. A. N.; Saa, S.

2016-12-01

The minimal SO(5) / SO(4) σ -model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.

11. Integration of Attributes from Non-Linear Characterization of Cardiovascular Time-Series for Prediction of Defibrillation Outcomes

PubMed Central

Shandilya, Sharad; Kurz, Michael C.; Ward, Kevin R.; Najarian, Kayvan

2016-01-01

Objective The timing of defibrillation is mostly at arbitrary intervals during cardio-pulmonary resuscitation (CPR), rather than during intervals when the out-of-hospital cardiac arrest (OOH-CA) patient is physiologically primed for successful countershock. Interruptions to CPR may negatively impact defibrillation success. Multiple defibrillations can be associated with decreased post-resuscitation myocardial function. We hypothesize that a more complete picture of the cardiovascular system can be gained through non-linear dynamics and integration of multiple physiologic measures from biomedical signals. Materials and Methods Retrospective analysis of 153 anonymized OOH-CA patients who received at least one defibrillation for ventricular fibrillation (VF) was undertaken. A machine learning model, termed Multiple Domain Integrative (MDI) model, was developed to predict defibrillation success. We explore the rationale for non-linear dynamics and statistically validate heuristics involved in feature extraction for model development. Performance of MDI is then compared to the amplitude spectrum area (AMSA) technique. Results 358 defibrillations were evaluated (218 unsuccessful and 140 successful). Non-linear properties (Lyapunov exponent > 0) of the ECG signals indicate a chaotic nature and validate the use of novel non-linear dynamic methods for feature extraction. Classification using MDI yielded ROC-AUC of 83.2% and accuracy of 78.8%, for the model built with ECG data only. Utilizing 10-fold cross-validation, at 80% specificity level, MDI (74% sensitivity) outperformed AMSA (53.6% sensitivity). At 90% specificity level, MDI had 68.4% sensitivity while AMSA had 43.3% sensitivity. Integrating available end-tidal carbon dioxide features into MDI, for the available 48 defibrillations, boosted ROC-AUC to 93.8% and accuracy to 83.3% at 80% sensitivity. Conclusion At clinically relevant sensitivity thresholds, the MDI provides improved performance as compared to AMSA

12. Non-linear analyses of heart rate variability during heavy exercise and recovery in cyclists.

PubMed

Casties, J-F; Mottet, D; Le Gallais, D

2006-10-01

We investigated the time course of RR interval variability during exercise and subsequent 50 minutes of recovery in seven well-trained male cyclists who performed an exercise with 3 successive 8 min stages at 40 %, 70 % and 90 % of their maximal oxygen uptake. The goal of the study was to check whether the decrease in the amplitude of heart rate variability during heavy exercise was accompanied by changes in the chaotic structure of the fluctuations. Heart rate variability was analysed in the temporal and frequency domain using traditional tools and using non-linear methods (Largest Lyapunov Exponent, Detrended Fluctuation Analysis, Minimum Embedding Dimension). When compared to rest, variability at the heaviest exercise intensity was significantly lower (RR: 0.94 +/- 0.22 vs. 0.34 +/- 0.01 ms; SDRR: 0.11 +/- 0.04 vs. 0.01 +/- 0.00 ms) due to a decrease in both LF (2101 +/- 1450 vs. 0.14 +/- 0.09 ms (2) . Hz (-1)) and HF spectral energy (1148 +/- 1126 vs. 7.88 +/- 9.24 ms (2) . Hz (-1)). Non-linear analyses showed that heart rate variability remained chaotic whatever the exercise intensity (the largest Lyapunov exponent was positive at 90 % of the maximal oxygen uptake), with a fractal organisation that tended towards white noise (DFA value close to 0.5) during heavy exercise. During recovery, temporal and spectral variables came back to their rest values within about 30 minutes following an exponential pattern. Non-linear analyses revealed that heartbeat dynamics were disorganised at the beginning of recovery, and involved more regulating systems than at rest, even after 50 minutes of recovery. We concluded that, during heavy exercise, heart rate variability was mainly influenced by other factors than autonomous nervous system, and suggest that mechanical or neurological couplings between the cardiac, locomotor and respiratory systems could play an important part in the observed changes.

13. Non-linear rotation-free shell finite-element models for aortic heart valves.

PubMed

Gilmanov, Anvar; Stolarski, Henryk; Sotiropoulos, Fotis

2017-01-04

Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann-Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves.

14. Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

PubMed

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

15. Renormalization and non-linear symmetries in quantum field theory

Velenich, Andrea

Most of the phenomena we experience, from the microscopic world to the universe at its largest scales, are out of equilibrium and their comprehensive formalization is one of the open problems in theoretical physics. Fluids of interacting particles cooled down or compressed quickly enough to become amorphous solids are an example of rich out-of-equilibrium systems with very slow relaxation dynamics. Even though the equilibrium phases are ordered, these systems remain trapped in glassy metastable states, with disordered microscopic structures. As a realistic model of this phenomenology, in the first part of this work I focused on a field theory of particles obeying a Brownian dynamics. The field-theoretic action displays a time-reversal symmetry leading to Fluctuation-Dissipation relations. For non-interacting particles I solved the field theory exactly, providing the explicit form of all the correlation functions, with their space and time dependence. As a non-perturbative result, the distribution of the density field has been proven to be Poissonian and not Gaussian. For interacting particles the field theory presents two major challenges: its apparent non-renormalizability and a non-linear implementation of the time-reversal symmetry. Non-linear field redefinitions can be used to make the symmetry linear and might even lead to the solution of the interacting equations of motion. However they also alter the renormalizability properties of a field theory. These challenges inspired the second part of the work, where a more abstract approach was taken. Using algebraic methods I investigated the effect of non-linear field redefinitions both on symmetry and on renormalization by focusing on simple scalar field theories as toy models. In the formal setting of the Hopf algebra of Feynman diagrams, symmetries take the form of Hopf ideals and enforce relations among scattering amplitudes; such relations can drastically reduce the number of independent couplings in a field

16. Attractor reconstruction for non-linear systems: a methodological note

USGS Publications Warehouse

Nichols, J.M.; Nichols, J.D.

2001-01-01

Attractor reconstruction is an important step in the process of making predictions for non-linear time-series and in the computation of certain invariant quantities used to characterize the dynamics of such series. The utility of computed predictions and invariant quantities is dependent on the accuracy of attractor reconstruction, which in turn is determined by the methods used in the reconstruction process. This paper suggests methods by which the delay and embedding dimension may be selected for a typical delay coordinate reconstruction. A comparison is drawn between the use of the autocorrelation function and mutual information in quantifying the delay. In addition, a false nearest neighbor (FNN) approach is used in minimizing the number of delay vectors needed. Results highlight the need for an accurate reconstruction in the computation of the Lyapunov spectrum and in prediction algorithms.

17. Non-linearities in Theory-of-Mind Development.

PubMed

Blijd-Hoogewys, Els M A; van Geert, Paul L C

2016-01-01

Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72-78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths.

18. Non-linearities in Theory-of-Mind Development

PubMed Central

Blijd-Hoogewys, Els M. A.; van Geert, Paul L. C.

2017-01-01

Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72–78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths. PMID:28101065

19. Non-Linear Dielectrics and Ferrites in ICEPIC

DTIC Science & Technology

2012-04-10

Technical Paper 3. DATES COVERED (From - To) 2010-2011 4. TITLE AND SUBTITLE Non-linear Dielectrics and Ferrites in ICEPIC 5a. CONTRACT...Electromagnetics Government Purpose Rights 14. ABSTRACT Models for non-linear dielectrics and magnetic ferrites are developed and coded into the particle...be longer than an FDTD time step. The ferrite model accounts for the non-linearity of the Landau-Lifshitz-Gibert equation, and the magnetization

20. Predictability of extremes in non-linear hierarchically organized systems

Kossobokov, V. G.; Soloviev, A.

2011-12-01

Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare

1. Construction of the wave operator for non-linear dispersive equations

Tsuruta, Kai Erik

In this thesis, we will study non-linear dispersive equations. The primary focus will be on the construction of the positive-time wave operator for such equations. The positive-time wave operator problem arises in the study of the asymptotics of a partial differential equation. It is a map from a space of initial data X into itself, and is loosely defined as follows: Suppose that for a solution ψlin to the dispersive equation with no non-linearity and initial data ψ +, there exists a unique solution ψ to the non-linear equation with initial data ψ0 such that ψ behaves as ψ lin as t → infinity. Then the wave operator is the map W+ that takes ψ + to ψ0. By its definition, W+ is injective. An important additional question is whether or not the map is also surjective. If so, then every non-linear solution emanating from X behaves, in some sense, linearly as it evolves (this is known as asymptotic completeness). Thus, there is some justification for treating these solutions as their much simpler linear counterparts. The main results presented in this thesis revolve around the construction of the wave operator(s) at critical non-linearities. We will study the "semi-relativistic" Schrodinger equation as well as the Klein-Gordon-Schrodinger system on R2 . In both cases, we will impose fairly general quadratic non-linearities for which conservation laws cannot be relied upon. These non-linearities fall below the scaling required to employ such tools as the Strichartz estimates. We instead adapt the "first iteration method" of Jang, Li, and Zhang to our setting which depends crucially on the critical decay of the non-linear interaction of the linear evolution. To see the critical decay in our problem, careful analysis is needed to treat the regime where one has spatial and/or time resonance.

2. Fault-tolerant control for a class of non-linear systems with dead-zone

Chen, Mou; Jiang, Bin; Guo, William W.

2016-05-01

In this paper, a fault-tolerant control scheme is proposed for a class of single-input and single-output non-linear systems with the unknown time-varying system fault and the dead-zone. The non-linear state observer is designed for the non-linear system using differential mean value theorem, and the non-linear fault estimator that estimates the unknown time-varying system fault is developed. On the basis of the designed fault estimator, the observer-based fault-tolerant tracking control is then developed using the backstepping technique for non-linear systems with the dead-zone. The stability of the whole closed-loop system is rigorously proved via Lyapunov analysis and the satisfactory tracking control performance is guaranteed in the presence of the unknown time-varying system fault and the dead-zone. Numerical simulation results are presented to illustrate the effectiveness of the proposed backstepping fault-tolerant control scheme for non-linear systems.

3. Non-linear electro-optical effects in the study of the helical smectic liquid crystals

Nowicka, K.; Kuczyński, W.

2016-04-01

Measurements of the non-linear electro-optical effects for the well-known prototype liquid crystal material (MHPOBC) are presented. The method to identify liquid crystalline phases and to determine temperatures of phase transitions based on the analysis of the second harmonic component of electro-optical response spectra is used. Applying that method, the values of the frequency (?) at which the second harmonic electro-optic response (EOR) possesses an extremum are determined for each smectic phase. We suggest that this characteristic frequency correspond to the phase-type mode processes. Furthermore, we show that the usually neglected results on heating can be useful in discussions of dynamical behaviour of second harmonic EOR in case of smectic phases.

4. Analysis of second order harmonic distortion due to transmitter non-linearity and chromatic and modal dispersion of optical OFDM SSB modulated signals in SMF-MMF fiber links

Patel, Dhananjay; Singh, Vinay Kumar; Dalal, U. D.

2017-01-01

Single mode fibers (SMF) are typically used in Wide Area Networks (WAN), Metropolitan Area Networks (MAN) and also find applications in Radio over Fiber (RoF) architectures supporting data transmission in Fiber to the Home (FTTH), Remote Antenna Units (RAUs), in-building networks etc. Multi-mode fibers (MMFs) with low cost, ease of installation and low maintenance are predominantly (85-90%) deployed in-building networks providing data access in local area networks (LANs). The transmission of millimeter wave signals through the SMF in WAN and MAN, along with the reuse of MMF in-building networks will not levy fiber reinstallation cost. The transmission of the millimeter waves experiences signal impairments due to the transmitter non-linearity and modal dispersion of the MMF. The MMF exhibiting large modal dispersion limits the bandwidth-length product of the fiber. The second and higher-order harmonics present in the optical signal fall within the system bandwidth. This causes degradation in the received signal and an unwanted radiation of power at the RAU. The power of these harmonics is proportional to the non-linearity of the transmitter and the modal dispersion of the MMF and should be maintained below the standard values as per the international norms. In this paper, a mathematical model is developed for Second-order Harmonic Distortion (HD2) generated due to non-linearity of the transmitter and chromatic-modal dispersion of the SMF-MMF optic link. This is also verified using a software simulation. The model consists of a Mach Zehnder Modulator (MZM) that generates two m-QAM OFDM Single Sideband (SSB) signals based on phase shift of the hybrid coupler (90° and 120°). Our results show that the SSB signal with 120° hybrid coupler has suppresses the higher-order harmonics and makes the system more robust against the HD2 in the SMF-MMF optic link.

5. The mathematics of non-linear metrics for nested networks

Wu, Rui-Jie; Shi, Gui-Yuan; Zhang, Yi-Cheng; Mariani, Manuel Sebastian

2016-10-01

Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness-complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness-complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.

6. Model of intermodulation distortion in non-linear multicarrier systems

Frigo, Nicholas J.

1994-02-01

A heuristic model is proposed which allows calculation of the individual spectral components of the intermodulation distortion present in a non-linear system with a multicarrier input. Noting that any given intermodulation product (IMP) can only be created by a subset of the input carriers, we partition them into 'signal' carriers (which create the IMP) and 'noise' carriers, modeled as a Gaussian process. The relationship between an input signal and the statistical average of its output (averaged over the Gaussian noise) is considered to be an effective transfer function. By summing all possible combinations of signal carriers which create power at the IMP frequencies, the distortion power can be calculated exactly as a function of frequency. An analysis of clipping in lightwave CATV links for AM-VSB signals is used to introduce the model, and is compared to a series of experiments.

7. Thermal Analysis of Non-linear Convective-Radiative Hyperbolic Lumped Systems with Simultaneous Variation of Temperature-Dependent Specific Heat and Surface Emissivity by MsDTM and BPES

Torabi, Mohsen; Yaghoobi, Hessameddin; Boubaker, Karem

2013-01-01

With the advent of temperatures near absolute zero, it is often claimed that at very low temperatures the effect of thermal wave propagation must be included by the hyperbolic heat conduction equation (HHCE). In this paper the non-linear convective-radiative HHCE is investigated. Opposite to common numerical analyses, analytical expressions are obtained for the temperature variations by the multi-step differential transformation method. Some conclusions about alteration of the specific heat of the material, temperature steeping, and Vernotte number have been formulated.

8. Discriminant power analyses of non-linear dimension expansion methods

Woo, Seongyoun; Lee, Chulhee

2016-05-01

Most non-linear classification methods can be viewed as non-linear dimension expansion methods followed by a linear classifier. For example, the support vector machine (SVM) expands the dimensions of the original data using various kernels and classifies the data in the expanded data space using a linear SVM. In case of extreme learning machines or neural networks, the dimensions are expanded by hidden neurons and the final layer represents the linear classification. In this paper, we analyze the discriminant powers of various non-linear classifiers. Some analyses of the discriminating powers of non-linear dimension expansion methods are presented along with a suggestion of how to improve separability in non-linear classifiers.

9. NonLinear Effects in Photorefractive Crystals

DTIC Science & Technology

1988-01-01

bloweth harde Christall cometh of the water As with Aristotalean dynamics, though, there were a few dissenting voices through the centuries. Agricola (Georg...longer. Our study is the first experimental look at transient power transfer among higher diffracted orders. 6.1.2 Videotape studies The business of

10. Computer modeling of batteries from non-linear circuit elements

NASA Technical Reports Server (NTRS)

Waaben, S.; Federico, J.; Moskowitz, I.

1983-01-01

A simple non-linear circuit model for battery behavior is given. It is based on time-dependent features of the well-known PIN change storage diode, whose behavior is described by equations similar to those associated with electrochemical cells. The circuit simulation computer program ADVICE was used to predict non-linear response from a topological description of the battery analog built from advice components. By a reasonable choice of one set of parameters, the circuit accurately simulates a wide spectrum of measured non-linear battery responses to within a few millivolts.

11. Design of an Internal Model Control strategy for single-phase grid-connected PWM inverters and its performance analysis with a non-linear local load and weak grid.

PubMed

Chaves, Eric N; Coelho, Ernane A A; Carvalho, Henrique T M; Freitas, Luiz C G; Júnior, João B V; Freitas, Luiz C

2016-09-01

This paper presents the design of a controller based on Internal Model Control (IMC) applied to a grid-connected single-phase PWM inverter. The mathematical modeling of the inverter and the LCL output filter, used to project the 1-DOF IMC controller, is presented and the decoupling of grid voltage by a Feedforward strategy is analyzed. A Proportional - Resonant Controller (P+Res) was used for the control of the same plant in the running of experimental results, thus moving towards the discussion of differences regarding IMC and P+Res performances, which arrived at the evaluation of the proposed control strategy. The results are presented for typical conditions, for weak-grid and for non-linear local load, in order to verify the behavior of the controller against such situations.

12. Dilatonic non-linear sigma models and Ricci flow extensions

Carfora, M.; Marzuoli, A.

2016-09-01

We review our recent work describing, in terms of the Wasserstein geometry over the space of probability measures, the embedding of the Ricci flow in the renormalization group flow for dilatonic non-linear sigma models.

13. Non-linear evolution of the cosmic neutrino background

SciTech Connect

Villaescusa-Navarro, Francisco; Viel, Matteo; Peña-Garay, Carlos E-mail: spb@ias.edu E-mail: viel@oats.inaf.it

2013-03-01

We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations which incorporate cold dark matter (CDM) and neutrinos as independent particle species. Our set of simulations explore the properties of neutrinos in a reference ΛCDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass 10{sup 11}−10{sup 15} h{sup −1}M{sub s}un, over a redshift range z = 0−2. We compute the halo mass function and show that it is reasonably well fitted by the Sheth-Tormen formula, once the neutrino contribution to the total matter is removed. More importantly, we focus on the CDM and neutrino properties of the density and peculiar velocity fields in the cosmological volume, inside and in the outskirts of virialized haloes. The dynamical state of the neutrino particles depends strongly on their momentum: whereas neutrinos in the low velocity tail behave similarly to CDM particles, neutrinos in the high velocity tail are not affected by the clustering of the underlying CDM component. We find that the neutrino (linear) unperturbed momentum distribution is modified and mass and redshift dependent deviations from the expected Fermi-Dirac distribution are in place both in the cosmological volume and inside haloes. The neutrino density profiles around virialized haloes have been carefully investigated and a simple fitting formula is provided. The neutrino profile, unlike the cold dark matter one, is found to be cored with core size and central density that depend on the neutrino mass, redshift and mass of the halo, for halos of masses larger than ∼ 10{sup 13.5}h{sup −1}M{sub s}un. For lower masses the neutrino profile is best fitted by a simple power-law relation in the range probed by the simulations. The results we obtain are numerically converged in terms of neutrino profiles at the 10% level for scales above ∼ 200 h{sup −1}kpc at z = 0, and are stable with

14. Searching for Non-linearities in Natural Language

Ribarov, Kiril; Smrz, Otakar

2003-08-01

Inspired by wide range of applicability of what is commonly referred to as chaos theories, we explore the nature of energy series of a signal of human speech in the light of nonlinear dynamics. Using the TISEAN software package, analyses on various recordings of the language energy series were carried out (single speaker — different speeches; single speech - different speakers; dialogues; talkshows). Also correlated to other tenths of experiments conveyed on different linguistic inputs as written and morphologically analyzed texts, the presented experiment outputs (up to our knowledge, similar experiments have not been performed yet) reveal the complex and tricky nature of the language and are in favor of certain linguistic hypotheses. However, without further research, they do not encourage us to make explicit claims about the language signal such as dimension estimations (although probably possible) or attractor reconstruction. Our main considerations include: (a) a look into the stochastic nature of the language aiming towards reduction of the currently very large number of parameters present in language models based on Hidden Markov Models on language n-grams; (b) visualization of the behavior of the language and revelation of what could possibly be behind the noisy' stream of sounds/letters/word-classes observed in our experiments; and last but not least (c) presentation of a new type of signal to the community exploring natural non-linear phenomena.

15. Organic non-linear optics and opto-electronics

Maldonado, J. L.; Ramos-Ortíz, G.; Rodríguez, M.; Meneses-Nava, M. A.; Barbosa-García, O.; Santillán, R.; Farfán, N.

2010-12-01

π-conjugated organic molecules and polymers are of great importance in physics, chemistry, material science and engineering. It is expected that, in the near future, organic materials will find widespread use in many technological applications. In the case of organic opto-electronic systems, the list of devices includes light emitting diodes (OLEDs), photovoltaic cells (OPVs), field-effect transistors (OFET), photorefractive materials for light manipulation, among others. These materials are also used for photonic applications: all-optical switching, modulators, optical correlators, plastic waveguides, all polymeric integrated circuits, solid-state lasers, and for biophotonic applications as in the case of the development of organic labels for multiphoton microscopy and photodynamic therapy. The advances in the developing of organic compounds with better mechanical, electrical, and optical (linear and non-linear) characteristics are of a great importance for this field. Here, we present the research on this area carried out at the Centro de Investigaciones en Óp-tica (CIO), in collaboration with Chemistry Departments of different institutions. This work focuses on the optical characterization of materials through several techniques such as TOF, FWM, TBC, THG Maker Fringes, HRS, Z-scan, and TPEF. Additionally, some applications, such as dynamic holography by using photorefractive polymers, and OPVs cells will be discussed.

16. Valuation of financial models with non-linear state spaces

Webber, Nick

2001-02-01

A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.

17. A Quantitative and Combinatorial Approach to Non-Linear Meanings of Multiplication

ERIC Educational Resources Information Center

Tillema, Erik; Gatza, Andrew

2016-01-01

We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…

18. Bifurcation and Resonance of a Mathematical Model for Non-Linear Motion of a Flooded Ship in Waves

Murashige, S.; Aihara, K.; Komuro, M.

1999-02-01

A flooded ship can exhibit undesirable non-linear roll motion even in waves of moderate amplitude. In order to understand the mechanism of this non-linear phenomenon, the non-linearly coupled dynamics of a ship and flood water are considered using a mathematical model for the simplified motion of a flooded ship in regular beam waves. This paper describes bifurcation and resonance of this coupled system. A bifurcation diagram shows that large-amplitude subharmonic motion exists in a wide range of parameters, and that the Hopf bifurcation is observed due to the dynamic effects of flood water. Resonance frequencies can be determined by linearization of this model. Comparison between the resonant points and the bifurcation curves suggests that non-linear resonance of this model can bring about large-amplitude subharmonic motion, even if it is in the non-resonate state of the linearized system.

19. THE RESPONSE OF DRUG EXPENDITURE TO NON-LINEAR CONTRACT DESIGN: EVIDENCE FROM MEDICARE PART D.

PubMed

Einav, Liran; Finkelstein, Amy; Schrimpf, Paul

2015-05-01

We study the demand response to non-linear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individuals' budget set created by the famous "donut hole," where insurance becomes discontinuously much less generous on the margin, to provide descriptive evidence of the drug purchase response to a price increase. We then specify and estimate a simple dynamic model of drug use that allows us to quantify the spending response along the entire non-linear budget set. We use the model for counterfactual analysis of the increase in spending from "filling" the donut hole, as will be required by 2020 under the Affordable Care Act. In our baseline model, which considers spending decisions within a single year, we estimate that "filling" the donut hole will increase annual drug spending by about $150, or about 8 percent. About one-quarter of this spending increase reflects "anticipatory" behavior, coming from beneficiaries whose spending prior to the policy change would leave them short of reaching the donut hole. We also present descriptive evidence of cross-year substitution of spending by individuals who reach the kink, which motivates a simple extension to our baseline model that allows - in a highly stylized way - for individuals to engage in such cross year substitution. Our estimates from this extension suggest that a large share of the$150 drug spending increase could be attributed to cross-year substitution, and the net increase could be as little as $45 per year. 20. THE RESPONSE OF DRUG EXPENDITURE TO NON-LINEAR CONTRACT DESIGN: EVIDENCE FROM MEDICARE PART D* PubMed Central Einav, Liran; Finkelstein, Amy; Schrimpf, Paul 2016-01-01 We study the demand response to non-linear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individuals’ budget set created by the famous “donut hole,” where insurance becomes discontinuously much less generous on the margin, to provide descriptive evidence of the drug purchase response to a price increase. We then specify and estimate a simple dynamic model of drug use that allows us to quantify the spending response along the entire non-linear budget set. We use the model for counterfactual analysis of the increase in spending from “filling” the donut hole, as will be required by 2020 under the Affordable Care Act. In our baseline model, which considers spending decisions within a single year, we estimate that “filling” the donut hole will increase annual drug spending by about$150, or about 8 percent. About one-quarter of this spending increase reflects “anticipatory” behavior, coming from beneficiaries whose spending prior to the policy change would leave them short of reaching the donut hole. We also present descriptive evidence of cross-year substitution of spending by individuals who reach the kink, which motivates a simple extension to our baseline model that allows – in a highly stylized way – for individuals to engage in such cross year substitution. Our estimates from this extension suggest that a large share of the $150 drug spending increase could be attributed to cross-year substitution, and the net increase could be as little as$45 per year. PMID:26769984

1. Non-Linear Transmission Line (NLTL) Microwave Source Lecture Notes the United States Particle Accelerator School

SciTech Connect

Russell, Steven J.; Carlsten, Bruce E.

2012-06-26

We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.

2. Visual discrimination and adaptation using non-linear unsupervised learning

Jiménez, Sandra; Laparra, Valero; Malo, Jesus

2013-03-01

Understanding human vision not only involves empirical descriptions of how it works, but also organization principles that explain why it does so. Identifying the guiding principles of visual phenomena requires learning algorithms to optimize specific goals. Moreover, these algorithms have to be flexible enough to account for the non-linear and adaptive behavior of the system. For instance, linear redundancy reduction transforms certainly explain a wide range of visual phenomena. However, the generality of this organization principle is still in question:10 it is not only that and additional constraints such as energy cost may be relevant as well, but also, statistical independence may not be the better solution to make optimal inferences in squared error terms. Moreover, linear methods cannot account for the non-uniform discrimination in different regions of the image and color space: linear learning methods necessarily disregard the non-linear nature of the system. Therefore, in order to account for the non-linear behavior, principled approaches commonly apply the trick of using (already non-linear) parametric expressions taken from empirical models. Therefore these approaches are not actually explaining the non-linear behavior, but just fitting it to image statistics. In summary, a proper explanation of the behavior of the system requires flexible unsupervised learning algorithms that (1) are tunable to different, perceptually meaningful, goals; and (2) make no assumption on the non-linearity. Over the last years we have worked on these kind of learning algorithms based on non-linear ICA,18 Gaussianization, 19 and principal curves. In this work we stress the fact that these methods can be tuned to optimize different design strategies, namely statistical independence, error minimization under quantization, and error minimization under truncation. Then, we show (1) how to apply these techniques to explain a number of visual phenomena, and (2) suggest the

3. Static compressive strength prediction of open-hole structure based on non-linear shear behavior and micro-mechanics

Li, Wangnan; Cai, Hongneng; Li, Chao

2014-11-01

This paper deals with the characterization of the strength of the constituents of carbon fiber reinforced plastic laminate (CFRP), and a prediction of the static compressive strength of open-hole structure of polymer composites. The approach combined with non-linear analysis in macro-level and a linear elastic micromechanical failure analysis in microlevel (non-linear MMF) is proposed to improve the prediction accuracy. A face-centered cubic micromechanics model is constructed to analyze the stresses in fiber and matrix in microlevel. Non-interactive failure criteria are proposed to characterize the strength of fiber and matrix. The non-linear shear behavior of the laminate is studied experimentally, and a novel approach of cubic spline interpolation is used to capture significant non-linear shear behavior of laminate. The user-defined material subroutine UMAT for the non-linear share behavior is developed and combined in the mechanics analysis in the macro-level using the Abaqus Python codes. The failure mechanism and static strength of open-hole compressive (OHC) structure of polymer composites is studied based on non-linear MMF. The UTS50/E51 CFRP is used to demonstrate the application of theory of non-linear MMF.

4. Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

5. Non-linear optical measurements using a scanned, Bessel beam

Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.

2015-03-01

Oftentimes cells are removed from the body for disease diagnosis or cellular research. This typically requires fluorescent labeling followed by sorting with a flow cytometer; however, possible disruption of cellular function or even cell death due to the presence of the label can occur. This may be acceptable for ex vivo applications, but as cells are more frequently moving from the lab to the body, label-free methods of cell sorting are needed to eliminate these issues. This is especially true of the growing field of stem cell research where specialized cells are needed for treatments. Because differentiation processes are not completely efficient, cells must be sorted to eliminate any unwanted cells (i.e. un-differentiated or differentiated into an unwanted cell type). In order to perform label-free measurements, non-linear optics (NLO) have been increasingly utilized for single cell analysis because of their ability to not disrupt cellular function. An optical system was developed for the measurement of NLO in a microfluidic channel similar to a flow cytometer. In order to improve the excitation efficiency of NLO, a scanned Bessel beam was utilized to create a light-sheet across the channel. The system was tested by monitoring twophoton fluorescence from polystyrene microbeads of different sizes. Fluorescence intensity obtained from light-sheet measurements were significantly greater than measurements made using a static Gaussian beam. In addition, the increase in intensity from larger sized beads was more evident for the light-sheet system.

6. Primordial Black Holes in non-linear perturbation theory

Hidalgo, Juan Carlos

2009-10-01

This thesis begins with a study of the origin of cosmological fluctuations with special attention to those cases in which the non-Gaussian correlation functions are large. The analysis shows that perturbations from an almost massless auxiliary field generically produce large values of the non-linear parameter f_NL. The effects of including non-Gaussian correlation functions in the statistics of cosmological structure are explored by constructing a non-Gaussian probability distribution function (PDF). Such PDF is derived for the comoving curvature perturbation from first principles in the context of quantum field theory, with n-point correlation functions as the only input. The non-Gaussian PDF is then used to explore two important problems in the physics of primordial black holes (PBHs): First, to compute non-Gaussian corrections to the number of PBHs generated from the primordial curvature fluctuations. The second application concerns new cosmological observables. The formation of PBHs is known to depend on two main physical characteristics: the strength of the gravitational field produced by the initial curvature inhomogeneity and the pressure gradient at the edge of the curvature configuration. We account for the probability of finding these configurations by using two parameters: The amplitude of the inhomogeneity and its second radial derivative, evaluated at the centre of the configuration. The implications of the derived probability for the fraction of mass in the universe in the form of PBHs are discussed.

7. Non-linear material characterisation using the noncollinear method

Croxford, Anthony J.; Wilcox, Paul D.; Drinkwater, Bruce W.

2010-04-01

Conventional ultrasonic NDT techniques are limited in their ability to detect small defects by the diffraction limit, that is there is much reduced sensitivity to defects smaller than the wavelength of the interrogating ultrasonic wave. While not a major issue for most inspection, this problem becomes particularly significant for the detection of fatigue damage prior to crack formation. In this regime conventional NDT has proven to be inadequate. For this reason significant effort has been expended on the development of non-linear techniques. These techniques rely on deviations of the material from linear stress strain behaviour which create harmonics in the resulting frequency response. Evidence suggests that changes to a materials condition, such as fatigue damage, change this non-linear response. This paper presents a non-linear inspection method using a non-collinear interaction. This technique has several advantages over other harmonic approaches in that there is spatial separation, modal separation and frequency separation of the non-linear signal. This allows the origin of the non-linear signal and underlying noise levels to be well defined. The capability of the technique is demonstrated using plastically strained material and samples subjected to low cycle fatigue.

8. Isolating Non-Linear Signatures of Two Colliding Black Holes

Garrido, Rita

2012-03-01

The early and late stages of the binary-black-hole collision can be approximated by perturbations to a background, solutions to linearization of the Einstein's equations. However, once the two black holes are within several radii of each other, and ultimately collide, the solution is intrinsically non-linear. The main objective is to intuitively understand the non-linear portion of the solution to the Einstein equation by performing simulations of such mergers. I will identify the non-linear regime through a process of elimination. The early stages of the coalescence are well known by post-Newtonian theory. The end state is approximated very well by perturbation theory, the waveforms decay as a damped sinusoidal with a frequency and decay time uniquely determined by the mass and spin of the final black hole in theory. I will isolate the non-linear portion of the waveform by fitting the early stages to the post-Newtonian solution and the late stages to the perturbative solution. What remains is the non-linear region. Once isolated, we will search through the physics parameter space of the binary black holes for bulk features. These features can then be used to fine-tune the search algorithms hunting for these collisions with LIGO.

9. Trade-off analysis in the Northern Andes to study the dynamics in agricultural land use.

PubMed

Stoorvogel, J J; Antle, J M; Crissman, C C

2004-08-01

In this paper we hypothesize that land use change can be induced by non-linearities and thresholds in production systems that impact farmers' decision making. Tradeoffs between environmental and economic indicators is a useful way to represent dynamic properties of agricultural systems. The Tradeoff Analysis (TOA) System is software designed to implement the integrated analysis of tradeoffs in agricultural systems. The TOA methodology is based on spatially explicit econometric simulation models linked to spatially referenced bio-physical simulation models to simulate land use and input decisions. The methodology has been applied for the potato-pasture production system in the Ecuadorian Andes. The land use change literature often describes non-linearity in land use change as a result of sudden changes in the political (e.g. new agricultural policies) or environmental setting (e.g. earthquakes). However, less attention has been paid to the non-linearities in production systems and their consequences for land use change. In this paper, we use the TOA system to study agricultural land use dynamics and to find the underlying processes for non-linearities. Results show that the sources of non-linearities are in the properties of bio-physical processes and in the decision making-process of farmers.

10. An on-site modal testing method for the detection of structural non-linearities Part II: Application

Lee, Gun-Myung; Trethewey, Martin W.

1992-03-01

The work presented in this paper discusses the practical implementation of an experimental testing/analysis method to detect non-linear structural behaviour in an effective on-site fashion. The testing/evaluation method is based on the linear analysis of non-linear systems with increasing amplitude random excitation signals and is presented in Part I of this work. In the second part of this work, the method is applied to two distinctly different types of structures; (1) a simple beam structure and; (2) an industrial robot. The analysis shows that the beam structure behaves in a linear fashion throughout the operating range. The robot structure exhibited non-linear characteristics over the frequency range of interest. The analysis of the robot data provided a means to classify the types of non-linearities present in the structure. These actual testing applications indicate the feasibility and capability of the proposed method.

11. A general non-linear multilevel structural equation mixture model

PubMed Central

Kelava, Augustin; Brandt, Holger

2014-01-01

In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh et al., 2004). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012; Kelava et al., 2014) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework. PMID:25101022

12. Non-linear system identification in flow-induced vibration

SciTech Connect

Spanos, P.D.; Zeldin, B.A.; Lu, R.

1996-12-31

The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.

13. Non-Linear Vibration Characteristics of Clamped Laminated Shallow Shells

ABE, A.; KOBAYASHI, Y.; YAMADA, G.

2000-07-01

This paper examines non-linear free vibration characteristics of first and second vibration modes of laminated shallow shells with rigidly clamped edges. Non-linear equations of motion for the shells based on the first order shear deformation and classical shell theories are derived by means of Hamilton's principle. We apply Galerkin's procedure to the equations of motion in which eigenvectors for first and second modes of linear vibration obtained by the Ritz method are employed as trial functions. Then simultaneous non-linear ordinary differential equations are derived in terms of amplitudes of the first and second vibration modes. Backbone curves for the first and second vibration modes are solved numerically by the Gauss-Legendre integration method and the shooting method respectively. The effects of lamination sequences and transverse shear deformation on the behavior are discussed. It is also shown that the motion of the first vibration mode affects the response for the second vibration mode.

14. Ghost Dark Energy with Non-Linear Interaction Term

Ebrahimi, E.

2016-06-01

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w D = p/ ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω D ). We find that in one case, w D cross the phantom line ( w D < -1). However in two other classes w D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w D , q. We study squared sound speed {vs2}, and find that for one case of non-linear interaction term {vs2} can achieves positive values at late time of evolution.

15. Pattern formation due to non-linear vortex diffusion

Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.

Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.

16. Non-linear effects in bunch compressor of TARLA

Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin

2016-03-01

Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.

17. Realization of non-linear coherent states by photonic lattices

SciTech Connect

Dehdashti, Shahram Li, Rujiang; Chen, Hongsheng; Liu, Jiarui Yu, Faxin

2015-06-15

In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.

18. Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

NASA Technical Reports Server (NTRS)

Taleghani, Barmac K.; Campbell, Joel F.

1999-01-01

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

19. Photocrosslinkable copolymers for non-linear optical applications

SciTech Connect

Kawatsuki, N.; Pakbaz, K.; Schmidt, H.W.

1993-12-31

New photocrosslinkable copolymers have been synthesized and applied as non-linear optical materials. The copolymers are based on methyl methacrylate, a photo-excitable benzophenone monomer, a non-linear optical active 4-[(2-hydroxyethyl)ethylamino]-4-nitro-azobenzene (disperse red 1) side chain monomer and a crosslinkable 2-butenyl monomer. These copolymers can be crosslinked by UV light at 366 nm in the poled state and show a stable alignment of NLO chromophore by monitoring the adsorption spectra. The crosslinked and poled film did not change its alignment after storing 4 weeks at room temperature.

20. BEAM-BASED NON-LINEAR OPTICS CORRECTIONS IN COLLIDERS.

SciTech Connect

PILAT, R.; LUO, Y.; MALITSKY, N.; PTITSYN, V.

2005-05-16

A method has been developed to measure and correct operationally the non-linear effects of the final focusing magnets in colliders, that gives access to the effects of multi-pole errors by applying closed orbit bumps, and analyzing the resulting tune and orbit shifts. This technique has been tested and used during 4 years of RHIC (the Relativistic Heavy Ion Collider at BNL) operations. I will discuss here the theoretical basis of the method, the experimental set-up, the correction results, the present understanding of the machine model, the potential and limitations of the method itself as compared with other non-linear correction techniques.

1. Step-response of a torsional device with multiple discontinuous non-linearities: Formulation of a vibratory experiment

Krak, Michael D.; Dreyer, Jason T.; Singh, Rajendra

2016-03-01

A vehicle clutch damper is intentionally designed to contain multiple discontinuous non-linearities, such as multi-staged springs, clearances, pre-loads, and multi-staged friction elements. The main purpose of this practical torsional device is to transmit a wide range of torque while isolating torsional vibration between an engine and transmission. Improved understanding of the dynamic behavior of the device could be facilitated by laboratory measurement, and thus a refined vibratory experiment is proposed. The experiment is conceptually described as a single degree of freedom non-linear torsional system that is excited by an external step torque. The single torsional inertia (consisting of a shaft and torsion arm) is coupled to ground through parallel production clutch dampers, which are characterized by quasi-static measurements provided by the manufacturer. Other experimental objectives address physical dimensions, system actuation, flexural modes, instrumentation, and signal processing issues. Typical measurements show that the step response of the device is characterized by three distinct non-linear regimes (double-sided impact, single-sided impact, and no-impact). Each regime is directly related to the non-linear features of the device and can be described by peak angular acceleration values. Predictions of a simplified single degree of freedom non-linear model verify that the experiment performs well and as designed. Accordingly, the benchmark measurements could be utilized to validate non-linear models and simulation codes, as well as characterize dynamic parameters of the device including its dissipative properties.

2. Non-linear dynamics of a spur gear pair

NASA Technical Reports Server (NTRS)

Kahraman, A.; Singh, R.

1990-01-01

The backlash nonlinearity excited primarily by transmission error between spur gear pairs is studied for both external and internal excitations. The digital simulation technique and the method of harmonic balance are used to develop steady state solutions for the internal sinuosidal excitations. The analytic predictions agreed well with available experimental data. Digital simulation is used to observe that at the chaotic and subharmonic resonances may exist in a gear pair depending on the mean or design load, mean to alternating force ratio, damping, and backlash.

3. Stress Induced in Periodontal Ligament under Orthodontic Loading (Part II): A Comparison of Linear Versus Non-Linear Fem Study

PubMed Central

Hemanth, M; Deoli, Shilpi; Raghuveer, H P; Rani, M S; Hegde, Chatura; Vedavathi, B

2015-01-01

Background: Simulation of periodontal ligament (PDL) using non-linear finite element method (FEM) analysis gives better insight into understanding of the biology of tooth movement. The stresses in the PDL were evaluated for intrusion and lingual root torque using non-linear properties. Materials and Methods: A three-dimensional (3D) FEM model of the maxillary incisors was generated using Solidworks modeling software. Stresses in the PDL were evaluated for intrusive and lingual root torque movements by 3D FEM using ANSYS software. These stresses were compared with linear and non-linear analyses. Results: For intrusive and lingual root torque movements, distribution of stress over the PDL was within the range of optimal stress value as proposed by Lee, but was exceeding the force system given by Proffit as optimum forces for orthodontic tooth movement with linear properties. When same force load was applied in non-linear analysis, stresses were more compared to linear analysis and were beyond the optimal stress range as proposed by Lee for both intrusive and lingual root torque. To get the same stress as linear analysis, iterations were done using non-linear properties and the force level was reduced. Conclusion: This shows that the force level required for non-linear analysis is lesser than that of linear analysis. PMID:26435629

4. Model Order and Identifiability of Non-Linear Biological Systems in Stable Oscillation.

PubMed

Wigren, Torbjörn

2015-01-01

The paper presents a theoretical result that clarifies when it is at all possible to determine the nonlinear dynamic equations of a biological system in stable oscillation, from measured data. As it turns out the minimal order needed for this is dependent on the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a simulated fourth order Hodgkin-Huxley spiking neuron model, which is identified using a non-linear second order differential equation model. The simulated result illustrates that the underlying higher order model of the spiking neuron cannot be uniquely determined given only the periodic measured data. The result of the paper is of general validity when the dynamics of biological systems in stable oscillation is identified, and illustrates the need to carefully address non-linear identifiability aspects when validating models based on periodic data.

5. Theoretically informed entangled polymer simulations: linear and non-linear rheology of melts.

SciTech Connect

Ramirez-Hernandez, Abelardo; Miller, Marcus; De Pablo, Juan J.

2013-01-02

In recent years, there has been a resurgence in developing models and theories for the non-equilibrium behavior of polymeric liquids. The so-called “tube” models, gradually refined over decades of research, can now provide a description of the linear and non-linear rheology of entangled polymers that is qualitatively consistent with experiments. Such approaches, however, have been limited to homopolymers. Here we present a general formalism that relies on the concept of slip links to describe the dynamics of high polymers. In this work, it is shown to be capable of describing quantitatively the linear response of pure homopolymers and blends, the non-linear rheology of highly entangled systems, and the dynamics of diblock copolymers.

6. Transient Vibration Prediction for Rotors on Ball Bearings Using Load-dependent Non-linear Bearing Stiffness

NASA Technical Reports Server (NTRS)

Fleming, David P.; Poplawski, J. V.

2002-01-01

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

7. Non-linear Langmuir waves in a warm quantum plasma

SciTech Connect

Dubinov, Alexander E. Kitaev, Ilya N.

2014-10-15

A non-linear differential equation describing the Langmuir waves in a warm quantum electron-ion plasma has been derived. Its numerical solutions of the equation show that ordinary electronic oscillations, similar to the classical oscillations, occur along with small-scale quantum Langmuir oscillations induced by the Bohm quantum force.

8. Tunneling control using classical non-linear oscillator

SciTech Connect

Kar, Susmita; Bhattacharyya, S. P.

2014-04-24

A quantum particle is placed in symmetric double well potential which is coupled to a classical non-linear oscillator via a coupling function. With different spatial symmetry of the coupling and under various controlling fashions, the tunneling of the quantum particle can be enhanced or suppressed, or totally destroyed.

9. Evolution equation for non-linear cosmological perturbations

SciTech Connect

Brustein, Ram; Riotto, Antonio E-mail: Antonio.Riotto@cern.ch

2011-11-01

We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations, with some possibly important differences. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.

10. The non-linear initiation of diapirs and plume heads

Bercovici, David; Kelly, Amanda

1997-04-01

A simple theory is devised to describe the non-linear feedback mechanisms involved in the initial growth of a single diapir or plume head from a low viscosity channel overlain by a much more viscous layer. Such feedbacks arise primarily from the relation between the growth of a proto-diapir (i.e. an undulation on the upper boundary of the low viscosity channel) and the draining of the low viscosity channel. In the period of time between its initial exponential growth (characterized by linear stability analysis) and its separation from the low viscosity channel as a fully formed diapir, the proto-diapir can undergo a significant cessation in its development due to deflation of the low viscosity channel; i.e. the proto-diapir's growth can essentially stall for a long period of time before it separates and begins its ascent through the overlying medium. The theory is used to determine a criterion for separation of the diapir from the low viscosity channel that is in terms of the geometrical and mechanical properties of the channel, instead of the ad hoc volume flux widely used in many models of mantle plumes and plume heads (e.g. Whitehead and Luther, 1975; Richards et al., 1989; Olson, 1990; Sleep, 1990; Bercovici and Mahoney, 1994). From this separation criterion, self-consistent scaling laws can be formulated to relate the size of the fully developed diapir and its trailing conduit to the properties of the initial channel, instead of to the ad hoc volume flux. Basic laboratory experiments involving highly viscous fluids are presented and demonstrate that the so-called 'stalling' period between initial growth and separation does indeed occur. These results suggest that nascent mantle plume heads may stall for extended periods at the base of the mantle and thereby contribute to variations in thickness of the D″ layer.

11. Non-Linear Stability of an Electrified Plane Interface in Porous Media

El-Dib, Yusry O.; Moatimid, Galal M.

2004-03-01

The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.

12. Non-linear homogenized and heterogeneous FE models for FRCM reinforced masonry walls in diagonal compression

Bertolesi, Elisa; Milani, Gabriele; Poggi, Carlo

2016-12-01

Two FE modeling techniques are presented and critically discussed for the non-linear analysis of tuff masonry panels reinforced with FRCM and subjected to standard diagonal compression tests. The specimens, tested at the University of Naples (Italy), are unreinforced and FRCM retrofitted walls. The extensive characterization of the constituent materials allowed adopting here very sophisticated numerical modeling techniques. In particular, here the results obtained by means of a micro-modeling strategy and homogenization approach are compared. The first modeling technique is a tridimensional heterogeneous micro-modeling where constituent materials (bricks, joints, reinforcing mortar and reinforcing grid) are modeled separately. The second approach is based on a two-step homogenization procedure, previously developed by the authors, where the elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. The non-linear structural analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). All the simulations here presented are performed using the commercial software Abaqus. Pros and cons of the two approaches are herein discussed with reference to their reliability in reproducing global force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.

13. Iterated non-linear model predictive control based on tubes and contractive constraints.

PubMed

Murillo, M; Sánchez, G; Giovanini, L

2016-05-01

This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle.

14. The quadratically damped oscillator: A case study of a non-linear equation of motion

Smith, B. R.

2012-09-01

The equation of motion for a quadratically damped oscillator, where the damping is proportional to the square of the velocity, is a non-linear second-order differential equation. Non-linear equations of motion such as this are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions. Like all second-order ordinary differential equations, it has a corresponding first-order partial differential equation, whose independent solutions constitute the constants of the motion. These constants readily provide an approximate solution correct to first order in the damping constant. They also reveal that the quadratically damped oscillator is never critically damped or overdamped, and that to first order in the damping constant the oscillation frequency is identical to the natural frequency. The technique described has close ties to standard tools such as integral curves in phase space and phase portraits.

15. Non-linear Young's double-slit experiment.

PubMed

San Roman, Julio; Ruiz, Camilo; Perez, Jose Antonio; Delgado, Diego; Mendez, Cruz; Plaja, Luis; Roso, Luis

2006-04-03

The Young's double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.

16. New non-linear photovoltaic effect in uniform bipolar semiconductor

SciTech Connect

Volovichev, I.

2014-11-21

A linear theory of the new non-linear photovoltaic effect in the closed circuit consisting of a non-uniformly illuminated uniform bipolar semiconductor with neutral impurities is developed. The non-uniform photo-excitation of impurities results in the position-dependant current carrier mobility that breaks the semiconductor homogeneity and induces the photo-electromotive force (emf). As both the electron (or hole) mobility gradient and the current carrier generation rate depend on the light intensity, the photo-emf and the short-circuit current prove to be non-linear functions of the incident light intensity at an arbitrarily low illumination. The influence of the sample size on the photovoltaic effect magnitude is studied. Physical relations and distinctions between the considered effect and the Dember and bulk photovoltaic effects are also discussed.

17. SSNN toolbox for non-linear system identification

Luzar, Marcel; Czajkowski, Andrzej

2015-11-01

The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.

18. Non-linear Poisson-Boltzmann theory for swollen clays

Leote de Carvalho, R. J. F.; Trizac, E.; Hansen, J.-P.

1998-08-01

The non-linear Poisson-Boltzmann (PB) equation for a circular, uniformly char ged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving the latter iteratively. This method proves efficient and robust, and can be readily generalized to other problems based on cell models, treated within non-linear Poisson-like theory. The solution to the PB equation is computed over a wide range of physical conditions, and the resulting osmotic equation of state is shown to be in semi-quantitative agreement with recent experimental data for Laponite clay suspensions, in the concentrated gel phase.

19. Minimax Techniques For Optimizing Non-Linear Image Algebra Transforms

Davidson, Jennifer L.

1989-08-01

It has been well established that the Air Force Armament Technical Laboratory (AFATL) image algebra is capable of expressing all linear transformations [7]. The embedding of the linear algebra in the image algebra makes this possible. In this paper we show a relation of the image algebra to another algebraic system called the minimax algebra. This system is used extensively in economics and operations research, but until now has not been investigated for applications to image processing. The relationship is exploited to develop new optimization methods for a class of non-linear image processing transforms. In particular, a general decomposition technique for templates in this non-linear domain is presented. Template decomposition techniques are an important tool in mapping algorithms efficiently to both sequential and massively parallel architectures.

20. Non-Linear Control Allocation Using Piecewise Linear Functions

DTIC Science & Technology

2003-08-01

A novel method is presented for the solution of the non- linear control allocation problem. Historically, control allocation has been performed by... linear control allocation problem to be cast as a piecewise linear program. The piecewise linear program is ultimately cast as a mixed-integer linear...piecewise linear control allocation method is shown to be markedly improved when compared to the performance of a more traditional control allocation approach that assumes linearity.

1. Non-linear stochastic growth rates and redshift space distortions

DOE PAGES

Jennings, Elise; Jennings, David

2015-04-09

The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a non-linear, stochastic relation between θ = ∇ ∙ v(x,t)/aH and δ. This provides a new phenomenological approach that examines the conditional mean <θ|δ>, together with the fluctuations of θ around this mean. We also measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from ~10 per cent at k < 0.2 h Mpc-1 to 25 per cent at kmore » ~ 0.45 h Mpc-1 at z = 0. Both the stochastic relation and non-linearity are more pronounced for haloes, M ≤ 5 × 1012 M⊙ h-1, compared to the dark matter at z = 0 and 1. Non-linear growth effects manifest themselves as a rotation of the mean <θ|δ> away from the linear theory prediction -fLTδ, where fLT is the linear growth rate. This rotation increases with wavenumber, k, and we show that it can be well-described by second-order Lagrangian perturbation theory (2LPT) fork < 0.1 h Mpc-1. Furthermore, the stochasticity in the θ – δ relation is not so simply described by 2LPT, and we discuss its impact on measurements of fLT from two-point statistics in redshift space. Furthermore, given that the relationship between δ and θ is stochastic and non-linear, this will have implications for the interpretation and precision of fLT extracted using models which assume a linear, deterministic expression.« less

2. Non-linear stochastic growth rates and redshift space distortions

SciTech Connect

Jennings, Elise; Jennings, David

2015-04-09

The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a non-linear, stochastic relation between θ = ∇ ∙ v(x,t)/aH and δ. This provides a new phenomenological approach that examines the conditional mean <θ|δ>, together with the fluctuations of θ around this mean. We also measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from ~10 per cent at k < 0.2 h Mpc-1 to 25 per cent at k ~ 0.45 h Mpc-1 at z = 0. Both the stochastic relation and non-linearity are more pronounced for haloes, M ≤ 5 × 1012 M h-1, compared to the dark matter at z = 0 and 1. Non-linear growth effects manifest themselves as a rotation of the mean <θ|δ> away from the linear theory prediction -fLTδ, where fLT is the linear growth rate. This rotation increases with wavenumber, k, and we show that it can be well-described by second-order Lagrangian perturbation theory (2LPT) fork < 0.1 h Mpc-1. Furthermore, the stochasticity in the θ – δ relation is not so simply described by 2LPT, and we discuss its impact on measurements of fLT from two-point statistics in redshift space. Furthermore, given that the relationship between δ and θ is stochastic and non-linear, this will have implications for the interpretation and precision of fLT extracted using models which assume a linear, deterministic expression.

3. NON-LINEAR MODELING OF THE RHIC INTERACTION REGIONS.

SciTech Connect

TOMAS,R.FISCHER,W.JAIN,A.LUO,Y.PILAT,F.

2004-07-05

For RHIC's collision lattices the dominant sources of transverse non-linearities are located in the interaction regions. The field quality is available for most of the magnets in the interaction regions from the magnetic measurements, or from extrapolations of these measurements. We discuss the implementation of these measurements in the MADX models of the Blue and the Yellow rings and their impact on beam stability.

4. Non-linear power spectra in the synchronous gauge

SciTech Connect

Hwang, Jai-chan; Noh, Hyerim; Jeong, Donghui; Gong, Jinn-Ouk; Biern, Sang Gyu E-mail: hr@kasi.re.kr E-mail: jinn-ouk.gong@apctp.org

2015-05-01

We study the non-linear corrections to the matter and velocity power spectra in the synchronous gauge (SG). For the leading correction to the non-linear power spectra, we consider the perturbations up to third order in a zero-pressure fluid in a flat cosmological background. Although the equations in the SG happen to coincide with those in the comoving gauge (CG) to linear order, they differ from second order. In particular, the second order hydrodynamic equations in the SG are apparently in the Lagrangian form, whereas those in the CG are in the Eulerian form. The non-linear power spectra naively presented in the original SG show rather pathological behavior quite different from the result of the Newtonian theory even on sub-horizon scales. We show that the pathology in the nonlinear power spectra is due to the absence of the convective terms in, thus the Lagrangian nature of, the SG. We show that there are many different ways of introducing the corrective convective terms in the SG equations. However, the convective terms (Eulerian modification) can be introduced only through gauge transformations to other gauges which should be the same as the CG to the second order. In our previous works we have shown that the density and velocity perturbation equations in the CG exactly coincide with the Newtonian equations to the second order, and the pure general relativistic correction terms starting to appear from the third order are substantially suppressed compared with the relativistic/Newtonian terms in the power spectra. As a result, we conclude that the SG per se is an inappropriate coordinate choice in handling the non-linear matter and velocity power spectra of the large-scale structure where observations meet with theories.

5. Non-linear characteristics of Rayleigh-Taylor instable perturbations

Fan, Zhengfeng; Luo, Jisheng

2008-04-01

The direct numerical simulation method is adopted to study the non-linear characteristics of Rayleigh-Taylor instable perturbations at the ablation front of a 200 μm planar CH ablation target. In the simulation, the classical electrical thermal conductivity is included, and NND difference scheme is used. The linear growth rates obtained from the simulation agree with the Takabe formula. The amplitude distribution of the density perturbation at the ablation front is obtained for the linear growth case. The non-linear characteristics of Rayleigh-Taylor instable perturbations are analyzed and the numerical results show that the amplitude distributions of the compulsive harmonics are very different from that of the fundamental perturbation. The characteristics of the amplitude distributions of the harmonics and their fast growth explain why spikes occur at the ablation front. The numerical results also show that non-linear effects have relations with the phase differences of double mode initial perturbations, and different phase differences lead to varied spikes.

6. Non-linear Oscillations of Compact Stars and Gravitational Waves

Passamonti, Andrea

2006-07-01

7. Non-linear modeling using fuzzy principal component regression for Vidyaranyapuram sewage treatment plant, Mysore - India.

PubMed

Sulthana, Ayesha; Latha, K C; Imran, Mohammad; Rathan, Ramya; Sridhar, R; Balasubramanian, S

2014-01-01

Fuzzy principal component regression (FPCR) is proposed to model the non-linear process of sewage treatment plant (STP) data matrix. The dimension reduction of voluminous data was done by principal component analysis (PCA). The PCA score values were partitioned by fuzzy-c-means (FCM) clustering, and a Takagi-Sugeno-Kang (TSK) fuzzy model was built based on the FCM functions. The FPCR approach was used to predict the reduction in chemical oxygen demand (COD) and biological oxygen demand (BOD) of treated wastewater of Vidyaranyapuram STP with respect to the relations modeled between fuzzy partitioned PCA scores and target output. The designed FPCR model showed the ability to capture the behavior of non-linear processes of STP. The predicted values of reduction in COD and BOD were analyzed by performing the linear regression analysis. The predicted values for COD and BOD reduction showed positive correlation with the observed data.

8. Vehicle dynamic analysis using neuronal network algorithms

Oloeriu, Florin; Mocian, Oana

2014-06-01

being a non-linear process identification algorithm. The common use of neuronal networks for non-linear processes is justified by the fact that both have the ability to organize by themselves. That is why the neuronal networks best define intelligent systems, thus the word neuronal' is sending one's mind to the biological neuron cell. The paper presents how to better interpret data fed from the on-board computer and a new way of processing that data to better model the real life dynamic behavior of the vehicle.

9. On the linear and non-linear electronic spectroscopy of chlorophylls: a computational study.

PubMed

Graczyk, Alicja; Żurek, Justyna M; Paterson, Martin J

2014-01-01

A theoretical analysis of linear and non-linear (two-photon absorption) electronic spectroscopy of all known porphyrinic pigments has been performed using linear and quadratic density functional response theory, with the long-range corrected CAM-B3LYP functional. We found that higher Soret transitions often contain non-Gouterman contributions and that each chlorophyll has the possibility for resonance enhanced TPA in the Soret region, although there is also significant TPA in the Q region.

10. Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1986-01-01

The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.

11. Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

Kraczek, Brent; Kanp, Jaroslaw

Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.

12. A review on non-linear aeroelasticity of high aspect-ratio wings

Afonso, Frederico; Vale, José; Oliveira, Éder; Lau, Fernando; Suleman, Afzal

2017-02-01

Current economic constraints and environmental regulations call for design of more efficient aircraft configurations. An observed trend in aircraft design to reduce the lift induced drag and improve fuel consumption and emissions is to increase the wing aspect-ratio. However, a slender wing is more flexible and subject to higher deflections under the same operating conditions. This effect may lead to changes in dynamic behaviour and in aeroelastic response, potentially resulting in instabilities. Therefore, it is important to take into account geometric non-linearities in the design of high aspect-ratio wings, as well as having accurate computational codes that couple the aerodynamic and structural models in the presence of non-linearities. Here, a review on the state-of-the-art on non-linear aeroelasticity of high aspect-ratio wings is presented. The methodologies employed to analyse high aspect-ratio wings are presented and their applications discussed. Important observations from the state-of-the-art studies are drawn and the current challenges in the field are identified.

13. Relativistic weak lensing from a fully non-linear cosmological density field

SciTech Connect

Thomas, D.B.; Bruni, M.; Wands, D. E-mail: marco.bruni@port.ac.uk

2015-09-01

In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- and B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a well-defined manner. Specifying General Relativity, we write down a complete set of equations for a GR+ΛCDM universe for computing all of the possible lensing terms from Newtonian N-body simulations. We illustrate this with the vector potential and show that, in a GR+ΛCDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a ΛCDM cosmology.

14. Solving deterministic non-linear programming problem using Hopfield artificial neural network and genetic programming techniques

Vasant, P.; Ganesan, T.; Elamvazuthi, I.

2012-11-01

A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.

15. Local instabilities and the transition to chaos of non-linear waves

1993-03-01

The object of this research contract was to study the singularities of non-linear structures through numerical simulations. The waiting times involved in the use of a Cray II prompted the lab to replace it with an HP 720 work station, which they found to be irreplaceable for the fine analysis of convection, despite the huge amount of calculations involved. The team simulated a fairly large number of two-dimensional phenomenological models, with satisfactory results. Examples described in this report include convection, dislocations in rolled structures, dislocation nucleation using the Landau-Ginzburg equation, the Pesch-Kramer equation (large-scale flows), non-linear wave defects, the optical model, and others.

16. Experimental and theoretical (FT-IR, FT-Raman, UV-vis, NMR) spectroscopic analysis and first order hyperpolarizability studies of non-linear optical material: (2E)-3-[4-(methylsulfanyl) phenyl]-1-(4-nitrophenyl) prop-2-en-1-one using density functional theory.

PubMed

Kumar, Amit; Deval, Vipin; Tandon, Poonam; Gupta, Archana; Deepak D'silva, E

2014-09-15

A combined experimental and theoretical investigation on FT-IR, FT-Raman, NMR, UV-vis spectra of a chalcone derivative (2E)-3-[4-(methylsulfanyl) phenyl]-1-(4-nitrophenyl) prop-2-en-1-one (4N4MSP) has been reported. 4N4MSP has two planar rings connected through conjugated double bond and it provides a necessary configuration to show non-linear optical (NLO) response. The molecular structure, fundamental vibrational frequencies and intensity of the vibrational bands are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) with B3LYP functional and 6-311++G(d,p) basis set combination. The analysis of the fundamental modes was made with the help of potential energy distribution (PED). Molecular electrostatic potential (MEP) surface was plotted over the geometry primarily for predicting sites and relative reactivities towards electrophilic and nucleophilic attack. The delocalization of electron density of various constituents of the molecule has been discussed with the aid of NBO analysis. The electronic properties, such as excitation energies, oscillator strength, wavelengths, HOMO and LUMO energies, were calculated by time-dependent density functional theory (TD-DFT) and the results complement the experimental findings. The recorded and calculated 1H chemical shifts in gas phase and MeOD solution are gathered for reliable calculations of magnetic properties. Thermodynamic properties like heat capacity (C°p,m), entropy (S°m), enthalpy (H°m) have been calculated for the molecule at the different temperatures. Based on the finite-field approach, the non-linear optical (NLO) parameters such as dipole moment, mean polarizability, anisotropy of polarizability and first order hyperpolarizability of 4N4MSP molecule are calculated. The predicted first hyperpolarizability shows that the molecule has a reasonably good nonlinear optical (NLO) behavior.

17. Global non-linear effect of temperature on economic production

Burke, Marshall; Hsiang, Solomon M.; Miguel, Edward

2015-11-01

Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.

18. Global non-linear effect of temperature on economic production.

PubMed

Burke, Marshall; Hsiang, Solomon M; Miguel, Edward

2015-11-12

Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.

19. Organic-inorganic hybrid glass: non-linear optical properties

Domínguez Cruz, R.; Mendez-Perez, A.; Romero Galván, G.; Mendoza-Panduro, M.; Trejo-Duran, M.; Alvarado-Mendez, E.; Estudillo-Ayala, J. M.; Rojas-Laguna, R.; Martínez-Richa, A.; Castano, V. M.

2008-04-01

In this paper we report the preliminary results about the optical characterization of a new kind of organic-inorganic hybrid glass named 4-((5-dichloromethylsily1)-penty)oxy-cyanobenzene (DCN) synthesized by sol-gel process. We obtain the sign and magnitude of the sample by the Z-scan technique using a low power He-Ne laser at 632 nm in CW operation. The experimental data show that the DNC glass has a negative Kerr optical non-linearity and is estimated a nonlinear coefficient as Δn˜10-6.

20. Disorder and Quantum Chromodynamics -- Non-Linear σ Models

Guhr, Thomas; Wilke, Thomas

2001-10-01

The statistical properties of Quantum Chromodynamics (QCD) show universal features which can be modeled by random matrices. This has been established in detailed analyses of data from lattice gauge calculations. Moreover, systematic deviations were found which link QCD to disordered systems in condensed matter physics. To furnish these empirical findings with analytical arguments, we apply and extend the methods developed in disordered systems to construct a non-linear σ model for the spectral correlations in QCD. Our goal is to derive connections to other low-energy effective theories, such as the Nambu-Jona-Lasinio model, and to chiral perturbation theory.

1. Disorder and Quantum Chromodynamics - Non-Linear σ Models

Guhr, Thomas; Wilke, Thomas

The statistical properties of Quantum Chromodynamics (QCD) show universal features which can be modeled by random matrices. This has been established in detailed analyses of data from lattice gauge calculations. Moreover, systematic deviations were found which link QCD to disordered systems in condensed matter physics. To furnish these empirical findings with analytical arguments, we apply and extend the methods developed in disordered systems to construct a non-linear σ model for the spectral correlations in QCD. Our goal is to derive connections to other low-energy effective theories, such as the Nambu-Jona-Lasinio model, and to chiral perturbation theory.

2. Non-linear isocurvature perturbations and non-Gaussianities

SciTech Connect

Langlois, David; Vernizzi, Filippo; Wands, David E-mail: filippo.vernizzi@cea.fr

2008-12-15

We study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended {delta}N formalism, we analyse in detail two illustrative examples. The first is a mixed curvaton-inflaton scenario in which fluctuations of both the inflaton and a curvaton (a light isocurvature field during inflation) contribute to the primordial density perturbation. The second example is that of double inflation involving two decoupled massive scalar fields during inflation. In the mixed curvaton-inflaton scenario we find that the bispectrum of primordial isocurvature perturbations may be large and comparable to the bispectrum of adiabatic curvature perturbations.

3. A non-linear UAV altitude PSO-PD control

Orlando, Calogero

2015-12-01

In this work, a nonlinear model based approach is presented for the altitude stabilization of a hexarotor unmanned aerial vehicle (UAV). The mathematical model and control of the hexacopter airframe is presented. To stabilize the system along the vertical direction, a Proportional Derivative (PD) control is taken into account. A particle swarm optimization (PSO) approach is used in this paper to select the optimal parameters of the control algorithm taking into account different objective functions. Simulation sets are performed to carry out the results for the non-linear system to show how the PSO tuned PD controller leads to zero the error of the position along Z earth direction.

4. 8-PSK Signaling over non-linear satellite channels

NASA Technical Reports Server (NTRS)

Horan, Sheila B.; Caballero, Ruben B. Eng.

1996-01-01

Space agencies are under pressure to utilize better bandwidth-efficient communication methods due to the actual allocated frequency bands becoming more congested. Also budget reductions is another problem that the space agencies must deal with. This budget constraint results in simpler spacecraft carrying less communication capabilities and also the reduction in staff to capture data in the earth stations. It is then imperative that the most bandwidth efficient communication methods be utilized. This thesis presents a study of 8-ary Phase Shift Keying (8PSK) modulation with respect to bandwidth, power efficiency, spurious emissions and interference susceptibility over a non-linear satellite channel.

5. Non-linear optical titanyl arsenates: Crystal growth and properties

Nordborg, Jenni Eva Louise

Crystals are appreciated not only for their appearance, but also for their unique physical properties which are utilized by the photonic industry in appliances that we come across every day. An important part of enabling the technical use of optical devices is the manufacture of crystals. This dissertation deals with a specific group of materials called the potassium titanyl phosphate (KIP) family, known for their non-linear optical and ferroelectric properties. The isomorphs vary in their linear optical and dielectric properties, which can be tuned to optimize device performance by forming solid solutions of the different materials. Titanyl arsenates have a wide range of near-infrared transmission which makes them useful for tunable infrared lasers. The isomorphs examined in the present work were primarily RbTiOASO4 (RTA) and CsTiOAsO4 (CTA) together with the mixtures RbxCs 1-xTiOAsO4 (RCTA). Large-scale crystals were grown by top seeding solution growth utilizing a three-zone furnace with excellent temperature control. Sufficiently slow cooling and constant upward lifting produced crystals with large volumes useable for technical applications. Optical quality RTA crystals up to 10 x 12 x 20 mm were grown. The greater difficulty in obtaining good crystals of CTA led to the use of mixed RCTA materials. The mixing of rubidium and cesium in RCTA is more favorable to crystal growth than the single components in pure RTA and CTA. Mixed crystals are rubidium-enriched and contain only 20-30% of the cesium concentration in the flux. The cesium atoms show a preference for the larger cation site. The network structure is very little affected by the cation substitution; consequently, the non-linear optical properties of the Rb-rich isomorphic mixtures of RTA and CTA can be expected to remain intact. Crystallographic methods utilizing conventional X-ray tubes, synchrotron radiation and neutron diffraction have been employed to investigate the properties of the atomic

6. Non-linear identification of a squeeze-film damper

NASA Technical Reports Server (NTRS)

Stanway, Roger; Mottershead, John; Firoozian, Riaz

1987-01-01

Described is an experimental study to identify the damping laws associated with a squeeze-film vibration damper. This is achieved by using a non-linear filtering algorithm to process displacement responses of the damper ring to synchronous excitation and thus to estimate the parameters in an nth-power velocity model. The experimental facility is described in detail and a representative selection of results is included. The identified models are validated through the prediction of damper-ring orbits and comparison with observed responses.

7. Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects

2015-07-01

Present work deals with the magneto-hydro-dynamic flow and heat transfer of Casson nanofluid over a non-linearly stretching sheet. Non-linear temperature distribution across the sheet is considered. More physically acceptable model of passively controlled wall nanoparticle volume fraction is accounted. The arising mathematical problem is governed by interesting parameters which include Casson fluid parameter, magnetic field parameter, power-law index, Brownian motion parameter, thermophoresis parameter, Prandtl number and Schmidt number. Numerical solutions are computed through fourth-fifth-order-Runge-Kutta integration approach combined with the shooting technique. Both temperature and nanoparticle volume fraction are increasing functions of Casson fluid parameter.

8. Non-linear interactions between {CO}_2 radiative and physiological effects on Amazonian evapotranspiration in an Earth system model

2016-11-01

We present a detailed analysis of mechanisms underlying the evapotranspiration response to increased {CO}_2 in HadGEM2-ES, focussed on western Amazonia. We use three simulations from CMIP5 in which atmospheric {CO}_2 increases at 1% per year reaching approximately four times pre-industrial levels after 140 years. Using 3-hourly data, we found that evapotranspiration (ET) change was dominated by decreased stomatal conductance (g_s ), and to a lesser extent by decreased canopy water and increased moisture gradient (specific humidity difference between surface and near-surface). There were large, non-linear decreases in ET in the simulation in which radiative and physiological forcings could interact. This non-linearity arises from non-linearity in the conductance term (includes aerodynamic and stomatal resistance and partitioning between the two, which is determined by canopy water availability), the moisture gradient, and negative correlation between these two terms. The conductance term is non-linear because GPP responds non-linearly to temperature and GPP is the dominant control on g_s in HadGEM2-ES. In addition, canopy water declines, mainly due to increases in potential evaporation, which further decrease the conductance term. The moisture gradient responds non-linearly owing to the non-linear response of temperature to {CO}_2 increases, which increases the Bowen ratio. Moisture gradient increases resulting from ET decline increase ET and thus constitute a negative feedback. This analysis highlights the importance of the g_s parametrisation in determining the ET response and the potential differences between offline and online simulations owing to feedbacks on ET via the atmosphere, some of which would not occur in an offline simulation.

9. Non-Linear Approach in Kinesiology Should Be Preferred to the Linear--A Case of Basketball.

PubMed

Trninić, Marko; Jeličić, Mario; Papić, Vladan

2015-07-01

In kinesiology, medicine, biology and psychology, in which research focus is on dynamical self-organized systems, complex connections exist between variables. Non-linear nature of complex systems has been discussed and explained by the example of non-linear anthropometric predictors of performance in basketball. Previous studies interpreted relations between anthropometric features and measures of effectiveness in basketball by (a) using linear correlation models, and by (b) including all basketball athletes in the same sample of participants regardless of their playing position. In this paper the significance and character of linear and non-linear relations between simple anthropometric predictors (AP) and performance criteria consisting of situation-related measures of effectiveness (SE) in basketball were determined and evaluated. The sample of participants consisted of top-level junior basketball players divided in three groups according to their playing time (8 minutes and more per game) and playing position: guards (N = 42), forwards (N = 26) and centers (N = 40). Linear (general model) and non-linear (general model) regression models were calculated simultaneously and separately for each group. The conclusion is viable: non-linear regressions are frequently superior to linear correlations when interpreting actual association logic among research variables.

10. Adaptive iterative learning control for a class of non-linearly parameterised systems with input saturations

Zhang, Ruikun; Hou, Zhongsheng; Ji, Honghai; Yin, Chenkun

2016-04-01

In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov-Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L2[0, T] convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.

11. Predicting haemodynamic networks using electrophysiology: The role of non-linear and cross-frequency interactions

PubMed Central

Tewarie, P.; Bright, M.G.; Hillebrand, A.; Robson, S.E.; Gascoyne, L.E.; Morris, P.G.; Meier, J.; Van Mieghem, P.; Brookes, M.J.

2016-01-01

Understanding the electrophysiological basis of resting state networks (RSNs) in the human brain is a critical step towards elucidating how inter-areal connectivity supports healthy brain function. In recent years, the relationship between RSNs (typically measured using haemodynamic signals) and electrophysiology has been explored using functional Magnetic Resonance Imaging (fMRI) and magnetoencephalography (MEG). Significant progress has been made, with similar spatial structure observable in both modalities. However, there is a pressing need to understand this relationship beyond simple visual similarity of RSN patterns. Here, we introduce a mathematical model to predict fMRI-based RSNs using MEG. Our unique model, based upon a multivariate Taylor series, incorporates both phase and amplitude based MEG connectivity metrics, as well as linear and non-linear interactions within and between neural oscillations measured in multiple frequency bands. We show that including non-linear interactions, multiple frequency bands and cross-frequency terms significantly improves fMRI network prediction. This shows that fMRI connectivity is not only the result of direct electrophysiological connections, but is also driven by the overlap of connectivity profiles between separate regions. Our results indicate that a complete understanding of the electrophysiological basis of RSNs goes beyond simple frequency-specific analysis, and further exploration of non-linear and cross-frequency interactions will shed new light on distributed network connectivity, and its perturbation in pathology. PMID:26827811

12. Filtering Non-Linear Transfer Functions on Surfaces.

PubMed

Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice

2013-07-18

Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to surface textures, as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. Our framework is also compatible with the case of transfer functions used to warp surface geometry.

13. Non-linear plasma wake growth of electron holes

Hutchinson, I. H.; Haakonsen, C. B.; Zhou, C.

2015-03-01

An object's wake in a plasma with small Debye length that drifts across the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind and probes in magnetized laboratory plasmas. The instability drive mechanism can equivalently be considered drift down the potential-energy gradient or drift up the density-gradient. The gradients arise because the plasma wake has a region of depressed density and electrostatic potential into which ions are attracted along the field. The non-linear consequences of the instability are analysed in this paper. At physical ratios of electron to ion mass, neither linear nor quasilinear treatment can explain the observation of large-amplitude perturbations that disrupt the ion streams well before they become ion-ion unstable. We show here, however, that electron holes, once formed, continue to grow, driven by the drift mechanism, and if they remain in the wake may reach a maximum non-linearly stable size, beyond which their uncontrolled growth disrupts the ions. The hole growth calculations provide a quantitative prediction of hole profile and size evolution. Hole growth appears to explain the observations of recent particle-in-cell simulations.

14. Charged relativistic fluids and non-linear electrodynamics

Dereli, T.; Tucker, R. W.

2010-01-01

The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.

15. Effects on non-linearities on aircraft poststall motion

SciTech Connect

Rohacs, J.; Thomasson, P.; Mosehilde, E.

1994-12-31

The poststall maneuverability controlled by thrust vectoring has become one of the important aspects of new fighter development projects. In simplified case, the motion of aircraft can be described by 6DOF nonlinear system. The lecture deals with the longitudinal motion of poststall maneuverable aircraft. The investigation made about the effects of non-linearities in aerodynamic coefficients having considerable non-linearities and hysteresisis an the poststall motions. There were used some different models of aerodynamic coefficients. The results of investigation have shown that the poststall domain of vectored aircraft can be divided into five different pHs in field of thrust - pitch vector angle, and the chaotic motions of aircraft can be found at the different frequencies of thrust deflection. There were defined an unstable right domain with an unstable oscillation and a field of overpulling at poststall motion. The certain frequency chaotic attractors were got at frequencies of Oxitation between the 0.15 and 0.65 rad/sec. The pitching moment derivatives had the big influence on the chaotic motions, while the lift coefficient derivatives bad the reasonable effects, only.

16. Non-linear plasma wake growth of electron holes

SciTech Connect

Hutchinson, I. H.; Haakonsen, C. B.; Zhou, C.

2015-03-15

An object's wake in a plasma with small Debye length that drifts across the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind and probes in magnetized laboratory plasmas. The instability drive mechanism can equivalently be considered drift down the potential-energy gradient or drift up the density-gradient. The gradients arise because the plasma wake has a region of depressed density and electrostatic potential into which ions are attracted along the field. The non-linear consequences of the instability are analysed in this paper. At physical ratios of electron to ion mass, neither linear nor quasilinear treatment can explain the observation of large-amplitude perturbations that disrupt the ion streams well before they become ion-ion unstable. We show here, however, that electron holes, once formed, continue to grow, driven by the drift mechanism, and if they remain in the wake may reach a maximum non-linearly stable size, beyond which their uncontrolled growth disrupts the ions. The hole growth calculations provide a quantitative prediction of hole profile and size evolution. Hole growth appears to explain the observations of recent particle-in-cell simulations.

17. Polycarbonate-Based Blends for Optical Non-linear Applications

Stanculescu, F.; Stanculescu, A.

2016-02-01

This paper presents some investigations on the optical and morphological properties of the polymer (matrix):monomer (inclusion) composite materials obtained from blends of bisphenol A polycarbonate and amidic monomers. For the preparation of the composite films, we have selected monomers characterised by a maleamic acid structure and synthesised them starting from maleic anhydride and aniline derivatives with -COOH, -NO2, -N(C2H5)2 functional groups attached to the benzene ring. The composite films have been deposited by spin coating using a mixture of two solutions, one containing the matrix and the other the inclusion, both components of the composite system being dissolved in the same solvent. The optical transmission and photoluminescence properties of the composite films have been investigated in correlation with the morphology of the films. The scanning electron microscopy and atomic force microscopy have revealed a non-uniform morphology characterised by the development of two distinct phases. We have also investigated the generation of some optical non-linear (ONL) phenomena in these composite systems. The composite films containing as inclusions monomers characterised by the presence of one -COOH or two -NO2 substituent groups to the aromatic nucleus have shown the most intense second-harmonic generation (SHG). The second-order optical non-linear coefficients have been evaluated for these films, and the effect of the laser power on the ONL behaviour of these materials has also been emphasised.

18. Non-linear leak currents affect mammalian neuron physiology

PubMed Central

Huang, Shiwei; Hong, Sungho; De Schutter, Erik

2015-01-01

In their seminal works on squid giant axons, Hodgkin, and Huxley approximated the membrane leak current as Ohmic, i.e., linear, since in their preparation, sub-threshold current rectification due to the influence of ionic concentration is negligible. Most studies on mammalian neurons have made the same, largely untested, assumption. Here we show that the membrane time constant and input resistance of mammalian neurons (when other major voltage-sensitive and ligand-gated ionic currents are discounted) varies non-linearly with membrane voltage, following the prediction of a Goldman-Hodgkin-Katz-based passive membrane model. The model predicts that under such conditions, the time constant/input resistance-voltage relationship will linearize if the concentration differences across the cell membrane are reduced. These properties were observed in patch-clamp recordings of cerebellar Purkinje neurons (in the presence of pharmacological blockers of other background ionic currents) and were more prominent in the sub-threshold region of the membrane potential. Model simulations showed that the non-linear leak affects voltage-clamp recordings and reduces temporal summation of excitatory synaptic input. Together, our results demonstrate the importance of trans-membrane ionic concentration in defining the functional properties of the passive membrane in mammalian neurons as well as other excitable cells. PMID:26594148

19. Linear and non-linear interdependence of EEG and HRV frequency bands in human sleep.

PubMed

Chaparro-Vargas, Ramiro; Dissanayaka, P Chamila; Patti, Chanakya Reddy; Schilling, Claudia; Schredl, Michael; Cvetkovic, Dean

2014-01-01

The characterisation of functional interdependencies of the autonomic nervous system (ANS) stands an evergrowing interest to unveil electroencephalographic (EEG) and Heart Rate Variability (HRV) interactions. This paper presents a biosignal processing approach as a supportive computational resource in the estimation of sleep dynamics. The application of linear, non-linear methods and statistical tests upon 10 overnight polysomnographic (PSG) recordings, allowed the computation of wavelet coherence and phase locking values, in order to identify discerning features amongst the clinical healthy subjects. Our findings showed that neuronal oscillations θ, α and σ interact with cardiac power bands at mid-to-high rank of coherence and phase locking, particularly during NREM sleep stages.

20. Hamiltonian Lattice Studies of Pionic Collective Excitations in the Non-linear Sigma Model

Chin, Siu A.

2001-04-01

The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin system with quantum fluctuations. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In particular, the mas gap of pionic collective excitations with quantum number of vector mesons can be determined as the chiral phase transition is approached. Results based on a newly discovered 4th order method of solving for the ground state of a quantum many-body Hamitonian will be presented.

1. Higgs physics beyond the SM: The non-linear EFT approach

Brivio, I.

2016-07-01

Depending on whether electroweak physics beyond the Standard Model is based on a linear or on a non-linear implementation of the electroweak symmetry breaking, a linear or a chiral Effective Lagrangian is more appropriate. In this talk, the main low-energy signals that allow to recognize whether the observed Higgs scalar is a dynamical (composite) particle or rather an elementary one are presented, in a model-independent way. The patterns of effective couplings produced upon the assumption of specific composite Higgs models are also discussed.=1

2. Modelling long term rockslide displacements with non-linear time-dependent relationships

De Caro, Mattia; Volpi, Giorgio; Castellanza, Riccardo; Crosta, Giovanni; Agliardi, Federico

2015-04-01

Rockslides undergoing rapid changes in behaviour pose major risks in alpine areas, and require careful characterization and monitoring both for civil protection and mitigation activities. In particular, these instabilities can undergo very slow movement with occasional and intermittent acceleration/deceleration stages of motion potentially leading to collapse. Therefore, the analysis of such instabilities remains a challenging issue. Rockslide displacements are strongly conditioned by hydrologic factors as suggested by correlations with groundwater fluctuations, snowmelt, with a frequently observed delay between perturbation and system reaction. The aim of this work is the simulation of the complex time-dependent behaviour of two case studies for which also a 2D transient hydrogeological simulation has been performed: Vajont rockslide (1960 to 1963) and the recent Mt. de La Saxe rockslide (2009 to 2012). Non-linear time-dependent constitutive relationships have been used to describe long-term creep deformation. Analyses have been performed using a "rheological-mechanical" approach that fits idealized models (e.g. viscoelastic, viscoplastic, elasto-viscoplastic, Burgers, nonlinear visco-plastic) to the experimental behaviour of specific materials by means of numerical constants. Bidimensional simulations were carried out using the finite difference code FLAC. Displacements time-series, available for the two landslides, show two superimposed deformation mechanisms: a creep process, leading to movements under "steady state" conditions (e.g. constant groundwater level), and a "dynamic" process, leading to an increase in displacement rate due to changes of external loads (e.g. groundwater level). For both cases sliding mass is considered as an elasto-plastic body subject to its self-weight, inertial and seepage forces varying with time according to water table fluctuation (due to snowmelt or changing in reservoir level) and derived from the previous hydrogeological

3. Linear and non-linear evolution of the vertical shear instability in accretion discs

Nelson, Richard P.; Gressel, Oliver; Umurhan, Orkan M.

2013-11-01

We analyse the stability and non-linear dynamics of power-law accretion disc models. These have mid-plane densities that follow radial power laws and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius, R. We employ two different hydrodynamic codes to perform high-resolution 2D axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the disc scaleheight, the thermal relaxation time of the fluid and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to guide our interpretation of the simulation results. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of perturbations whose most obvious character is modes with horizontal and vertical wavenumbers that satisfy |kR/kZ| ≫ 1. Instability occurs only when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time-scale. These discs appear to exhibit the Goldreich-Schubert-Fricke or vertical shear' linear instability. Closer inspection of the simulation results uncovers the growth of two distinct modes. The first are characterized by very short radial wavelength perturbations that grow rapidly at high latitudes in the disc, and descend down towards the mid-plane on longer time-scales. We refer to these as finger modes' because they display kR/kZ ≫ 1. The second appear at slightly later times in the main body of the disc, including near the mid-plane. These body modes' have somewhat longer radial wavelengths. Early on they manifest themselves as fundamental breathing modes, but quickly become corrugation modes as symmetry about the mid-plane is broken. The corrugation modes are a prominent feature

4. Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics

Nazem, M.; Carter, J. P.; Airey, D. W.

2010-06-01

In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.

5. Social Data Analysis by Non-Linear Imbedding

DTIC Science & Technology

2013-09-20

DISTRIBUTION A: Distribution approved for public release. 1989 1990 1991 Middle East 2 7 6 Weapon Nonproliferation 2 6 5 Anti- Apartheid & Human Rights...the Non-Proliferation of Nuclear Weapons) #3570 (Status of the International Convention on the Suppression and Punishment of the crime of Apartheid

6. Non-linear analysis of stick/slip motion

Pratt, T. K.; Williams, R.

1981-02-01

The steady state relative motion of two masses with dry (Coulomb) friction contact is investigated. The bodies are assumed to have the same mass and stiffness and are subjected to harmonic excitation. By means of a combined analytical—numerical procedure, results are obtained for arbitrary values of Coulomb friction, excitation frequency, and natural frequencies of the bodies. For certain values of these parameters, multiple lockups per cycle are possible. In this respect, the problem investigated here is a natural extension of the one considered by Den Hartog, who in obtaining his closed form solution assumed a maximum of two lockups per cycle.

7. The use of non-linearity techniques (correlation dimension) to analyze western Mediterranean rainfall time series

Pérez Lluch, María. Carmen; Pascual-Aguilar, Juan Antonio; Andreu, Vicente

2010-05-01

The Mediterranean climate patterns are characterized by the great rain variability between years combined whit recurrent drought periods and highly intense rain events. These last becomes critical in this area because incise, usually, immediately after the summer dry period, when the vegetation cover is less capable to protect the soil against rainfall aggressiveness and the wildfire period is finishing. These circumstances favour the intensification of erosion processes and the incidence of landslides, floods, etc. Within the scope of the Valencia Community (Western Mediterranean Region), rain displays a high variability as a result of the Mediterranean sea influence and certain local factors, which favour that great part of the precipitations, take place at micro-scale level, assuming a random behaviour of precipitations. In order to have a better knowledge on rain dynamics and to detect the possible differences caused by the regionalization, four temporal series (40 years) have been selected pertaining to climate stations (Castellón, Valencia, Sueca and Alicante) located in the coastal zone of the study area (Valencia Community, Spain). They are characterized by three concrete climatic regions, and are analysed under the deterministic chaos perspective. A non-linear technique, correlation dimension, is used to carry out this analysis. This technique allows calculating the necessary variables to explain the rain behaviour and to establish suitable models that assume their complexity. The results suggest a possible chaotic behaviour in the four series analysed, obtaining a great variability in the zones of Sueca and Castellón. Statistically, the comparison of the results with the coefficient of variation shows coincidences in almost all the series considered. The only exception was the station of Sueca, where an inverse relation is obtained. Similarly, from a geographic perspective, the obtained results are related favourably to the particular characteristics of

8. Image enhancement by non-linear extrapolation in frequency space

NASA Technical Reports Server (NTRS)

Anderson, Charles H. (Inventor); Greenspan, Hayit K. (Inventor)

1998-01-01

An input image is enhanced to include spatial frequency components having frequencies higher than those in an input image. To this end, an edge map is generated from the input image using a high band pass filtering technique. An enhancing map is subsequently generated from the edge map, with the enhanced map having spatial frequencies exceeding an initial maximum spatial frequency of the input image. The enhanced map is generated by applying a non-linear operator to the edge map in a manner which preserves the phase transitions of the edges of the input image. The enhanced map is added to the input image to achieve a resulting image having spatial frequencies greater than those in the input image. Simplicity of computations and ease of implementation allow for image sharpening after enlargement and for real-time applications such as videophones, advanced definition television, zooming, and restoration of old motion pictures.

9. Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

10. Non-linear optical crystal vibration sensing device

DOEpatents

Kalibjian, R.

1994-08-09

A non-linear optical crystal vibration sensing device including a photorefractive crystal and a laser is disclosed. The laser produces a coherent light beam which is split by a beam splitter into a first laser beam and a second laser beam. After passing through the crystal the first laser beam is counter-propagated back upon itself by a retro-mirror, creating a third laser beam. The laser beams are modulated, due to the mixing effect within the crystal by vibration of the crystal. In the third laser beam, modulation is stable and such modulation is converted by a photodetector into a usable electrical output, intensity modulated in accordance with vibration applied to the crystal. 3 figs.

11. Non-linear optical crystal vibration sensing device

DOEpatents

Kalibjian, Ralph

1994-01-11

A non-linear optical crystal vibration sensing device (10) including a photorefractive crystal (26) and a laser (12). The laser (12 ) produces a coherent light beam (14) which is split by a beam splitter (18) into a first laser beam (20) and a second laser beam (22). After passing through the crystal (26) the first laser beam (20) is counter-propagated back upon itself by a retro-mirror (32), creating a third laser beam (30). The laser beams (20, 22, 30) are modulated, due to the mixing effect within the crystal (26) by vibration of the crystal (30). In the third laser beam (30), modulation is stable and such modulation is converted by a photodetector (34) into a usable electrical output, intensity modulated in accordance with vibration applied to the crystal (26).

12. Method and system for non-linear motion estimation

NASA Technical Reports Server (NTRS)

Lu, Ligang (Inventor)

2011-01-01

A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.

13. Non-linear radial spinwave modes in thin magnetic disks

SciTech Connect

Helsen, M. De Clercq, J.; Vansteenkiste, A.; Van Waeyenberge, B.; Weigand, M.

2015-01-19

We present an experimental investigation of radial spin-wave modes in magnetic nano-disks with a vortex ground state. The spin-wave amplitude was measured using a frequency-resolved magneto-optical spectrum analyzer, allowing for high-resolution resonance curves to be recorded. It was found that with increasing excitation amplitude up to about 10 mT, the lowest-order mode behaves strongly non-linearly as the mode frequency redshifts and the resonance peak strongly deforms. This behavior was quantitatively reproduced by micromagnetic simulations. Micromagnetic simulations showed that at higher excitation amplitudes, the spinwaves are transformed into a soliton by self-focusing, and collapse onto the vortex core, dispersing the energy in short-wavelength spinwaves. Additionally, this process can lead to switching of the vortex polarization through the injection of a Bloch point.

14. Non-linear hydrodynamical simulations of delta Scuti star pulsations

Templeton, M. R.; Guzik, J. A.; McNamara, B. J.

1998-12-01

We present the initial results of non-linear hydrodynamic simulations of the pulsation modes of delta Scuti stars. These models use the Ostlie and Cox (1993) Lagrangian hydrodynamic code, adapted to use the most recent OPAL (1996) opacities, the Stellingwerf (1974) periodic relaxation method of obtaining stable limit cycle pulsations, and time-dependent convection. Initial tests of first- and second-overtone pulsation models are consistent with the models of Bono, et al (1997) showing asymmetric lightcurves for first overtone rather than fundamental pulsations. Future modeling work will test several stellar models with varying masses, ages, metal and helium abundances and envelope abundance gradients. Ultimately, we hope to determine the role that abundances and, more specifically, helium abundance gradients in delta Scuti envelopes play in light curve shape. This work will be applied to a test sample of known radially-pulsating delta Scuti field stars and the newly-discovered delta Scuti/SX Phoenicis variables in the Galactic Bulge.

15. Neural networks: What non-linearity to choose

NASA Technical Reports Server (NTRS)

1991-01-01

Neural networks are now one of the most successful learning formalisms. Neurons transform inputs (x(sub 1),...,x(sub n)) into an output f(w(sub 1)x(sub 1) + ... + w(sub n)x(sub n)), where f is a non-linear function and w, are adjustable weights. What f to choose? Usually the logistic function is chosen, but sometimes the use of different functions improves the practical efficiency of the network. The problem of choosing f as a mathematical optimization problem is formulated and solved under different optimality criteria. As a result, a list of functions f that are optimal under these criteria are determined. This list includes both the functions that were empirically proved to be the best for some problems, and some new functions that may be worth trying.

16. Ferrite core non-linearity in coils for magnetic neurostimulation.

PubMed

RamRakhyani, Anil Kumar; Lazzi, Gianluca

2014-10-01

The need to correctly predict the voltage across terminals of mm-sized coils, with ferrite core, to be employed for magnetic stimulation of the peripheral neural system is the motivation for this work. In such applications, which rely on a capacitive discharge on the coil to realise a transient voltage curve of duration and strength suitable for neural stimulation, the correct modelling of the non-linearity of the ferrite core is critical. A demonstration of how a finite-difference model of the considered coils, which include a model of the current-controlled inductance in the coil, can be used to correctly predict the time-domain voltage waveforms across the terminals of a test coil is presented. Five coils of different dimensions, loaded with ferrite cores, have been fabricated and tested: the measured magnitude and width of the induced pulse are within 10% of simulated values.

17. Non-linear diffusion and pattern formation in vortex matter

Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Griessen, R.; Einfeld, J.; Woerdenweber, R.

2000-03-01

Penetration of magnetic flux in YBa_2Cu_3O7 superconducting thin films and crystals in externally applied magnetic fields is visualized with a magneto-optical technique. A variety of flux patterns due to non-linear vortex behavior is observed: 1. Roughening of the flux front^1 with scaling exponents identical to those observed in burning paper^2. Two regimes are found where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. 2. Roughening of the flux profile similar to the Oslo model for rice-piles. 3. Fractal penetration of flux^3 with Hausdorff dimension depending on the critical current anisotropy. 4. Penetration as 'flux-rivers'. 5. The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori^4. By comparison with numerical simulations, it is shown that most of the observed behavior can be explained in terms of non-linear diffusion of vortices. ^1R. Surdeanu, R.J. Wijngaarden, E. Visser, J.M. Huijbregtse, J.H. Rector, B. Dam and R. Griessen, Phys.Rev. Lett. 83 (1999) 2054 ^2J. Maunuksela, M. Myllys, O.-P. Kähkönen, J. Timonen, N. Provatas, M.J. Alava, T. Ala-Nissila, Phys. Rev. Lett. 79, 1515 (1997) ^3R. Surdeanu, R.J. Wijngaarden, B. Dam, J. Rector, R. Griessen, C. Rossel, Z.F. Ren and J.H. Wang, Phys Rev B 58 (1998) 12467 ^4C. Reichhardt, C.J. Olson and F. Nori, Phys. Rev. B 58, 6534 (1998)

18. Linear and non-linear effects of gradient artifact filtering methods in simultaneous EEG-FMRI - biomed 2010.

PubMed

Cusenza, Monica; Accardo, Agostino; Monti, Fabrizio; Bramanti, Placido

2010-01-01

Simultaneous EEG-fMRI is a powerful emerging tool in functional neuroimaging that exploits the relationship between neuronal electrophysiological activity and its hemodynamic response. It has found application in the study of both spontaneous and evoked brain activity. Combining the complementary advantages of the two techniques it provides a measurement with high temporal and spatial resolution, allowing a reliable localization of event generators. However, EEG data recorded inside MRI scanner are heavily corrupted by different types of artifacts due to the interactions between the patient, EEG electrodes wires and the magnetic fields inside the scanner. In particular, gradient switching and RF pulses, necessary to acquire fMRI data, generate large artifacts that can completely obscure EEG signals. Many methods have been proposed to eliminate or at least reduce gradient artifact. In this paper both a qualitative and a quantitative evaluation of two different algorithms used for gradient artifact removal are presented. Linear and non-linear characteristics of EEG, such as power spectra, fractal dimension and beta scaling exponent, are evaluated for EEGs recorded outside and inside the scanner, in MR static and dynamic conditions. The study highlights how residual artifacts after correction and artifacts induced by correction itself could still considerably affect EEG signals. The results suggest that the quality of both these gradient artifact filtering methods is not yet sufficient to preserve EEG characteristics and thus it must be further improved. The aim of this study is to make neurophysiologists aware of the filtering effects that can compromise linear and non-linear analysis of EEG recorded during functional MRI.

19. Spectral coupling issues in a two-degree-of-freedom system with clearance non-linearities

1992-06-01

In an earlier study [14], the frequency response characteristics of a multi-degree-of-freedom system with clearance non-linearities were presented. The current study is an extension of this prior work and deals specifically with the issue of dynamic interactions between resonances. The harmonic balance method, digital solutions and analog computer simulation are used to investigate a two-degree-of-freedom system under a mean load, when subjected to sinusoidal excitations. The existence of harmonic, periodic and chaotic solutions is demonstrated using digital simulation. The method of harmonic balance is employed to construct approximate solutions at the excitation frequency which are then used to classify weak, moderate and strong non-linear spectral interactions. The effects of parameters such as damping ratio, mean load, alternating load and frequency spacing between the resonances have been quantified. The applicability of the methodology is demonstrated through the following practical examples: (i) neutral gear rattle in an automotive transmission system; and (ii) steady state characteristics of a spur gear pair with backlash. In the second case, measured dynamic transmission error data at the gear mesh frequency are used to investigate spectral interactions. Limitations associated with solution methods and interaction classification schemes are also discussed.

20. Real-time estimation and detection of non-linearity in bio-signals using wireless brain-computer interface.

PubMed

Ganesan, S; Victoire, T Aruldoss Albert; Vijayalakshmy, G

2014-01-01

In this paper, the work is mainly concentrated on removing non-linear parameters to make the physiological signals more linear and reducing the complexity of the signals. This paper discusses three different types of techniques that can be successfully utilised to remove non-linear parameters in EEG and ECG. (i) Transformation technique using Discrete Walsh-Hadamard Transform (DWHT); (ii) application of fuzzy logic control and (iii) building the Adaptive Neuro-Fuzzy Inference System (ANFIS) model for fuzzy. This work has been inspired by the need to arrive at an efficient, simple, accurate and quicker method for analysis of bio-signal.

1. Discriminating Non-Linearity from Linearity: Its Cognitive Foundations in Five-Year-Olds

ERIC Educational Resources Information Center

Ebersbach, Mirjam; Van Dooren, Wim; Goudriaan, Margje N.; Verschaffel, Lieven

2010-01-01

People often have difficulties in understanding situations that involve non-linear processes. Also, the topic of non-linear functions is introduced relatively late in the curriculum. Previous research has nevertheless shown that already children aged 6 years and older are able to discriminate non-linear from linear processes. Within the present…

2. Dynamics in Epistasis Analysis.

PubMed

Awdeh, Aseel; Phenix, Hilary; Kaern, Mads; Perkins, Theodore

2017-01-16

Finding regulatory relationships between genes, including the direction and nature of influence between them, is a fundamental challenge in the field of molecular genetics. One classical approach to this problem is epistasis analysis. Broadly speaking, epistasis analysis infers the regulatory relationships between a pair of genes in a genetic pathway by considering the patterns of change in an observable trait resulting from single and double deletion of genes. While classical epistasis analysis has yielded deep insights on numerous genetic pathways, it is not without limitations. Here, we explore the possibility of dynamic epistasis analysis, in which, in addition to performing genetic perturbations of a pathway, we drive the pathway by a time-varying upstream signal. We explore the theoretical power of dynamical epistasis analysis by conducting an identifiability analysis of Boolean models of genetic pathways, comparing static and dynamic approaches. We find that even relatively simple input dynamics greatly increases the power of epistasis analysis to discriminate alternative network structures. Further, we explore the question of experiment design, and show that a subset of short time-varying signals, which we call dynamic primitives, allow maximum discriminative power with a reduced number of experiments.

3. Towards a non-linear theory for fluid pressure and osmosis in shales

Droghei, Riccardo; Salusti, Ettore

2015-04-01

In exploiting deep hydrocarbon reservoirs, often injections of fluid and/or solute are used. To control and avoid troubles as fluid and gas unexpected diffusions, a reservoir characterization can be obtained also from observations of space and time evolution of micro-earthquake clouds resulting from such injections. This is important since several among the processes caused by fluid injections can modify the deep matrix. Information about the evolution of such micro-seismicity clouds therefore plays a realistic role in the reservoir analyses. To reach a better insight about such processes, and obtain a better system control, we here analyze the initial stress necessary to originate strong non linear transients of combined fluid pressure and solute density (osmosis) in a porous matrix. All this can indeed perturb in a mild (i.e. a linear diffusion) or dramatic non linear way the rock structure, till inducing rock deformations, micro-earthquakes or fractures. I more detail we here assume first a linear Hooke law relating strain, stress, solute density and fluid pressure, and analyze their effect in the porous rock dynamics. Then we analyze its generalization, i.e. the further non linear effect of a stronger external pressure, also in presence of a trend of pressure or solute in the whole region. We moreover characterize the zones where a sudden arrival of such a front can cause micro-earthquakes or fractures. All this allows to reach a novel, more realistic insight about the control of rock evolution in presence of strong pressure fronts. We thus obtain a more efficient reservoir control to avoid large geological perturbations. It is of interest that our results are very similar to those found by Shapiro et al.(2013) with a different approach.

4. Simulating the effect of non-linear mode coupling in cosmological parameter estimation

Kiessling, A.; Taylor, A. N.; Heavens, A. F.

2011-09-01

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment and to optimize the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimization it is usually assumed that the power-spectrum covariance matrix is diagonal in Fourier space. However, in the low-redshift Universe, non-linear mode coupling will tend to correlate small-scale power, moving information from lower to higher order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naïve Gaussian Fisher matrix forecasts with a maximum likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2D and tomographic shear analysis of a Euclid-like survey. In both cases, we find that the 68 per cent confidence area of the Ωm-σ8 plane increases by a factor of 5. However, the marginal errors increase by just 20-40 per cent. We propose a new method to model the effects of non-linear shear-power mode coupling in the Fisher matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68 per cent confidence regions of the full maximum likelihood analysis in the Ωm-σ8 plane to high accuracy for both 2D and tomographic weak lensing surveys. Finally, we perform a multiparameter analysis of Ωm, σ8, h, ns, w0 and wa to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The 6D volume of the 1σ error contours for the non-linear Fisher analysis is a factor of 3 larger than for the Gaussian case, and the shape of the 68 per cent confidence

5. Non-linear plasma transport in graphene channels and application to the detection of terahertz signals

Rudin, Sergey; Rupper, Greg

2012-02-01

The non-linear electron plasma response to electromagnetic signal applied to a gated graphene conduction channel can be used to make a graphene based Dyakonov-Shur terahertz detector. The hydrodynamic model predicts a resonance response to electromagnetic radiation at the plasma oscillation frequency. With less damping and higher mobility, the graphene conduction channels may provide higher quality plasma response than possible with semiconductor channels. Our analysis of plasma oscillations in a graphene channel is based on the hydrodynamic equations which we derive from the Boltzmann equation accounting for both electrons and holes, and including the effects of viscosity and finite mobility.

6. A non-linear mathematical model for a three species ecosystem: Hippos in Lake Edward.

PubMed

Bologna, Mauro; Chandía, Kristopher J; Flores, J C

2016-01-21

In this work we study a non-linear mathematical model based on three different interacting species. We apply our model to Lake Edward ecosystem consisting in hippos, tilapia fishes and human inhabitants. In this case, we estimate the values of the key parameters using actual data and show the reliability of the proposed model as a predictive tool. We also show, via numerical calculations and parameter values that the ecosystem associated to the lake is very far from reaching a stable equilibrium. Through our analysis we provide the conditions for a possible coexistence among the three species.

7. Rapid Non-Linear Uncertainty Propagation via Analytical Techniques

Fujimoto, K.; Scheeres, D. J.

2012-09-01

Space situational awareness (SSA) is known to be a data starved problem compared to traditional estimation problems in that observation gaps per object may span over days if not weeks. Therefore, consistent characterization of the uncertainty associated with these objects including non-linear effects is crucial in maintaining an accurate catalog of objects in Earth orbit. Simultaneously, the motion of satellites in Earth orbit is well-modeled in that it is particularly amenable to having their solution and their uncertainty described through analytic or semi-analytic techniques. Even when stronger non-gravitational perturbations such as solar radiation pressure and atmospheric drag are encountered, these perturbations generally have deterministic components that are substantially larger than their time-varying stochastic components. Analytic techniques are powerful because time propagation is only a matter of changing the time parameter, allowing for rapid computational turnaround. These two ideas are combined in this paper: a method of analytically propagating non-linear orbit uncertainties is discussed. In particular, the uncertainty is expressed as an analytic probability density function (pdf) for all time. For a deterministic system model, such pdfs may be obtained if the initial pdf and the system states for all time are also given analytically. Even when closed-form solutions are not available, approximate solutions exist in the form of Edgeworth series for pdfs and Taylor series for the states. The coefficients of the latter expansion are referred to as state transition tensors (STTs), which are a generalization of state transition matrices to arbitrary order. Analytically expressed pdfs can be incorporated in many practical tasks in SSA. One can compute the mean and covariance of the uncertainty, for example, with the moments of the initial pdf as inputs. This process does not involve any sampling and its accuracy can be determined a priori. Analytical

8. Filtering Non-Linear Transfer Functions on Surfaces.

PubMed

Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice

2014-07-01

Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few

9. Wave intensity amplification and attenuation in non-linear flow: implications for the calculation of local reflection coefficients.

PubMed

Mynard, Jonathan; Penny, Daniel J; Smolich, Joseph J

2008-12-05

Local reflection coefficients (R) provide important insights into the influence of wave reflection on vascular haemodynamics. Using the relatively new time-domain method of wave intensity analysis, R has been calculated as the ratio of the peak intensities (R(PI)) or areas (R(CI)) of incident and reflected waves, or as the ratio of the changes in pressure caused by these waves (R(DeltaP)). While these methods have not yet been compared, it is likely that elastic non-linearities present in large arteries will lead to changes in the size of waves as they propagate and thus errors in the calculation of R(PI) and R(CI). To test this proposition, R(PI), R(CI) and R(DeltaP) were calculated in a non-linear computer model of a single vessel with various degrees of elastic non-linearity, determined by wave speed and pulse amplitude (DeltaP(+)), and a terminal admittance to produce reflections. Results obtained from this model demonstrated that under linear flow conditions (i.e. as DeltaP(+)-->0), R(DeltaP) is equivalent to the square-root of R(PI) and R(CI) (denoted by R(PI)(p) and R(CI)(p)). However for non-linear flow, pressure-increasing (compression) waves undergo amplification while pressure-reducing (expansion) waves undergo attenuation as they propagate. Consequently, significant errors related to the degree of elastic non-linearity arise in R(PI) and R(CI), and also R(PI)(p) and R(CI)(p), with greater errors associated with larger reflections. Conversely, R(Delta)(P) is unaffected by the degree of non-linearity and is thus more accurate than R(PI) and R(CI).

10. Origin of the effective mobility in non-linear active micro-rheology

2016-10-01

The distinction between the damping coefficient and the effective non-linear mobility of driven particles in active micro-rheology of supercooled liquids is explained in terms of individual and collective dynamics. The effective mobility arises as a collective effect which gives insight into the energy landscape of the system. On the other hand, the damping coefficient is a constant that modulates the effect of external forces over the thermal energy which particles have at their disposition to perform Brownian motion. For long times, these thermal fluctuations become characterized in terms of an effective temperature that is a consequence of the dynamic coupling between kinetic and configurational degrees of freedom induced by the presence of the strong external force. The interplay between collective mobility and effective temperature allows to formulate a generalized Stokes-Einstein relation that may be used to determine the collective diffusion coefficient. The explicit relations we deduce reproduce simulation data remarkably well.

11. Optimum Damping in a Non-Linear Base Isolation System

Jangid, R. S.

1996-02-01

Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations; i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping.

12. CMB hemispherical asymmetry from non-linear isocurvature perturbations

SciTech Connect

Assadullahi, Hooshyar; Wands, David; Firouzjahi, Hassan; Namjoo, Mohammad Hossein E-mail: firouz@mail.ipm.ir E-mail: david.wands@port.ac.uk

2015-04-01

We investigate whether non-adiabatic perturbations from inflation could produce an asymmetric distribution of temperature anisotropies on large angular scales in the cosmic microwave background (CMB). We use a generalised non-linear δ N formalism to calculate the non-Gaussianity of the primordial density and isocurvature perturbations due to the presence of non-adiabatic, but approximately scale-invariant field fluctuations during multi-field inflation. This local-type non-Gaussianity leads to a correlation between very long wavelength inhomogeneities, larger than our observable horizon, and smaller scale fluctuations in the radiation and matter density. Matter isocurvature perturbations contribute primarily to low CMB multipoles and hence can lead to a hemispherical asymmetry on large angular scales, with negligible asymmetry on smaller scales. In curvaton models, where the matter isocurvature perturbation is partly correlated with the primordial density perturbation, we are unable to obtain a significant asymmetry on large angular scales while respecting current observational constraints on the observed quadrupole. However in the axion model, where the matter isocurvature and primordial density perturbations are uncorrelated, we find it may be possible to obtain a significant asymmetry due to isocurvature modes on large angular scales. Such an isocurvature origin for the hemispherical asymmetry would naturally give rise to a distinctive asymmetry in the CMB polarisation on large scales.

13. Tailored Excitation using Non-Linear B0-Shims

PubMed Central

Duan, Qi; van Gelderen, Peter; Duyn, Jeff

2011-01-01

In high field MRI, RF flip angle inhomogeneity due to wavelength effects can lead to spatial variations in contrast and sensitivity. Improved flip angle homogeneity can be achieved through multi-dimensional excitation, but long RF pulse durations limit practical application. A recent approach to reduce RF pulse duration is based on parallel excitation through multiple RF channels. Here, an alternative approach to shorten multi-dimensional excitation is proposed that makes use of non-linear spatial variations in the stationary (B0) magnetic field during a B0-sensitive excitation pulse. As initial demonstration, the method was applied to 2D gradient echo (GE) MRI of human brain at 7T. Using B0 shims with up to second order spatial dependence, it is demonstrated that root-mean-squared flip angle variation can be reduced from 20% to 11% with RF pulse lengths that are practical for general GE imaging applications without requiring parallel excitation. The method is expected to improve contrast and sensitivity in GE MRI of human brain at high field. PMID:22222623

14. Amplitude relations in non-linear sigma model

Chen, Gang; Du, Yi-Jian

2014-01-01

In this paper, we investigate tree-level scattering amplitude relations in U( N) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell U(1) identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy U(1)-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total 2 m-point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation.

15. Channel Capacity of Non-Linear Transmission Systems

Ellis, Andrew D.; Zhao, Jian

Since their introduction in the late 1970s, the capacity of optical communication links has grown exponentially, fuelled by a series of key innovations including movement between the three telecommunication windows of 850 nm, 1,310 nm and 1,550 nm, distributed feedback laser, erbium-doped fibre amplifiers (EDFAs), dispersion-shifted and dispersion-managed fibre links, external modulation, wavelength division multiplexing, optical switching, forward error correction (FEC), Raman amplification, and most recently, coherent detection, electronic signal processing and optical orthogonal frequency division multiplexing (OFDM). Throughout this evolution, one constant factor has been the use of single-mode optical fibre, whose fundamental principles dated back to the 1800s, when Irish scientist, John Tyndall demonstrated in a lecture to the Royal Society in London that light could be guided through a curved stream of water [1]. Following many developments, including the proposal for waveguides by J.J. Thompson [2], the presentation of detailed calculations for dielectric waveguides by Snitzer [3], the proposal [4] and fabrication [5] of ultra low loss fibres, single-mode fibres were first adopted for non-experimental use in Dorset, UK in 1975, and are still in use today, despite the evolving designs to control chromatic dispersion and non-linearity.

16. A non linear analytical model of switched reluctance machines

Sofiane, Y.; Tounzi, A.; Piriou, F.

2002-06-01

Nowadays, the switched reluctance machine are widely used. To determine their performances and to elaborate control strategy, we generally use the linear analytical model. Unhappily, this last is not very accurate. To yield accurate modelling results, we use then numerical models based on either 2D or 3D Finite Element Method. However, this approach is very expensive in terms of computation time and remains suitable to study the behaviour of eventually a whole device. However, it is not, a priori, adapted to elaborate control strategy for electrical machines. This paper deals with a non linear analytical model in terms of variable inductances. The theoretical development of the proposed model is introduced. Then, the model is applied to study the behaviour of a whole controlled switched reluctance machine. The parameters of the structure are identified from a 2D numerical model. They can also be determined from an experimental bench. Then, the results given by the proposed model are compared to those issue from the 2D-FEM approach and from the classical linear analytical model.

17. Non-linear modulation of short wavelength compressional Alfven eigenmodes

SciTech Connect

Fredrickson, E. D.; Gorelenkov, N. N.; Podesta, M.; Gerhardt, S. P.; Bell, R. E.; Diallo, A.; LeBlanc, B.; Bortolon, A.; Crocker, N. A.; Levinton, F. M.; Yuh, H.

2013-04-15

Most Alfvenic activity in the frequency range between toroidal Alfven eigenmodes and roughly one half of the ion cyclotron frequency on National Spherical Torus eXperiment [Ono et al., Nucl. Fusion 40, 557 (2000)], that is, approximately 0.3 MHz up to Almost-Equal-To 1.2 MHz, are modes propagating counter to the neutral beam ions. These have been modeled as Compressional and Global Alfven Eigenmodes (CAE and GAE) and are excited through a Doppler-shifted cyclotron resonance with the beam ions. There is also a class of co-propagating modes at higher frequency than the counter-propagating CAE and GAE. These modes have been identified as CAE, and are seen mostly in the company of a low frequency, n = 1 kink-like mode. In this paper, we present measurements of the spectrum of these high frequency CAE (hfCAE) and their mode structure. We compare those measurements to a simple model of CAE and present a predator-prey type model of the curious non-linear coupling of the hfCAE and the low frequency kink-like mode.

18. Experimental study of a linear/non-linear flux rope

SciTech Connect

DeHaas, Timothy; Gekelman, Walter; Van Compernolle, Bart

2015-08-15

Flux ropes are magnetic structures of helical field lines, accompanied by spiraling currents. Commonly observed on the solar surface extending into the solar atmosphere, flux ropes are naturally occurring and have been observed by satellites in the near earth and in laboratory environments. In this experiment, a single flux rope (r = 2.5 cm, L = 1100 cm) was formed in the cylindrical, magnetized plasma of the Large Plasma Device (LaPD, L = 2200 cm, r{sub plasma} = 30 cm, n{sub o} = 10{sup 12 }cm{sup −3}, T{sub e} = 4 eV, He). The flux rope was generated by a DC discharge between an electron emitting cathode and anode. This fixes the rope at its source while allowing it to freely move about the anode. At large currents (I > πr{sup 2}B{sub 0}c/2 L), the flux rope becomes helical in structure and oscillates about a central axis. Under varying Alfven speeds and injection current, the transition of the flux rope from stable to kink-unstable was examined. As it becomes non-linear, oscillations in the magnetic signals shift from sinusoidal to Sawtooth-like, associated with elliptical motion of the flux rope; or the signal becomes intermittent as its current density increases.

19. Fitness Effects of Network Non-Linearity Induced by Gene Expression Noise

Ray, Christian; Cooper, Tim; Balazsi, Gabor

2012-02-01

In the non-equilibrium dynamics of growing microbial cells, metabolic enzymes can create non-linearities in metabolite concentration because of non-linear degradation (utilization): an enzyme can saturate in the process of metabolite utilization. Increasing metabolite production past the saturation point then results in an ultrasensitive metabolite response. If the production rate of a metabolite depends on a second enzyme or other protein-mediated process, uncorrelated gene expression noise can thus cause transient metabolite concentration bursts. Such bursts are physiologically unnecessary and may represent a source of selection against the ultrasensitive switch, especially if the fluctuating metabolic intermediate is toxic. Selection may therefore favor correlated gene expression fluctuations for enzymes in the same pathway, such as by same-operon membership in bacteria. Using a modified experimental lac operon system, we are undertaking a combined theoretical-experimental approach to demonstrate that (i) the lac operon has an implicit ultrasensitive switch that we predict is avoided by gene expression correlations induced by same-operon membership; (ii) bacterial growth rates are sensitive to crossing the ultrasensitive threshold. Our results suggest that correlations in intrinsic gene expression noise are exploited by evolution to ameliorate the detrimental effects of nonlinearities in metabolite concentrations.

PubMed

Bonamore, Giorgio; Carmignani, Fabrizio; Colombo, Emilio

2015-02-01

The effect of unemployment on mortality is the object of a lively literature. However, this literature is characterized by sharply conflicting results. We revisit this issue and suggest that the relationship might be non-linear. We use data for 265 territorial units (regions) within 23 European countries over the period 2000-2012 to estimate a multivariate regression of mortality. The estimating equation allows for a quadratic relationship between unemployment and mortality. We control for various other determinants of mortality at regional and national level and we include region-specific and time-specific fixed effects. The model is also extended to account for the dynamic adjustment of mortality and possible lagged effects of unemployment. We find that the relationship between mortality and unemployment is U shaped. In the benchmark regression, when the unemployment rate is low, at 3%, an increase by one percentage point decreases average mortality by 0.7%. As unemployment increases, the effect decays: when the unemployment rate is 8% (sample average) a further increase by one percentage point decreases average mortality by 0.4%. The effect changes sign, turning from negative to positive, when unemployment is around 17%. When the unemployment rate is 25%, a further increase by one percentage point raises average mortality by 0.4%. Results hold for different causes of death and across different specifications of the estimating equation. We argue that the non-linearity arises because the level of unemployment affects the psychological and behavioural response of individuals to worsening economic conditions.

1. Inference of dense spectral reflectance images from sparse reflectance measurement using non-linear regression modeling

Deglint, Jason; Kazemzadeh, Farnoud; Wong, Alexander; Clausi, David A.

2015-09-01

One method to acquire multispectral images is to sequentially capture a series of images where each image contains information from a different bandwidth of light. Another method is to use a series of beamsplitters and dichroic filters to guide different bandwidths of light onto different cameras. However, these methods are very time consuming and expensive and perform poorly in dynamic scenes or when observing transient phenomena. An alternative strategy to capturing multispectral data is to infer this data using sparse spectral reflectance measurements captured using an imaging device with overlapping bandpass filters, such as a consumer digital camera using a Bayer filter pattern. Currently the only method of inferring dense reflectance spectra is the Wiener adaptive filter, which makes Gaussian assumptions about the data. However, these assumptions may not always hold true for all data. We propose a new technique to infer dense reflectance spectra from sparse spectral measurements through the use of a non-linear regression model. The non-linear regression model used in this technique is the random forest model, which is an ensemble of decision trees and trained via the spectral characterization of the optical imaging system and spectral data pair generation. This model is then evaluated by spectrally characterizing different patches on the Macbeth color chart, as well as by reconstructing inferred multispectral images. Results show that the proposed technique can produce inferred dense reflectance spectra that correlate well with the true dense reflectance spectra, which illustrates the merits of the technique.

2. Non-linear finite-amplitude transfer of basal perturbations to a glacier surface

Raymond, M.; Gudmundsson, G. H.; Funk, M.

2003-04-01

Disturbances of surface topography and velocity fields on ice streams can be caused by spatial variations in basal properties. Understanding the relationship between basal and surface perturbations allows estimates of the role of basal control on the dynamics of ice streams to be made. This relationship is well understood for linear medium and small-amplitude basal perturbations where analytical methods can be applied. Studies of the non-linear problems have so far been limited to special cases where semi-analytical methods can be used. Here the transfer of basal variability to a glacier surface is investigated using a numerical model for non-linear ice rheology. Two dimensional steady-state transfer functions for both sinusoidal bedrock undulations and variations in till resistance are determined using Glen's flow law and the full momentum equation system. Amplitude ratios and phase shifts are calculated for wavelengths up to thousand times the mean ice thickness and compared with predictions based on small-amplitude perturbation theory.

3. Non-linearities in hydrological connectivity and microbiological flux in nested catchments - implications of environmental change

Tetzlaff, D.; Soulsby, C.; Birkel, C.; Capell, R.; Speed, M.

2009-12-01

The non-linearities of catchment hydrological behaviour are strongly influenced by the connectivity of hillslopes and channel networks, particularly where overland flow is an important runoff mechanism. Such surface connectivity also controls the flux of microbiological pollutants (coliform bacteria) from areas of live stock grazing which can have serious health implications for potable water supplies. We report a nested catchment study where hydrological and tracer monitoring over a two year period has been coupled with regular sampling for faecal indicator organisms (FIOs). The study has been based in catchments with mixed landuse where FIOs are derived from livestock (sheep and cows) in agricultural land and wild animals (red deer) on moorlands. At all scales (3-1800km2), high levels of FIO were transient and episodic and strongly correlated with periods of high hydrological connectivity. We show how this non-linearity in connectivity can be captured within a dynamic hydrological model. The model was used, along with climate change predictions, to assess possible scenarios of change in connectivity and microbiological contamination in catchments with different land use.

4. Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank

PubMed Central

Bardoscia, Marco; Caccioli, Fabio; Perotti, Juan Ignacio; Vivaldo, Gianna; Caldarelli, Guido

2016-01-01

We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013. PMID:27701457

5. Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank.

PubMed

Bardoscia, Marco; Caccioli, Fabio; Perotti, Juan Ignacio; Vivaldo, Gianna; Caldarelli, Guido

2016-01-01

We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013.

6. Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

7. Tidal propagation and its non-linear characteristics in the Head Bay of Bengal

2017-03-01

The Head Bay of Bengal is highly vulnerable to flooding events caused due to monsoons, cyclones and sea-level rise, owing to its funnel-like shape, high tidal range, presence of numerous river drainage systems, low-lying topography, and shallow bathymetry. Tides dominate the hydrodynamic behaviour and coastal processes in this region and its propagation is quite distinct. The present study uses ADCIRC hydrodynamic model customized for the Head Bay of Bengal, discretized using unstructured finite elements and validated against limited available observations in this data sparse region. The water-level elevations derived from ADCIRC simulation was used to understand the pattern of non-linear tidal propagation with respect to complex coastal geomorphology prevalent in this region. The study finds a marginal amplification of diurnal tide, nearly double amplification of semi-diurnal components, and existence of a degenerate amphidromic point near Meghna delta consistent with previous studies. The spatial and temporal variability of tidal spectral components were examined by applying the techniques of wavelet, harmonic, and time-series analysis at various locations. Maximum amplification of tides occurs at the head of the bay, along a zone enclosing the mouth of tidal inlets; and for regions northward, the tides decay with progressively increasing phase lags. The study signifies dominance of a forced fortnightly tide and tidal asymmetry leading to flood-dominance in the rivers Hooghly, Meghna, and Tetulia. The non-linear properties of tides have been elucidated, and their origin and spatio-temporal variability in these riverine systems were further investigated. Shallow depth and sharp depth gradients were discerned to be the important conditions for the origin of non-linear components. It has been deduced that non-linear tides are generated in regions where propagating tides are accumulated, and amplified in regions where they are funneled. A study of tidal energetics

8. Importance of the spatial heterogeneity in the non-linear response of a small Mediterranean catchment

Ruiz Pérez, Guiomar; Medici, Chiara; Latron, Jérôme; Llorens, Pilar; Gallart, Francesc; Francés, Félix

2013-04-01

It is well known that Mediterranean catchments are characterized by a complex hydrological behavior and strong non-linearities (Ye et al., 1998, Piñol et al., 1999). Therefore, modeling hydrology of a small Mediterranean catchment still represents a great challenge for modelers. To this end, the practical superiority of distributed or semi-distributed approaches over lumped ones remains an open question (see e.g. Loague and Freeze, 1985; Michaud and Sorooshian, 1994; Refsgaard and Knudsen, 1996; Loumagne et al., 1999; Zhang et al., 2003). In fact, a variety of earlier studies have inter-compared distributed versus lumped model simulations reaching opposite conclusions. With the present work, we tried to answer the following research question: Are observed non-linearities due to spatial heterogeneity or to non-linear mechanisms that should be taken into account in a model conceptual scheme? To address these issues the hydrological modeling of the Can Vila catchment (Vallcebre, Eastern Pyrenees, Spain) was carried out. Three hydrological models were considered: two lumped models called LU3 and LU4 (Medici et al., 2008), and a fully distributed model called TETIS (Francés et al., 2007). The TETIS model has the same conceptual schema as the LU3 model at cell-scale and the LU4 model's structure is based on the LU3 model, but it splits the aquifer storage in two tanks: shallow aquifer and deep aquifer. Percolation to the deep aquifer occurs only when soil water content exceeds a threshold value. So, the difference between the LU3 model and the TETIS model is the incorporation of the spatial heterogeneity and the difference between the LU3 model and the LU4 model is an additional strong non-linearity with the threshold which actives the deep percolation. The graphical comparison with the observations and the goodness of fit indexes employed showed that: (1) the LU3 model could not reproduce reasonably well the wet and dry period with the same set of parameters while (2

9. Flight Dynamics Analysis Branch

NASA Technical Reports Server (NTRS)

Stengle, Tom; Flores-Amaya, Felipe

2000-01-01

This report summarizes the major activities and accomplishments carried out by the Flight Dynamics Analysis Branch (FDAB), Code 572, in support of flight projects and technology development initiatives in fiscal year 2000. The report is intended to serve as a summary of the type of support carried out by the FDAB, as well as a concise reference of key accomplishments and mission experience derived from the various mission support roles. The primary focus of the FDAB is to provide expertise in the disciplines of flight dynamics, spacecraft trajectory, attitude analysis, and attitude determination and control. The FDAB currently provides support for missions and technology development projects involving NASA, government, university, and private industry.

10. Non-Linear Slosh Damping Model Development and Validation

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeff

2015-01-01

Propellant tank slosh dynamics are typically represented by a mechanical model of spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control (GN&C) analysis. For a partially-filled smooth wall propellant tank, the critical damping based on classical empirical correlation is as low as 0.05%. Due to this low value of damping, propellant slosh is potential sources of disturbance critical to the stability of launch and space vehicles. It is postulated that the commonly quoted slosh damping is valid only under the linear regime where the slosh amplitude is small. With the increase of slosh amplitude, the critical damping value should also increase. If this nonlinearity can be verified and validated, the slosh stability margin can be significantly improved, and the level of conservatism maintained in the GN&C analysis can be lessened. The purpose of this study is to explore and to quantify the dependence of slosh damping with slosh amplitude. Accurately predicting the extremely low damping value of a smooth wall tank is very challenging for any Computational Fluid Dynamics (CFD) tool. One must resolve thin boundary layers near the wall and limit numerical damping to minimum. This computational study demonstrates that with proper grid resolution, CFD can indeed accurately predict the low damping physics from smooth walls under the linear regime. Comparisons of extracted damping values with experimental data for different tank sizes show very good agreements. Numerical simulations confirm that slosh damping is indeed a function of slosh amplitude. When slosh amplitude is low, the damping ratio is essentially constant, which is consistent with the empirical correlation. Once the amplitude reaches a critical value, the damping ratio becomes a linearly increasing function of the slosh amplitude. A follow-on experiment validated the developed nonlinear damping relationship. This discovery can

11. Non-linear interactions in a boundary layer developing over an array of cubes using stochastic estimation

Blackman, Karin; Perret, Laurent

2016-09-01

In the present work, a boundary layer developing over a rough-wall consisting of staggered cubes with a plan area packing density, λp = 25%, is studied within a wind tunnel using combined particle image velocimetry and hot-wire anemometry to investigate the non-linear interactions between large-scale momentum regions and small-scale structures induced by the presence of the roughness. Due to the highly turbulent nature of the roughness sub-layer and measurement equipment limitations, temporally resolved flow measurements are not feasible, making the conventional filtering methods used for triple decomposition unsuitable for the present work. Thus, multi-time delay linear stochastic estimation is used to decompose the flow into large-scales and small-scales. Analysis of the scale-decomposed skewness of the turbulent velocity (u') shows a significant contribution of the non-linear term uL ' uS ' 2 ¯ , which represents the influence of the large-scales ( uL ' ) onto the small-scales ( uS ' ). It is shown that this non-linear influence of the large-scale momentum regions occurs with all three components of velocity in a similar manner. Finally, through two-point spatio-temporal correlation analysis, it is shown quantitatively that large-scale momentum regions influence small-scale structures throughout the boundary layer through a non-linear top-down mechanism.

12. The Parkinsonian Subthalamic Network: Measures of Power, Linear, and Non-linear Synchronization and their Relationship to L-DOPA Treatment and OFF State Motor Severity

PubMed Central

West, Timothy; Farmer, Simon; Berthouze, Luc; Jha, Ashwani; Beudel, Martijn; Foltynie, Thomas; Limousin, Patricia; Zrinzo, Ludvic; Brown, Peter; Litvak, Vladimir

2016-01-01

In this paper we investigated the dopaminergic modulation of neuronal interactions occurring in the subthalamic nucleus (STN) during Parkinson's disease (PD). We utilized linear measures of local and long range synchrony such as power and coherence, as well as Detrended Fluctuation Analysis for Phase Synchrony (DFA-PS)- a recently developed non-linear method that computes the extent of long tailed autocorrelations present in the phase interactions between two coupled signals. Through analysis of local field potentials (LFPs) taken from the STN we seek to determine changes in the neurodynamics that may underpin the pathophysiology of PD in a group of 12 patients who had undergone surgery for deep brain stimulation. We demonstrate up modulation of alpha-theta (5–12 Hz) band power in response to L-DOPA treatment, whilst low beta band power (15–20 Hz) band-power is suppressed. We also find evidence for significant local connectivity within the region surrounding STN although there was evidence for its modulation via administration of L-DOPA. Further to this we present evidence for a positive correlation between the phase ordering of bilateral STN interactions and the severity of bradykinetic and rigidity symptoms in PD. Although, the ability of non-linear measures to predict clinical state did not exceed standard measures such as beta power, these measures may help identify the connections which play a role in pathological dynamics. PMID:27826233

13. Non-linear elastic properties of the lingual and facial tissues assessed by indentation technique. Application to the biomechanics of speech production.

PubMed

Gerard, J M; Ohayon, J; Luboz, V; Perrier, P; Payan, Y

2005-12-01

This paper aims at characterizing the mechanical behavior of two human anatomical structures, namely the tongue and the cheek. For this, an indentation experiment was provided, by measuring the mechanical response of tongue and cheek tissues removed from the fresh cadaver of a 74 year old woman. Non-linear relationships were observed between the force applied to the tissues and the corresponding displacements. To infer the mechanical constitutive laws from these measurements, a finite element (FE) analysis was provided. This analysis aimed at simulating the indentation experiment. An optimization process was used to determine the FE constitutive laws that provided the non-linear force/displacements observed during the indentation experiments. The tongue constitutive law was used for simulations provided by a 3D FE biomechanical model of the human tongue. This dynamical model was designed to study speech production. Given a set of tongue muscular commands, which levels correspond to the force classically measured during speech production, the FE model successfully simulated the main tongue movements observed during speech data.

14. The Parkinsonian Subthalamic Network: Measures of Power, Linear, and Non-linear Synchronization and their Relationship to L-DOPA Treatment and OFF State Motor Severity.

PubMed

West, Timothy; Farmer, Simon; Berthouze, Luc; Jha, Ashwani; Beudel, Martijn; Foltynie, Thomas; Limousin, Patricia; Zrinzo, Ludvic; Brown, Peter; Litvak, Vladimir

2016-01-01

In this paper we investigated the dopaminergic modulation of neuronal interactions occurring in the subthalamic nucleus (STN) during Parkinson's disease (PD). We utilized linear measures of local and long range synchrony such as power and coherence, as well as Detrended Fluctuation Analysis for Phase Synchrony (DFA-PS)- a recently developed non-linear method that computes the extent of long tailed autocorrelations present in the phase interactions between two coupled signals. Through analysis of local field potentials (LFPs) taken from the STN we seek to determine changes in the neurodynamics that may underpin the pathophysiology of PD in a group of 12 patients who had undergone surgery for deep brain stimulation. We demonstrate up modulation of alpha-theta (5-12 Hz) band power in response to L-DOPA treatment, whilst low beta band power (15-20 Hz) band-power is suppressed. We also find evidence for significant local connectivity within the region surrounding STN although there was evidence for its modulation via administration of L-DOPA. Further to this we present evidence for a positive correlation between the phase ordering of bilateral STN interactions and the severity of bradykinetic and rigidity symptoms in PD. Although, the ability of non-linear measures to predict clinical state did not exceed standard measures such as beta power, these measures may help identify the connections which play a role in pathological dynamics.

15. Inverse modelling of NOx emissions over eastern China: uncertainties due to chemical non-linearity

Gu, Dasa; Wang, Yuhang; Yin, Ran; Zhang, Yuzhong; Smeltzer, Charles

2016-10-01

Satellite observations of nitrogen dioxide (NO2) have often been used to derive nitrogen oxides (NOx = NO + NO2) emissions. A widely used inversion method was developed by Martin et al. (2003). Refinements of this method were subsequently developed. In the context of this inversion method, we show that the local derivative (of a first-order Taylor expansion) is more appropriate than the "bulk ratio" (ratio of emission to column) used in the original formulation for polluted regions. Using the bulk ratio can lead to biases in regions of high NOx emissions such as eastern China due to chemical non-linearity. Inverse modelling using the local derivative method is applied to both GOME-2 and OMI satellite measurements to estimate anthropogenic NOx emissions over eastern China. Compared with the traditional method using bulk ratio, the local derivative method produces more consistent NOx emission estimates between the inversion results using GOME-2 and OMI measurements. The results also show significant changes in the spatial distribution of NOx emissions, especially over high emission regions of eastern China. We further discuss a potential pitfall of using the difference of two satellite measurements to derive NOx emissions. Our analysis suggests that chemical non-linearity needs to be accounted for and that a careful bias analysis is required in order to use the satellite differential method in inverse modelling of NOx emissions.

16. Characterization of atherosclerotic arterial tissue using multimodal non-linear optical microscopy

Cicchi, Riccardo; Matthäus, Christian; Meyer, Tobias; Lattermann, Annika; Dietzek, Benjamin; Brehm, Bernhard R.; Popp, Jürgen; Pavone, Francesco S.

2013-06-01

Atherosclerosis is among the most widespread cardiovascular diseases and one of the leading cause of death in the Western World. Characterization of arterial tissue in atherosclerotic condition is extremely interesting from the diagnostic point of view. Routinely used diagnostic methods, such as histopathological examination, are limited to morphological analysis of the examined tissues, whereas an exhaustive characterization requires a morpho-functional approach. Non-linear microscopy techniques have the potential to bridge this gap by providing morpho-functional information in a label-free way. Here we employed multiple non-linear microscopy techniques, including CARS, TPF, and SHG to provide intrinsic optical contrast from various tissue components in both arterial wall and atherosclerotic plaques. CARS and TPF microscopy were used to respectively image lipid depositions within plaques and elastin in the arterial wall. Cholesterol deposition in the lumen and collagen in the arterial wall were selectively imaged by SHG microscopy and distinguished by forward-backward SHG ratio. Image pattern analysis allowed characterizing collagen organization in different tissue regions. The presented method has the potential to find a stable place in clinical setting as well as to be applied in vivo in the near future.

17. Prediction of formability for non-linear deformation history using generalized forming limit concept (GFLC)

Volk, Wolfram; Suh, Joungsik

2013-12-01

The prediction of formability is one of the most important tasks in sheet metal process simulation. The common criterion in industrial applications is the Forming Limit Curve (FLC). The big advantage of FLCs is the easy interpretation of simulation or measurement data in combination with an ISO standard for the experimental determination. However, the conventional FLCs are limited to almost linear and unbroken strain paths, i.e. deformation histories with non-linear strain increments often lead to big differences in comparison to the prediction of the FLC. In this paper a phenomenological approach, the so-called Generalized Forming Limit Concept (GFLC), is introduced to predict the localized necking on arbitrary deformation history with unlimited number of non-linear strain increments. The GFLC consists of the conventional FLC and an acceptable number of experiments with bi-linear deformation history. With the idea of the new defined "Principle of Equivalent Pre-Forming" every deformation state built up of two linear strain increments can be transformed to a pure linear strain path with the same used formability of the material. In advance this procedure can be repeated as often as necessary. Therefore, it allows a robust and cost effective analysis of beginning instability in Finite Element Analysis (FEA) for arbitrary deformation histories. In addition, the GFLC is fully downwards compatible to the established FLC for pure linear strain paths.

18. Describing Adequacy of cure with maximum hardness ratios and non-linear regression.

PubMed

Bouschlicher, Murray; Berning, Kristen; Qian, Fang

2008-01-01

Knoop Hardness (KH) ratios (HR) > or = 80% are commonly used as criteria for the adequate cure of a composite. These per-specimen HRs can be misleading, as both numerator and denominator may increase concurrently, prior to reaching an asymptotic, top-surface maximum hardness value (H(MAX)). Extended cure times were used to establish H(MAX) and descriptive statistics, and non-linear regression analysis were used to describe the relationship between exposure duration and HR and predict the time required for HR-H(MAX) = 80%. Composite samples 2.00 x 5.00 mm diameter (n = 5/grp) were cured for 10 seconds, 20 seconds, 40 seconds, 60 seconds, 90 seconds, 120 seconds, 180 seconds and 240 seconds in a 2-composite x 2-light curing unit design. A microhybrid (Point 4, P4) or microfill resin (Heliomolar, HM) composite was cured with a QTH or LED light curing unit and then stored in the dark for 24 hours prior to KH testing. Non-linear regression was calculated with: H = (H(MAX)-c)(1-e(-kt)) +c, H(MAX) = maximum hardness (a theoretical asymptotic value), c = constant (t = 0), k = rate constant and t = exposure duration describes the relationship between radiant exposure (irradiance x time) and HRs. Exposure durations for HR-H(MAX) = 80% were calculated. Two-sample t-tests for pairwise comparisons evaluated relative performance of the light curing units for similar surface x composite x exposure (10-90s). A good measure of goodness-of-fit of the non-linear regression, r2, ranged from 0.68-0.95. (mean = 0.82). Microhybrid (P4) exposure to achieve HR-H(MAX = 80% was 21 seconds for QTH and 34 seconds for the LED light curing unit. Corresponding values for microfill (HM) were 71 and 74 seconds, respectively. P4 HR-H(MAX) of LED vs QTH was statistically similar for 10 to 40 seconds, while HM HR-H(MAX) of LED was significantly lower than QTH for 10 to 40 seconds. It was concluded that redefined hardness ratios based on maximum hardness used in conjunction with non-linear regression

19. Superharmonic resonances in a two-dimensional non-linear photonic-crystal nano-electro-mechanical oscillator

Chowdhury, A.; Yeo, I.; Tsvirkun, V.; Raineri, F.; Beaudoin, G.; Sagnes, I.; Raj, R.; Robert-Philip, I.; Braive, R.

2016-04-01

We investigate the non-linear mechanical dynamics of a nano-optomechanical mirror formed by a suspended membrane pierced by a photonic crystal. By applying to the mirror a periodic electrostatic force induced by interdigitated electrodes integrated below the membrane, we evidence superharmonic resonances of our nano-electro-mechanical system; the constant phase shift of the oscillator across the resonance tongues is observed on the onset of principal harmonic and subharmonic excitation regimes.

20. Non-Linear Pattern Formation in Bone Growth and Architecture

PubMed Central

Salmon, Phil

2014-01-01

The three-dimensional morphology of bone arises through adaptation to its required engineering performance. Genetically and adaptively bone travels along a complex spatiotemporal trajectory to acquire optimal architecture. On a cellular, micro-anatomical scale, what mechanisms coordinate the activity of osteoblasts and osteoclasts to produce complex and efficient bone architectures? One mechanism is examined here – chaotic non-linear pattern formation (NPF) – which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others. At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of “group intelligence” exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called “particle swarm optimization” (PSO). This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating “socially” in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites. This represents problem-solving by social intelligence, and could potentially add further realism to in silico computer simulation of bone modeling. What insights has NPF provided to bone biology? One example concerns the genetic disorder juvenile Pagets disease or idiopathic hyperphosphatasia, where the anomalous parallel trabecular architecture characteristic of this pathology is consistent with an NPF paradigm by analogy with known experimental NPF systems. Here, coupling or “feedback” between osteoblasts and osteoclasts is the critical element. This NPF paradigm implies a profound link between bone regulation and its architecture: in bone the architecture is the regulation. The former is the

1. Non-linear pattern formation in bone growth and architecture.

PubMed

Salmon, Phil

2014-01-01

The three-dimensional morphology of bone arises through adaptation to its required engineering performance. Genetically and adaptively bone travels along a complex spatiotemporal trajectory to acquire optimal architecture. On a cellular, micro-anatomical scale, what mechanisms coordinate the activity of osteoblasts and osteoclasts to produce complex and efficient bone architectures? One mechanism is examined here - chaotic non-linear pattern formation (NPF) - which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others. At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of "group intelligence" exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called "particle swarm optimization" (PSO). This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating "socially" in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites. This represents problem-solving by social intelligence, and could potentially add further realism to in silico computer simulation of bone modeling. What insights has NPF provided to bone biology? One example concerns the genetic disorder juvenile Pagets disease or idiopathic hyperphosphatasia, where the anomalous parallel trabecular architecture characteristic of this pathology is consistent with an NPF paradigm by analogy with known experimental NPF systems. Here, coupling or "feedback" between osteoblasts and osteoclasts is the critical element. This NPF paradigm implies a profound link between bone regulation and its architecture: in bone the architecture is the regulation. The former is the emergent

2. Linear and non-linear bias: predictions versus measurements

Hoffmann, K.; Bel, J.; Gaztañaga, E.

2017-02-01

We study the linear and non-linear bias parameters which determine the mapping between the distributions of galaxies and the full matter density fields, comparing different measurements and predictions. Associating galaxies with dark matter haloes in the Marenostrum Institut de Ciències de l'Espai (MICE) Grand Challenge N-body simulation, we directly measure the bias parameters by comparing the smoothed density fluctuations of haloes and matter in the same region at different positions as a function of smoothing scale. Alternatively, we measure the bias parameters by matching the probability distributions of halo and matter density fluctuations, which can be applied to observations. These direct bias measurements are compared to corresponding measurements from two-point and different third-order correlations, as well as predictions from the peak-background model, which we presented in previous papers using the same data. We find an overall variation of the linear bias measurements and predictions of ∼5 per cent with respect to results from two-point correlations for different halo samples with masses between ∼1012and1015 h-1 M⊙ at the redshifts z = 0.0 and 0.5. Variations between the second- and third-order bias parameters from the different methods show larger variations, but with consistent trends in mass and redshift. The various bias measurements reveal a tight relation between the linear and the quadratic bias parameters, which is consistent with results from the literature based on simulations with different cosmologies. Such a universal relation might improve constraints on cosmological models, derived from second-order clustering statistics at small scales or higher order clustering statistics.

3. Effects of Initial Geometric Imperfections On the Non-Linear Response of the Space Shuttle Superlightweight Liquid-Oxygen Tank

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H., Jr.

2002-01-01

The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.

4. Random forests in non-invasive sensorimotor rhythm brain-computer interfaces: a practical and convenient non-linear classifier.

PubMed

Steyrl, David; Scherer, Reinhold; Faller, Josef; Müller-Putz, Gernot R

2016-02-01

There is general agreement in the brain-computer interface (BCI) community that although non-linear classifiers can provide better results in some cases, linear classifiers are preferable. Particularly, as non-linear classifiers often involve a number of parameters that must be carefully chosen. However, new non-linear classifiers were developed over the last decade. One of them is the random forest (RF) classifier. Although popular in other fields of science, RFs are not common in BCI research. In this work, we address three open questions regarding RFs in sensorimotor rhythm (SMR) BCIs: parametrization, online applicability, and performance compared to regularized linear discriminant analysis (LDA). We found that the performance of RF is constant over a large range of parameter values. We demonstrate - for the first time - that RFs are applicable online in SMR-BCIs. Further, we show in an offline BCI simulation that RFs statistically significantly outperform regularized LDA by about 3%. These results confirm that RFs are practical and convenient non-linear classifiers for SMR-BCIs. Taking into account further properties of RFs, such as independence from feature distributions, maximum margin behavior, multiclass and advanced data mining capabilities, we argue that RFs should be taken into consideration for future BCIs.

5. Structural dynamics analysis

NASA Technical Reports Server (NTRS)

Housner, J. M.; Anderson, M.; Belvin, W.; Horner, G.

1985-01-01

Dynamic analysis of large space antenna systems must treat the deployment as well as vibration and control of the deployed antenna. Candidate computer programs for deployment dynamics, and issues and needs for future program developments are reviewed. Some results for mast and hoop deployment are also presented. Modeling of complex antenna geometry with conventional finite element methods and with repetitive exact elements is considered. Analytical comparisons with experimental results for a 15 meter hoop/column antenna revealed the importance of accurate structural properties including nonlinear joints. Slackening of cables in this antenna is also a consideration. The technology of designing actively damped structures through analytical optimization is discussed and results are presented.

6. Vibration and chaos control of non-linear torsional vibrating systems

El-Bassiouny, A. F.

2006-07-01

Vibration of a mechanical system is often an undesirable phenomenon, as it may cause damage, disturbance, discomfort and, sometimes, destruction of systems and structures. To reduce vibration, many methods can be used. The most famous method is using dynamic absorbers or dampers. In the present work, a non-linear elastomeric damper or absorber is used to control the torsional vibrations of the crankshaft in internal combustion engines, when subjected to both external and parametric excitation torques. The multiple time scale perturbation method is applied to determine the equations governing the modulation of both amplitudes and phases of the crankshaft and the absorber. These equations are used to determine the steady-state amplitudes and system stability. Numerical integration of the basic equations is applied to investigate the effects of the different parameters on system behavior. A comparison is made with the available published work. Some recommendations are given at the end of the work.

7. Relativistic cosmic ray spectra in the full non-linear theory of shock acceleration

NASA Technical Reports Server (NTRS)

Eichler, D.; Ellison, D. C.

1985-01-01

The non-linear theory of shock acceleration was generalized to include wave dynamics. In the limit of rapid wave damping, it is found that a finite ave velocity tempers the acceleration of high Mach number shocks and limits the maximum compression ratio even when energy loss is important. For a given spectrum, the efficiency of relativistic particle production is essentially independent of v sub Ph. For the three families shown, the percentage of kinetic energy flux going into relativistic particles is (1) 72%, 2) 44%, and (3) 26% (this includes the energy loss at the upper energy cuttoff). Even small v sub ph, typical of the HISM, produce quasi-universal spectra that depend only weakly on the acoustic Mach number. These spectra should be close enough to e(-2) to satisfy cosmic ray source requirements.

8. Scalar field-perfect fluid correspondence and non-linear perturbation equations

SciTech Connect

Mainini, Roberto

2008-07-15

The properties of dynamical dark energy (DE) and, in particular, the possibility that it can form or contribute to stable inhomogeneities have been widely debated in recent literature, and also in association with a possible coupling between DE and dark matter (DM). In order to clarify this issue, in this paper we present a general framework for the study of the non-linear phases of structure formation, showing the equivalence of two possible descriptions of DE: a scalar field {phi} self-interacting through a potential V ({phi}) and a perfect fluid with an assigned negative equation of state w(a). This enables us to show that, in the presence of coupling, the mass of DE quanta may increase where large DM condensations are present, with the result that also DE may be involved in the clustering process.

9. Visualizing the spatial gene expression organization in the brain through non-linear similarity embeddings.

PubMed

Mahfouz, Ahmed; van de Giessen, Martijn; van der Maaten, Laurens; Huisman, Sjoerd; Reinders, Marcel; Hawrylycz, Michael J; Lelieveldt, Boudewijn P F

2015-02-01

The Allen Brain Atlases enable the study of spatially resolved, genome-wide gene expression patterns across the mammalian brain. Several explorative studies have applied linear dimensionality reduction methods such as Principal Component Analysis (PCA) and classical Multi-Dimensional Scaling (cMDS) to gain insight into the spatial organization of these expression patterns. In this paper, we describe a non-linear embedding technique called Barnes-Hut Stochastic Neighbor Embedding (BH-SNE) that emphasizes the local similarity structure of high-dimensional data points. By applying BH-SNE to the gene expression data from the Allen Brain Atlases, we demonstrate the consistency of the 2D, non-linear embedding of the sagittal and coronal mouse brain atlases, and across 6 human brains. In addition, we quantitatively show that BH-SNE maps are superior in their separation of neuroanatomical regions in comparison to PCA and cMDS. Finally, we assess the effect of higher-order principal components on the global structure of the BH-SNE similarity maps. Based on our observations, we conclude that BH-SNE maps with or without prior dimensionality reduction (based on PCA) provide comprehensive and intuitive insights in both the local and global spatial transcriptome structure of the human and mouse Allen Brain Atlases.

10. Non-linear Resistivity of a Two-Dimensional Electron Gas in a Magnetic Field

Vavilov, Maxim G.; Aleiner, Igor L.; Glazman, Leonid I.

2007-03-01

We develop a theory of nonlinear response to an electric field of a two-dimensional electron gas (2DEG) placed in a classically strong magnetic field. The latter leads to a non-linear current-voltage characteristic at a relatively weak electric field. The origin of the non-linearity is two-fold: the formation of a non-equilibrium electron distribution function, and the geometrical resonance in the inter-Landau-levels transitions rates. We find the dependence of the current-voltage characteristics on the electron relaxation rates in the 2DEG. Our results can be applied for analysis of measurements at low [1] and high [2,3] current densities. [1] J. Zhang, S. Vitkalov, A. A. Bykov, A. K. Kalagin and A. K. Bakarov, cond-mat/0607741. [2] C. L. Yang, J. Zhang, R. R. Du, J. A. Simmons and J. L. Reno, Phys. Rev. Lett. 89, 076801 (2002). [3] W. Zhang, H. -S. Chiang, M. A. Zudov, L. N. Pfeiffer and K. W. West, cond-mat/0608727.

11. Haematite natural crystals: non-linear initial susceptibility at low temperature

Guerrero-Suarez, S.; Martín-Hernández, F.

2016-06-01

Several works have reported that haematite has non-linear initial susceptibility at room temperature, like pyrrhotite or titanomagnetite, but there is no explanation for the observed behaviours yet. This study sets out to determine which physical property (grain size, foreign cations content and domain walls displacements) controls the initial susceptibility. The performed measurements include microprobe analysis to determine magnetic phases different to haematite; initial susceptibility (300 K); hysteresis loops, SIRM and backfield curves at 77 and 300 K to calculate magnetic parameters and minor loops at 77 K, to analyse initial susceptibility and magnetization behaviours below Morin transition. The magnetic moment study at low temperature is completed with measurements of zero field cooled-field cooled and AC susceptibility in a range from 5 to 300 K. The minor loops show that the non-linearity of initial susceptibility is closely related to Barkhausen jumps. Because of initial magnetic susceptibility is controlled by domain structure it is difficult to establish a mathematical model to separate magnetic subfabrics in haematite-bearing rocks.

12. Cerebral autoregulation of preterm neonates--a non-linear control system?

PubMed

Zernikow, B; Michel, E; Kohlmann, G; Steck, J; Schmitt, R M; Jorch, G

1994-05-01

The low frequency cerebral blood flow velocity (CBFV) oscillations in neonates are commonly attributed to an under-dampened immature linear type cerebral autoregulation, and the 'instability' is regarded as causative for peri-intraventricular haemorrhage/periventricular leukomalacia. In contrast, oscillations susceptible to frequency entrainment are a fundamental part of the stable function of non-linear control systems. To classify the autoregulation an observational study was done on the relationship between CBFV oscillations, heart rate variability, and artificial ventilation. In 10 preterm neonates (gestational age 26 to 35 weeks) we serially Doppler traced arterial CBFV continuously for 12 minutes between days 1 and 49 of life. The individual time series of CBFV and heart rate were subjected to spectral analysis. Forty six of 47 tracings showed significant low frequency CBFV oscillations. Low frequency heart rate oscillations were not a prerequisite thereof. All patients with < 30% of total power in the low frequency band of CBFV oscillations were on the ventilator. Three of them demonstrated a shift of spectral power from low frequency to a frequency equal or harmonic to the ventilator rate indicating entrainment. The findings of CBFV oscillations combined with entrainment classify the autoregulation as a non-linear system. It is suggested that entrainment by periodic high amplitude stimuli might challenge the regulatory capacity to its limits thus increasing the risk for cerebral damage.

13. Non-linear blending of dual-energy CT data improves depiction of late iodine enhancement in chronic myocardial infarction.

PubMed

Wichmann, Julian L; Hu, Xiaohan; Kerl, J Matthias; Schulz, Boris; Bodelle, Boris; Frellesen, Claudia; Lehnert, Thomas; Vogl, Thomas J; Bauer, Ralf W

2014-08-01

To compare non-linear and linear blending of cardiac dual-energy computed tomography (DECT) for optimal visualization of late iodine enhancement (LIE) in patients with chronic myocardial infarction (CMI). LIE-DECT data from 20 patients with known CMI were retrospectively analyzed. Images were reconstructed using non-linear blending center and width settings in the range of 0-500. Linear blending was performed with weighting factors 0.8 (80% 100 kV, 20% 140 kV), 0.6 and 0.3. 100-/140-kV data and blended images were analyzed. Contrast and percentage signal differences between infarcted and healthy myocardium and the left ventricle blood pool were computed. Statistical analysis was performed using repeated-measures analysis of variance and post hoc t tests. Non-linear blending showed the highest signal differences for all contrasts and analyses. Repeated-measures ANOVA tests confirmed the statistical differences between the investigated blending techniques (P < 0.01). Paired-samples post hoc t tests confirmed the significance of these results (P < 0.04). The ideal non-linear blending settings for best demarcation of CMI from healthy myocardium were a center of 65.8 ± 23.2 and a width of 0.0 ± 0.0. Non-linear blending of LIE-DECT improves display of LIE in patients with CMI in comparison with linear blending and non-post-processed image data from 100-/140-kV.

14. Non-linear optical flow cytometry using a scanned, Bessel beam light-sheet.

PubMed

Collier, Bradley B; Awasthi, Samir; Lieu, Deborah K; Chan, James W

2015-05-29

Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers.

15. A comparison/validation of a fractional derivative model with an empirical model of non-linear shock waves in swelling shales

Droghei, Riccardo; Salusti, Ettore

2013-04-01

Control of drilling parameters, as fluid pressure, mud weight, salt concentration is essential to avoid instabilities when drilling through shale sections. To investigate shale deformation, fundamental for deep oil drilling and hydraulic fracturing for gas extraction ("fracking"), a non-linear model of mechanic and chemo-poroelastic interactions among fluid, solute and the solid matrix is here discussed. The two equations of this model describe the isothermal evolution of fluid pressure and solute density in a fluid saturated porous rock. Their solutions are quick non-linear Burger's solitary waves, potentially destructive for deep operations. In such analysis the effect of diffusion, that can play a particular role in fracking, is investigated. Then, following Civan (1998), both diffusive and shock waves are applied to fine particles filtration due to such quick transients , their effect on the adjacent rocks and the resulting time-delayed evolution. Notice how time delays in simple porous media dynamics have recently been analyzed using a fractional derivative approach. To make a tentative comparison of these two deeply different methods,in our model we insert fractional time derivatives, i.e. a kind of time-average of the fluid-rocks interactions. Then the delaying effects of fine particles filtration is compared with fractional model time delays. All this can be seen as an empirical check of these fractional models.

16. Advanced Non-Linear Control Algorithms Applied to Design Highly Maneuverable Autonomous Underwater Vehicles (AUVs)

DTIC Science & Technology

2007-08-01

Advanced non- linear control algorithms applied to design highly maneuverable Autonomous Underwater Vehicles (AUVs) Vladimir Djapic, Jay A. Farrell...hierarchical such that an ”inner loop” non- linear controller (outputs the appropriate thrust values) is the same for all mission scenarios while a...library of ”outer-loop” non- linear controllers are available to implement specific maneuvering scenarios. On top of the outer-loop is the mission planner

17. Dynamic Contingency Analysis Tool

SciTech Connect

2016-01-14

The Dynamic Contingency Analysis Tool (DCAT) is an open-platform and publicly available methodology to help develop applications that aim to improve the capabilities of power system planning engineers to assess the impact and likelihood of extreme contingencies and potential cascading events across their systems and interconnections. Outputs from the DCAT will help find mitigation solutions to reduce the risk of cascading outages in technically sound and effective ways. The current prototype DCAT implementation has been developed as a Python code that accesses the simulation functions of the Siemens PSS�E planning tool (PSS/E). It has the following features: It uses a hybrid dynamic and steady-state approach to simulating the cascading outage sequences that includes fast dynamic and slower steady-state events. It integrates dynamic models with protection scheme models for generation, transmission, and load. It models special protection systems (SPSs)/remedial action schemes (RASs) and automatic and manual corrective actions. Overall, the DCAT attempts to bridge multiple gaps in cascading-outage analysis in a single, unique prototype tool capable of automatically simulating and analyzing cascading sequences in real systems using multiprocessor computers.While the DCAT has been implemented using PSS/E in Phase I of the study, other commercial software packages with similar capabilities can be used within the DCAT framework.

18. Control methods to improve non-linear HVAC system operations

cascade control method is applied to improve the stability of cooling coil valve operation in single zone air handling unit systems, and return fan speed for building pressure control. The system dynamic response is studied using root locus analysis. It was found that the cascade control improved the stability range in two applications under consideration and made the HVAC feedback control loops more robust and adaptive.

19. Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

SciTech Connect

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. The goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.

20. Peculiar velocities into the next generation: cosmological parameters from large surveys without bias from non-linear structure

Abate, Alexandra; Bridle, Sarah; Teodoro, Luis F. A.; Warren, Michael S.; Hendry, Martin

2008-10-01

We investigate methods to best estimate the normalization of the mass density fluctuation power spectrum (σ8) using peculiar velocity data from a survey like the six-degree Field Galaxy Velocity Survey (6dFGSv). We focus on two potential problems: (i) biases from non-linear growth of structure and (ii) the large number of velocities in the survey. Simulations of ΛCDM-like models are used to test the methods. We calculate the likelihood from a full covariance matrix of velocities averaged in grid cells. This simultaneously reduces the number of data points and smoothes out non-linearities which tend to dominate on small scales. We show how the averaging can be taken into account in the predictions in a practical way, and show the effect of the choice of cell size. We find that a cell size can be chosen that significantly reduces the non-linearities without significantly increasing the error bars on cosmological parameters. We compare our results with those from a principal components analysis following Watkins et al. and Feldman et al. to select a set of optimal moments constructed from linear combinations of the peculiar velocities that are least sensitive to the non-linear scales. We conclude that averaging in grid cells performs equally well. We find that for a survey such as 6dFGSv we can estimate σ8 with less than 3 per cent bias from non-linearities. The expected error on σ8 after marginalizing over Ωm is approximately 16 per cent.

1. Neural network-based robust actuator fault diagnosis for a non-linear multi-tank system.

PubMed

Mrugalski, Marcin; Luzar, Marcel; Pazera, Marcin; Witczak, Marcin; Aubrun, Christophe

2016-03-01

The paper is devoted to the problem of the robust actuator fault diagnosis of the dynamic non-linear systems. In the proposed method, it is assumed that the diagnosed system can be modelled by the recurrent neural network, which can be transformed into the linear parameter varying form. Such a system description allows developing the designing scheme of the robust unknown input observer within H∞ framework for a class of non-linear systems. The proposed approach is designed in such a way that a prescribed disturbance attenuation level is achieved with respect to the actuator fault estimation error, while guaranteeing the convergence of the observer. The application of the robust unknown input observer enables actuator fault estimation, which allows applying the developed approach to the fault tolerant control tasks.

2. A Non-Linear Approach to Spacecraft Trajectory Control in the Vicinity of a Libration Point

NASA Technical Reports Server (NTRS)

Luquette, Richard J.; Sanner, Robert M.

2001-01-01

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, station-keeping, control algorithm for trajectories in the vicinity of a libration point. The control law guarantees exponential convergence, based on a Lyaponov analysis. Controller performance is evaluated using FreeFlyer(R) and MATLAB(R) for a spacecraft stationed near the L2 libration point in the Earth-Moon system, tracking a pre-defined reference trajectory. Evaluation metrics are fuel usage and tracking accuracy. Simulation results are compared with a linear-based controller for a spacecraft tracking the same reference trajectory. Although the analysis is framed in the context of station-keeping, the control algorithm is equally applicable to a formation flying problem with an appropriate definition of the reference trajectory.

3. Effect of cellulosic fiber scale on linear and non-linear mechanical performance of starch-based composites.

PubMed

Karimi, Samaneh; Abdulkhani, Ali; Tahir, Paridah Md; Dufresne, Alain

2016-10-01

Cellulosic nanofibers (NFs) from kenaf bast were used to reinforce glycerol plasticized thermoplastic starch (TPS) matrices with varying contents (0-10wt%). The composites were prepared by casting/evaporation method. Raw fibers (RFs) reinforced TPS films were prepared with the same contents and conditions. The aim of study was to investigate the effects of filler dimension and loading on linear and non-linear mechanical performance of fabricated materials. Obtained results clearly demonstrated that the NF-reinforced composites had significantly greater mechanical performance than the RF-reinforced counterparts. This was attributed to the high aspect ratio and nano dimension of the reinforcing agents, as well as their compatibility with the TPS matrix, resulting in strong fiber/matrix interaction. Tensile strength and Young's modulus increased by 313% and 343%, respectively, with increasing NF content from 0 to 10wt%. Dynamic mechanical analysis (DMA) revealed an elevational trend in the glass transition temperature of amylopectin-rich domains in composites. The most eminent record was +18.5°C shift in temperature position of the film reinforced with 8% NF. This finding implied efficient dispersion of nanofibers in the matrix and their ability to form a network and restrict mobility of the system.

4. Info-gap robustness for the correlation of tests and simulations of a non-linear transient

Hemez, François M.; Ben-Haim, Yakov

2004-11-01

An alternative to the theory of probability is applied to the problem of assessing the robustness, to uncertainty in model parameters, of the correlation between measurements and computer simulations. The analysis is based on the theory of information-gap uncertainty, which models the clustering of uncertain events in families of nested sets instead of assuming a probability structure. The system investigated is the propagation of a transient impact through a layer of hyper-elastic material. The two sources of non-linearity are (1) the softening of the constitutive law representing the hyper-elastic material and (2) the contact dynamics at the interface between metallic and crushable materials. The robustness of the correlation between test and simulation, to sources of parameter variability, is first studied to identify the parameters of the model that significantly influence the agreement between measurements and predictions. Model updating under non-probabilistic uncertainty is then illustrated, based on two complementary immunity functions: the robustness to uncertainty and the opportunity from uncertainty. Finally an info-gap model is embedded within a probability density function to represent uncertainty in the knowledge of the model's parameters and their correlation structure. Although computationally expensive, it is demonstrated that info-gap reasoning can greatly enhance our understanding of a moderately complex system when the theory of probability cannot be applied due to insufficient information.

5. Structural, optical and dielectric studies of novel non-linear Bisglycine Lithium Nitrate piezoelectric single crystal

Dalal, Jyoti; Sinha, Nidhi; Kumar, Binay

2014-11-01

The novel non-linear semiorganic Bisglycine Lithium Nitrate (BGLiN) single crystals were grown by slow evaporation technique. The structural analysis revealed that it belongs to non-centrosymmetric orthorhombic structure. The presence of various functional groups in the grown crystal was confirmed by FTIR and Raman analysis. Surface morphology of the grown crystal was studied by scanning electron microscopy. The optical studies show that crystal has good transmittance (more than 80%) in the entire visible region and a wide band gap (5.17 eV). The optical constants such as extinction coefficient (K), the reflectance (R) and refractive index (n) as a function of photon energy were calculated from the optical measurements. With the help of these optical constants the electric susceptibility (χc) and both the real (εr) and imaginary (εi) parts of the dielectric constants were also calculated which are required to develop optoelectronic devices. In photoluminescence studies, a broad emission band centered at 404 nm was found in addition to a small band at 352 nm. A broad transition (from 29 to 33 °C) was observed with low dielectric constant value. A high piezoelectric charge coefficient (d33) of 14 pC/N was measured at room temperature which implies its usefulness for various sensor applications. The second harmonic generation efficiency of crystal was found to be 1.5 times to that of KDP. From thermo gravimetric analysis and differential thermal analysis, thermal stability and melting point (246 °C) were investigated. The dielectric behavior, optical characterization, piezoelectric behavior and the non-linear optical properties of the Bisglycine Lithium Nitrate single crystals were reported for the first time which established the usefulness of these crystals for various piezo- and opto-electronics applications.

6. Non-linear education gradient across the nutrition transition: mothers’ overweight and the population education transition

PubMed Central

Salinas, Daniel; Baker, David P

2015-01-01

7. Non-linear relativistic contributions to the cosmological weak-lensing convergence

SciTech Connect

Andrianomena, Sambatra; Clarkson, Chris; Patel, Prina; Umeh, Obinna; Uzan, Jean-Philippe E-mail: chris.clarkson@gmail.com E-mail: umeobinna@gmail.com

2014-06-01

Relativistic contributions to the dynamics of structure formation come in a variety of forms, and can potentially give corrections to the standard picture on typical scales of 100 Mpc. These corrections cannot be obtained by Newtonian numerical simulations, so it is important to accurately estimate the magnitude of these relativistic effects. Density fluctuations couple to produce a background of gravitational waves, which is larger than any primordial background. A similar interaction produces a much larger spectrum of vector modes which represent the frame-dragging rotation of spacetime. These can change the metric at the percent level in the concordance model at scales below the equality scale. Vector modes modify the lensing of background galaxies by large-scale structure. This gives in principle the exciting possibility of measuring relativistic frame dragging effects on cosmological scales. The effects of the non-linear tensor and vector modes on the cosmic convergence are computed and compared to first-order lensing contributions from density fluctuations, Doppler lensing, and smaller Sachs-Wolfe effects. The lensing from gravitational waves is negligible so we concentrate on the vector modes. We show the relative importance of this for future surveys such as Euclid and SKA. We find that these non-linear effects only marginally affect the overall weak lensing signal so they can safely be neglected in most analyses, though are still much larger than the linear Sachs-Wolfe terms. The second-order vector contribution can dominate the first-order Doppler lensing term at moderate redshifts and are actually more important for survey geometries like the SKA.

8. Non-Linear Cosmological Power Spectra in Real and Redshift Space

NASA Technical Reports Server (NTRS)

Taylor, A. N.; Hamilton, A. J. S.

1996-01-01

We present an expression for the non-linear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self-gravitating fields. Some exact solutions are found for power-law initial spectra. We have extended this analysis into red-shift space and found a solution for the non-linear, anisotropic redshift-space power spectrum in the limit of plane-parallel redshift distortions. The quadrupole-to-monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, beta. The point of zero-crossing of the quadrupole, kappa(sub o), is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of N-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole-to-monopole ratio found in the merged QDOT plus 1.2-Jy-IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta greater than 0.5 at the 95 percent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n = -2 un the translinear regime. The zero-crossing scale of the quadrupole is k(sub 0) = 0.5 +/- 0.1 h Mpc(exp -1) and from this we infer that the amplitude of clustering is sigma(sub 8) = 0.7 +/- 0.05. We suggest that the success of this model is due to non-linear redshift-space effects arising from infall on to caustic and is not dominated by virialized cluster cores

9. Comparison of linear and non-linear blade model predictions in Bladed to measurement data from GE 6MW wind turbine

Collier, W.; Milian Sanz, J.

2016-09-01

10. Geometric phase in the Hopf bundle and the stability of non-linear waves

Grudzien, Colin J.; Bridges, Thomas J.; Jones, Christopher K. R. T.

2016-11-01

We develop a stability index for the traveling waves of non-linear reaction-diffusion equations using the geometric phase induced on the Hopf bundle S 2 n - 1 ⊂Cn. This can be viewed as an alternative formulation of the winding number calculation of the Evans function, whose zeros correspond to the eigenvalues of the linearization of reaction-diffusion operators about the wave. The stability of a traveling wave can be determined by the existence of eigenvalues of positive real part for the linear operator. Our method of geometric phase for locating and counting eigenvalues is inspired by the numerical results in Way's Dynamics in the Hopf bundle, the geometric phase and implications for dynamical systems Way (2009). We provide a detailed proof of the relationship between the phase and eigenvalues for dynamical systems defined on C2 and sketch the proof of the method of geometric phase for Cn and its generalization to boundary-value problems. Implementing the numerical method, modified from Way (2009), we conclude with open questions inspired from the results.

11. Wave Driven Non-linear Flow Oscillator for the 22-Year Solar Cycle

NASA Technical Reports Server (NTRS)

Mayr, Hans G.; Wolff, Charles L.; Hartle, Richard E.; Einaudi, Franco (Technical Monitor)

2000-01-01

In the Earth's atmosphere, a zonal flow oscillation is observed with periods between 20 and 32 months, the Quasi Biennial Oscillation. This oscillation does not require external time dependent forcing but is maintained by non-linear wave momentum deposition. It is proposed that such a mechanism also drives long-period oscillations in planetary and stellar interiors. We apply this mechanism to generate a flow oscillation for the 22-year solar cycle. The oscillation would occur just below the convective envelope where waves can propagate. Using scale analysis, we present results from a simplified model that incorporates Hines' gravity wave parameterization. Wave amplitudes less than 10 m/s can produce reversing zonal flows of 25 m/s that should be sufficient to generate a corresponding oscillation in the poloidal magnetic field. Low buoyancy frequency and the associated increase in turbulence help to produce the desired oscillation period of the flow.

12. Synthesis of monodispersed palladium nanoparticles using tannic acid and its optical non-linearity

Meena Kumari, M.; Aromal, S. Aswathy; Philip, Daizy

2013-02-01

Palladium nanoparticles with average size 11.3 nm have been synthesized via a one-step reduction and capping method. This colloidal route using tannic acid does not require any other surfactant or capping agent to direct the growth of palladium nanoparticles. The effect of temperature on the conversion of Pd2+ ion to Pd0 is investigated. The growth process of nanoparticles is monitored using UV-visible spectra. The morphology and phase transformation have been confirmed by transmission electron microscopy and X-ray diffraction. An attempt to reveal the capping mechanism of tannic acid is done through FTIR analysis. The optical non-linearity of the samples was studied using open aperture Z-scan technique. The significance of this protocol for the generation of environmentally benign palladium nanoparticles lies mainly in its simplicity and cost effectiveness.

13. Non-linear characteristics and long-range correlations in Asian stock markets

Jiang, J.; Ma, K.; Cai, X.

2007-05-01

We test several non-linear characteristics of Asian stock markets, which indicates the failure of efficient market hypothesis and shows the essence of fractal of the financial markets. In addition, by using the method of detrended fluctuation analysis (DFA) to investigate the long range correlation of the volatility in the stock markets, we find that the crossover phenomena exist in the results of DFA. Further, in the region of small volatility, the scaling behavior is more complicated; in the region of large volatility, the scaling exponent is close to 0.5, which suggests the market is more efficient. All these results may indicate the possibility of characteristic multifractal scaling behaviors of the financial markets.

14. Non-linear interactions of plasma waves in the context of solar particle acceleration

Gallegos-Cruz, A.; Perez-Peraza, J.

2001-08-01

Stochastic particle acceleration in plasmas by means of MHD turbulence in-volves a wide range of alternatives according to, the specific wave mode, the frequency regime of the turbulence, the kind of particles to be accelerated, the assumed plasma model and so on. At present most of the alternatives have been studied with relatively deepness, though some features are not yet com-pletely understood. One of them is the delimitation of the real importance of non-lineal effects of turbulence waves in the process of particle acceleration. In this work we analyse such effects taking into account the temporal evolution of the turbulence. For illustration we exemplify our analysis with the fast MHD mode. Our results show that in some specific stages of the turbulence evolu-tion, non-linear interactions have important effects in the process of particle acceleration.

15. Computational Modelling and Optimal Control of Ebola Virus Disease with non-Linear Incidence Rate

Takaidza, I.; Makinde, O. D.; Okosun, O. K.

2017-03-01

The 2014 Ebola outbreak in West Africa has exposed the need to connect modellers and those with relevant data as pivotal to better understanding of how the disease spreads and quantifying the effects of possible interventions. In this paper, we model and analyse the Ebola virus disease with non-linear incidence rate. The epidemic model created is used to describe how the Ebola virus could potentially evolve in a population. We perform an uncertainty analysis of the basic reproductive number R 0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time control interventions (education, vaccination, quarantine and safe handling) and provide the cost effective combination of the interventions.

16. Stochastic Estimation and Non-Linear Wall-Pressure Sources in a Separating/Reattaching Flow

NASA Technical Reports Server (NTRS)

Naguib, A.; Hudy, L.; Humphreys, W. M., Jr.

2002-01-01

Simultaneous wall-pressure and PIV measurements are used to study the conditional flow field associated with surface-pressure generation in a separating/reattaching flow established over a fence-with-splitter-plate geometry. The conditional flow field is captured using linear and quadratic stochastic estimation based on the occurrence of positive and negative pressure events in the vicinity of the mean reattachment location. The results shed light on the dominant flow structures associated with significant wall-pressure generation. Furthermore, analysis based on the individual terms in the stochastic estimation expansion shows that both the linear and non-linear flow sources of the coherent (conditional) velocity field are equally important contributors to the generation of the conditional surface pressure.

17. Non-linear signal detection improvement by radiation damping in single-pulse NMR spectra.

PubMed

Schlagnitweit, Judith; Morgan, Steven W; Nausner, Martin; Müller, Norbert; Desvaux, Hervé

2012-02-01

When NMR lines overlap and at least one of them is affected by radiation damping, the resonance line shapes of all lines are no longer Lorentzian. We report the appearance of narrow signal distortions, which resemble hole-burnt spectra. This new experimental phenomenon facilitates the detection of tiny signals hidden below the main resonance. Theoretical analysis based on modified Maxwell-Bloch equations shows that the presence of strong transverse magnetization creates a feedback through the coil, which influences the magnetization of all spins with overlapping resonance lines. In the time domain this leads to cross-precession terms between magnetization densities, which ultimately cause non-linear behavior. Numerical simulations corroborate this interpretation.

18. Non-linear state transitions in neural systems: from ion to networks

Liljenström, Hans; Braun, Hans; Århem, Peter

2001-03-01

The activity of neural systems often seems to depend on non-linear threshold effects, where microscopic fluctuations may cause rapid and large effects at a macroscopic level. Single ion channels are found to be capable of eliciting action potentials in small hippocampal interneurons. Computer simulations show that spontaneous neuronal activity can induce global oscillations in networks of neurons. For a small change in some parameter values, the global activity instead becomes chaotic-like. We use experimental as well as computational methods to investigate mechanisms by which neural systems can amplify weak signals and control the system at a larger scale. We also investigate if there are non-random processes in ion channel kinetics and use topological methods for the analysis, also of computer simulations.

19. In vitro exposure: Linear and non-linear thermodynamic events in Petri dishes.

PubMed

Paffi, Alessandra; Liberti, Micaela; Apollonio, Francesca; Sheppard, Asher; Balzano, Quirino

2015-10-01

We conducted an electromagnetic-thermal analysis of Petri dishes filled with different medium volumes under different radio frequency exposure conditions with the aim of identifying linear and non-linear parameters that might explain contradictory results of many in vitro bioelectromagnetic experiments. We found that power loss density and temperature depend on shape, size, and orientation of the exposed sample with respect to direction of incident energy, showing that the liquid medium acts as a receiving antenna. In addition, we investigated the possibility of convection from thermodynamic principles within the liquid medium. For a 35 mm diameter Petri dish, a 2 or 4 ml medium volume is too small to support vertical convection. Conversely, horizontal convective motion is possible for H-polarization exposures at 1.8 GHz.

20. Evidence of fast non-linear feedback in EBR-II rod-drop measurements

SciTech Connect

Grimm, K.N.; Meneghetti, D.

1987-06-01

Feedback reactivities determine the time dependence of a reactor during and after a transient initiating event. Recent analysis of control-rod drops in the Experimental Breeder Reactor II (EBR-II) Reactor has indicated that some relatively fast feedback may exist which cannot be accounted for by the linear feedback mechanisms. The linear and deduced non-linear feedback reactivities from a control-rod drop in EBR-II run 93A using detailed temperature coefficients of reactivity in the EROS kinetics code have been reported. The transient analyses have now been examined in more detail for times close to the drop to ascertain if additional positive reactivity is being built-in early in the drop which could be gradually released later in the drop.
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