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Vortex Simulation of Axisymmetrical Flows in Cylindrical Geometries.Part II:Application to Pipes Incorporating an Orifice Plate
Institute of Scientific and Technical Information of China (English)
The Random Vortex Method extended to an axisymmetrical flow is used in the study of the flow field inside pipes incorporating an orifice plate with different contraction ratios and different inlet velocity profiles.Three test-cases,each having experimental measurements available in the literature,are studied,.In particular,instantaneous and average velocity fields along with the turbulent statistics for high Reynolds number flows are computed and compared to the corresponding experimental results These comparisons show the ability and the limitations of the method.The results of the numerical simulations are used in the physical analysis of the flow fields and thus allow for a better understanding of the dynamics of the flow in pipes incorporating an orifice plate.
Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry
Energy Technology Data Exchange (ETDEWEB)
Brizard, Alain J. [Department of Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States); Duthoit, François-Xavier [CEA, IRFM, F-13108 Saint-Paul-lez-Durance (France); SNU Division of Graduate Education for Sustainabilization of Foundation Energy, Seoul National University, Seoul 151-742 (Korea, Republic of)
The generating function for the canonical transformation from the parallel canonical coordinates (s,p{sub ||}) to the action-angle coordinates (ζ, J) for trapped/passing guiding-center orbits in axisymmetric tokamak geometry is presented. Drawing on the analogy between the phase-space portraits of the librating/rotating pendulum and the trapped/passing guiding-center orbits, the generating function is expressed in terms of the Jacobi zeta function, which can then readily be used to obtain an explicit expression for the bounce-center transformation for trapped/passing-particle guiding-center orbits in axisymmetric tokamak geometry.
Late-time tails in a stationary axisymmetric EMDA black hole geometry
Institute of Scientific and Technical Information of China (English)
Pan Qi-Yuan; Jing Ji-Liang
The late-time tails of massless and self-interacting (SI) (massive) scalar fields are investigated analytically in a stationary axisymmetric Einstein-Maxwell dilaton-axion (EMDA) black hole geometry. It is shown that the asymptotic behaviour of massless perturbations is dominated by an inverse power-law decaying tail and the intermediate asymptotic behaviour of SI (massive) perturbations is dominated by an oscillatory one.
On the prediction of swirling flowfields found in axisymmetric combustor geometries
Rhode, D. L.; Lilley, D. G.; Mclaughlin, D. K.
The paper reports research restricted to steady turbulence flow in axisymmetric geometries under low speed and nonreacting conditions. Numerical computations are performed for a basic two-dimensional axisymmetrical flow field similar to that found in a conventional gas turbine combustor. Calculations include a stairstep boundary representation of the expansion flow, a conventional k-epsilon turbulence model and realistic accomodation of swirl effects. A preliminary evaluation of the accuracy of computed flowfields is accomplished by comparisons with flow visualizations using neutrally-buoyant helium-filled soap bubbles as tracer particles. Comparisons of calculated results show good agreement, and it is found that a problem in swirling flows is the accuracy with which the sizes and shapes of the recirculation zones may be predicted, which may be attributed to the quality of the turbulence model.
Predictions and measurements of isothermal flowfields in axisymmetric combustor geometries. Ph.D. Thesis. Final Report
Rhodes, D. L.; Lilley, D. G.
Numerical predictions, flow visualization experiments and time-mean velocity measurements were obtained for six basic nonreacting flowfields (with inlet swirl vane angles of 0 (swirler removed), 45 and 70 degrees and sidewall expansion angles of 90 and 45 degrees) in an idealized axisymmetric combustor geometry. A flowfield prediction computer program was developed which solves appropriate finite difference equations including a conventional two equation k-epsilon eddy viscosity turbulence model. The wall functions employed were derived from previous swirling flow measurements, and the stairstep approximation was employed to represent the sloping wall at the inlet to the test chamber. Recirculation region boundaries have been sketched from the entire flow visualization photograph collection. Tufts, smoke, and neutrally buoyant helium filled soap bubbles were employed as flow tracers. A five hole pitot probe was utilized to measure the axial, radial, and swirl time mean velocity components.
Asymptotic Tails of Massive Scalar Fields in a Stationary Axisymmetric EMDA Black Hole Geometry
Institute of Scientific and Technical Information of China (English)
PAN Qi-Yuan; JING Ji-Liang
The late-time tail behaviour of massive scalar fields is studied analytically in a stationary axisymmetric EinsteinMaxwell Dilaton-Axion (EMDA) black hole geometry. It is shown that the asymptotic behaviour of massive perturbations is dominated by the oscillatory inverse power-law decaying tail t-(l+3/2) sin(μt) at the intermediate late times, and by the asymptotic tail t-5/6 sin(μt) at asymptotically late times, with μ being field mass. Our result seems to suggest that the intermediate tails t-(l+3/2) sin(μt) and the asymptotically tails t-5/6 sin(μt) may be a quite general feature for evolution of massive scalar fields in any four-dimensional asymptotically flat rotating black hole backgrounds.
Wanas, M I
The present work is a review of a series of papers, published in the last ten years, comprising an attempt to find a suitable avenue from geometry to quantum. It shows clearly that, any non-symmetric geometry admits some built-in quantum features. These features disappear completely once the geometry becomes symmetric (torsion-less). It is shown that, torsion of space-time plays an important role in both geometry and physics. It interacts with the spin of the moving particle and with its charge. The first interaction, {\\bf{Spin-Torsion Interaction}}, has been used to overcome the discrepancy in the results of the COW-experiment. The second interaction, {\\bf{Charge-Torsion Interaction}}, is similar to the Aharonov-Bohm effect. As a byproduct, a new version of Absolute Parallelism (AP) geometry, the Parameterized Absolute Parallelism (PAP) geometry, has been established and developed. This version can be used to construct field theories that admit some quantum features. Riemannian geometry and conventional AP-g...
A comparison of specularly reflective boundary conditions and rotationally invariant formulations for Discrete Ordinate Methods in axisymmetric geometries
Cai, Jian; Roy, Somesh; Modest, Michael F.
In simulations of periodic or symmetric geometries, computational domains are reduced by imaginary boundaries that exploit the symmetry conditions. Two boundary conditions are proposed for Discrete Ordinate Methods to solve axisymmetric radiation problems. Firstly, a specularly reflective boundary condition similar to that is used in Photon Monte Carlo methods is developed for Discrete Ordinate Methods. Secondly, the rotational invariant formulation is revisited for axisymmetric wedge geometries. Correspondingly, a new rotationally invariant boundary condition specially designed for axisymmetric problems on wedge shape is proposed to enforce the rotational invariance properties possessed by the radiative transfer equation (RTE) but violated by three-dimensional conventional Discrete Ordinate Methods. Both boundary conditions have the advantage that the discretization and linear equation solution procedures of conventional three-dimensional DOM are not affected by changing to a reduced geometry. Consistency, accuracy and efficiency of the new boundary conditions are demonstrated by multiple numerical examples involving periodic symmetry and axisymmetry. A comparison between specularly reflective boundary conditions and the rotationally invariant formulation shows that the latter offers several advantages for wedge geometries. In other symmetry conditions, when the rotational invariant formulation is not applicable, specular reflective boundary conditions are still effective.
Generalized geometry lectures on type II backgrounds
Tsimpis, Dimitrios
The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some past and recent results on the generalized complex structure of supersymmetric type II vacua in various dimensions.
Oscillations of magnetic stars: II. Axisymmetric toroidal and non-axisymmetric shear Alfven modes in a spherical shell
Reese, D; Rieutord, M
We carry out numerical and mathematical investigations of shear Alfven waves inside of a spherical shell filled with an incompressible conducting fluid, and bathed in a strong dipolar magnetic field. We focus on axisymmetric toroidal and non-axisymmetric modes, in continuation of a previous work by Rincon & Rieutord (2003). Analytical expressions are obtained for toroidal eigenmodes and their corresponding frequencies at low diffusivities. These oscillations behave like magnetic shear layers, in which the magnetic poles play a key role, and hence become singular when diffusivities vanish. It is also demonstrated that non-axisymmetric modes are split into two categories, namely poloidal or toroidal types, following similar asymptotic behaviours as their axisymmetric counterparts when the diffusivities become arbitrarily small.
Variational calculation of neoclassical ion heat flux and poloidal flow in the banana regime for axisymmetric magnetic geometry
Parker, Jeffrey B.; Catto, Peter J.
We present a numerical solution of the drift-kinetic equation retaining the linearized Fokker-Planck collision operator which is valid for general axisymmetric magnetic geometry in the low collisionality limit. We use the well-known variational principle based on entropy production and expand in basis functions. Uniquely, we expand in pitch-angle basis functions which are eigenfunctions of the transit-averaged test particle collision operator. These eigenfunctions, which depend on the geometry, are extremely well suited to this problem, with only one or two basis functions required to obtain an accurate solution. As a simple example of the technique, the neoclassical ion heat flux and poloidal flow are calculated for circular flux surfaces and compared with analytic approximations for arbitrary aspect ratio.
Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry
Duthoit, F -X; Peysson, Y; Decker, J
The perturbation analysis of the bounce action-angle coordinates $(J,\\zeta)$ for charged particles trapped in an axisymmetric dipole magnetic field is presented. First, the lowest-order bounce action-angle coordinates are derived for deeply-trapped particles in the harmonic-oscillator approximation. Next, the Lie-transform perturbation method is used to derive higher-order anharmonic action-angle corrections. Explicit expressions (with anharmonic corrections) for the canonical parallel coordinates $s(J,\\zeta)$ and $p_{\\|}(J,\\zeta)$ are presented, which satisfy the canonical identity $\\{s,\\; p_{\\|}\\}(J,\\zeta) \\equiv 1$. Lastly, analytical expressions for the bounce and drift frequencies (which include anharmonic corrections) yield excellent agreement with exact numerical results.
Gas uptake in a three-generation model geometry during steady expiration: comparison of axisymmetric and three-dimensional models.
Madasu, Srinath; Borhan, Ali; Ultman, James
Mass transfer coefficients were predicted and compared for uptake of a formaldehyde-air gas system using an axisymmetric single path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM) in three-generation model geometry at steady expiratory flow. The flow and concentration fields in the ASPM were solved using Galerkin's finite-element method and in the CFDM using a commercial finite-element software, FIDAP. Numerical results were compared for two different inlet flow rates, wall mass transfer coefficients, and bifurcation angles. The mass transfer coefficients variation with bifurcation unit from the ASPM and CFDM compared qualitatively and quantitatively closely at all flows and lower wall mass transfer coefficients for both 40 degrees and 70 degrees bifurcation angles. However, at higher wall mass transfer coefficients, quantitatively they were within 40% for both the bifurcation angles. Also, at higher flow and wall mass transfer coefficients, they were off qualitatively for a 70 degrees bifurcation angle although the uptake compared qualitatively. This is due to the normalization of uptake within a bifurcation unit with the average of inlet and outlet average concentrations. Both CFDM and ASPM predict the same trends of increase in mass transfer coefficients with inlet flow and wall mass transfer coefficients. Also, the local values of the mass transfer coefficients compared closely at all conditions. These results validate the simplified ASPM and the complex CFDM. Mass transfer coefficients increase with bifurcation angles and with a flat inlet velocity profile compared to a parabolic velocity profile since the flow is non-fully developed and hence, the uptake increases.
Axiomatic differential geometry II-2 - differential forms
Nishimura, Hirokazu
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of Pure and Applied Mathematics, 64 (2010), 85-102] to our present axiomatic framework.
Geometry of the TJ-II in Astra 6.0
International Nuclear Information System (INIS)
One of the most exploited features of the TJ-II Heliac, a facility in the Laboratorio Nacional de Fusion (CIEMAT, Madrid), is its ability to explore plasmas in different magnetic configurations. For this reason, there are available libraries that provide the metrics and associated magnitudes for many among all possible configurations. On the other hand, the transport codes that can normally be used to perform transport calculations cannot dea properly with these geometries, which is especially delicate when there are induced plasma currents. In the present work we adopt ASTRA, a transport analysis shell, to study the approximations performed when calculations that impose axi-symmetry (as ASTRA does) are performed on magnetic configurations that are not really axi-symmetric. After describing how we obtain those TJ-II metric averages that must be set in ASTRA, we perform two comparisons: (i) we obtain the vacuum rotational transform as deduced from the metric coefficients but imposing axisymmetry, and compare the results with the rotational transform yielded by the existing libraries; and (ii) we build a ID transport code with TJ-II metrics so its results can be compared with those of ASTRA. In both cases, the differences found indicate that evaluating the evolution of the rotational transform under ohmic induction and transport evolution is acceptable assuming that the geometry itself does not evolve. (Author) 11 refs
Line geometry and electromagnetism II: wave motion
Delphenich, D. H.
The fundamental role of line geometry in the study of wave motion is first introduced in the general context by way of the tangent planes to the instantaneous wave surfaces, in which it is first observed that the possible frequency-wave number 1-forms are typically constrained by a dispersion law that is derived from a constitutive law by way of the field equations. After a general review of the basic concepts that relate to quadratic line complexes, these geometric notions are applied to the...
Line geometry and electromagnetism II: wave motion
Delphenich, D H
The fundamental role of line geometry in the study of wave motion is first introduced in the general context by way of the tangent planes to the instantaneous wave surfaces, in which it is first observed that the possible frequency-wave number 1-forms are typically constrained by a dispersion law that is derived from a constitutive law by way of the field equations. After a general review of the basic concepts that relate to quadratic line complexes, these geometric notions are applied to the study of electromagnetic waves, in particular.
A finite volume approach to the problem of heat transfer in axisymmetric annulus geometry with internal heating element using local analytical solution techniques
Energy Technology Data Exchange (ETDEWEB)
Salama, A. [Atomic Energy Authority (AEA), Cairo (Egypt). Nuclear Research Center
In this paper we implement the local analytical solution technique to the problem of heat transfer in axisymmetric annulus geometry with internal heating element. This method has shown to be very accurate in estimating the temperature field for axisymmetric problems even for coarse mesh. It is shown that this method reduces to the analytical solution for unidirectional heat transfer in the radial direction in homogeneous media. The technique is based on finding an analytical expression for the temperature field in the radial direction within each grid cell. This means that the temperature field in each cell is allowed to change in a nonlinear fashion along the radial direction. We compare this technique with the traditional finite volume technique and show that; with only few cells in the radial direction, this technique arrives at the mesh-independent solution quite accurately whereas it required denser mesh to arrive closer to this solution using traditional techniques. This method is proposed to the 1D codes that are currently being used to simulate thermalhydraulic characteristics of reactor systems. Furthermore, we also implement the experimental temperature field algorithm in which the governing equations are approximated for each cell as it would without extra manipulation to the governing equations. This technique is very simple and separates the physics from the solving part.
A stabilized finite element formulation for the solution of the Navier-Stokes equations in axisymmetric geometry
International Nuclear Information System (INIS)
The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NSSOLVERMPI2DA program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)
Supermassive Black Holes in Galactic Nuclei with Tidal Disruption of Stars: Paper II - Axisymmetric Nuclei
Zhong, Shiyan; Spurzem, Rainer
Tidal Disruption of stars by supermassive central black holes from dense rotating star clusters is modelled by high-accuracy direct N-body simulation. As in a previous paper on spherical star clusters we study the time evolution of the stellar tidal disruption rate and the origin of tidally disrupted stars, now according to several classes of orbits which only occur in axisymmetric systems (short axis tube and saucer). Compared with that in spherical systems, we found a higher TD rate in axisymmetric systems. The enhancement can be explained by an enlarged loss-cone in phase space which is raised from the fact that total angular momentum $\\bf J$ is not conserved. As in the case of spherical systems, the distribution of the last apocenter distance of tidally accreted stars peaks at the classical critical radius. However, the angular distribution of the origin of the accreted stars reveals interesting features. Inside the influence radius of the supermassive black hole the angular distribution of disrupted star...
Geometry of the TJ-II in Astra 6.0; Geometria del TJ-II en Astra 6.0
Energy Technology Data Exchange (ETDEWEB)
Lopez-Bruna, D.; Romero, J.A.; Castejon, F.
One of the most exploited features of the TJ-II Heliac, a facility in the Laboratorio Nacional de Fusion (CIEMAT, Madrid), is its ability to explore plasmas in different magnetic configurations. For this reason, there are available libraries that provide the metrics and associated magnitudes for many among all possible configurations. On the other hand, the transport codes that can normally be used to perform transport calculations cannot dea properly with these geometries, which is especially delicate when there are induced plasma currents. In the present work we adopt ASTRA, a transport analysis shell, to study the approximations performed when calculations that impose axi-symmetry (as ASTRA does) are performed on magnetic configurations that are not really axi-symmetric. After describing how we obtain those TJ-II metric averages that must be set in ASTRA, we perform two comparisons: (i) we obtain the vacuum rotational transform as deduced from the metric coefficients but imposing axisymmetry, and compare the results with the rotational transform yielded by the existing libraries; and (ii) we build a ID transport code with TJ-II metrics so its results can be compared with those of ASTRA. In both cases, the differences found indicate that evaluating the evolution of the rotational transform under ohmic induction and transport evolution is acceptable assuming that the geometry itself does not evolve. (Author) 11 refs.
A Particle Simulation for the Axisymmetric Pulsar Magnetosphere: II. the case of dipole field
Wada, Tomohide
The main issue of the pulsar magnetosphere is how the rotation power is converted into both particle beams which causes pulsed emissions, and a highly relativistic wind of electron-positron plasmas which forms surrounding nebulae shining in X-rays and TeV gamma-rays. As a sequel of the first paper (Wada & Shibata 2007), we carried out a three dimensional particle simulation for the axisymmetric global magnetosphere. We present the results of additional calculations, which are higher resolution model and higher pair creation rate cases, and a detailed analysis for the solution. We confined to demonstrate the cases of low pair creation rate, i.e., the magnetic field is fixed dipole. The radiation drag of the plasma is taken in a form with the curvature radius along the dipole magnetic field. The electrostatic interactions are calculated by a programmable special purpose computer, GRAPE-DR (Makino et al 2007). Once pair creation is onset in the outer gaps, the both signed particles begin to drift across the ...
Gas uptake in a three-generation model geometry with a flat inlet velocity during steady inspiration: comparison of axisymmetric and three-dimensional models.
Madasu, Srinath; Borhan, Ali; Ultman, James
Mass transfer coefficients were predicted and compared for uptake of reactive gas system using an axisymmetric single-path model (ASPM) with experimentally predicted values in a two-generation geometry and with a three-dimensional computational fluid dynamics model (CFDM) in a three-generation model geometry at steady inspiratory flow with a flat inlet velocity profile. The flow and concentration fields in the ASPM were solved using Galerkin's finite element method and in the CFDM using a commercial finite element software FIDAP. ASPM predicted average gas phase mass transfer coefficients within 25% of the experimental values. Numerical results in terms of overall mass transfer coefficients from the two models within each bifurcation unit were compared for two different inlet flow rates, wall mass transfer coefficients, and bifurcation angles. The overall mass transfer coefficients variation with bifurcation unit from the ASPM and CFDM compared qualitatively and quantitatively closely at lower wall mass transfer coefficients for both 40 degree and 70 degree bifurcation angles. But at higher wall mass transfer coefficients, quantitatively they were off in the range of 2-10% for 40 degree bifurcation angle and in the range of 4-15% for 70 degree bifurcation angle. Both CFDM and ASPM predict the same trends of increase in mass transfer coefficients with inlet flow, wall mass transfer coefficients, and during inspiration compared to expiration. Higher mass transfer coefficients were obtained with a flat velocity profile compared to a parabolic velocity profile using ASPM. These results validate the simplified ASPM and the complex CFDM.
Shubnikov state in complex geometry Type-II Technetium device
International Nuclear Information System (INIS)
We investigate numerically the flux quantum configurations and some thermodynamic properties of a superconducting Technetium film by using the link variables technique for one shape of circular geometry. The Technetium exhibits superconductivity properties indicated by to an extrapolated critical magnetic field value of Hc(T = 0) = 1410 Oe, a Ginzburg-Landau parameter of κ = 0.92, and a critical temperature Tc = 7.86K, being the magnetic behavior of this material characteristic of a type-II superconductor with a weak-coupling superconductor of the BCS type. The studied sample is a circular sector with angular width θ = 7π/4 surrounded by a dielectric material and submitted to external magnetic field applied perpendicular to its plane. We evaluate the magnetic moment density, Shubnikov state and free Gibbs energy as a function of the external magnetic field
Coordinate-free Classic Geometries II. Conformal Structure
Anan'in, Sasha; Grossi, Carlos H
We study grassmannian classic geometries in the spirit of the previous paper. The interrelation between a (pseudo-)riemannian projective classic geometry and the conformal structure on its absolute is explained.
Supersymmetric Background of Type II Theories and Generalized Geometry
International Nuclear Information System (INIS)
I will present an outline of generalised geometry and I show how it provides a natural description of supersymmetric backgrounds. The discussion will be in slightly different terms to those appearing in the majority of the literature. It appears that: -) generalized geometry is a natural extension of differential geometry, -) we have brackets, metrics, spinors etc, in generalized geometry, and -) N=1 vacuum equations look more natural in this language. This document is composed of the slides of the presentation. (author)
Synthetic line and continuum linear-polarisation signatures of axisymmetric type II supernova ejecta
Dessart, Luc
We present synthetic single-line and continuum linear-polarisation signatures due to electron scattering in axially-symmetric Type II supernovae (SNe) which we calculate using a Monte Carlo and a long-characteristic radiative-transfer code. Aspherical ejecta are produced by prescribing a latitudinal scaling or stretching of SN ejecta inputs obtained from 1-D non-LTE time-dependent calculations. We study polarisation signatures as a function of inclination, shape factor, wavelength, line identity, post-explosion time. At early times, cancellation and optical-depth effects make the polarisation intrinsically low, causing complicated sign reversals with inclination or continuum wavelength, and across line profiles. While the line polarisation is positive (negative) for an oblate (prolate) morphology at the peak and in the red wing, the continuum polarisation may be of any sign. These complex polarisation variations are produced not just by the asymmetric distribution of scatterers but also of the flux. Our early...
Mathematical aspects of molecular replacement. II. Geometry of motion spaces.
Chirikjian, Gregory S; Yan, Yan
Molecular replacement (MR) is a well established computational method for phasing in macromolecular crystallography. In MR searches, spaces of motions are explored for determining the appropriate placement of rigid models of macromolecules in crystallographic asymmetric units. In the first paper of this series, it was shown that this space of motions, when endowed with an appropriate composition operator, forms an algebraic structure called a quasigroup. In this second paper, the geometric properties of these MR search spaces are explored and analyzed. This analysis includes the local differential geometry, global geometry and symmetry properties of these spaces.
Incidence Geometry in a Weyl Chamber II: $SL_n$
Esole, Mboyo; Jagadeesan, Ravi; Noël, Alfred G
We study the polyhedral geometry of the hyperplanes orthogonal to the weights of the first and the second fundamental representations of $sl_n$ inside the dual fundamental Weyl chamber. We obtain generating functions that enumerate the flats and the faces of a fixed dimension. In addition, we describe the extreme rays of the incidence geometry and classify simplicial faces. From the perspective of supersymmetric gauge theories with 8 supercharges in five dimensional spacetime, the poset of flats is isomorphic to the network of mixed Coulomb-Higgs branches. On the other hand, the poset of faces is conjectured to be isomorphic to the network of crepant partial resolutions of an elliptic fibration with gauge algebra $sl_n$ and "matter representation" given by the sum of the first two fundamental representations.
Pedoe, Dan
""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he
Coordination chemistry and solution structure of Fe(II)-peplomycin. Two possible coordination geometries.
Li, Yang; Lehmann, Teresa
The solution structure of Fe(II)-peplomycin was determined from NMR data collected for this molecule. As found previously for Fe(II)- and Co(II)-bound bleomycin; the coordination sphere of the metal is composed of the primary and secondary amines in β-aminoalanine, the pyrimidine and imidazole rings in the pyrimidinylpropionamide, and β-hydroxyhistidine moieties, respectively, the amine nitrogen in β-hydroxyhistidine, and either the carbamoyl group in mannose or a solvent molecule. The two most discussed coordination geometries for the aforementioned ligands in metallo-bleomycins have been tested against the NMR data generated for Fe(II)-peplomycin. The interpretation of the experimental evidence obtained through molecular dynamics indicates that both geometries are equally likely in solution for this compound in the absence of DNA, but arguments are offered to explain why one of these geometries is preferred in the presence of DNA.
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...... matematik, geometri, og fysik til at forstå, hvad det er, der foregår....
Evaluation of gas radiation heat transfer in a 2D axisymmetric geometry using the line-by-line integration and WSGG models
Centeno, Felipe Roman; Brittes, Rogério; França, Francis. H. R.; Ezekoye, Ofodike A.
The weighted-sum-of-gray-gases (WSGG) model is widely used in engineering computations of radiative heat transfer due to its relative simplicity, robustness and flexibility. This paper presents the computation of radiative heat transfer in a 2D axisymmetric chamber using two WSGG models to compute radiation in H2O and CO2 mixtures. The first model considers a fixed ratio between the molar concentrations of H2O and CO2, while the second allows the solution for arbitrary ratios. The correlations for both models are based on the HITEMP2010 database. The test case considers typical conditions found in turbulent methane flames, with steep variations in the temperature field as well as in the molar concentrations of the participating species. To assess the accuracy of the WSGG model, the results are compared with a solution obtained by line-by-line integration (LBL) of the spectrum.
A Non-axisymmetric Spherical α2-Dynamo
Institute of Scientific and Technical Information of China (English)
Using the Chebyshev-tau method, the generation of oscillatory nonaxisymmetric stellar magnetic fields by the α2-dynamo is studied in spherical geometry. Following the boundary conditions given by Schubert & Zhang, the spherical α2-dynamo consists of a fully convective spherical shell with inner radius ri and outer radius ro. A comparison of the critical dynamo numbers of axisymmetric and φ-dependent modes for different thicknesses of the convective shell and different α-profiles leads to the following qualitative results: (I) when the angular factor of α-profile is sinnθ cosθ (n = 1, 2, 4) the solutions of the α2-dynamo are oscillatory and non-axisymmetric, (ii) the thinner the convective shell, the more easily is the nonaxisymmetric mode excited and the higher is the latitudinal wave number, (iii) the thickness of the outer convective shell has an effect on the symmetries of the magnetic fields.
Hybrid guiding-centre/full-orbit simulations in non-axisymmetric magnetic geometry exploiting general criterion for guiding-centre accuracy
Pfefferlé, David; Cooper, Wilfred A
To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also the local shear of the field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (Mega Amp Spherical Tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation to the simpler situation $\\vec{B}(x,y,z) = B_0 [\\sin(kx) \\vec{e_y} + \\cos(kx)\\vec{e_z}]$, for which...
Magnetic Flux Lines in Complex Geometry Type-II Superconductors Studied by the Time Dependent Ginzburg-Landau Equation
DEFF Research Database (Denmark)
Alstrøm, Tommy Sonne; Sørensen, Mads Peter; Pedersen, Niels Falsig;
The time-dependent Ginzburg-Landau equation is solved numerically for type-II superconductors of complex geometry using the finite element method. The geometry has a marked influence on the magnetic vortex distribution and the vortex dynamics. We have observed generation of giant vortices...
LRS Bianchi Type II Massive String Cosmological Models with Magnetic Field in Lyra's Geometry
Directory of Open Access Journals (Sweden)
Raj Bali
Full Text Available Bianchi type II massive string cosmological models with magnetic field and time dependent gauge function ( in the frame work of Lyra's geometry are investigated. The magnetic field is in -plane. To get the deterministic solution, we have assumed that the shear ( is proportional to the expansion (. This leads to , where and are metric potentials and is a constant. We find that the models start with a big bang at initial singularity and expansion decreases due to lapse of time. The anisotropy is maintained throughout but the model isotropizes when . The physical and geometrical aspects of the model in the presence and absence of magnetic field are also discussed.
Type II InAs/GaAsSb quantum dots: Highly tunable exciton geometry and topology
Energy Technology Data Exchange (ETDEWEB)
Llorens, J. M.; Wewior, L.; Cardozo de Oliveira, E. R.; Alén, B., E-mail: email@example.com [IMM-Instituto de Microelectrónica de Madrid (CNM-CSIC), Isaac Newton 8, PTM, E-28760 Tres Cantos, Madrid (Spain); Ulloa, J. M.; Utrilla, A. D.; Guzmán, A.; Hierro, A. [Institute for Systems based on Optoelectronics and Microtechnology (ISOM), Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040 Madrid (Spain)
External control over the electron and hole wavefunctions geometry and topology is investigated in a p-i-n diode embedding a dot-in-a-well InAs/GaAsSb quantum structure with type II band alignment. We find highly tunable exciton dipole moments and largely decoupled exciton recombination and ionization dynamics. We also predicted a bias regime where the hole wavefunction topology changes continuously from quantum dot-like to quantum ring-like as a function of the external bias. All these properties have great potential in advanced electro-optical applications and in the investigation of fundamental spin-orbit phenomena.
Shielding NSLS-II light source: Importance of geometry for calculating radiation levels from beam losses
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. The principles used to provide supplemental shielding to the NSLS-II accelerators and
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.
Identification of different coordination geometries by XAFS in copper(II) complexes with trimesic acid
Gaur, A.; Klysubun, W.; Soni, Balram; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
X-ray absorption spectroscopy (XAS) is very useful in revealing the information about geometric and electronic structure of a transition-metal absorber and thus commonly used for determination of metal-ligand coordination. But XAFS analysis becomes difficult if differently coordinated metal centers are present in a system. In the present investigation, existence of distinct coordination geometries around metal centres have been studied by XAFS in a series of trimesic acid Cu(II) complexes. The complexes studied are: Cu3(tma)2(im)6 8H2O (1), Cu3(tma)2(mim)6 17H2O (2), Cu3(tma)2(tmen)3 8.5H2O (3), Cu3(tma) (pmd)3 6H2O (ClO4)3 (4) and Cu3(tma)2 3H2O (5). These complexes have not only Cu metal centres with different coordination but in complexes 1-3, there are multiple coordination geometries present around Cu centres. Using XANES spectra, different coordination geometries present in these complexes have been identified. The variation observed in the pre-edge features and edge features have been correlated with the distortion of the specific coordination environment around Cu centres in the complexes. XANES spectra have been calculated for the distinct metal centres present in the complexes by employing ab-initio calculations. These individual spectra have been used to resolve the spectral contribution of the Cu centres to the particular XANES features exhibited by the experimental spectra of the multinuclear complexes. Also, the variation in the 4p density of states have been calculated for the different Cu centres and then correlated with the features originated from corresponding coordination of Cu. Thus, these spectral features have been successfully utilized to detect the presence of the discrete metal centres in a system. The inferences about the coordination geometry have been supported by EXAFS analysis which has been used to determine the structural parameters for these complexes.
Black holes in the Einstein -Gauss-Bonnet theory and the geometry of their thermodynamics-II
Biswas, Ritabrata; Chakraborty, Subenoy
In the present work we study (i) charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) black hole in EGB gravity with Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
Axisymmetric flows from fluid injection into a confined porous medium
Guo, Bo; Zheng, Zhong; Celia, Michael A.; Stone, Howard A.
We study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced fluid relative to injected fluid, and Γ, which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R2/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid (Γ ≪ 1 and M interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity (Γ ≪ 1 and M = 1), where we find a self-similar solution that predicts a distinct parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid (Γ ≪ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow (Γ ≫ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. "Axisymmetric gravity currents in a porous medium," J. Fluid Mech. 543, 293-302 (2005)]. The various axisymmetric flows are summarized in a Γ-M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime. The implications of the regime diagram are discussed using practical
Axisymmetric Plume Simulations with NASA's DSMC Analysis Code
Stewart, B. D.; Lumpkin, F. E., III
A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.
A stabilized finite element formulation for the solution of the Navier-Stokes equations in axisymmetric geometry; Uma formulacao estabilizada de elementos finitos para solucao das equacoes de Navier-Stokes em geometria axissimetrica
Energy Technology Data Exchange (ETDEWEB)
Souza, Altivo Monteiro de
The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS{sub S}OLVER{sub M}PI{sub 2}D{sub A} program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)
Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules. Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms. We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity.
Axisymmetric multiwormholes revisited
Clément, Gérard
The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the n cuts associated with the wormhole mouths. The resulting Riemann manifold has 2^n sheets interconnected by 2^{n-1}n wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.
Axisymmetric multiwormholes revisited
Clément, Gérard
The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the $n$ cuts associated with the wormhole mouths. The resulting Riemann manifold has $2^n$ sheets interconnected by $2^{n-1}n$ wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.
Axisymmetric Coanda-assisted vectoring
Energy Technology Data Exchange (ETDEWEB)
Allen, Dustin; Smith, Barton L. [Utah State University, Mechanical and Aerospace Engineering, Logan, UT (United States)
An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach<0.3). The control jet attaches to the convex wall and vectors according to known Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r-{theta} directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets. (orig.)
Axisymmetric Coanda-assisted vectoring
Allen, Dustin; Smith, Barton L.
An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r - θ directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets.
Axisymmetric control in tokamaks
International Nuclear Information System (INIS)
Vertically elongated tokamak plasmas are intrinsically susceptible to vertical axisymmetric instabilities as a result of the quadrupole field which must be applied to produce the elongation. The present work analyzes the axisymmetric control necessary to stabilize elongated equilibria, with special application to the Alcator C-MOD tokamak. A rigid current-conserving filamentary plasma model is applied to Alcator C-MOD stability analysis, and limitations of the model are addressed. A more physically accurate nonrigid plasma model is developed using a perturbed equilibrium approach to estimate linearized plasma response to conductor current variations. This model includes novel flux conservation and vacuum vessel stabilization effects. It is found that the nonrigid model predicts significantly higher growth rates than predicted by the rigid model applied to the same equilibria. The nonrigid model is then applied to active control system design. Multivariable pole placement techniques are used to determine performance optimized control laws. Formalisms are developed for implementing and improving nominal feedback laws using the C-MOD digital-analog hybrid control system architecture. A proportional-derivative output observer which does not require solution of the nonlinear Ricatti equation is developed to help accomplish this implementation. The nonrigid flux conserving perturbed equilibrium plasma model indicates that equilibria with separatrix elongation of at least sep = 1.85 can be stabilized robustly with the present control architecture and conductor/sensor configuration
Coordination geometries of Zn(II) and Cd(II) in phosphotriesterase: Influence of water molecules in the active site
DEFF Research Database (Denmark)
Krauss, M; Olsen, Lars; Antony, J;
Models of the metal ion binding sites of native ZnZn and of cadmium-substituted ZnCd and CdCd phosphotriesterase, including full amino acid side chains, were geometry optimized with quantum mechanical methods, with effective fragment potentials (EFP) representing the protein environment surrounding...... the active site. One to three water molecules were included in the active site in addition to the bridging hydroxide. Comparison with recent X-ray diffraction results Benning, M. M.; Shim, H.; Raushel, F. M.; Holden, H. M. Biochemistry 2001, 40, 2712-22 is hindered by the presence of ethylene glycol...... molecules in the active site. We suggest that the ethylene glycol required for crystallization distorts the structure of the water network in the active site and that the theoretical structures provide a better description of the system in aqueous solution. Cd-113 NMR isotropic shielding calculations were...
Optical knots and contact geometry II. From Hopf links to transverse and cosmetic knots
Kholodenko, Arkady L
In 1985 Moffatt conjectured that in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. Using methods of contact geometry Etnyre and Ghrist in 2000 developed the existence-type proof of the Moffatt conjecture. The alternative proof, also of existence-type, was proposed by Enciso and Peralta -Salas in 2012. In all three papers the Beltrami equation was used as point of departure. However, only work by Etnyre and Ghrist takes full advantage of contact-geometric nature of the Beltrami equation. In this work we propose the constructive proof of the Moffatt conjecture based on ideas and methods of contact geometry. We discuss in sufficient detail various physical processes generating such knotted structures. By employing the correspondence between ideal hydrodynamics and electrodynamics discussed in part I, the Moffatt conjecture is proved for Maxwellian electrodynamics. The potential relevance of the obtained results for source-free Yang-Mills and gravity fields is also br...
On geometry of deformed black holes: II. Schwarzschild hole surrounded by a Bach-Weyl ring
Basovník, M
We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro-)vacuum exact solutions of Einstein's equations, we first considered the Majumdar--Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach--Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still...
Special geometry of euclidean supersymmetry II. Hypermultiplets and the c-map
Energy Technology Data Exchange (ETDEWEB)
Cortes, Vicente [Institut de Mathematiques Elie Cartan, Universite Henri Poincare - Nancy I, B.P. 239, F-54506 Vandoeuvre-les-Nancy (France); Mayer, Christoph [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Mohaupt, Thomas [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Saueressig, Frank [Institute for Theoretical Physics and Spinoza Institute, Postbus 80.195, 3508 TD Utrecht (Netherlands)
We construct two new versions of the c-map which allow us to obtain the target manifolds of hypermultiplets in euclidean theories with rigid N = 2 supersymmetry. While the minkowskian para-c-map is obtained by dimensional reduction of the minkowskian vector multiplet lagrangian over time, the euclidean para-c-map corresponds to the dimensional reduction of the euclidean vector multiplet lagrangian. In both cases the resulting hypermultiplet target spaces are para-hyper-Kaehler manifolds. We review and prove the relevant results of para-complex and para-hypercomplex geometry. In particular, we give a second, purely geometrical construction of both c-maps, by proving that the cotangent bundle N = T*M of any affine special (para-)Kaehler manifold M is para-hyper-Kaehler.
Stability of Axisymmetric Liquid Bridges
Rubinstein, Boris
We study stability of axisymmetric liquid bridges between two axisymmetric solid bodies in the absence of gravity under arbitrary asymmetric perturbations which are expanded into a set of angular Fourier modes. We determine the stability region boundary for every angular mode in case of both fixed and free contact lines. Application of this approach allows us to demonstrate existence of stable convex nodoid menisci between two spheres.
Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring
Basovník, M.; Semerák, O.
We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of Einstein's equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather nontrivial landscapes outside the horizon.
Supergravity as Generalised Geometry II: $E_{d(d)} \\times \\mathbb{R}^+$ and M theory
Coimbra, André; Waldram, Daniel
We reformulate eleven-dimensional supergravity, including fermions, in terms of generalised geometry, for spacetimes that are warped products of Minkowski space with a $d$-dimensional manifold $M$ with $d\\leq7$. The reformation has a $E_{d(d)} \\times \\mathbb{R}^+$ structure group and is has a local $\\tilde{H}_d$ symmetry, where $\\tilde{H}_d$ is the double cover of the maximally compact subgroup of $E_{d(d)}$. The bosonic degrees for freedom unify into a generalised metric, and, defining the generalised analogue $D$ of the Levi-Civita connection, one finds that the corresponding equations of motion are the vanishing of the generalised Ricci tensor. To leading order, we show that the fermionic equations of motion, action and supersymmetry variations can all be written in terms of $D$. Although we will not give the detailed decompositions, this reformulation is equally applicable to type IIA or IIB supergravity restricted to a $(d-1)$-dimensional manifold. For completeness we give explicit expressions in terms o...
Axisymmetric annular curtain stability
International Nuclear Information System (INIS)
A temporal stability analysis was carried out to investigate the stability of an axially moving viscous annular liquid jet subject to axisymmetric disturbances in surrounding co-flowing viscous gas media. We investigated in this study the effects of inertia, surface tension, the gas-to-liquid density ratio, the inner-to-outer radius ratio and the gas-to-liquid viscosity ratio on the stability of the jet. With an increase in inertia, the growth rate of the unstable disturbances is found to increase. The dominant (or most unstable) wavenumber decreases with increasing Reynolds number for larger values of the gas-to-liquid viscosity ratio. However, an opposite tendency for the most unstable wavenumber is predicted for small viscosity ratio in the same inertia range. The surrounding gas density, in the presence of viscosity, always reduces the growth rate, hence stabilizing the flow. There exists a critical value of the density ratio above which the flow becomes stable for very small viscosity ratio, whereas for large viscosity ratio, no stable flow appears in the same range of the density ratio. The curvature has a significant destabilizing effect on the thin annular jet, whereas for a relatively thick jet, the maximum growth rate decreases as the inner radius increases, irrespective of the surrounding gas viscosity. The degree of instability increases with Weber number for a relatively large viscosity ratio. In contrast, for small viscosity ratio, the growth rate exhibits a dramatic dependence on the surface tension. There is a small Weber number range, which depends on the viscosity ratio, where the flow is stable. The viscosity ratio always stabilizes the flow. However, the dominant wavenumber increases with increasing viscosity ratio. The range of unstable wavenumbers is affected only by the curvature effect. (paper)
Classification of Stellar Orbits in Axisymmetric Galaxies
Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood
It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.
Axisymmetric fretting analysis in coated cylinder
Indian Academy of Sciences (India)
M Ramesh; Satish V Kailas; K R Y Simha
Fretting is essentially a contact fatigue phenomenon, although bulk stresses and material properties contribute to final failure. The near surface state of stress developed under oscillatory contact between machine elements plays a major role in deciding the severity of fretting. It is possible to enhance tribological properties by coating the surface. There is rather scanty literature available on fretting analysis of coated components. Presence of such coatings has a large influence on the near surface state of stress. The effect of coatings on the severity of fretting is the focus of this paper. Results obtained for both hard and soft coatings are compared with the results obtained for the homogeneous case. The component geometry and loading are chosen to be cylindrical to enable 3D elastic axisymmetric fretting analysis. The results are compared with 2D models (strip and half-plane) to examine their utility and validity for understanding axisymmetric fretting. Contact pressure and frictional shear loading cases are solved separately and superposed appropriately depending on the coefficient of friction considered. Results for different values of coefficient of friction and elastic mismatch are illustrated through contour plots of stresses and strains. These results are expected to be helpful for identifying fretting failure zones and fracture mechanisms in coated components. Analytical results presented here could serve as useful benchmarks for calibrating numerical codes and experimental techniques.
Classification of Stellar Orbits in Axisymmetric Galaxies
Li, Baile; Khan, Fazeel
It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly- flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on Gyr timescales (Khan et al. 2013). Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contai...
From x-ray telescopes to neutron scattering: using axisymmetric mirrors to focus a neutron beam
Khaykovich, B.; Gubarev, M. V.; Bagdasarova, Y.; Ramsey, B. D.; Moncton, D.E.
We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in x-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We have implemented a system containing four nested Ni mirror pairs, which was tested by focusing a polychromatic neutron beam at the MIT Reactor. In ...
Tuning of coordination geometry via cooperation of inter- and intramolecular hydrogen bonds in bis(benzoylacetonato)manganese(II) adducts with pyridine derivatives
Cvrtila, Ivica; Stilinovic, Vladimir; Kaitner, Branko
In order to study the effects of intramolecular hydrogen bonding on coordination geometry of a relatively rigid octahedral system, eight coordination compounds derived from bis(benzoylacetonato)manganese(II) and seven pyridine derivatives (three of them o-aminopyridines) were prepared. Four compound
Numerical computation of gravitational field for general axisymmetric objects
Fukushima, Toshio
We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (i) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (ii) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (i) finite uniform objects covering rhombic spindles and circular toroids, (ii) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (iii) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.
Non-axisymmetric flow characteristics in centrifugal compressor
Wang, Leilei; Lao, Dazhong; Liu, Yixiong; Yang, Ce
The flow field distribution in centrifugal compressor is significantly affected by the non-axisymmetric geometry structure of the volute. The experimental and numerical simulation methods were adopted in this work to study the compressor flow field distribution with different flow conditions. The results show that the pressure distributionin volute is characterized by the circumferential non-uniform phenomenon and the pressure fluctuation on the high static pressure zone propagates reversely to upstream, which results in the non-axisymmetric flow inside the compressor. The non-uniform level of pressure distribution in large flow condition is higher than that in small flow condition, its effect on the upstream flow field is also stronger. Additionally, the non-uniform circumferential pressure distribution in volute brings the non-axisymmetric flow at impeller outlet. In different flow conditions,the circumferential variation of the absolute flow angle at impeller outlet is also different. Meanwhile, the non-axisymmetric flow characteristics in internal impeller can be also reflected by the distribution of the mass flow. The high static pressure region of the volute corresponds to the decrease of mass flow in upstream blade channel, while the low static pressure zone of the volute corresponds to the increase of the mass flow. In small flow condition, the mass flow difference in the blade channel is bigger than that in the large flow condition.
Streamline topology of axisymmetric flows
DEFF Research Database (Denmark)
Brøns, Morten
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...
Institute of Scientific and Technical Information of China (English)
An analytical approach is described for the axisymmetric flow through a permeable near-sphere with a modification to boundary conditions in order to account permeability. The Stokes equation was solved by a regular perturbation technique up to the second order correction in epsilon representing the deviation from the radius of nondeformed sphere. The drag and the flow rate were calculated and the results were evaluated from the point of geometry and the permeability of the surface. An attempt also was made to apply the theory to the filter feeding problem. The filter appendages of small ecologically important aquatic organisms were modeled as axisymmetric permeable bodies, therefore a rough model for this problem was considered here as an oblate spheroid or near-sphere.
Linear Stability of Hill's Vortex to Axisymmetric Perturbations
Protas, Bartosz
We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape differentiation to the contour dynamics formulation of the problem in a 3D axisymmetric geometry. This approach allows us to systematically account for the effect of boundary deformations on the linearized evolution of the vortex under the constraint of constant circulation. The resulting singular integro-differential operator defined on the vortex boundary is discretized with a highly accurate spectral approach. This operator has two unstable and two stable eigenvalues complemented by a continuous spectrum of neutrally-stable eigenvalues. By considering a family of suitably regularized (smoothed) eigenvalue problems solved with a range of numerical resolutions we demonstrate that the corresponding eigenfunctions are in fact singular objects in the form of infinitely sharp peaks localiz...
Palladium(II)-Catalyzed Annulation between ortho-Alkenylphenols and Allenes. Key Role of the Metal Geometry in Determining the Reaction Outcome
2-Alkenylphenols react with allenes, upon treatment with catalytic amounts of Pd(II) and Cu(II), to give benzoxepine products in high yields and with very good regio- and diastereoselectivities. This contrasts with the results obtained with Rh catalysts, which provided chromene-like products through a pathway involving a β-hydrogen elimination step. Computational studies suggest that the square planar geometry of the palladium is critical to favor the reductive elimination process required for the formation of the oxepine products.
Stationary and Axisymmetric Perfect-Fluid Solutions with Conformal Motion
Mars, Marc; Senovilla, Jose M M
Stationary and axisymmetric perfect-fluid metrics are studied under the assumption of the existence of a conformal Killing vector field and in the general case of differential rotation. The possible Lie algebras for the conformal group and corresponding canonical line-elements are explicitly given. It turns out that only four different cases appear, the abelian and other three called I, II and III. We explicitly find all the solutions in the abelian and I cases. For the abelian case the gener...
Experiments in axisymmetric supersonic jets
Moore, Cyrille Dennis
An experimental study of the effects of exit Mach number and density ratio on the development of axisymmetric jets is described in this thesis. Jet exit Mach numbers of 1.41, 2.0, and 3.0, were studied for jets of helium, argon, and nitrogen. The jets exit into a gas at rest (velocity ratio = 0), in order to better isolate the effects of compressibility and density ratio. Density ratios vary from 0.23 to 5.5.In order to generate shock free-jets, unique nozzles were designed and constructed for each gas and Mach number combination. A plating method for the construction of the nozzles was developed to ensure high-accuracy and a good surface finish at a cost significantly less than direct-machining techniques.The spreading rate of the jet for several downstream locations is measured with a pitot probe. Centerline data are used to characterise the length of the potential core of the jet, which correlates well with the relative spreading rates. Limited frequency data is obtained through the use of piezo-resistive pressure probes. This method is promising for flows that are not conducive to hot-wire probes.Spark shadography is used to visualize both the mean and instantaneous flow, with the minimum spark time being 20 nanoseconds. The convection velocity of large-scale disturbances is estimated from the visible Mach-type acoustic waves emanating from the jet.For a wide range of jet Mach and Reynolds numbers, the convection velocity of the large scale disturbances in the potential core region of the jet is approximately 0.8 times the jet velocity, the approximate velocity of the first helical instability mode of the jet.The main objectives of the present work were to investigate the effects of compressibility and density on the initial development of the axisymmetric jet. Although the data are not sufficient to determine if the convective Mach number concept used in 2-d shear layer research will work in the case of an axisymmetric jet, it is clear that the axisymmetric
Non-existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics
International Nuclear Information System (INIS)
In this work we explore the possible existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics. Considering static and spherically symmetric (2 + 1)- and (3 + 1)-dimensional wormhole spacetimes, we verify the presence of an event horizon and the non-violation of the null energy condition at the throat. For the former spacetime, the principle of finiteness is imposed, in order to obtain regular physical fields at the throat. Next, we analyse (2 + 1)-dimensional stationary and axisymmetric wormhole, and also verify the presence of an event horizon, rendering the geometry non-traversable. Relative to (3 + 1)-dimensional stationary and axisymmetric wormhole geometry, we find that the field equations impose specific conditions that are incompatible with the properties of wormholes. Thus, we prove the non-existence of the general class of traversable wormhole solutions, outlined above, within the context of nonlinear electrodynamics
Multi-objective optimization of weld geometry in hybrid fiber laser-arc butt welding using Kriging model and NSGA-II
Gao, Zhongmei; Shao, Xinyu; Jiang, Ping; Wang, Chunming; Zhou, Qi; Cao, Longchao; Wang, Yilin
An integrated multi-objective optimization approach combining Kriging model and non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to predict and optimize weld geometry in hybrid fiber laser-arc welding on 316L stainless steel in this paper. A four-factor, five-level experiment using Taguchi L25 orthogonal array is conducted considering laser power ( P), welding current ( I), distance between laser and arc ( D) and traveling speed ( V). Kriging models are adopted to approximate the relationship between process parameters and weld geometry, namely depth of penetration (DP), bead width (BW) and bead reinforcement (BR). NSGA-II is used for multi-objective optimization taking the constructed Kriging models as objective functions and generates a set of optimal solutions with pareto-optimal front for outputs. Meanwhile, the main effects and the first-order interactions between process parameters are analyzed. Microstructure is also discussed. Verification experiments demonstrate that the optimum values obtained by the proposed integrated Kriging model and NSGA-II approach are in good agreement with experimental results.
A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields
Jiang, J
Increasing observations are becoming available about a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. It indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric alpha2-Omega dynamo model is set up to discuss the characteristics of the axisymmetric m=0 and the first non-axisymmetric m=1 modes and to provide further the theoretical bases to explain the active longitude, flip-flop and other non-axisymmetric phenomena. The model consists of a updated solar internal differential rotation, a turbulent diffusivity varied with depth and an alpha-effect working at the tachocline in rotating spherical systems. The difference between the alpha2-Omega and the alpha-Omega models and the conditions to favor the non-axisymmetric modes with the solar-like parameters are also presented.
Two-dimensional axisymmetric formulation of high order spherical harmonics methods for radiative heat transfer
Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo
The spherical harmonics (PN) method is a radiative transfer equation solver, which approximates the radiative intensity as a truncated series of spherical harmonics. For general 3-D configurations, N(N + 1) / 2 intensity coefficients must be solved from a system of coupled second-order elliptic PDEs. In 2-D axisymmetric applications, the number of equations and intensity coefficients reduces to (N + 1) 2 / 4 if the geometric relations of the intensity coefficients are taken into account. This paper presents the mathematical details for the transformation and its implementation on the OpenFOAM finite volume based CFD software platform. The transformation and implementation are applicable to any arbitrary axisymmetric geometry, but the examples to test the new formulation are based on a wedge grid, which is the most common axisymmetric geometry in CFD simulations, because OpenFOAM and most other platforms do not have true axisymmetric solvers. Two example problems for the new axisymmetric PN formulation are presented, and the results are verified with that of the general 3-D PN solver, a Photon Monte Carlo solver and exact solutions.
Radion stability and induced, on-brane geometries in an effective scalar-tensor theory of gravity II
Kar, Sayan; SenGupta, Soumitra
In our earlier article (Phys.Rev. {\\bf D 88} 083506,(2013)) we had obtained spherically symmetric, static on-brane geometries in the Kanno-Soda effective scalar-tensor theory of gravity. The solution found was the extremal Reissner--Nordstrom black hole (the Majumdar-Papapetrou solution). In this article, we extend our analysis to more general, spherically symmetric, static geometries which are non-extremal in nature. The solution is nothing other than the well-known Reissner--Nordstrom solution. We find the radion field profiles for the various cases and also look into the issue of radion stability. Finally, the energy-momentum tensor for the effective on-brane matter is obtained and we observe that it can satisfy all energy conditions for a certain region of the parameter space of the solution.
Differential geometry of the ruled surfaces optically generated by mirror scanning devices: II. Generation of helicoids and hyperbolic paraboloids.
Li, Yajun
The theory developed in Part I of this study [Y. Li, "Differential geometry of the ruled surfaces optically generated by mirror-scanning devices. I. Intrinsic and extrinsic properties of the scan field," J. Opt. Soc. Am. A28, 667 (2011)] for the ruled surfaces optically generated by single-mirror scanning devices is extended to multimirror scanning systems for an investigation of optical generation of the well-known ruled surfaces, such as helicoid, Plücker's conoid, and hyperbolic paraboloid.
Axisymmetric fully spectral code for hyperbolic equations
Macedo, Rodrigo P
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge-Kutta ("SDIRK"-) method. The SDIRK-method also supplies the code with a good initial-guess. The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hol...
Stability of perturbed geodesics in $nD$ axisymmetric spacetimes
Coimbra-Araujo, C H
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. It is plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric $n$-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where it is studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed $5D$ and $6D$ axisymmetric spacetime; (ii) a simple Randall-Sundrum $5D$ spacetime; (iii) general $5D$ and $6D$ Randall-Sundrum spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Schwarzschild and Chazy-C...
Two field-induced slow magnetic relaxation processes in a mononuclear Co(ii) complex with a distorted octahedral geometry.
Li, Jing; Han, Yuan; Cao, Fan; Wei, Rong-Min; Zhang, Yi-Quan; Song, You
A distorted octahedral Co(II) complex is reported with homoscorpionate ligands. This complex comprised a field-induced single-molecule magnet, showing two slow relaxation processes under a low dc field (magnetic data, we show for the first time that one of the slow relaxation processes in the low dc field originates from intermolecular dipolar interactions. Interestingly, the Raman process is predominant in the spin reversal relaxation process. The origin of the behaviours of the complex was elucidated by ab initio calculations. PMID:27180637
Stability of perturbed geodesics in nD axisymmetric spacetimes
Coimbra-Araújo, C. H.; Anjos, R. C.
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall–Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto–Nagai and Chazy–Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS–Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Stability of perturbed geodesics in nD axisymmetric spacetimes
Coimbra-Araújo, C. H.; Anjos, R. C.
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall-Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto-Nagai and Chazy-Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS-Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Pyrone-based Cu(II) complexes, their characterization, DFT based conformational drift from square planar to square pyramidal geometry and biological activities
Indian Academy of Sciences (India)
Pradeep Kumar Vishwakarma; Jan Mohammad Mir; Ram Charitra Maurya
This work deals with the synthesis and characterization of a series of three -Dehydroacetic acid- 4-phenyl-3-thiosemicarbazide (H2dha-ptsc) Schiff base Cu(II) complexes based on combined experimental and theoretical approach, having the general composition formula as [Cu(dha-ptsc)(L-L)], where L-L is H2O, 2,2-bipyridine (bipy) or 1,10-phenanthroline (phen). H2O containing complex acts as origin for the latter two complexes and in due course, the geometry of the complex changes from square planar to square pyramidal. DFT calculations were carried out for both the geometrical forms. B3LYP/LANL2DZ level of theory was used to carry out the required computations. From the overall DFT computations, square pyramidal geometry was found to be more stable as compared to the square planar conformation for the complexes under investigation. Super oxide dismutation, thermal behaviour and electrochemical activity were also studied. The results have shown satisfactory super oxide scavenging potential, high degree of thermal resistance and efficient redox properties for the title complexes. Moreover, charge analysis and nonlinear optical properties were computed to establish a comprehensive note of atomic constituents differing in nature of charge delocalization.
Spread of excitation in 3-D models of the anisotropic cardiac tissue. II. Effects of fiber architecture and ventricular geometry.
Franzone, P C; Guerri, L; Pennacchio, M; Taccardi, B
We investigate a three-dimensional macroscopic model of wave-front propagation related to the excitation process in the left ventricular wall represented by an anisotropic bidomain. The whole left ventricle is modeled, whereas, in a previous paper, only a flat slab of myocardial tissue was considered. The direction of cardiac fibers, which affects the anisotropic conductivity of the myocardium, rotates from the epi- to the endocardium. If the ventricular wall is conceived as a set of packed surfaces, the fibers may be tangent to them or more generally may cross them obliquely; the latter case is described by an "imbrication angle." The effect of a simplified Purkinje network also is investigated. The cardiac excitation process, more particularly the depolarization phase, is modeled by a nonlinear elliptic equation, called an eikonal equation, in the activation time. The numerical solution of this equation is obtained by means of the finite element method, which includes an upwind treatment of the Hamiltonian part of the equation. By means of numerical simulations in an idealized model of the left ventricle, we try to establish whether the eikonal approach contains the essential basic elements for predicting the features of the activation patterns experimentally observed. We discuss and compare these results with those obtained in our previous papers for a flat part of myocardium. The general rules governing the spread of excitation after local stimulations, previously delineated for the flat geometry, are extended to the present, more realistic monoventricular model.
Material laws and related uncommon phenomena in the electromagnetic response of type-II superconductors in longitudinal geometry
Ruiz, H. S.; Badía-Majós, A.; López, C.
Relying on our theoretical approach for the superconducting critical state problem in 3D magnetic field configurations, we present an exhaustive analysis of the electrodynamic response for the so-called longitudinal transport problem in the slab geometry. A wide set of experimental conditions have been considered, including modulation of the applied magnetic field either perpendicular or parallel (longitudinal) to the transport current density. The main objective of our work was to characterize the role of the macroscopic material law that should properly account for the underlying mechanisms of flux cutting and depinning. The intriguing occurrence of negative current patterns and the enhancement of the transport current flow along the center of the superconducting sample are reproduced as a straightforward consequence of the magnetically induced internal anisotropy. Moreover, we show that, related to a maximal projection of the current density vector onto the local magnetic field, a maximal transport current density occurs somewhere within the sample. The elusive measurement of the flux cutting threshold (critical value of such parallel component J_{ {c} \\parallel } ) is suggested on the basis of local measurements of the transport current density. Finally, we show that a high correlation exists between the evolution of the transport current density and the appearance of paramagnetic peak structures in terms of the applied longitudinal magnetic field.
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
M. Jakomin; F. Kosel
In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the lar...
Integral-Field Spectroscopy of the Post Red Supergiant IRC +10420: evidence for an axi-symmetric wind
Davies, Ben; Sahu, Kailash C
We present NAOMI/OASIS adaptive-optics assisted integral-field spectroscopy of the transitional massive hypergiant IRC +10420, an extreme mass-losing star apparently in the process of evolving from a Red Supergiant toward the Wolf-Rayet phase. To investigate the present-day mass-loss geometry of the star, we study the appearance of the line-emission from the inner wind as viewed when reflected off the surrounding nebula. We find that, contrary to previous work, there is strong evidence for wind axi-symmetry, based on the equivalent-width and velocity variations of H$\\alpha$ and Fe {\\sc ii} $\\lambda$6516. We attribute this behaviour to the appearance of the complex line-profiles when viewed from different angles. We also speculate that the Ti {\\sc ii} emission originates in the outer nebula in a region analogous to the Strontium Filament of $\\eta$ Carinae, based on the morphology of the line-emission. Finally, we suggest that the present-day axisymmetric wind of IRC +10420, combined with its continued blueward...
Structure of stationary and axisymmetric metrics
International Nuclear Information System (INIS)
We study the structure of stationary and axisymmetric metrics solving the vacuum Einstein equations of general relativity in four and higher dimensions, building on recent work in Phys. Rev. D 70, 124002 (2004). We write the Einstein equations in a new form that naturally identifies the sources for such metrics. The sources live in a one-dimensional subspace and the entire metric is uniquely determined by them. We study in detail the structure of stationary and axisymmetric metrics in four dimensions, and consider as an example the sources of the Kerr black hole
Boundary element method for internal axisymmetric flow
Directory of Open Access Journals (Sweden)
Gokhman Alexander
Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.
Guggenheimer, Heinrich W
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a
Kinetically Stabilized Axisymmetric Tandem Mirrors: Summary of Studies
Energy Technology Data Exchange (ETDEWEB)
Post, R F
The path to practical fusion power through plasma confinement in magnetic fields, if it is solely based on the present front-runner, the tokamak, is clearly long, expensive, and arduous. The root causes for this situation lie in the effects of endemic plasma turbulence and in the complexity the tokamak's ''closed'' field geometry. The studies carried out in the investigations described in the attached reports are aimed at finding an approach that does not suffer from these problems. This goal is to be achieved by employing an axisymmetric ''open'' magnetic field geometry, i.e. one generated by a linear array of circular magnet coils, and employing the magnetic mirror effect in accomplishing the plugging of end leakage. More specifically, the studies were aimed at utilizing the tandem-mirror concept in an axisymmetric configuration to achieve performance superior to the tokamak, and in a far simpler system, one for which the cost and development time could be much lower than that for the tokamak, as exemplified by ITER and its follow-ons. An important stimulus for investigating axisymmetric versions of the tandem mirror is the fact that, beginning from early days in fusion research there have been examples of axisymmetric mirror experiments where the plasma exhibited crossfield transport far below the turbulence-enhanced rates characteristic of tokamaks, in specific cases approaching the ''classical'' rate. From the standpoint of theory, axisymmetric mirror-based systems have special characteristics that help explain the low levels of turbulence that have been observed. Among these are the facts that there are no parallel currents in the equilibrium state, and that the drift surfaces of all of the trapped particles are closed surfaces, as shown early on by Teller and Northrop. In addition, in such systems it is possible to arrange that the radial boundary of the confined plasma terminates without
Axisymmetric Toroidal Equilibrium with Sheared Toroidal Flows
Institute of Scientific and Technical Information of China (English)
Since the early 1960' s, the developments of the tokamak research make plasma flows a reality in many devices where neutral beam injections were used as heating in general and refueling in particular. Compared to the static axi-symmetric toroidal equilibrium that
Axisymmetric Toroidal Equilibrium with Sheared Toroidal Flows
Institute of Scientific and Technical Information of China (English)
Problem of the axisymmetric toroidal equilibrium with pure sheared toroidal flow is involved. For standard tokamak equilibrium, general approximate solutions are analytically pursued for arbitrary current profile and non-circular cross-section. Equilibrium properties including the flow-induced density asymmetry are analyzed.
Magneto-hydrodynamically stable axisymmetric mirrors
Energy Technology Data Exchange (ETDEWEB)
Ryutov, D. D.; Cohen, B. I.; Molvik, A. W. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Berk, H. L. [University of Texas, Austin, Texas 78712 (United States); Simonen, T. C. [University of California, Berkeley, California 94720 (United States)
Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.
Magneto-hydrodynamically stable axisymmetric mirrorsa)
Ryutov, D. D.; Berk, H. L.; Cohen, B. I.; Molvik, A. W.; Simonen, T. C.
Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.
Topological fluid mechanics of Axisymmetric Flow
DEFF Research Database (Denmark)
Brøns, Morten
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field v...
Optimizing a neutron-beam focusing device for the direct geometry time-of-flight spectrometer TOFTOF at the FRM II reactor source
Rasmussen, N. G.; Simeoni, G. G.; Lefmann, K.
A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (adjustable supermirror curvature) and the compact size (only 0.5 m long). We have simulated the neutron transport across the entire guide system. We present a detailed computer characterization of the existing device, along with the study of the factors mostly influencing the future improvement. We have optimized the simulated prototype as a function of the neutron wavelength, accounting also for all relevant features of a real instrument like the non-reflecting side edges. The results confirm the "chromatic" displacement of the focal point (flux density maximum) at fixed supermirror curvature, and the ability of a variable curvature to keep the focal point at the sample position. Our simulations are in excellent agreement with theoretical predictions and the experimentally measured beam profile. With respect to the possibility of a further upgrade, we find that supermirror coatings with m-values higher than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum.
Pottmann, Helmut
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Maor, Eli
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks
Energy Technology Data Exchange (ETDEWEB)
Stacey, W. M. [Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Bae, C. [National Fusion Research Institute, Daejoen (Korea, Republic of)
A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric "neoclassical toroidal viscosity" mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.
Lefschetz, Solomon
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Mechanism of non-axisymmetric pipe-wall thinning in pipeline with elbow and orifice under influence of swirling flow
Energy Technology Data Exchange (ETDEWEB)
Fujisawa, Nobuyuki, E-mail: email@example.com [Visualization Research Center, Niigata University, Niigata (Japan); Kanatani, Nobuaki [Graduate School of Science and Technology, Niigata University, Niigata (Japan); Yamagata, Takayuki, E-mail: firstname.lastname@example.com [Visualization Research Center, Niigata University, Niigata (Japan); Takano, Tsuyoshi [Graduate School of Science and Technology, Niigata University, Niigata (Japan)
Highlights: • Pipe-wall thinning due to flow accelerated corrosion is studied. • Pipeline geometry consists of elbow and orifice in swirling flow. • Velocity field and mass transfer rate are measured in pipeline. • Non-axisymmetric pipe-wall thinning occurs behind orifice. - Abstract: In this study, the mechanism of non-axisymmetric pipe-wall thinning that led to a pipeline break in the Mihama nuclear power plant in 2004 is evaluated in a scale-model experiment in a water tunnel having an elbow and orifice under the influence of swirling flow. The velocity fields are measured by stereo particle image velocimetry, and the mass transfer rate is measured by a benzoic acid dissolution method at Reynolds number Re = 3 × 10{sup 4} with and without swirling flow. The non-axisymmetric swirling flow is found to be generated behind the elbow, even when the axisymmetric swirling flow is supplied in the upstream of the elbow. The secondary flow generated in the elbow is not suppressed in the pipeline 10 diameters downstream of elbow in the swirling flow, and in this flow geometry, the non-axisymmetry of the flow is greatly magnified downstream of the orifice. The measured mass transfer rates downstream of the orifice under the influence of swirling flow indicate that the Sherwood number distribution on one side of the pipe is enhanced and that on the other side is reduced owing to the appearance of the non-axisymmetric swirling flow, which results in the occurrence of non-axisymmetric pipe-wall thinning downstream of the orifice.
From x-ray telescopes to neutron scattering: Using axisymmetric mirrors to focus a neutron beam
Energy Technology Data Exchange (ETDEWEB)
Khaykovich, B., E-mail: email@example.com [Nuclear Reactor Laboratory, Massachusetts Institute of Technology, 138 Albany Street, Cambridge, MA 02139 (United States); Gubarev, M.V. [Marshall Space Flight Center, NASA, VP62, Huntsville, AL 35812 (United States); Bagdasarova, Y. [Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Ramsey, B.D. [Marshall Space Flight Center, NASA, VP62, Huntsville, AL 35812 (United States); Moncton, D.E. [Nuclear Reactor Laboratory, Massachusetts Institute of Technology, 138 Albany Street, Cambridge, MA 02139 (United States); Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States)
We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in X-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We implemented a system containing four nested Ni mirror pairs, which was tested by the focusing of a polychromatic neutron beam at the MIT Reactor. In addition, we have carried out extensive ray-tracing simulations of the mirrors and their performance in different situations. The major advantages of the Wolter mirrors are nesting for large angular collection and aberration-free performance. We discuss how these advantages can be utilized to benefit various neutron scattering methods, such as imaging, SANS, and time-of-flight spectroscopy.
From x-ray telescopes to neutron scattering: Using axisymmetric mirrors to focus a neutron beam
International Nuclear Information System (INIS)
We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in X-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We implemented a system containing four nested Ni mirror pairs, which was tested by the focusing of a polychromatic neutron beam at the MIT Reactor. In addition, we have carried out extensive ray-tracing simulations of the mirrors and their performance in different situations. The major advantages of the Wolter mirrors are nesting for large angular collection and aberration-free performance. We discuss how these advantages can be utilized to benefit various neutron scattering methods, such as imaging, SANS, and time-of-flight spectroscopy.
Pinch-off of axisymmetric vortex pairs in the limit of vanishing vortex line curvature
Sadri, V.; Krueger, P. S.
Pinch-off of axisymmetric vortex pairs generated by flow between concentric cylinders with radial separation ΔR was studied numerically and compared with planar vortex dipole behavior. The axisymmetric case approaches planar vortex dipole behavior in the limit of vanishing ΔR. The flow was simulated at a jet Reynolds number of 1000 (based on ΔR and the jet velocity), jet pulse length-to-gap ratio ( /L Δ R ) in the range 10-20, and gap-to-outer radius ratio ( /Δ R R o ) in the range 0.01-0.1. Contrary to investigations of strictly planar flows, vortex pinch-off was observed for all gap sizes investigated. This difference was attributed to the less constrained geometry considered, suggesting that even very small amounts of vortex line curvature and/or vortex stretching may disrupt the absence of pinch-off observed in strictly planar vortex dipoles.
Magnetic design of the axisymmetric throttle-coil addition to the tandem mirror experiment-upgrade
International Nuclear Information System (INIS)
The TMX-U magnet set has incorporated new axisymmetric throttle coils and fan-reversing transition magnets. This new magnet geometry, which will allow for the experimental verification of new physics issues related to axicell tandem mirrors, encompasses both engineering and physics considerations. Engineering considerations include structural integrity plus neutral beam and diagnostic access. Physics issues include the stability and radial transport of the confined plasma. We have calculated the magnetic field using the magnetic field code, EFFI, and the plasma stability and surface curvatures using the plasma stability code, TEBASCO. Our magnet design allows the axisymmetric throttle mirror to be varied from the end-cell mirror value of 2 to a peak of 6 T
Orbital effect in the stationary axisymmetric field
Institute of Scientific and Technical Information of China (English)
Gong Tian-Xi; Wang Yong-Jiu
This paper uses an elegant mathematical method to calculate the orbital effects in the axisymmetric field created by the spinning mass with electric charge and a large number of magnetic monopoles. In comparison with that in the Reissner-Nordstrom (R-N) field, the correction terms caused by the spinning mass decrease the advanced effect as the revolution direction of the test particle coincides with that of the Kerr field, however, the correction terms caused by the spinning charged mass increase the advance effect as the revolution direction of the test particle coincides with that of the Kerr-Newman-Kasnya (KNK) field. Generalizing the effect in the axisymmetric field, it obtains interesting results by discussing the parameters of the celestial body, these parameters provide a feasible experimental verification of the general relativity.
Global stability analysis of axisymmetric boundary layers
Vinod, N
This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes(LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes are nega...
Orbital effect in the stationary axisymmetric field
International Nuclear Information System (INIS)
This paper uses an elegant mathematical method to calculate the orbital effects in the axisymmetric field created by the spinning mass with electric charge and a large number of magnetic monopoles. In comparison with that in the Reissner–Nordström (R–N) field, the correction terms caused by the spinning mass decrease the advanced effect as the revolution direction of the test particle coincides with that of the Kerr field, however, the correction terms caused by the spinning charged mass increase the advance effect as the revolution direction of the test particle coincides with that of the Kerr–Newman–Kasnya (KNK) field. Generalizing the effect in the axisymmetric field, it obtains interesting results by discussing the parameters of the celestial body, these parameters provide a feasible experimental verification of the general relativity. (general)
An axisymmetric steady state vortex ring model
Wang, Ruo-Qian
Based on the solution of Atanasiu et al. (2004), a theoretical model for axisymmetric vortex flows is derived in the present study by solving the vorticity transport equation for an inviscid, incompressible fluid in cylindrical coordinates. The model can describe a variety of axisymmetric flows with particular boundary conditions at a moderately high Reynolds number. This paper shows one example: a high Reynolds number laminar vortex ring. The model can represent a family of vortex rings by specifying the modulus function using a Rayleigh distribution function. The characteristics of this vortex ring family are illustrated by numerical methods. For verification, the model results compare well with the recent direct numerical simulations (DNS) in terms of the vorticity distribution and streamline patterns, cross-sectional areas of the vortex core and bubble, and radial vorticity distribution through the vortex center. Most importantly, the asymmetry and elliptical outline of the vorticity profile are well capt...
Collapse of Non-Axisymmetric Cavities
Enriquez, Oscar R.; Peters, Ivo R.; Gekle, Stephan; Schmidt, Laura; Versluis, Michel; van der Meer, Devaraj; Lohse, Detlef
A round disk with a harmonic disturbance impacts on a water surface and creates a non-axisymmetric cavity which collapses under the influence of hydrostatic pressure. We use disks deformed with mode m=2 to m=6. For all mode numbers we find clear evidence for a phase inversion of the cavity wall during the collapse. We present a fluid dynamics video showing high speed imaging of different modes, pointing out the characteristic features during collapse.
Institute of Scientific and Technical Information of China (English)
A method for analyzing the elasticity problem of cubic quasicrystal is developed. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the solutions of elastic field of cubic quasicrystal with a penny-shaped crack are obtained,and the stress intensity factor and strain energy release rate are determined.
Numerical description of cavitation on axisymmetric bodies
Energy Technology Data Exchange (ETDEWEB)
Hickox, C.E.; Hailey, C.E.; Wolfe, W.P.; Watts, H.A.; Gross, R.J.; Ingber, M.S.
This paper reports on ongoing studies which are directed toward the development of predictive techniques for the modeling of steady cavitation on axisymmetric bodies. The primary goal of the modeling effort is the prediction of cavity shape and pressure distribution from which forces and moments can be calculated. Here we present an overview of the modeling techniques developed and compare predictions with experimental data obtained from water tunnel tests for both limited and supercavitation. 14 refs., 4 figs.
Analysis of Axisymmetric Crushing of Frusta
M.M.A. Khan; H. Abbas; N K Gupta
The paper presents a curved-fold model with variable straight length for the axisymmetric crushing of thin frusta. The folding considered in the model is partly inside and partly outside. The variation of circumferential strain during the formation of a fold has been taken into account. The size of the fold and mean, as well as variation of crushing load, has been computed mathematically. The study is purely analytical and does not involve any empirical constant; and hence, can be used...
Axisymmetric long liquid bridges stability and resonances
Meseguer Ruiz, José; Sanz Andres, Angel Pedro; Perales Perales, José Manuel
In this paper mathematical expressions for minimum-volume stability limits and resonance frequencies of axisymmetric long liquid bridges are presented. These expressions are valid for a wide range of liquid bridge configurations, accounting for ef-fects like unequal disks and axial microgravity in the case of minimum-volume stability limits,and unequal disks, axial microgravity,non-zero viscosity and liquid bridge volume different from the cylindrical one in the case of resonance frequenc...
Axisymmetric oscillations of magnetic neutron stars
Lee, U
We calculate axisymmetric oscillations of rotating neutron stars composed of the surface fluid ocean, solid crust, and fluid core, taking account of a dipole magnetic field as strong as $B_S\\sim 10^{15}$G at the surface. The adiabatic oscillation equations for the solid crust threaded by a dipole magnetic field are derived in Newtonian dynamics, on the assumption that the axis of rotation is aligned with the magnetic axis so that perturbations on the equilibrium can be represented by series expansions in terms of spherical harmonic functions $Y_l^m(\\theta,\\phi)$ with different degrees $l$ for a given azimuthal wave number $m$ around the the magnetic axis. Although the three component models can support a rich variety of oscillation modes, axisymmetric ($m=0$) toroidal $_{l}t_n$ and spheroidal $_ls_n$ shear waves propagating in the solid crust are our main concerns, where $l$ and $n$ denote the harmonic degree and the radial order of the modes, respectively. In the absence of rotation, axisymmetric spheroidal ...
Stabilization of the vertical instability by non-axisymmetric coils
Turnbull, A. D.; Reiman, A. H.; Lao, L. L.; Cooper, W. A.; Ferraro, N. M.; Buttery, R. J.
In a published Physical Review Letter (Reiman 2007 Phys. Rev. Lett. 99 135007), it was shown that axisymmetric (or vertical) stability can be improved by placing a set of parallelogram coils above and below the plasma oriented at an angle to the constant toroidal planes. The physics of this stabilization can be understood as providing an effective additional positive stability index. The original work was based on a simplified model of a straight tokamak and is not straightforwardly applicable to a finite aspect ratio, strongly shaped plasma such as in DIII-D. Numerical calculations were performed in a real DIII-D -like configuration to provide a proof of principal that 3-D fields can, in fact raise the elongation limits as predicted. A four field period trapezioid-shaped coil set was developed in toroidal geometry and 3D equilibria were computed using trapezium coil currents of 10 kA , 100 kA , and 500 kA . The ideal magnetohydrodynamics growth rates were computed as a function of the conformal wall position for the n = 0 symmetry-preserving family. The results show an insignificant relative improvement in the stabilizing wall location for the two lower coil current cases, of the order of 10‑3 and less. In contrast, the marginal wall position is increased by 7% as the coil current is increased to 500 kA , confirming the main prediction from the original study in a real geometry case. In DIII-D the shift in marginal wall position of 7% would correspond to being able to move the existing wall outward by 5 to 10 cm. While the predicted effect on the axisymmetric stability is real, it appears to require higher coil currents than could be provided in an upgrade to existing facilities. Additional optimization over the pitch of the coils, the number of field periods and the coil positions, as well as plasma parameters, such as the internal inductivity {{\\ell}\\text{i}} , β , and {{q}95} would mitigate this but seem unlikely to change the conclusion.
Basin structure of the San Fernando and Santa Clarita Valleys and geometry of the Northridge and San Fernando faults as determined from the Los Angeles Region Seismic Experiment, Phase II (LARSE II)
Lutter, W. J.; Ryberg, T.; Fuis, G. S.; Murphy, J. M.; Okaya, D. A.
We acquired combined refraction and low-fold reflection data along a north-south-trending profile through the epicentral regions of the 1994 M 6.7 Northridge and 1971 M 6.7 San Fernando earthquakes as part of the Los Angeles Region Seismic Experiment, Phase II (LARSE II). The chief goal of LARSE is to image sedimentary basins and faults in the Los Angeles region to better understand and mitigate earthquake hazards associated with sedimentary basins and hidden faults. The LARSE II profile crossed the San Fernando and Santa Clarita Valleys, locations of the Northridge and San Fernando earthquakes, respectively. Refraction and reflection data show asymmetric basins beneath both valleys. Stacked wide-angle basin-bottom reflections and iso-velocity lines dip gently northward from the Santa Monica Mts, on the south margin of the San Fernando Valley, to 5-6 km below sea level in the northern part of the San Fernando Valley. Similar reflections and iso-velocity lines dip southward from the Sierra Pelona, on the north margin of the Santa Clarita Valley, to 3.5-4.5 km below sea level at the San Gabriel fault, in the central part of the Santa Clarita Valley. In both valleys, the basin-bottom reflections are generally slightly below the 5 km/s iso-velocity line, indicating that ``basement'' beneath these two valleys has velocities generally upwards of 5 km/s. In the San Fernando Valley, the basin-bottom reflections are truncated on the north by what we interpret to be the Northridge Hills blind thrust fault. In the Santa Clarita Valley, these reflections are truncated on the south at the steeply north-dipping San Gabriel fault. The region between these two faults, including the Santa Susana Mts and the southern part of the Santa Clarita Valley is characterized by complexity in both the velocity model and reflectivity. Below ~10-km depth, reflectivity is higher in the hanging walls of the Northridge and San Fernando faults than in the footwalls. The Northridge fault dips ~30o
Robinson, Gilbert de B
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Connes, Alain
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Berger, Marcel
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Desseyn, H. O.; And Others
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural
Low Cost Method of Manufacturing Cooled Axisymmetric Scramjets Project
National Aeronautics and Space Administration — Scramjet engine developers are working on advanced axisymmetric engine concepts that may not be feasible due to limitations of currently available manufacturing...
Preferential axisymmetric field growth in kinematic geodynamo models
Livermore, Philip W.; Jackson, Andrew
Earth's magnetic field, generated by fluid motion and inductive processes in Earth's core, has a predominantly axisymmetric dipolar component. Yet indefinite self-excitation of purely axisymmetric fields through any dynamo mechanism is specifically disallowed, begging the question of why the geodynamo sustains this dominant axisymmetric component. By considering a number of different fluid flow models modified from existing studies, we show that axisymmetric fields are consistently the most easily regenerated magnetic fields on short timescales, despite the fact that on long timescales they must die away. We argue that this transient field generation may play an important role in generating Earth's magnetic field, especially in the recovery after reversals.
Axisymmetric oscillations of magnetic neutron stars
Lee, Umin
We calculate axisymmetric oscillations of rotating neutron stars composed of the surface fluid ocean, solid crust and fluid core, taking account of a dipole magnetic field as strong as BS ~ 1015 G at the surface. The adiabatic oscillation equations for the solid crust threaded by a dipole magnetic field are derived in Newtonian dynamics, on the assumption that the axis of rotation is aligned with the magnetic axis so that perturbations on the equilibrium can be represented by series expansions in terms of spherical harmonic functions Yml(θ, φ) with different degrees l for a given azimuthal wave number m around the magnetic axis. Although the three component models can support a rich variety of oscillation modes, axisymmetric (m = 0) toroidal ltn and spheroidal lsn shear waves propagating in the solid crust are our main concerns, where l and n denote the harmonic degree and the radial order of the modes, respectively. In the absence of rotation, axisymmetric spheroidal and toroidal modes are completely decoupled, and we consider the effects of rotation on the oscillation modes only in the limit of slow rotation. We find that the oscillation frequencies of the fundamental toroidal torsional modes ltn in the crust are hardly affected by the magnetic field as strong as BS ~ 1015 G at the surface. As the radial order n of the shear modes in the crust becomes higher, however, both spheroidal and toroidal modes become susceptible to the magnetic field, and their frequencies in general get higher with increasing BS. We also find that the surface g modes and the crust/ocean interfacial modes are suppressed by a strong magnetic field, and that there appear magnetic modes in the presence of a strong magnetic field.
Axisymmetric instability in a thinning electrified jet.
Dharmansh; Chokshi, Paresh
The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated. PMID:27176407
Comment on "Conformally flat stationary axisymmetric metrics"
Barnes, A; Senovilla, José MM
Garcia and Campuzano claim to have found a previously overlooked family of stationary and axisymmetric conformally flat spacetimes, contradicting an old theorem of Collinson. In both these papers it is tacitly assumed that the isometry group is orthogonally transitive. Under the same assumption, we point out here that Collinson's result still holds if one demands the existence of an axis of symmetry on which the axial Killing vector vanishes. On the other hand if the assumption of orthogonal transitivity is dropped, a wider class of metrics is allowed and it is possible to find explicit counterexamples to Collinson's result.
Reversed straining in axisymmetric compression test
DEFF Research Database (Denmark)
Arentoft, Mogens; Wanheim, Tarras; Lindegren, Maria;
in an expansion of the bore. After unloading, the container will try to reduce this expansion and thus in many cases cause a reversed plastic deformation of the work-piece. This will have an effect on the resulting diameter of the work-piece and – above all – on the resulting mechanical properties. In order...... to simulate these conditions a reversed axisymmetrical material tester is designed and constructed. Three different materials were tested, aluminum alloy AA6082, technically pure copper (99.5%) and cold forging steel Ma8, at different temperatures found during cold forging....
Travelling waves in axisymmetric pipe flows
International Nuclear Information System (INIS)
The weakly nonlinear dynamics of axisymmetric Poiseuille pipe flows is investigated. It is shown that small perturbations of the laminar flow with amplitude ε ∼ O(Re−2.5) obey a coupled system of nonlinear Korteweg–de Vries-type equations. To leading order, these support inviscid soliton-type solutions and periodic waves in the form of toroidal vortex tubes that, due to viscous effects, slowly decay in time on a longer time scale t ∼ O(ε−2.5). (paper)
Distribution of Topological Defects on Axisymmetric Surface
Institute of Scientific and Technical Information of China (English)
SI Tie-Yan; DUAN Yi-Shi
We propose a general method of determining the distribution of topological defects on axisymmetric surface,and study the distribution of topological defects on biconcave-discoid surface, which is the geometric configuration of red blood cell. There are three most possible cases of the distribution of the topological defects on the biconcave surface:four defects charged with 1/2, two defects charged with +1, or one defect charged with 2. For the four defect charged with 1/2, they sit at the vertices of a square imbedded in the equator of biconcave surface.
Analysis of Axisymmetric Crushing of Frusta
Directory of Open Access Journals (Sweden)
M.M.A. Khan
Full Text Available The paper presents a curved-fold model with variable straight length for the axisymmetric crushing of thin frusta. The folding considered in the model is partly inside and partly outside. The variation of circumferential strain during the formation of a fold has been taken into account. The size of the fold and mean, as well as variation of crushing load, has been computed mathematically. The study is purely analytical and does not involve any empirical constant; and hence, can be used in general. The model's predictions have been compared with experimental results and a reasonably good agreement has been observed. "
Institute of Scientific and Technical Information of China (English)
CAI Yuan-qiang; XU Chang-jie; ZHENG Zao-feng; WU Da-zhi
Based on Biot's dynamic consolidation equations, by means of Laplace-Hankel transform technology, the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arbitrary excitations were derived. Influence of the reflected wave generated by the boundary was revealed. Numerical results indicate that the vibration frequency has some effect on the vertical displacement of saturated soil. The vertical displacement at the surface of saturated soil lags in phase with the load. Furthermore, the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied, but when the load becomes stable, the effect is inapparent.
Snap-through of the system of open shallow axi-symmetric bimetallic shell by non-linear theory
Jakomin, Marko; Kosel, Tadej; Kosel, Franc; Batista, Milan
The paper deals with stresses, strains and buckling conditions in the thin axi-symmetric shallow bimetallic shells with circular opening at the top of the shell. According to the third order theory by the Czech researcher E. Chawalla, which takes into account the equilibrium state of forces and moments acting on the deformed system, the paper presents a model for mathematical description of the system's geometry, stresses, thermo-elastic strains and displacements. The mathematical formulation...
Axi-Symmetric Simulation of the Slump Flow Test for Self-Compacting
DEFF Research Database (Denmark)
Thrane, Lars Nyholm; Szabo, Peter; Geiker, Mette Rica;
One of the main obstacles for further development of Self-Compacting Concrete (SCC)is to relate the fresh concrete properties, form geometry, reinforcement configuration, and casting technique to the form filling ability. Simulation of the filling ability might provide a tool in obtaining this goal....... This paper presents a numerical axi-symmetric approach for simulation of the slump flow test. Simulations are compared to experimental test results on the rheological properties and slump flow. Former rheological investigations on SCC indicate a non-Newtonian behaviour according to the Bingham model....
Detailed Decomposition of Galaxy Images. II. Beyond Axisymmetric Models
Peng, Chien Y; Impey, Chris D; Rix, Hans-Walter
We present a two-dimensional (2-D) fitting algorithm (GALFIT, Version 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2-D fitting algorithms by allowing for irregular, curved, logarithmic and power-law spirals, ring and truncated shapes in otherwise traditional parametric functions like the Sersic, Moffat, King, Ferrer, etc., profiles. One can mix and match these new shape features freely, with or without constraints, apply them to an arbitrary number of model components and of numerous profile types, so as to produce realistic-looking galaxy model images. Yet, despite the potential for extreme complexity, the meaning of the key parameters like the Sersic index, effective radius or luminosity remain intuitive and essentially unchanged. The new features have an interesting potential for use to quantify the degree of asymmetry of galaxies, to quantify low surface brightness tidal features beneath and bey...
Petersen, Peter
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
Momentum and Heat Transfer in MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet
Directory of Open Access Journals (Sweden)
T. R. Mahapatra
Full Text Available In this paper we present a mathematical analysis for the magneto hydrodynamic (MHD axi-symmetric stagnation-point flow and heat transfer over a shrinking sheet which shrinks axi-symmetrically in its own plane. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then these equations are solved numerically by shooting technique. Thermal conductivity is assumed to vary linearly with the temperature. Temperature profiles are obtained for two different types of heating process namely (i the sheet with prescribed surface temperature (PST and (ii the sheet with prescribed surface heat flux (PHF. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.
Axisymmetric bending oscillations of stellar disks
Sellwood, J A
Self-gravitating stellar disks with random motion support both exponentially growing and, in some cases, purely oscillatory axisymmetric bending modes, unlike their cold disk counterparts. A razor-thin disk with even a very small degree of random motion in the plane is both unstable and possesses a discrete spectrum of neutral modes, irrespective of the sharpness of the edge. Random motion normal to the disk plane has a stabilizing effect but at the same time allows bending waves to couple to the internal vibrations of the particles, which causes the formerly neutral modes to decay through Landau damping. Focusing first on instabilities, I here determine the degree of random motion normal to the plane needed to suppress global, axisymmetric, bending instabilities in a family of self-gravitating disks. As found previously, bending instabilities are suppressed only when the thickness exceeds that expected from a na\\"\\i ve local criterion when the degree of pressure support within the disk plane is comparable to...
Linear lateral vibration of axisymmetric liquid briges
Ferrera, C.; Montanero, J. M.; Cabezas, M. G.
A liquid bridge is a mass of liquid sustained by the action of the surface tension force between two parallel supporting disks Apart from their basic scientific interest a liquid bridge can be considered as the simplest idealization of the configuration appearing in the floating zone technique used for crystal growth and purification of high melting point materials footnote Messeguer et al emph Crystal Growth Res bf 5 27 1999 This has conferred considerable interest on the study of liquid bridges not only in fluid mechanics but also in the field of material engineering The axisymmetric dynamics of an isothermal liquid bridge has been frequently analysed over the past years The studies have considered different phenomena such as free oscillations footnote Montanero emph E J Mech B Fluids bf 22 169 2003 footnote Acero and Montanero emph Phys Fluids bf 17 078105 2005 forced vibrations footnote Perales and Messeguer emph Phys Fluids A bf 4 1110 1992 g-jitter effects footnote Messeguer and Perales emph Phys Fluids A bf 3 2332 1991 extensional deformation footnote Zhang et al emph J Fluid Mech bf 329 207 1996 and breakup process footnote Espino et al emph Phys Fluids bf 14 3710 2002 among others Works considering the nonaxisymmetric dynamical behaviour of a liquid bridge has been far less common footnote Sanz and Diez emph J Fluid Mech bf 205 503 1989 In the present study the linear vibration of an axisymmetric liquid
Institute of Scientific and Technical Information of China (English)
谢锡麟; 麻伟巍; 周慧良
The dynamical behaviors of coherent structures in countercurrent axisymmetric shear flows are experimentally studied. The forward velocity U1 and the velocity ratio R = (U1 - U2)/(U1 +U2), where U2 denotes the suction velocity, are considered as the control parameters. Two kinds of vortex structures, i.e., axisymmetric and helical structures, were discovered with respect to different regimes in the R versus U1 diagram. In the case of U1 ranging from 3 to 20 m/s and R from 1 to 3, the axisymmetric structures play an important role. Based on the dynamical behaviors of axisymmetric structures, a critical forward velocity Ucr1 = 6.8 m/s was defined, subsequently, the subcritical velocity regime: U1 > Ucr1 and the supercritical velocity regime: U1 < Ucr1. In the subcritical velocity regime,the flow system contains shear layer self-excited oscillations in a certain range of the velocity ratio with respect to any forward velocity. In the supercritical velocity regime, the effect of the velocity ratio could be explained by the relative movement and the spatial evolution of the axisymmetric structure undergoes the following stages: (1) Kelvin-Helmholtz instability leading to vortex rolling up, (2) first time vortex agglomeration, (3) jet column self-excited oscillation, (4) shear layer self-excited oscillation,(5) "ordered tearing", (6) turbulence in the case of U1 < 4 m/s (the "ordered tearing" does not exist when U1 > 4m/s), correspondingly, the spatial evolution of the temporal asymptotic behavior of a dynamical system can be described as follows: (1) Hopf bifurcation, (2) subharmonic bifurcation, (3)reversed superharmonic bifurcation, (4) superharmonic bifurcation, (5) chaos ("weak turbulence") in the case of U1 < 4 m/s (superharmonic bifurcation does not exist when U1 > 4 m/s). The proposed new terms, superharmonic and reversed superharmonic bifurcations, are characterized of the frequency doubling rather than the period doubling. A kind of unfamiliar
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
Analogue Kerr-like geometries in a MHD inflow
Noda, Sousuke; Takahashi, Masaaki
We present a model of the analogue black hole in magnetohydrodynamic (MHD) flow. For a two dimensional axisymmetric stationary trans-magnetosonic inflow with a sink, using the dispersion relation of the MHD waves, we introduce the effective geometries for magnetoacoustic waves propagating in the MHD flow. Investigating the properties of the effective potentials for magnetoacoustic rays, we find that the effective geometries can be classified into five types which include analogue spacetimes of the Kerr black hole, ultra spinning stars with ergoregions and spinning stars without ergoregions. We address the effects of the magnetic pressure and the magnetic tension on each magnetoacoustic geometries.
Compact neutron imaging system using axisymmetric mirrors
Khaykovich, Boris; Moncton, David E; Gubarev, Mikhail V; Ramsey, Brian D; Engelhaupt, Darell E
A dispersed release of neutrons is generated from a source. A portion of this dispersed neutron release is reflected by surfaces of a plurality of nested, axisymmetric mirrors in at least an inner mirror layer and an outer mirror layer, wherein the neutrons reflected by the inner mirror layer are incident on at least one mirror surface of the inner mirror layer N times, wherein N is an integer, and wherein neutrons reflected by the outer mirror are incident on a plurality of mirror surfaces of the outer layer N+i times, where i is a positive integer, to redirect the neutrons toward a target. The mirrors can be formed by a periodically reversed pulsed-plating process.
Lagrangian mixing in an axisymmetric hurricane model
Directory of Open Access Journals (Sweden)
B. Rutherford
Full Text Available This paper discusses the extension of established Lagrangian mixing measures to make them applicable to data extracted from a 2-D axisymmetric hurricane simulation. Because of the non-steady and unbounded characteristics of the simulation, the previous measures are extended to a moving frame approach to create time-dependent mixing rates that are dependent upon the initial time of particle integration, and are computed for nonlocal regions. The global measures of mixing derived from finite-time Lyapunov exponents, relative dispersion, and a measured mixing rate are applied to distinct regions representing different characteristic feautures within the model. It is shown that these time-dependent mixing rates exhibit correlations with maximal tangential winds during a quasi-steady state, establishing a connection between mixing and hurricane intensity.
The Parker instability in axisymmetric filaments: Final equilibria with longitudinal magnetic field
Sanchez-Salcedo, F J
We study the final equilibrium states of the Parker instability arising from an initially unstable cylindrical equilibrium configuration of gas in the presence of a radial gravitational field and a longitudinal magnetic field. The aim of this work is to compare the properties of the nonlinear final equilibria with those found in a system with Cartesian geometry. Maps of the density and magnetic field lines, when the strength of the gravitational field is constant, are given in both geometries. In the axisymmetric model, the magnetic field tends to expand in radius, forming magnetic arcades, while knots of gas are formed because the plasma drains radially and strangulates the magnetic field lines, leading to the formation of magnetic bottlenecks. We find that the magnetic buoyancy and the drainage of gas along field lines are less efficient under axial symmetry than in a Cartesian atmosphere. As a consequence, the column density enhancement arising in gas condensations in the axially-symmetric model is smaller...
Numerical and experimental investigation of unsteady three-dimensional separation on axisymmetric bodies
International Nuclear Information System (INIS)
Highlights: • Flow visualizations from experiments and simulations for two axisymmetric bodies. • Improved understanding of mean flow separation topology for hemisphere cylinder. • Modal analysis of unsteady fluid dynamics. • Discussion of possible hydrodynamic instabilities. -- Abstract: The understanding of unsteady three-dimensional separation is lagging behind the understanding of two-dimensional separation due to its greater complexity and the limited amount of data for universal or canonical flow problems. Three-dimensional separation occurs, for example, when low aspect ratio devices such as submarines and torpedoes are operated at large angles of attack, α. Two low aspect ratio geometries, the DARPA Suboff bare hull geometry, which is a prototypical submarine shape, and a hemisphere-cylinder geometry were investigated. Numerical simulations and water tunnel experiments for the Suboff geometry for a Reynolds number based on diameter of Re=10,000 show little flow separation at α=30°. A hemisphere-cylinder geometry was derived by replacing the Suboff forebody with a hemisphere. Simulations and water tunnel experiments were carried out for Re=2000 and 5000. For α=10° a large shedding separation bubble is observed on the leeward side. For α=30° two counter-rotating leeward vortices appear and shedding is reduced. Proper orthogonal decomposition and Fourier analysis in time are employed for investigating the unsteady fluid dynamics. Conclusions are drawn with respect to the mean flow topology and possibly relevant hydrodynamic instabilities
Non-Axisymmetric Equilibrium Reconstruction for Stellarators, Reversed Field Pinches and Tokamaks
International Nuclear Information System (INIS)
Full text: Equilibrium reconstruction is the process of minimizing the mismatch between modeled and observed signals by changing the parameters that specify the equilibrium. While stellarator equilibria are inherently non-axisymmetric, non-axisymmetric effects are also crucial for understanding stability and confinement of high-performance reversed field pinch and tokamak plasmas. Therefore, two-dimensional reconstruction tools are not adequate for fully exploring 3D plasmas. The V3FIT and STELLOPT codes are 3D equilibrium reconstruction codes, both based on the VMEC 3D equilibrium code. VMEC models field-period symmetric 3D flux surface geometry but does not treat magnetic islands and chaotic regions. VMEC requires the specification of the pressure and either rotational transform or toroidal current profiles, as functions of either the toroidal or poloidal flux. VMEC can treat both axisymmetric and non-axisymmetric configurations, both free- and fixed-boundary equilibria, and both stellarator-symmetric and non-stellarator-symmetric equilibria. Both V3FIT and STELLOPT can utilize signals from magnetic diagnostics, soft X-rays (SXR), Thomson scattering, and geometrical information from plasma limiters. STELLOPT can also utilize Motional Stark Effect (MSE) signals. Both calculate a finite difference approximation to a Jacobian for the signal-mismatch minimization. V3FIT and STELLOPT differ in the details of their minimization algorithms, their utilization of auxiliary profiles (like electron density and soft x-ray emissivity), and in their computation of model signals. V3FIT is currently in use on stellarators (HSX, CTH), reversed field pinches (RFX-mod) and tokamaks (DIII-D) for a wide variety of studies: interpretation of Pfirsch-Schliiter and bootstrap currents, design of new magnetic diagnostics, magnetic island generation, vertical instabilities, density-limit disruption activity, conformance of multiple data sources to a single set of flux surfaces, quasi
Coupled neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas
Lyons, Brendan C.
Neoclassical effects (e.g., the bootstrap current and neoclassical toroidal viscosity [NTV]) have a profound impact on many magnetohydrodynamic (MHD) instabilities, including tearing modes, edge-localized modes (ELMs), and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We present the first results of the DK4D code, a dynamic drift-kinetic equation (DKE) solver being developed for this application. In this study, DK4D solves a set of time-dependent, axisymmetric DKEs for the non-Maxwellian part of the electron and ion distribution functions (fNM) with linearized Fokker-Planck-Landau collision operators. The plasma is formally assumed to be in the low- to finite-collisionality regimes. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that fNM carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by an appropriate set of extended MHD equations. We will discuss computational methods used and benchmarks to other neoclassical models and codes. Furthermore, DK4D has been coupled to a reduced, transport-timescale MHD code, allowing for self-consistent simulations of the dynamic formation of the ohmic and bootstrap currents. Several applications of this hybrid code will be presented, including an ELM-like pressure collapse. We will also discuss plans for coupling to the spatially three-dimensional, extended MHD code M3D-C1 and generalizing to nonaxisymmetric geometries, with the goal of performing self-consistent hybrid simulations of tokamak instabilities and calculations of NTV torque. This work supported by the U.S. Department of Energy (DOE) under Grant Numbers DE-FC02-08ER54969 and DE-AC02-09CH11466.
Asymmetric and axisymmetric dynamics of tropical cyclones
Directory of Open Access Journals (Sweden)
J. Persing
Full Text Available We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D and axisymmetric (AX model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f-plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally-averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics and are generally not represented properly by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast time scales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since during the 3-D intensification process the convection has not yet organized
Modeling and simulation of axisymmetric stagnation flames
Sone, Kazuo
Laminar flame modeling is an important element in turbulent combustion research. The accuracy of a turbulent combustion model is highly dependent upon our understanding of laminar flames and their behavior in many situations. How much we understand combustion can only be measured by how well the model describes and predicts combustion phenomena. One of the most commonly used methane combustion models is GRI-Mech 3.0. However, how well the model describes the reacting flow phenomena is still uncertain even after many attempts to validate the model or quantify uncertainties. In the present study, the behavior of laminar flames under different aerodynamic and thermodynamic conditions is studied numerically in a stagnation-flow configuration. In order to make such a numerical study possible, the spectral element method is reformulated to accommodate the large density variations in methane reacting flows. In addition, a new axisymmetric basis function set for the spectral element method that satisfies the correct behavior near the axis is developed, and efficient integration techniques are developed to accurately model axisymmetric reacting flow within a reasonable amount of computational time. The numerical method is implemented using an object-oriented programming technique, and the resulting computer program is verified with several different verification methods. The present study then shows variances with the commonly used GRI-Mech 3.0 chemical kinetics model through a direct simulation of laboratory flames that allows direct comparison to experimental data. It is shown that the methane combustion model based on GRI-Mech 3.0 works well for methane-air mixtures near stoichiometry. However, GRI-Mech 3.0 leads to an overprediction of laminar flame speed for lean mixtures and an underprediction for rich mixtures. This result is slightly different from conclusion drawn in previous work, in which experimental data are compared with a one-dimensional numerical solutions
Numerical Simulation of Fibre Suspension Flow through an Axisymmetric Contraction and Expansion Passages by Brownian Configuration Field Method
Lu, Zhumin; Dou, Hua-Shu; Phan-Thien, Nhan; Yeo, Khoon Seng
In this paper, the finite element method is combined with the Brownian Configuration Field (BFC) method to simulate the fibre suspension flow in axisymmetric contraction and expansion passages. In order to solve for the high stress at high concentration, the Discrete Adaptive Viscoelastic Stress Splitting (DAVSS) method is employed. For the axisymmetric contraction and expansion passages with different geometry ratios, the results obtained are compared to available constitutive models and experiments. The predicted vortex length for dilute suspensions agrees well with experimental data in literature. Our numerical results show clearly the effect on vortex enhancement with increase of the volume fractions and the aspect ratios. Effect of aspect ratio of fibres on the vortex length is also studied. It is found that for the lower expansion ratio flows the vortex dimension in the corner region is fairly independent of fibre concentration and aspect ratio of fibres while the said vortex dimension increases with th...
Non-axisymmetric, scale-free, razor-thin discs
Syer, D; Syer, Dave; Tremaine, Scott
Galaxies exhibit a variety of non-axisymmetric structure (bars, spiral structure, lopsided structure, etc.). These suggest the following general problem: what are the possible stationary configurations of a two-dimensional self-gravitating fluid other than an axisymmetric razor-thin disc? We address a modest component of this problem: we seek non-axisymmetric razor-thin discs of two-dimensional barotropic fluid that are stationary in an inertial frame. We distinguish between `razor-thin' and `two-dimensional,' applying the latter term to the equation of state. Furthermore we assume that our systems are scale-free, which reduces the partial differential equations describing the system to ordinary differential equations. We also allow for the presence of an axisymmetric background potential. This simple and highly idealized problem already exhibits a rich variety of solutions, the richest being for m=1 symmetry.
Axisymmetric Consolidation of Unsaturated Soils by Differential Quadrature Method
Wan-Huan Zhou
Axisymmetric consolidation in a sand drain foundation is a common problem in foundation engineering. In unsaturated soils, the excess pore-water and pore-air pressures simultaneously change during the consolidation procedure; and the solutions are not easy to obtain. The present paper uses the differential quadrature method (DQM) for axisymmetric consolidation of unsaturated soils in a sand drain foundation. The radial seepage of sand drain foundation is considered based on the framework of F...
Parametric study of axisymmetric fusion devices
International Nuclear Information System (INIS)
Three different axisymmetric magnetic mirror fusion machines are examined in order to optimize the ratio the fusion power produced by them to the power injected into them to maintain the plasma. These three devices were chosen to study the continuum between a simple mirror and a tandem mirror. This allowed the evolutionary process leading from the simple to the tandem mirror to be examined in detail. The Kelley mirror, which corresponds to the middle step, was examined in depth for the first time. A computer code that models the plasma in these machines was written to investigate the steady-state operation of these machines. The balance equations are solved by using an ordinary differential equation solver, LSODE, to numerically solve the system of differential equations. The computer model was used to examine parameter space to optimize Q for each of the three machines. When feasible, a comparison with a Fokker-Planck code was made for the optimal Q case for each machine. Finally, the possible roles these devices might fill was discussed
Axisymmetric, Ventilated Supercavitation in Unsteady, Horizontal Flow
Kawakami, Ellison; Lee, Seung-Jae; Arndt, Roger
Drag reduction and/or speed augmentation of marine vehicles by means of supercavitation is a topic of great interest. During the initial launch of a supercavitating vehicle, an artificial supercavity is required until the vehicle can reach conditions at which a natural supercavity can be sustained. Previous studies at Saint Anthony Falls Laboratory (SAFL) focused on the behavior of ventilated supercavities in steady horizontal flows. In open waters, vehicles can encounter unsteady flows, especially when traveling under waves. A study has been carried out at SAFL to investigate the effects of unsteady flow on axisymmetric supercavities. An attempt is made to duplicate sea states seen in open waters. In an effort to track cavity dimensions throughout a wave cycle, an automated cavity tracking script has been developed. Using a high speed camera and the proper software, it is possible to synchronize cavity dimensions with pressure measurements taken inside the cavity. Results regarding supercavity shape, ventilation demand, cavitation parameters and closure methods are presented. It was found that flow unsteadiness caused a decrease in the overall length of the supercavity while having only a minimal effect on the maximum diameter. The supercavity volume varied with cavitation number and a possible relationship between the two is being explored. (Supported by ONR)
Axisymmetric Vortex Simulations with Various Turbulence Models
Directory of Open Access Journals (Sweden)
Brian Howard Fiedler
Full Text Available The CFD code FLUENTTM has been applied to a vortex within an updraft above a frictional lower boundary. The sensitivity of vortex intensity and structure to the choice of turbulent model is explored. A high Reynolds number of 108 is employed to make the investigation relevant to the atmospheric vortex known as a tornado. The simulations are axisymmetric and are integrated forward in time to equilibrium. In a variety of turbulence models tested, the Reynolds Stress Model allows for the greatest intensification of the vortex, with the azimuthal wind speed near the surface being 2.4 times the speed of the updraft, consistent with the destructive nature of tornadoes. The Standard k-e Model, which is simpler than the Reynolds Stress Model but still more detailed than what is commonly available in numerical weather prediction models, produces an azimuthal wind speed near the surface of at most 0.6 times the updraft speed.
Exact vectorial law for axisymmetric MHD turbulence
Galtier, S.
3D incompressible MHD turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar (1950) may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations a la von Karman-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field. We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector and we derive an exact vectorial law which is parametrized by the intensity of anisotropy. The critical balance proposed by Goldreich & Sridhar (1995) is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to the mean field are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.
Exact Vectorial Law for Axisymmetric Magnetohydrodynamics Turbulence
Galtier, S.
Three-dimensional incompressible magnetohydrodynamics turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations à la von Kármán-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field B0 . We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector r and we derive an exact vectorial law which is parameterized by the intensity of anisotropy. The critical balance proposed by Goldreich & Sridhar is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to B0 are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.
Transport of Colloids along Corners: Visualization of Evaporation-Induced Flows beyond the Axisymmetric Condition.
Vélez-Cordero, J Rodrigo; Yáñez Soto, Bernardo; Arauz-Lara, José L
Nonhomogeneous evaporation fluxes have been shown to promote the formation of internal currents in sessile droplets, explaining the patterns that suspended particles leave after the droplet has dried out. Although most evaporation experiments have been conducted using spherical-cap-shaped drops, which are essentially in an axisymmetric geometry, here we show an example of nonhomogeneous evaporation in asymmetric geometries, which is visualized by following the motion of colloidal particles along liquid fingers forming a meniscus at square corners. It is found that the particle's velocity increases with the diffusive evaporation factor [Formula: see text] for the three tested fluids: water, isopropyl alcohol (IPA), and ethanol (EtOH). Here, [Formula: see text] is the vapor diffusivity in air, RH is the relative amount of vapor in the atmosphere, and cs is the saturated vapor concentration. We observed that in IPA and EtOH the internal currents promote a 3D spiral motion, whereas in water the particle's trajectory is basically unidirectional. By adding 0.25 critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS) surfactant in water, a velocity blast was observed in the whole circulation flow pattern, going from [Formula: see text] to nearly [Formula: see text] in the longitudinal velocity component. To assess the effect of breaking the axisymmetric condition on the evaporation flux profile, we numerically solved the diffusive equation in model geometries that preserve the value of the contact angle θ but introduce an additional angle ϕ that characterizes the solid substrate. By testing different combinations of θ and ϕ, we corroborated that the evaporation flux increases when the substrate and the gas-liquid curves meet at corners with increasing sharpness.
Extreme Black Holes and Near-Horizon Geometries
Li, Ka Ki; Li, Carmen
In this thesis we study near-horizon geometries of extreme black holes. We first consider stationary extreme black hole solutions to the Einstein-Yang-Mills theory with a compact semi-simple gauge group in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon AdS2 symmetry and deduce its near-horizon geometry must be that of the abelian embedded extreme Kerr-Newman (AdS) black hole. We sho...
Asymmetric and axisymmetric dynamics of tropical cyclones
Persing, J.; Montgomery, M. T.; McWilliams, J. C.; Smith, R. K.
We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics during a key spin-up period, and more generally are not solely diffusive. The effects of these eddies are thus not properly represented by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast timescales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since
Axisymmetric Control in Alcator C-Mod
Tinios, Gerasimos
This thesis investigates the degree to which linear axisymmetric modeling of the response of a tokamak plasma can reproduce observed experimental behavior. The emphasis is on the vertical instability. The motivation for this work lies in the fact that, once dependable models have been developed, modern control theory methods can be used to design feedback laws for more effective and efficient tokamak control. The models are tested against experimental data from the Alcator C-Mod tokamak. A linear model for each subsystem of the closed-loop system constituting an Alcator C-Mod discharge under feedback control has been constructed. A non-rigid, approximately flux-conserving, perturbed equilibrium plasma response model is used in the comparison to experiment. A detailed toroidally symmetric model of the vacuum vessel and the supporting superstructure is used. Modeling of the power supplies feeding the active coils has been included. Experiments have been conducted with vertically unstable plasmas where the feedback was turned off and the plasma response was observed in an open -loop configuration. The closed-loop behavior has been examined by injecting step perturbations into the desired vertical position of the plasma. The agreement between theory and experiment in the open-loop configuration was very satisfactory, proving that the perturbed equilibrium plasma response model and a toroidally symmetric electromagnetic model of the vacuum vessel and the structure can be trusted for the purpose of calculations for control law design. When the power supplies and the feedback computer hardware are added to the system, however, as they are in the closed-loop configuration, they introduce nonlinearities that make it difficult to explain observed behavior with linear theory. Nonlinear simulation of the time evolution of the closed-loop experiments was able to account for the discrepancies between linear theory and experiment. (Copies available exclusively from MIT Libraries
Resonance and cut-off surfaces in the ion cyclotron frequency range in toroidal geometry
International Nuclear Information System (INIS)
Resonances and cut-offs of the fast Alfven and ion-cyclotron waves have been studied for a multicomponent plasma in a toroidal axisymmetric geometry. The resonance and cut-off frequencies are given by eigenvalues of ordinary differential equations on the rosonance and cut-off sufaces, respectively. These surfaces coincide with magnetic surfaces. (author)
Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21-Ge29
Yoo, S.; Zeng, X. C.
We performed a constrained search for the geometries of low-lying neutral germanium clusters GeN in the size range of 21⩽N⩽29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N ˜65.
Computation of supersonic jet mixing noise for an axisymmetric convergent-divergent nozzle
Khavaran, Abbas; Krejsa, Eugene A.; Kim, Chan M.
The turbulent mixing noise of a supersonic jet is calculated for an axisymmetric convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy is adopted. The acoustics solution is based upon the methodology followed in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors (Ribner's assumption). Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The CFD solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.
Light propagation in the field of a moving axisymmetric body: theory and application to Juno
Hees, A; Poncin-Lafitte, C Le
Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the Time Transfer Functions formalism to study light propagation in the field of moving axisymmetric bodies, which extends the field of application of previous works. We first derive a space-time metric adapted to describe the geometry of an ensemble of moving bodies. Then, we show that the expression of the Time Transfer Functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a change of variables. We also give a general expression of the Time Transfer Function in the case where the motion of the body is arbitrary. This result is given in the form of an integral easily computable numerically. We also provide the derivatives of the Time Transfer Function in this case, which are mandatory to compute Doppler and astrometric observables. We particularize our results in the case of moving axisymmetric bodies. Finally, ...
Assessment of a parabolic analysis for axisymmetric internal flows in rocket and turbomachinery ducts
Power, G. D.; Anderson, O. L.
The flow paths in gas turbine passages encompass a wide range of flow properties such as Reynolds number and Mach number as well as many other variable flow conditions such as swirl, free-stream turbulence, and laminar/turbulent transition. An existing computer program, the Axisymmetric Diffuser Duct (ADD) code, which calculates compressible, turbulent, swirling flow through axisymmetric ducts has been modified to include the effects of free-stream turbulence and laminar/turbulent transition. The program has been evaluated on a matrix of test cases to determine its accuracy, robustness, and limits of applicability. This improved version of the ADD code calculates solutions which compare well with available data and can now be applied to a wider range of problems than previously possible. In addition a concept called local enhancement was developed and tested on a simple two-dimensional geometry in order to demonstrate a method to reduce computer time. In this concept the pressure distribution is calculated on a coarse grid using the ADD code and the viscous layer is locally enhanced using a boundary layer analysis. By applying this concept, an order of magnitude reduction in computer time was possible without any loss in accuracy.
Experimental study on the effects of nose geometry on drag over axisymmetric bodies in supersonic flow
Brooker, B. Tyler
A new nose shape that was determined using the penetration mechanics to have the least penetration drag has been tested in the supersonic wind tunnel of the University of Alabama to determine the aerodynamic characteristics of this nose shape. The aerodynamic drag measured on the new nose shape and on four additional nose shapes are compared to each other. The results show that the new nose shape has the least aerodynamic drag. The measurements were made at Mach numbers ranging from 1.85 to 3.1. This study also required the maintenance of several components of the University of Alabama's 6-inch by 6-inch supersonic wind tunnel and modification of the existing data acquisition programs. These repairs and modifications included the repair and recalibration of the supersonic wind tunnel, repair of the four component force balance, and the modification of the tunnel's control program.
Surface complexation and precipitate geometry for aqueous Zn(II) sorption on ferrihydrite I: X-ray absorption extended fine structure spectroscopy analysis
Waychunas, G.A.; Fuller, C.C.; Davis, J.A.
"Two-line" ferrihydrite samples precipitated and then exposed to a range of aqueous Zn solutions (10-5 to 10-3 M), and also coprecipitated in similar Zn solutions (pH 6.5), have been examined by Zn and Fe K-edge X-ray absorption spectroscopy. Typical Zn complexes on the surface have Zn-O distances of 1.97(0.2) A?? and coordination numbers of about 4.0(0.5), consistent with tetrahedral oxygen coordination. This contrasts with Zn-O distances of 2.11(.02) A?? and coordination numbers of 6 to 7 in the aqueous Zn solutions used in sample preparation. X-ray absorption extended fine structure spectroscopy (EXAFS) fits to the second shell of cation neighbors indicate as many as 4 Zn-Fe neighbors at 3.44(.04) A?? in coprecipitated samples, and about two Zn-Fe neighbors at the same distance in adsorption samples. In both sets of samples, the fitted coordination number of second shell cations decreases as sorption density increases, indicating changes in the number and type of available complexing sites or the onset of competitive precipitation processes. Comparison of our results with the possible geometries for surface complexes and precipitates suggests that the Zn sorption complexes are inner sphere and at lowest adsorption densities are bidentate, sharing apical oxygens with adjacent edge-sharing Fe(O,OH)6 octahedra. Coprecipitation samples have complexes with similar geometry, but these are polydentate, sharing apices with more than two adjacent edge-sharing Fe(O,OH)6 polyhedra. The results are inconsistent with Zn entering the ferrihydrite structure (i.e., solid solution formation) or formation of other Zn-Fe precipitates. The fitted Zn-Fe coordination numbers drop with increasing Zn density with a minimum of about 0.8(.2) at Zn/(Zn + Fe) of 0.08 or more. This change appears to be attributable to the onset of precipitation of zinc hydroxide polymers with mainly tetrahedral Zn coordination. At the highest loadings studied, the nature of the complexes changes further
Stationary and axisymmetric solutions of higher-dimensional general relativity
International Nuclear Information System (INIS)
We study stationary and axisymmetric solutions of General Relativity, i.e., pure gravity, in four or higher dimensions. D-dimensional stationary and axisymmetric solutions are defined as having D-2 commuting Killing vector fields. We derive a canonical form of the metric for such solutions that effectively reduces the Einstein equations to a differential equation on an axisymmetric D-2 by D-2 matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a D-2 by D-2 matrix field living in two-dimensional flat space). This generalizes the Papapetrou form of the metric for stationary and axisymmetric solutions in four dimensions, and furthermore generalizes the work on Weyl solutions in four and higher dimensions. We analyze then the sources for the solutions, which are in the form of thin rods along a line in the three-dimensional flat space that the matrix field can be seen to live in. As examples of stationary and axisymmetric solutions, we study the five-dimensional rotating black hole and the rotating black ring, write the metrics in the canonical form and analyze the structure of the rods for each solution
Axisymmetric modes of rotating relativistic stars in the cowling approximation
International Nuclear Information System (INIS)
Axisymmetric pulsations of rotating neutron stars can be excited in several scenarios, such as core-collapse, crust and core-quakes and binary mergers and could become detectable either in gravitational waves or high-energy radiation. Here, we present a comprehensive study of all low-order axisymmetric modes of uniformly and rapidly rotating relativistic stars. Initial stationary configurations are appropriately perturbed and are numerically evolved using an axisymmetric, nonlinear relativistic hydrodynamics code, assuming time-independence of the gravitational field (Cowling approximation). The simulations are performed using a high-resolution shock-capturing finite-difference scheme accurate enough to maintain the initial rotation law for a large number of rotational periods, even for stars at the mass-shedding limit. Through Fourier transforms of the time evolution of selected fluid variables, we compute the frequencies of quasi-radial and non-radial modes with spherical harmonic indices l=0, 1, 2 and 3, for a sequence of rotating stars from the non-rotating limit to the mass-shedding limit. The frequencies of the axisymmetric modes are affected significantly by rotation only when the rotation rate exceeds about 50% of the maximum allowed. As expected, at large rotation rates, apparent mode crossings between different modes appear. In addition to the above modes, several axisymmetric inertial modes are also excited in our numerical evolutions. (orig.)
Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies
International Nuclear Information System (INIS)
The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma.At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process,and a new code SYMTRAN (by Hua and Fowler)that solves the coupled radial and axial particle and energy transport in a K-S T-M. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values.The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma.Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging.Our studies have confirmed the viability of the K-S T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution.In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K-S T-M
Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies
International Nuclear Information System (INIS)
The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma. At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employed a low-beta code written especially to analyze the beam injection/stabilization process, and a new code SYMTRAN (by Hua and Fowler) that solves the coupled radial and axial particle and energy transport in a K-S TM. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values. The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma. Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging. Our studies have confirmed the viability of the K-S-T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution. In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
Directory of Open Access Journals (Sweden)
M. Jakomin
Full Text Available In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the large displacements theory. We numerically calculate the deformation curve and the snap-through temperature using the fourth-order Runge-Kutta method and a nonlinear shooting method. We show how the temperature of both snap-through depends on the point where one type of the rotational curve transforms into another.
ECOM: a fast and accurate solver for toroidal axisymmetric MHD equilibria
Lee, Jungpyo
We present ECOM (Equilibrium solver via COnformal Mapping), a fast and accurate fixed boundary solver for toroidally axisymmetric magnetohydrodynamic equilibria with or without a toroidal flow. ECOM combines conformal mapping and Fourier and integral equation methods on the unit disk to achieve exponential convergence for the poloidal flux function as well as its first and second partial derivatives. As a consequence of its high order accuracy, for dense grids and tokamak-like elongations ECOM computes key quantities such as the safety factor and the magnetic shear with higher accuracy than the finite element based code CHEASE [H. L\\"utjens \\textit{et al.}, Computer physics communications 97, 219 (1996)] at equal run time. ECOM has been developed to provide equilibrium quantities and details of the flux contour geometry as inputs to stability, wave propagation and transport codes.
Non-Axisymmetric Flows on Hot Jupiters with Oblique Magnetic Fields
Batygin, Konstantin
Giant planets that reside in close proximity to their host stars are subject to extreme irradiation, which gives rise to thermal ionization of trace Alkali metals in their atmospheres. On objects where the atmospheric electrical conductivity is substantial, the global circulation couples to the background magnetic field, inducing supplementary fields and altering the nature of the flow. To date, a number of authors have considered the influence of a spin-pole aligned dipole magnetic field on the dynamical state of a weakly-ionized atmosphere and found that magnetic breaking may lead to significantly slower winds than predicted within a purely hydrodynamical framework. Here, we consider the effect of a tilted dipole magnetic field on the circulation and demonstrate that in addition to regulating wind velocities, an oblique field generates stationary non-axisymmetric structures that adhere to the geometry of the magnetic pole. Using a kinematic perturbative approach, we derive a closed-form solution for the per...
Near surface stress analysis strategies for axisymmetric fretting
Indian Academy of Sciences (India)
M Ramesh; Satish V Kailas; K R Y Simha
Fretting is essentially a surface phenomenon, but bulk stresses and material properties contribute to subsequent failure. This feature of fretting demands a thorough understanding of near surface stresses under the joint action of normal, shear and thermal loading. Axisymmetric fretting is of great concern in piping and coupling design. In this paper, we develop design tools for Near Surface Analysis (NSA) for understanding axisymmetric fretting. Axisymmetric Fretting Analysis (AFA) becomes formidable owing to localised tractions that call for Fourier transform techniques. We develop two different NSA strategies based on two-dimensional plane strain models: 2D strip model (2DS) and half-plane Flamant model (2DF). We compare the results of 2DS and 2DF with the exact results for AFA obtained using Love's stress function in conjunction with Fourier transform. There is a good correspondence between stress components obtained from 2D-models.
Study of axisymmetric flow problems by Hele-Shaw models
Rao, P. V.; Sachan, J. S.
Hele-Shaw models have been applied for solving two-dimensional, irrotational flow problems such as flow past bodies or radial seepage flow. The gap between the two plates is varied as a cubic parabola in the radial direction. Results are presented for seven axisymmetric models, including a cylindrical body with 60-deg conical head forms, an axisymmetric sluice entrance with a compound elliptical transition and radial flow to a well with a free surface. Pressure distributions were computed and compared with water-tunnel data, wind-tunnel data, finite-differential solutions and exact solutions.
Axisymmetric solitary waves on the surface of a ferrofluid
Bourdin, Elise; Falcon, Eric
We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both elevation and depression solitary waves are observed with profiles in good agreement with theoretical predictions based on the magnetic analogue of the Korteweg-deVries equation. We also report the first measurements of the velocity and the dispersion relation of axisymmetric linear waves propagating on the cylindrical ferrofluid layer that are found in good agreement with theoretical predictions.
Potential flow past axisymmetric bodies at angle of attack
Kuhlman, J. M.; Shu, J.-Y.
The Karamcheti (1966) suggestion concerning the use of higher order singularity techniques has been developed for the calculation of incompressible flow past an axisymmetric body at angle of attack. Attention is given to the results of a convergence study using this axial singularity method, where solution accuracy has been investigated for ellipsoids of slenderness ratio in the 1-10 range for both axial and inclined flow. Effects of singularity type, element number and size distribution, and singularity line inset distance, are noted, and a paneling scheme is developed which yields accurate results for the class of axisymmetric bodies having continuous body slopes with discontinuous curvature jumps.
A regularity criterion for the angular velocity component in axisymmetric Navier-Stokes equations
Ondrej Kreml; Milan Pokorny
We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].
A regularity criterion for the angular velocity component in axisymmetric Navier-Stokes equations
Directory of Open Access Journals (Sweden)
Ondrej Kreml
Full Text Available We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].
Soft metal ions, Cd(II) and Hg(II), induce triple-stranded alpha-helical assembly and folding of a de novo designed peptide in their trigonal geometries.
Li, X; K. Suzuki; Kanaori, K; Tajima, K; Kashiwada, A.; Hiroaki, H; Kohda, D; Tanaka, T
We previously reported the de novo design of an amphiphilic peptide [YGG(IEKKIEA)4] that forms a native-like, parallel triple-stranded coiled coil. Starting from this peptide, we sought to regulate the assembly of the peptide by a metal ion. The replacement of the Ile18 and Ile22 residues with Ala and Cys residues, respectively, in the hydrophobic positions disrupted of the triple-stranded alpha-helix structure. The addition of Cd(II), however, resulted in the reconstitution of the triple-str...
Stationary axisymmetric spacetimes with a conformally coupled scalar field
Astorino, Marco
Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This family contains, amongst other things, rotating extensions of the BBMB black hole and also its angular and mass multipolar generalisations. Further addition of NUT charge is also discussed.
Unified characteristics line theory of spacial axisymmetric plastic problem
Institute of Scientific and Technical Information of China (English)
俞茂宏; 李建春; 张永强
The unified strength theory proposed by Yu in 1991 is extended to spacial axisymmetric problem. A unified spacial axismymmetric characteristics line theory based on the unified strength theory is proposed. This theory takes account of different effects of intermediate principal stress on yielding or failure and the SD effect (tensile-compression strength difference) of materials. Various conventional axisymmetric characteristics line theories, whihc are based on the Haar-von Karman plastic condition, Szczepinski hypothesis, Tresca criterion, von Mises criterion and Mohr-Coulomb theory, are special cases of the new theory. Besides, a series of new spacial axisymmetric characteristics fields for different materials can be introduced. It forms a unified spacial axisymmetric characteristics theory. Two examples are calculated with the new theory, the results are compared with those obtained by the finite element program UEPP and those based on the Mohr-Coulomb strength theory. It is shown that the new theory is reliable and feasible. The economic benefit can be obtained from the engineering application of the new theory.
Fluid dynamics analysis of a rotating axisymmetric part using FIDAP
Giles, G. E.; Kirkpatrick, J. R.; Wendel, M. W.; Bullock, J. S., IV
The effect of fluid flow on electrochemical plating on a rotating axisymmetric part was investigated by using a finite element computer code, FIDAP. The results from these investigations compare well with analytical results for laminar flow conditions. The addition of a nonrotating shield was also investigated for laminar flow conditions. An attempt to extend these analyses to turbulent conditions was unsuccessful.
Consistent lattice Boltzmann methods for incompressible axisymmetric flows
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.
Hawking radiation via tunnelling from general stationary axisymmetric black holes
Institute of Scientific and Technical Information of China (English)
Zhang Jing-Yi; Fan Jun-Hui
Hawking radiation is viewed as a tunnelling process. In this way the emission rates of massless particles and massive particles tunnelling across the event horizon of general stationary axisymmetric black holes are calculated,separately. The emission spectra of these two different kinds of outgoing particles have the same functional form and both are consistent with an underlying unitary theory.
Geometric integrator for charged particle orbits in axisymmetric fusion devices
Kasilov, S. V.; Runov, A. M.; Kernbichler, W.
A semi-analytical geometric integrator of guiding centre orbits in an axisymmetric tokamak is described. The integrator preserves all three invariants of motion up to computer accuracy at the expense of reduced orbit accuracy and it is roughly an order of magnitude more efficient than a direct solution of the equations of guiding centre motion with a standard high order adaptive ODE integrator.
Stability of a compound sessile drop at the axisymmetric configuration.
Zhang, Ying; Chatain, Dominique; Anna, Shelley L; Garoff, Stephen
The equilibrium configuration of compound sessile drops has been calculated previously in the absence of gravity. Using the Laplace equations, we establish seven dimensionless parameters describing the axisymmetric configuration in the presence of gravity. The equilibrium axisymmetric configuration can be either stable or unstable depending on the fluid properties. A stability criterion is established by calculating forces on a perturbed Laplacian shape. In the zero Bond number limit, the stability criterion depends on the density ratio, two ratios of interfacial tensions, the volume ratio of the two drops, and the contact angle. We use Surface Evolver to examine the stability of compound sessile drops at small and large Bond numbers and compare with the zero Bond number approximation. Experimentally, we realize a stable axisymmetric compound sessile drop in air, where the buoyancy force exerted by the air is negligible. Finally, using a pair of fluids in which the density ratio can be tuned nearly independently of the interfacial tensions, the stability transition is verified for the axisymmetric configuration. Even though the perturbations are different for the theory, simulations and experiments, both simulations and experiments agree closely with the zero Bond number approximation, exhibiting a small discrepancy at large Bond number. PMID:26433481
Modelling axisymmetric cod-ends made of different mesh types
DEFF Research Database (Denmark)
Priour, D.; Herrmann, Bent; O'Neill, F.G.
Cod-ends are the rearmost part of trawl fishing gears. They collect the catch, and for many important species it is where fish selection takes place. Generally speaking they are axisymmetric, and their shape is influenced by the catch volume, the mesh shape, and the material characteristics...
Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry
Energy Technology Data Exchange (ETDEWEB)
Long-Poe Ku and Allen H. Boozer
If quasi-axisymmetry is preserved, non-axisymmetric shaping can be used to design tokamaks that do not require current drive, are resilient to disruptions, and have robust plasma stability without feedback. Suggestions for addressing the critical issues of tokamaks can only be validated when presented with sufficient specificity that validating experiments can be designed. The purpose of this paper is provide that specificity for non-axisymmetric shaping. To our knowledge, no other suggestions for the solution of a number of tokamak issues, such as disruptions, have reached this level of specificity. Sequences of three-field-period quasi-axisymmetric plasmas are studied. These sequences address the questions: (1) What can be achieved at various levels of non-axisymmetric shaping? (2) What simplifications to the coils can be achieved by going to a larger aspect ratio? (3) What range of shaping can be achieved in a single experimental facility? The sequences of plasmas found in this study provide a set of interesting and potentially important configurations.
Institute of Scientific and Technical Information of China (English)
ZARRABI K; LAWRENCE Ng
A multiaxial paradigm for predicting creep damage/lives of components is described. Although in principle the paradigm is general, it is verified using axisymmetric experimental data. It is shown that the proposed paradigm is capable of predicting creep lives with an error of less than 2%. It is also shown that the proposed paradigm is more accurate than the reference stress method.
Mahé, Louis; Roy, Marie-Françoise
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Digital Differential Geometry Processing
Institute of Scientific and Technical Information of China (English)
Xin-Guo Liu; Hu-Jun Bao; Qun-Sheng Peng
The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient,Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.
The lifecycle of axisymmetric internal solitary waves
Directory of Open Access Journals (Sweden)
J. M. McMillan
Full Text Available The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r-p with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r-1.
Meyer, Walter J
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
Institute of Scientific and Technical Information of China (English)
GUO Enli; MO Xiaohuan
In this paper,a survey on Riemann-Finsler geometry is given.Non-trivial examples of Finsler metrics satisfying different curvature conditions are presented.Local and global results in Finsler geometry are analyzed.
An axisymmetric boundary element formulation of sound wave propagation in fluids including viscous and thermal losses
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff's decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses...... are solved using extended boundary conditions that account for: i) negligible temperature fluctuations at the boundary, and ii) normal and tangential matching of the boundary's particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers...... as is the case with the existing Finite Element Method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions....
The Role of Axisymmetric Reconnection Events in JET Discharges with Extreme Shear Reversal
Energy Technology Data Exchange (ETDEWEB)
B.C. Stratton; J.A. Breslau; R.V. Budny; S.C. Jardin; W. Park; H.R. Strauss; L.E. Zakharov; B. Alper; V. Drozdov; N.C. Hawkes; S. Reyes-Cortes; and Contributors to the EFDA-JET Work Programme
Injection of Lower Hybrid Heating and Current Drive into the current ramp-up phase of Joint European Torus (JET) discharges can produce extremely reversed q-profiles characterized by a core region of very small or zero current density (within Motional Stark Effect diagnostic measurement errors) and q(subscript min) > 1. T(subscript e)-profiles show sawtooth-like collapses and the presence of an internal transport barrier. Accurate equilibrium reconstructions of these discharges are obtained using the ESC code, which was recently extended to allow equilibrium reconstructions in which a free boundary solver determines the plasma boundary and a fixed boundary solver provides the magnetic geometry and current density profile. The core current density does not appear to go negative, although current diffusion calculations indicate that sufficient non-inductive current drive to cause this is present. This is explained by nonlinear resistive MHD simulations in toroidal geometry which predict that these discharges undergo n=0 reconnection events (axisymmetric sawteeth) that redistribute the current to hold the core current density near zero.
Collection-efficient, axisymmetric vacuum sublimation module for the purification of solid materials
May, Michael; Paul, Elizabeth; Katovic, Vladimir
A vacuum sublimation module of axisymmetric geometry was developed and employed to purify solid-phase materials. The module provides certain practical advantages and it comprises: a metering valve, glass collector, glass lower body, main seal, threaded bushing, and glass internal cartridge (the latter to contain starting material). A complementary process was developed to de-solvate, sublime, weigh, and collect solid chemical materials exemplified by oxalic acid, ferrocene, pentachlorobenzene, chrysene, and urea. The oxalic acid sublimate was analyzed by titration, melting range, Fourier Transform Infrared (FT-IR) Spectroscopy, cyclic voltammetry, and its (aqueous phase) electrolytically generated gas. The analytical data were consistent with a high-purity, anhydrous oxalic acid sublimate. Cyclic voltammograms of 0.11 mol. % oxalic acid in water displayed a 2.1 V window on glassy carbon electrode beyond which electrolytic decomposition occurs. During module testing, fifteen relatively pure materials were sublimed with (energy efficient) passive cooling and the solid-phase recovery averaged 95 mass %. Key module design features include: compact vertical geometry, low-angle conical collector, uniformly compressed main seal, modest power consumption, transparency, glovebox compatibility, cooling options, and preferential conductive heat transfer. To help evaluate the structural (module) heat transfer, vertical temperature profiles along the dynamically evacuated lower body were measured versus electric heater power: for example, an input of 18.6 W generated a temperature 443-K at the bottom. Experimental results and engineering calculations indicate that during sublimation, solid conduction is the primary mode of heat transfer to the starting material.
Taylor, M
Two charge BPS horizon free supergravity geometries are important in proposals for understanding black hole microstates. In this paper we construct a new class of geometries in the NS1-P system, corresponding to solitonic strings carrying fermionic as well as bosonic condensates. Such geometries are required to account for the full microscopic entropy of the NS1-P system. We then briefly discuss the properties of the corresponding geometries in the dual D1-D5 system.
Emergent Geometry of KP Hierarchy. II
Zhou, Jian
We elaborate on a construction of quantum LG superpotential associated to a tau-function of the KP hierarchy in the case that resulting quantum spectral curve lies in the quantum two-torus. This construction is applied to Hurwitz numbers, one-legged topological vertex and resolved conifold with external D-brane to give a natural explanation of some earlier work on the relevant quantum curves.
Axi-symmetric forward spiral extrusion, a kinematic and experimental study
International Nuclear Information System (INIS)
Research highlights: → The accumulated strain in AFSE, a new extrusion process, is the result of circumferential velocity gradient along extrusion axis. → The effective strain depends on the radius and helix angle only while independent of the chamfer geometry. → Embedded wires were used to verify the validity of the derived velocity field during AFSE. → The velocity field and the observations conform well and the proposed kinematics is a reliable model for AFSE. - Abstract: A modified axi-symmetric forward spiral extrusion process has been proposed here to allow for a near zero area reduction process. The axi-symmetric forward spiral extrusion, AFSE, can be carried out through a die with a number of engraved spiral grooves. This paper investigates the kinematics of the AFSE process. A velocity field is derived using principle of mass conservation along the extrusion axis. The proposed model has been developed to calculate strain components in the deformation zone during the process. An experimental method has been designed which uses composite lead samples with embedded copper wires to trace the strain path to verify the proposed velocity field. A good agreement between experimental results and the proposed analytical model was observed. The proposed velocity field, verified by experimental results, shows that the deformation develops away from the AFSE die-sample interface. A linear gradient of velocity in the radial direction was observed which is in good agreement with the proposed velocity field. Based on the estimated strains, velocity gradient, and nearly no change in sample cross section during AFSE, the process seems to have good potential for application as a new severe plastic deformation process in both continuous and batch modes.
The turbulent flow in an enclosed corotating disk pair: axisymmetric numerical simulation and Reynolds stress modelling
Energy Technology Data Exchange (ETDEWEB)
Randriamampianina, A.; Schiestel, R. [UMR CNRS, Marseille (France). Institut de Recherche sur les Phenomenes; Wilson, M. [University of Bath (United Kingdom). Dept. of Mechanical Engineering
We present axisymmetric numerical simulation and modelling of the turbulent flow between corotating disks with a stationary outer casing, the enclosed corotating disk pair configuration. This follows previous work on laminar flow for an identical geometry defined by a gap ratio G=0.6 (=s/(b-a)) and a/b=0.5, where a and b are the inner and outer radii, and s is the inter-disk distance [J. Fluid Mech. 434 (2001) 39]. The rotation rate considered in the present case is equivalent to Re=1.46 x 10{sup 5}, where Re (={omega}b{sup 2}/{nu}) is the rotational Reynolds number. This corresponds to a value at which mean flow measurements have been obtained for the same configuration [Flow in a rotating cavity with a peripheral inlet and outlet of cooling air, in: ASME Int. Gas Turbine and Aeroengine Cong., paper 96-GT-309, Birmingham]. In computed laminar regimes, it was found previously for this aspect ratio that the flow structure is first characterized by a shift-and-reflect symmetry at lower values of Re before bifurcating to symmetry breaking at higher rotation rates. For the rotation rate under consideration here, the flow is turbulent and shows an unsteady behaviour in the mean, characterized by flapping of the flow between the two disks, inducing symmetry breaking with respect to the inter-disk midplane. Similarities are observed between the centripetal flow coming from the stationary casing and an impinging jet in a cavity. Comparisons are made between the computed results from the axisymmetric numerical simulation (ANS), a Reynolds Stress Transport Model (RSM) and the available experimental data. The RSM predictions are in close agreement with the mean flow measurements. The ANS results give a more detailed description of the flow characteristics, but suffer from the axisymmetry assumption that is not compatible with the three-dimensional turbulence. (author)
Geometry essentials for dummies
Ryan, Mark
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Mobility of an axisymmetric particle near an elastic interface
Daddi-Moussa-Ider, Abdallah; Gekle, Stephan
Using a fully analytical theory, we compute the leading order corrections to the translational, rotational and translation-rotation coupling mobilities of an arbitrary axisymmetric particle immersed in a Newtonian fluid moving near an elastic cell membrane that exhibits resistance towards stretching and bending. The frequency-dependent mobility corrections are expressed as general relations involving separately the particle's shape-dependent bulk mobility and the shape-independent parameters such as the membrane-particle distance, the particle orientation and the characteristic frequencies associated with shearing and bending of the membrane. This makes the equations applicable to an arbitrary-shaped axisymmetric particle provided that its bulk mobilities are known, either analytically or numerically. For a spheroidal particle, these general relations reduce to simple expressions in terms of the particle's eccentricity. We find that the corrections to the translation-rotation coupling mobility are primarily d...
Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
Dolan, Sam R
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we classify the equatorial circular photon orbits of Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordstr\\"om di-holes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a torus around a di-hole, via a selection of Poincar\\'e sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electrovacuum; but not in pure vacuum.
Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
Dolan, Sam R.; Shipley, Jake O.
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordström diholes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a dihole, via a selection of Poincaré sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electro vacuum, but not in pure vacuum.
Axisymmetric equilibria of a gravitating plasma with incompressible flows
Throumoulopoulos, G N
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. {\\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime $\\beta_0\\approx \\gamma_0\\approx \\delta_0 \\approx\\epsilon_0\\ll 1$, where $\\beta_0$, $\\gamma_0$, $\\delta_0$, and $\\...
Application of the PTT model to axisymmetric free surface flows
Merejolli, R.; Paulo, G. S.; Tomé, M. F.
This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters ɛ and ξ are investigated.
The axisymmetric jet in a rotating reference frame
Energy Technology Data Exchange (ETDEWEB)
Lawrie, A G W; Scott, J F; Godeferd, F; Cambon, C [LMFA, Ecole Centrale de Lyon (France); Duran-Matute, M; Flor, J-B [LEGI, Universite Joseph Fourier, Grenoble (France); Danaila, L, E-mail: email@example.com [CORIA, Universite de Rouen (France)
The axisymmetric jet is a geometrically simple, statistically stationary example of inhomogenous turbulence. Considering conservation of volume and momentum, Morton et al. (1956) offered a prediction of jet development, characterised solely by an unknown, constant entrainment coefficient. The presence of background rotation complicates the kinematics of the entrainment, and without special treatment, the jet suffers a helical instability. Here, we present one technique which stabilises the axisymmetric jet, yet preserves its desirable turbulent properties. The jet offers a steady-state flow in which there is an axial variation of local Rossby number, and after decay along the axis to a critical value, cones of inertial waves emerge. In this paper, we demonstrate these features using our numerical software MOBILE, offer our solution to stabilise the jet, and explain the mechanisms involved.
Dynamics and thermodynamics of axisymmetric flows: I. Theory
Leprovost, N; Chavanis, P H; Leprovost, Nicolas; Chavanis, Pierre-Henri
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We derive relaxation equations which can be used as numerical algorithm to construct stable stationary solutions of axisymmetric flows. In a second part, we develop a thermodynamical approach to the equilibrium states at some fixed coarse-grained scale. We show that the resulting distribution can be divided in a universal part coming from the conservation of robust invariants and one non-universal determined by the initial conditions through the fragile invariants (for freely evolving systems) or by a prior distribution encoding non-ideal effects such as viscosity, small-scale forcing and dissipation (for forced systems). Finally, we derive a parameterization of inviscid mixing to describe the dynamics of the system at the coarse-grained scale.
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Axisymmetric smoothed particle hydrodynamics with self-gravity
García Senz, Domingo; Relano, A.; Cabezón Gómez, Rubén Martín; Bravo Guil, Eduardo
The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a Sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ablative implosion of a small capsule). New material concerning the standard SPH formalism is given. That includes the numerical handli...
International Nuclear Information System (INIS)
Extensive studies over the past decade showed that HD and MHD nonaxisymmetric instabilities exist in the solar tachocline for a wide range of toroidal field profiles, amplitudes, and latitude locations. Axisymmetric instabilities (m = 0) do not exist in two dimensions, and are excited in quasi-three-dimensional shallow-water systems only for very high field strengths (2 mG). We investigate here MHD axisymmetric instabilities in a three-dimensional thin-shell model of the solar/stellar tachocline, employing a hydrostatic, non-Boussinesq system of equations. We deduce a number of general properties of the instability by use of an integral theorem, as well as finding detailed numerical solutions for unstable modes. Toroidal bands become unstable to axisymmetric perturbations for solar-like field strengths (100 kG). The e-folding time can be months down to a few hours if the field strength is 1 mG or higher, which might occur in the solar core, white dwarfs, or neutron stars. These instabilities exist without rotation, with rotation, and with differential rotation, although both rotation and differential rotation have stabilizing effects. Broad toroidal fields are stable. The instability for modes with m = 0 is driven from the poleward shoulder of banded profiles by a perturbation magnetic curvature stress that overcomes the stabilizing Coriolis force. The nonaxisymmetric instability tips or deforms a band; with axisymmetric instability, the fluid can roll in latitude and radius, and can convert bands into tubes stacked in radius. The velocity produced by this instability in the case of low-latitude bands crosses the equator, and hence can provide a mechanism for interhemispheric coupling.
Non-axisymmetric oscillations of differentially rotating relativistic stars
Passamonti, Andrea; Stavridis, Adamantios; Kokkotas, Kostas
Non-axisymmetric oscillations of differentially rotating stars are studied using both slow rotation and Cowling approximation. The equilibrium stellar models are relativistic polytropes where differential rotation is described by the relativistic j-constant rotation law. The oscillation spectrum is studied versus three main parameters: the stellar compactness $M/R$, the degree of differential rotation $A$ and the number of maximun couplings $\\ell_{\\rm max}$. It is shown that the rotational sp...
Study on the Interaction of Non-axisymmetric Binary Vortices
Institute of Scientific and Technical Information of China (English)
In the context of advection dynamics, 19 experiments (Exps.) are performed using a quasi-geostrophic barotropic vorticity equation model to explore the condition for the mergence of binary vortices and the self-organization of the larger scale vortex. Results show that the initial distance between the centers of binary vortices and the non-axisymmetric distributions of their initial vorticity are two factors affecting the mergence of binary vortices. There is a critical distance for the mergence of initial symmetric binary vortices, however, the mergence of initial non-axisymmetric binary vortices is also affected by the asymmetric structure of initial vortices. The self-organization processes in 19 experiments can be classified into two types: one is the merging of identical, axisymmetric binary vortices in which the interaction of the two vortices undergoes slowly change, rapid change, and the formation, stretching, and development of the filaments of vorticity, and the two vortices merge into a symmetric vortex, with its vorticity piled up in the inner region coming from the two initial vortices, and the vorticity of the spiral band in the outer region from the stretching of the filaments of the two initial vortices. And the other type is the merging of the two non-axisymmetric initial vortices of an elliptic vortex and an eccentric vortex hi which the elliptic vortex, on the one hand, mutually rotates, and on the other hand moves towards the center of the computational domain, at the same time expands its vorticity area, and at last forms the inner core of resultant state vortex; and the eccentric vortex mutually rotates, meanwhile continuously stretches, and finally forms the spiral band of resultant state vortex. The interaction process is characteristic of the vorticity piled up in the inner core region of resultant state vortex originating from the elliptic vortex and the vorticity in spiral band mainly from the successive stretch and rupture of the
Viscosity Effects on the Dynamics of Long Axisymmetric Liquid Bridges
Meseguer Ruiz, José; Perales Perales, José Manuel
In this paper the dynamics of axisymmetric liquid columns held by capillary forces between two circular, concentric, solid disks is considered. The problem has been solved by using an one-dimensional model known in the literature as the Cosserat model, which includes viscosity effects, where the axial velocity is considered constant in each section of the liquid bridge. The dynamic response of the bridge to an excitation consisting of a small amplitude vibration of the supporting disks has be...
Bis(thiosemicarbazonato) chelates of Co(II), Ni(II), Cu(II), Pd(II) and Pt(II)
Chandra, Sulekh; Singh, R.
Bis chelates of Co(II), Ni(II), Cu(II), Pd(II) and Pt(II) with the enolic form of diethyl ketone and methyl n-propyl thiosemicarbazones were synthesized and characterized by elemental analyses, magnetic moments, i.r. and electronic and electron spin resonance spectral studies. All the complexes were found to have the composition ML 2 [where M = Co(II), Ni(II), Cu(II), Pd(ii) and Pt(II) and L = thiosemicarbazones of diethyl ketone and methyl n-propyl ketone]. Co(II) and Cu(II) complexes are paramagnetic and may have polymeric six-coordinate octahedral and square planar geometries, respectively. The Ni(II), Pd(II) and Pt(II) complexes are diamagnetic and may have square planar geometries. Pyridine adducts (ML 2·2Py) of Ni(II) and Cu(II) complexes were also prepared and characterized.
Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt
This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank
Advances in finite element 3D modeling and meshing of axisymmetrical pressure vessels for the computation of limit loads
International Nuclear Information System (INIS)
Full text: This work will present a new technology for modeling the geometry of pressure vessels, using thin axi-symmetrical shells. An ObjectARX application is being developed based on the ObjectARX programming environment, which provides an object oriented C++ programming interface for developers to use, customize and extend AutoCAD. The application will perform the modeling and the discretization of vessels into axi-symmetrical finite elements for limit and shakedown analysis of pressure vessels. It uses AutoCAD as a graphical platform, taking advantage of AutoCAD's open architecture, which provides direct access to AutoCAD graphic system, database structures and native command definition. The application customized entities; objects and commands can be ordered by command line, toolbars or menu and will be virtually indistinguishable from built-in AutoCAD's related. Modeling the geometry required the construction of a mother class denominated shell, from which the following primitives were derived: spherical, toroidal, conical and cylindrical. For the discretization of the shell geometry two entities were created, element and node. The class constraint imposes restrictions on displacements to the element nodes at the edges of the vessel. The mother class load contains the characteristics of the entities ring load and pressure load. Finally, the class material is derived from AutoCAD object and has only numerical data and no graphical representation. All data are saved into AutoCAD database and can be easily exported to analysis in a text format through an appropriate interface. Further, the work will present advances on the development of the technique proposed by Franco and Ponter for the finite element formulation of shakedown problems in symmetrically loaded shells of revolution. An upper bound formulation for estimating limit and shakedown loads for pressure vessels is recounted. The error estimator using the energy norm and adaptive strategies for remeshing
Osborne, Ianna
CMS faces real challenges with upgrade of the CMS detector through 2020. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The...
Bárány, Imre; Vilcu, Costin
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
Jonsson, Rickard; Westman, Hans
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz and Lasota 1997, Class. Quantum Grav. 14 (1997) A23). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, w...
The Axisymmetric Tandem Mirror: A Magnetic Mirror Concept Game Changer Magnet Mirror Status Study Group
Energy Technology Data Exchange (ETDEWEB)
Simonen, T; Cohen, R; Correll, D; Fowler, K; Post, D; Berk, H; Horton, W; Hooper, E B; Fisch, N; Hassam, A; Baldwin, D; Pearlstein, D; Logan, G; Turner, B; Moir, R; Molvik, A; Ryutov, D; Ivanov, A A; Kesner, J; Cohen, B; McLean, H; Tamano, T; Tang, X Z; Imai, T
Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT
The Axisymmetric Tandem Mirror: A Magnetic Mirror Concept Game Changer Magnet Mirror Status Study Group
International Nuclear Information System (INIS)
Experimental results, theory and innovative ideas now point with increased confidence to the possibility of a Gas Dynamic Trap (GDT) neutron source which would be on the path to an attractively simple Axisymmetric Tandem Mirror (ATM) power plant. Although magnetic mirror research was terminated in the US 20 years ago, experiments continued in Japan (Gamma 10) and Russia (GDT), with a very small US effort. This research has now yielded data, increased understanding, and generated ideas resulting in the new concepts described here. Early mirror research was carried out with circular axisymmetric magnets. These plasmas were MHD unstable due to the unfavorable magnetic curvature near the mid-plane. Then the minimum-B concept emerged in which the field line curvature was everywhere favorable and the plasma was situated in a MHD stable magnetic well (70% average beta in 2XII-B). The Ioffe-bar or baseball-coil became the standard for over 40 years. In the 1980's, driven by success with minimum-B stabilization and the control of ion cyclotron instabilities in PR6 and 2XII-B, mirrors were viewed as a potentially attractive concept with near-term advantages as a lower Q neutron source for applications such as a hybrid fission fuel factory or toxic waste burner. However there are down sides to the minimum-B geometry: coil construction is complex; restraining magnetic forces limit field strength and mirror ratios. Furthermore, the magnetic field lines have geodesic curvature which introduces resonant and neoclassical radial transport as observed in early tandem mirror experiments. So what now leads us to think that simple axisymmetric mirror plasmas can be stable? The Russian GDT experiment achieves on-axis 60% beta by peaking of the kinetic plasma pressure near the mirror throat (where the curvature is favorable) to counter-balance the average unfavorable mid-plane curvature. Then a modest augmentation of plasma pressure in the expander results in stability. The GDT
O'Leary, Michael
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Split Special Lagrangian Geometry
Harvey, F. Reese; Lawson Jr, H. Blaine
One purpose of this article is to draw attention to the seminal work of J. Mealy in 1989 on calibrations in semi-riemannian geometry where split SLAG geometry was first introduced. The natural setting is provided by doing geometry with the complex numbers C replaced by the double numbers D, where i with i^2 = -1 is replaced by tau with tau^2 = 1. A rather surprising amount of complex geometry carries over, almost untouched, and this has been the subject of many papers. We briefly review this ...
Fundamental concepts of geometry
Meserve, Bruce E
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Emission-Line Profiles of Accretion Disks with a Non-Axisymmetric Pattern
SANBUICHI, Kiyotaka; FUKUE, Jun; Kojima, Yasufumi
In several cases, accretion disks may have non-axisymmetric patterns, such as one-armed oscillations and spiral shock waves. In such cases the line emissivity may also become non-axisymmetric. We examined the emission-line profiles for geometrically thin/thick, (non-) relativistic accretion disks while taking acount of the non-axisymmetric emissivity. The emission-line profiles were calculated numerically using a code based on the ray-tracing method. The emission-line profiles are usually ...
Bergshoeff, Eric A.; Riccioni, Fabio; Alvarez-Gaumé, L.
We probe doubled geometry with dual fundamental branes. i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundam
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance introdu...
Euclidean Geometry via Programming.
Filimonov, Rossen; Kreith, Kurt
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
Precision analysis of non-conformal reconstruction for the surface acoustic field on axisymmetric structures
Institute of Scientific and Technical Information of China (English)
HE Yuanan; HE Zuoyong
Reconstruction of the surface acoustic field of axisymmetric body with arbitrary boundary conditions using near-field acoustic data is studied. The method of numerical reconstruction based on orthonormalization function expansion (OFE) and boundary element integral (BEI) is presented which can overcome the singular integral problem in the boundary integral equations. By numerical examples, the precision of reconstruction for the non-conformal surface with the axisymmetric or non-axisymmetric vibrating on axisymmetric body is given.The results of the numerical simulation are shown that this kind of reconstruction method is available for engineering.
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Axisymmetric Turbulent Wakes with New Nonequilibrium Similarity Scalings
Nedić, J.; Vassilicos, J. C.; Ganapathisubramani, B.
The recently discovered nonequilibrium turbulence dissipation law implies the existence of axisymmetric turbulent wake regions where the mean flow velocity deficit decays as the inverse of the distance from the wake-generating body and the wake width grows as the square root of that distance. This behavior is different from any documented boundary-free turbulent shear flow to date. Its existence is confirmed in wind tunnel experiments of wakes generated by plates with irregular edges placed normal to an incoming free stream. The wake characteristics of irregular bodies such as buildings, bridges, mountains, trees, coral reefs, and wind turbines are critical in many areas of environmental engineering and fluid mechanics.
Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
Rigas, G; Brackston, R D; Morrison, J F
A modelling methodology to reproduce the experimental measurements of a turbulent flow under the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake- flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries which occur at the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.
Stability and Halo Formation in Axisymmetric Intense Beams
Gluckstern, R L; Gluckstern, Robert L.; Kurennoy, Sergey S.
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression - mismatch space is explored for the uniform (KV) distribution of the particle transverse-phase-space density, as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results show an agreement with predictions of the analytical model for halo formation (R.L. Gluckstern, Phys. Rev. Letters, 73 (1994) 1247).
Stability and Halo Formation in Axisymmetric Intense Beams.
Gluckstern, Robert L.; Kurennoy, Sergey S.
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression - mismatch space is explored for the uniform distribution of the particle transverse phase space density (Kapchinsky-Vladimirsky), as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results obtained are compared and show an agreement with the predictions of the analytical model for halo formation developed earlier (R.L. Gluckstern, Phys. Rev. Lett., 73), 1247 (1994)..
Stability and halo formation in axisymmetric intense beams
Energy Technology Data Exchange (ETDEWEB)
Gluckstern, R.L. [Univ. of Maryland, College Park, MD (United States); Kurennoy, S.S. [Los Alamos National Lab., NM (United States)
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression-mismatch space is explored for the uniform (KV) distribution of the particle transverse-phase-space density, as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results show an agreement with predictions of the analytical model for halo formation.
A high-precision algorithm for axisymmetric flow
Directory of Open Access Journals (Sweden)
A. Gokhman
Full Text Available We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.
Fusion-product transport in axisymmetric tokamaks: losses and thermalization
International Nuclear Information System (INIS)
High-energy fusion-product losses from an axisymmetric tokamak plasma are studied. Prompt-escape loss fluxes (i.e. prior to slowing down) are calculated including the non-separable dependence of flux as a function of poloidal angle and local angle-of-incidence at the first wall. Fusion-product (fp) thermalization and heating are calculated assuming classical slowing down. The present analytical model describes fast ion orbits and their distribution function in realistic, high-β, non-circular tokamak equilibria. First-orbit losses, trapping effects, and slowing-down drifts are also treated
An axisymmetric PFEM formulation for bottle forming simulation
Ryzhakov, Pavel B.
A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisymmetric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.
Angle-action estimation in a general axisymmetric potential
Sanders, Jason
The usefulness of angle-action variables in galaxy dynamics is well known, but their use is limited due to the difficulty of their calculation in realistic galaxy potentials. Here we present a method for estimating angle-action variables in a realistic Milky Way axisymmetric potential by locally fitting a St\\"ackel potential over the region an orbit probes. The quality of the method is assessed by comparison with other known methods for estimating angle-action variables of a range of disc and...
Accuracy Improvement in Magnetic Field Modeling for an Axisymmetric Electromagnet
Ilin, Andrew V.; Chang-Diaz, Franklin R.; Gurieva, Yana L.; Il,in, Valery P.
This paper examines the accuracy and calculation speed for the magnetic field computation in an axisymmetric electromagnet. Different numerical techniques, based on an adaptive nonuniform grid, high order finite difference approximations, and semi-analitical calculation of boundary conditions are considered. These techniques are being applied to the modeling of the Variable Specific Impulse Magnetoplasma Rocket. For high-accuracy calculations, a fourth-order scheme offers dramatic advantages over a second order scheme. For complex physical configurations of interest in plasma propulsion, a second-order scheme with nonuniform mesh gives the best results. Also, the relative advantages of various methods are described when the speed of computation is an important consideration.
Axisymmetric fundamental solutions for a finite layer with impeded boundaries
Institute of Scientific and Technical Information of China (English)
程泽海; 陈云敏; 凌道盛; 唐晓武
Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary-value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.
Exact solutions to some axisymmetric problems in magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Sheriazdanov, G.B.
Steady-state axisymmetric flow of an incompressible perfectly conducting fluid is analyzed with allowance for the circular motion and the azimuthal component of the magnetic field. In the case of a nonviscous fluid, an equation of motion integral is obtained which relates the Bernoulli function to the azimuthal component of the velocity and magnetic fields. For the case of the rotation of a viscous fluid as a solid, the Bernoulli integral depends on the stream function, Reynolds and Alfven numbers, and the twisting parameter. 5 references.
Marginally stable circular orbits in stationary axisymmetric spacetimes
Beheshti, Shabnam
We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs are explicitly calculated for concrete examples of physical interest.
Axisymmetric Vibration of Piezo-Lemv Composite Hollow Multilayer Cylinder
Directory of Open Access Journals (Sweden)
E. S. Nehru
Full Text Available Axisymmetric vibration of an infinite piezolaminated multilayer hollow cylinder made of piezoelectric layers of 6 mm class and an isotropic LEMV (Linear Elastic Materials with Voids layers is studied. The frequency equations are obtained for the traction free outer surface with continuity conditions at the interfaces. Numerical results are carried out for the inner, middle, and outer hollow piezoelectric layers bonded by LEMV (It is hypothetical material layers and the dispersion curves are compared with that of a similar 3-layer model and of 3 and 5 layer models with inner, middle, and outer hollow piezoelectric layers bonded by CFRP (Carbon fiber reinforced plastics.
A Generalization of Abel Inversion to non axisymmetric density distribution
Tomassini, P
Abel Inversion is currently used in laser-plasma studies in order to estimate the electronic density $n_e$ from the phase-shift map $\\delta \\phi$ obtained via interferometry. The main limitation of the Abel method is due to the assumption of axial symmetry of the electronic density, which is often hardly fulfilled. In this paper we present an improvement to the Abel inversion technique in which the axial symmetry condition is relaxed by means of a truncated Legendre Polinomial expansion in the azimutal angle. With the help of simulated interferograms, we will show that the generalized Abel inversion generates accurate densities maps when applied to non axisymmetric density sources.
Space reconstruction of the morphology and kinematics of axisymmetric radio sources
Diep, P. N.; Phuong, N. T.; Hoai, D. T.; Nhung, P. T.; Thao, N. T.; Tuan-Anh, P.; Darriulat, P.
The unprecedented quality of the observations available from the Atacama Large Millimetre/sub-millimetre Array (ALMA) calls for analysis methods making the best of them. Reconstructing in space the morphology and kinematics of radio sources is an underdetermined problem that requires imposing additional constraints for its solution. The hypothesis of rotational invariance, which is a good approximation to, or at least a good reference for the description of the gas envelopes of many evolved stars and protostars, is particularly efficient in this role. In the first part of the article, a systematic use of simulated observations allows us for identifying the main problems and for constructing quantities aimed at solving them. In particular the evaluation of the orientation of the star axis in space and the differentiation between expansion along the star axis and rotation about it are given special attention. The use of polar rather than Cartesian sky coordinates to display the results of the analysis is shown to often better match the morphology and kinematics of actual stars. The radial dependence of the gas density and temperature and the possible presence of velocity gradients are briefly considered. In the second part, these results are applied to a few stars taken as examples with the aim of evaluating their usefulness when applied to concrete cases. A third part takes stock of what precedes and formulates some guidelines for modelling the radio emission of axisymmetric radio sources, limited however to the mathematics and geometry of the problem, physics considerations being generally ignored.
Spreading of non-planar non-axisymmetric gravity and turbidity currents
Zgheib, Nadim; Bonometti, Thomas; Balachandar, S.
The dynamics of non-axisymmetric turbidity currents is considered here. The study comprises a series of experiments for which a finite volume of particle-laden solution is released into fresh water. A mixture of water and polystyrene particles of diameter 280 cylinder at the center of a large tank filled with fresh water. Cylinders with four different cross-sections are examined: a circle, a plus-shape, a rectangle and a rounded rectangle in which the sharp corners are smoothened. The time evolution of the front is recorded as well the spatial distribution of the thickness of the final deposit via the use of a laser triangulation technique. The dynamics of the front and final deposit are significantly influenced by the initial geometry, displaying substantial azimuthal variation especially for the rectangular case where the current extends farther and deposits more particles along the initial minor axis of the rectangular cross section. Interestingly, this departure from axisymmetry cannot be predicted by current theoretical methods such as the Box Model. Several parameters are varied to assess the dependence on the settling velocity, initial height aspect ratio, local curvature and mixture density. NSF-PIRE OISE-0968313.
Collection-efficient, axisymmetric vacuum sublimation module for the purification of solid materials.
May, Michael; Paul, Elizabeth; Katovic, Vladimir
A vacuum sublimation module of axisymmetric geometry was developed and employed to purify solid-phase materials. The module provides certain practical advantages and it comprises: a metering valve, glass collector, glass lower body, main seal, threaded bushing, and glass internal cartridge (the latter to contain starting material). A complementary process was developed to de-solvate, sublime, weigh, and collect solid chemical materials exemplified by oxalic acid, ferrocene, pentachlorobenzene, chrysene, and urea. The oxalic acid sublimate was analyzed by titration, melting range, Fourier Transform Infrared (FT-IR) Spectroscopy, cyclic voltammetry, and its (aqueous phase) electrolytically generated gas. The analytical data were consistent with a high-purity, anhydrous oxalic acid sublimate. Cyclic voltammograms of 0.11 mol. % oxalic acid in water displayed a 2.1 V window on glassy carbon electrode beyond which electrolytic decomposition occurs. During module testing, fifteen relatively pure materials were sublimed with (energy efficient) passive cooling and the solid-phase recovery averaged 95 mass %. Key module design features include: compact vertical geometry, low-angle conical collector, uniformly compressed main seal, modest power consumption, transparency, glovebox compatibility, cooling options, and preferential conductive heat transfer. To help evaluate the structural (module) heat transfer, vertical temperature profiles along the dynamically evacuated lower body were measured versus electric heater power: for example, an input of 18.6 W generated a temperature 443-K at the bottom. Experimental results and engineering calculations indicate that during sublimation, solid conduction is the primary mode of heat transfer to the starting material. PMID:26628150
Riemann-Finsler Geometry with Applications to Information Geometry
Institute of Scientific and Technical Information of China (English)
Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce RiemannFinsler geometry, by which we establish Information Geometry on a much broader base,so that the potential applications of Information Geometry will be beyond statistics.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Santo, J
The ALICE Geometry Database project consists of the development of a set of data structures to store the geometrical information of the ALICE Detector. This Database will be used in Simulation, Reconstruction and Visualisation and will interface with existing CAD systems and Geometrical Modellers.At the present time, we are able to read a complete GEANT3 geometry, to store it in our database and to visualise it. On disk, we store different geometry files in hierarchical fashion, and all the nodes, materials, shapes, configurations and transformations distributed in this tree structure. The present status of the prototype and its future evolution will be presented.
Discrete and computational geometry
Devadoss, Satyan L
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well a
Bonola, Roberto
This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important.Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance. Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such
Application of the Least Squares Method in Axisymmetric Biharmonic Problems
Directory of Open Access Journals (Sweden)
Vasyl Chekurin
Full Text Available An approach for solving of the axisymmetric biharmonic boundary value problems for semi-infinite cylindrical domain was developed in the paper. On the lateral surface of the domain homogeneous Neumann boundary conditions are prescribed. On the remaining part of the domain's boundary four different biharmonic boundary pieces of data are considered. To solve the formulated biharmonic problems the method of least squares on the boundary combined with the method of homogeneous solutions was used. That enabled reducing the problems to infinite systems of linear algebraic equations which can be solved with the use of reduction method. Convergence of the solution obtained with developed approach was studied numerically on some characteristic examples. The developed approach can be used particularly to solve axisymmetric elasticity problems for cylindrical bodies, the heights of which are equal to or exceed their diameters, when on their lateral surface normal and tangential tractions are prescribed and on the cylinder's end faces various types of boundary conditions in stresses in displacements or mixed ones are given.
Non-axisymmetric instabilities in discs with imposed zonal flows
Vanon, R
We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick (2007), which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is $\\gtrsim 8H$, where $H$ is the disc's scale height, regardless of the value of the adiabatic index $\\gamma$. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisym...
Aerodynamics characteristic of axisymmetric surface protuberance in supersonic regime
Qamar, Adnan
The present work deals with the problem of an axi-symmetric surface protuberance mounted on a spherical nosed body of revolution. The numerical computations are carried out for laminar supersonic viscous flow for trapezoidal shape axi-symmetric protuberances. A free stream Mach number ranging from 3 to 8 in steps of 1 at a fixed free stream Reynolds number of 1.8x10(4) has been used in the present study. The steady solutions are obtained using a time marching approach. A newly developed Particle Velocity Upwinding (PVU) scheme has been used for the computation. The spatial flow pattern exhibits a strong bow shock in front of the hemispherical nose, which engulfs the entire base body. Near the protuberance, the fluid particle decelerates due to the adverse pressure created by the protuberance and thus the flow separates in front of the protuberance. This point of separation is found to be a function of Mach number and the protuberance shape. A low-pressure expansion region dominates the base region of the obstacle. The reattachment point for the base separation is also a function of Mach number. As the Mach number is increased the reattachment point shifts toward the protuberances base. A weak recompression shock is also seen in the base, which affects the separated zone behind the protuberance. The important design parameters such as skin friction, heat transfer, drag, and surface pressure coefficients are reported extensively.
Two-Dimensional Axisymmetric Collapse of Thermally Unstable Primordial Clouds
Baek, C H; Ryu, D; Baek, Chang Hyun; Kang, Hyesung; Ryu, Dongsu
We have performed two-dimensional hydrodynamic simulations of the collapse of isolated axisymmetric clouds condensing via radiative cooling in a primordial background gas. In order to study the development of the so-called ``shape-instability'', we have considered two types of axisymmetric clouds, oblate and prolate clouds of various sizes and with axial ratios of $0.5 \\leq {R_{\\rm c,R}} /{R_{\\rm c,z}} \\leq 2$. We find that the degree of oblateness or prolateness is enhanced during the initial cooling phase. But it can be reversed later, if the initial contrast in cooling times between the cloud gas and the background gas is much greater than one. In such cases an oblate cloud collapses to a structure composed of an outer thin disk and a central prolate component. A prolate cloud, on the other hand, becomes a thin cigar-shape structure with a central dense oblate component. The reversal of shape in the central part of the cooled clouds is due to supersonic motions either along the disk plane in the case of ob...
Mechanical Geometry Theorem Proving Based on Groebner Bases
Institute of Scientific and Technical Information of China (English)
A new method for the mechanical elementary geometry theorem proving is presented by using Groebner bases of polynomial ideals.It has two main advantages over the approach proposed in literature:(i)It is complete and not a refutational procdure;(ii) The subcases of the geometry statements which are not generally true can be differentiated clearly.
Emenaker, Charles E.
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Directory of Open Access Journals (Sweden)
Richter William
Full Text Available This is the translation of the Mizar article containing readable Mizar proofs of some axiomatic geometry theorems formulated by the great Polish mathematician Alfred Tarski [8], and we hope to continue this work.
Elementary differential geometry
Pressley, Andrew
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecture...
Lectures on Symplectic Geometry
Silva, Ana Cannas
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Induced geometry from disformal transformation
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Fang-Fang Yuan
Full Text Available In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.
Induced geometry from disformal transformation
Energy Technology Data Exchange (ETDEWEB)
Yuan, Fang-Fang, E-mail: email@example.com [School of Physics, Nankai University, Tianjin 300071 (China); Huang, Peng, E-mail: email@example.com [School of Astronomy and Space Science, Sun Yat-Sen University, Guangzhou 510275 (China)
In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.
Intermediate algebra & analytic geometry
Gondin, William R
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Punzi, Raffaele; Wohlfarth, Mattias N R
We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Energy Technology Data Exchange (ETDEWEB)
Punzi, Raffaele [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: firstname.lastname@example.com; Schuller, Frederic P. [Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14467 Potsdam (Germany)], E-mail: email@example.com; Wohlfarth, Mattias N.R. [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: email@example.com
We reveal the non-metric geometry underlying {omega}{yields}0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Ashtekar, Abhay
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate students in physics. As an illustrative application, I indicate how some of the detailed features of the micro-structure of geometry can be tested using black hole thermodynamics. Current and future directions of research in this area are discussed.
Compositional Geometry and Programming
Bantchev, Boyko
Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014 Functional, or compositional, geometry is a method of constructing complex pictures from simpler ones, apllying binding operations. The method is naturally related to functional programming and can be used as a tool for education or self-education in programming. The paper introduces to compositional geometry, bringing attention to its severa...
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Wave Propagation in Axi-Symmetrical Magmatic Conduits Due to an Internal Source
De Negri, R. S.; Sanchez-Sesma, F. J.; Arciniega-Ceballos, A.
The classical Trefftz's method is implemented to simulate wave propagation in and around axi-symmetrical magmatic conduits. In this fluid-solid system the fluid (magma) is confined by an elastic unbounded medium that represents the surrounding rock. Our aim is to associate wave behavior with mechanical and geometrical conduit characteristics. The source is assumed to be at a point along the conduit centered axis medium are constructed in both cases as linear combinations of particular solutions.Within the fluid such solutions are spherical standing waves that are smooth at the origins. In the elastic solid region the field is constructed with monopoles and dipoles for the P waves and spheroidal dipoles for SV waves. The particular solutions satisfy the elastodynamic equations that govern the wave motion at those media and are associated to origins (selected points) distributed along the conduit axis. For the surrounding rock the solutions are sources that satisfy Sommerfeld's radiation condition. These sets of solutions are assumed to be complete. This conjecture is exact in 2D acoustic problems. The conduit can be closed or open at the ends and the surrounding elastic domain is unbounded. In order to find the coefficients of Trefftz's wave expansions, boundary conditions at the fluid-solid interface (null shear and continuity of pressures and normal velocities) are satisfied in the least squares sense. The solution is obtained in the frequency domain and the source time function can be introduced using Fourier analysis.Regardless the low order of the formulation our results display a rich variety of behaviors. For a uniform infinite cylinder we reproduced the exact analytical solution. In addition, this approach allows identifying some important effects of the conduit geometry, including changes of sections. Lateral and longitudinal resonances of irregular axi-symmetric conduits are well resolved. The stiffness of the solid domain with respect to the fluid
Osborne, I.; Brownson, E.; Eulisse, G.; Jones, C. D.; Lange, D. J.; Sexton-Kennedy, E.
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Tokamak magnetohydrodynamic equilibrium states with axisymmetric boundary and a 3D helical core.
Cooper, W A; Graves, J P; Pochelon, A; Sauter, O; Villard, L
Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures.
Geodesic Acoustic Mode in Toroidally Axisymmetric Plasmas with Non-Circular Cross Sections
Institute of Scientific and Technical Information of China (English)
SHI Bing-Ren; LI Ji-Quan; DONG Jia-Qi
@@ The geodesic acoustic mode in general toroidally axisymmetric plasmas such as Tokamak and spherical torus is studied in detail. The mode structure is found and the dispersion equation is derived and solved for arbitrary toroidally axi-symmetric plasmas. Besides the finite aspect ratio, effects of elongation and triangularity on this mode are clarified.
Spectral approach to axisymmetric evolution of Einstein's equations
Schell, Christian
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the occurrence of coordinate singularities on the axis of symmetry and at the origin. Spherical harmonics are manifestly regular on the axis and hence take care of that issue automatically. In addition a spectral approach has computational advantages when the equations are implemented. Therefore we spectrally decompose all the variables in the appropriate harmonics. A central point in the formulation is the gauge choice. One of our results is that the commonly used maximal-isothermal gauge turns out to be incompatible with tensor harmonic expansions, and we introduce a new gauge that is better suited. We also address the regularisation of the coordinate singularity at the origin.
Axisymmetric Nonlinear Waves And Structures in Hall Plasmas
Islam, Tanim
A Hall plasma consists of a plasma with not all species frozen into the magnetic field. In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature -- whistler drift modes that propagate along the electron drift as a Burger's shock, and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral -- are analyzed. We derive analytical and numerical solutions in an electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to electron-ion-gas Hall plasmas, in which the ions are coupled to the motion of gases in low ionized plasmas (lower ionosphere and protostellar disks), and to dusty Hall plasmas (such as molecular clouds), in which the much heavier charged dust may be collisionally coupled to the gas.
Fluidic Control of Aerodynamic Forces on an Axisymmetric Body
Abramson, Philip; Vukasinovic, Bojan; Glezer, Ari
The aerodynamic forces and moments on a wind tunnel model of an axisymmetric bluff body are modified by induced local vectoring of the separated base flow. Control is effected by an array of four integrated aft-facing synthetic jets that emanate from narrow, azimuthally-segmented slots, equally distributed around the perimeter of the circular tail end within a small backward facing step that extends into a Coanda surface. The model is suspended in the wind tunnel by eight thin wires for minimal support interference with the wake. Fluidic actuation results in a localized, segmented vectoring of the separated base flow along the rear Coanda surface and induces asymmetric aerodynamic forces and moments to effect maneuvering during flight. The aerodynamic effects associated with quasi-steady and transitory differential, asymmetric activation of the Coanda effect are characterized using direct force and PIV measurements.
Institute of Scientific and Technical Information of China (English)
By using Brown-York quasilocal energy theory we calculate the quasilocal energy of a stationary axisymmetic EMDA black hole and explore the universality of Martinez's conjecture in string theory. We show that the energy is positive and monotonically decreases to the ADM mass at spatial infinity, and the Martinez's conjecture, the Brown York quasilocal energy at the outer horizon reduces to twice its irreducible mass, is still valid for stationary axisymmetric EMDA black hole. From the result we also find that the Kerr-Sen spacetime keeps up with Martinez's conjecture. This is different from the Bose-Naing result that the quasilocal energy of the Kerr Sen spacetime does not approach the Martinez's conjecture.
Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases
Chaussade, Marie; Faou, Erwan; Yosibash, Zohar
Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam\\'e system) are determined by an asymptotic analysis as the thickness ($2\\varepsilon$) tends to zero. The departing point is the Koiter shell model that we reduce by asymptotic analysis to a scalar modelthat depends on two parameters: the angular frequency $k$ and the half-thickness $\\varepsilon$. Optimizing $k$ for each chosen $\\varepsilon$, we find power laws for $k$ in function of $\\varepsilon$ that provide the smallest eigenvalues of the scalar reductions.Corresponding eigenpairs generate quasimodes for the 3D Lam\\'e system by means of several reconstruction operators, including boundary layer terms. Numerical experiments demonstrate that in many cases the constructed eigenpair corresponds to the first eigenpair of the Lam\\'e system.Geometrical conditions are necessary to this approach: The Gaussian curvature has to be nonnegative and the azimuthal curvature has to dominate the meridian ...
Time and "angular" dependent backgrounds from stationary axisymmetric solutions
Obregón, O; Ryan, M P; Obregon, Octavio; Quevedo, Hernando; Ryan, Michael P.
Backgrounds depending on time and on "angular" variable, namely polarized and unpolarized $S^1 \\times S^2$ Gowdy models, are generated as the sector inside the horizons of the manifold corresponding to axisymmetric solutions. As is known, an analytical continuation of ordinary $D$-branes, $iD$-branes allows one to find $S$-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzchild and the Kerr metrics. The possibility of studying the $i$-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generalized $S$-branes depending not only on time but also on an ``angular'' variable.
Axisymmetric equilibria with pressure anisotropy and plasma flow
Evangelias, Achilleas
In this Master thesis we investigate the influence of pressure anisotropy and incompressible flow of arbitrary direction on the equilibrium properties of magnetically confined, axisymmetric toroidal plasmas. The main novel contribution is the derivation of a pertinent generalised Grad-Shafranov equation. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy, through an anisotropy function assumed to be uniform on the magnetic surfaces, and plasma flow, via the...
Axisymmetric equilibria with pressure anisotropy and plasma flow
Evangelias, A
A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of...
An Axisymmetrical Acoustic BEM Formulation Including Visco-Thermal Losses
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
Sound waves in air experience losses due to viscous friction and thermal exchange, which become particularly relevant in a thin boundary layer over the domain boundaries. The lossless wave equation can still be used when the thickness of the boundary layer is small as compared with the setup...... dimensions. However, this is not usually true for small devices such as microphones, hearing aids, couplers, MEMS devices, mobile phones, etc., and then the losses need to be modeled. In this paper a numerical implementation of the Boundary Element Method (BEM) which includes visco-thermal losses...... is presented. The formulation is based on the Kirchoff method, where acoustic, thermal and viscous effects are decoupled everywhere except at the boundaries. This BEM formulation does not impose geometrical restrictions to the setup and can be applied to any axisymmetrical object, as long as the division...
Non-Radial Oscillations in an Axisymmetric MHD Incompressible Fluid
Indian Academy of Sciences (India)
A. Satya Narayanan
It is well known from Helioseismology that the Sun exhibits oscillations on a global scale, most of which are non-radial in nature. These oscillations help us to get a clear picture of the internal structure of the Sun as has been demonstrated by the theoretical and observational (such as GONG) studies. In this study we formulate the linearised equations of motion for non-radial oscillations by perturbing the MHD equilibrium solution for an axisymmetric incompressible fluid. The fluid motion and the magnetic field are expressed as scalars , , and , respectively. In deriving the exact solution for the equilibrium state, we neglect the contribution due to meridional circulation. The perturbed quantities *, *, *, * are written in terms of orthogonal polynomials. A special case of the above formulation and its stability is discussed.
Modular Coils and Plasma Configurations for Quasi-axisymmetric Stellarators
Energy Technology Data Exchange (ETDEWEB)
L.P. Ku and A.H. Boozer
Characteristics of modular coils for quasi-axisymmetric stellarators that are related to the plasma aspect ratio, number of field periods and rotational transform have been examined systematically. It is observed that, for a given plasma aspect ratio, the coil complexity tends to increase with the increased number of field periods. For a given number of field periods, the toroidal excursion of coil winding is reduced as the plasma aspect ratio is increased. It is also clear that the larger the coil-plasma separation is, the more complex the coils become. It is further demonstrated that it is possible to use other types of coils to complement modular coils to improve both the physics and the modular coil characteristics.
Cellular blebs: pressure-driven, axisymmetric, membrane protrusions
Woolley, Thomas E.
Blebs are cellular protrusions that are used by cells for multiple purposes including locomotion. A mechanical model for the problem of pressure-driven blebs based on force and moment balances of an axisymmetric shell model is proposed. The formation of a bleb is initiated by weakening the shell over a small region, and the deformation of the cellular membrane from the cortex is obtained during inflation. However, simply weakening the shell leads to an area increase of more than 4 %, which is physically unrealistic. Thus, the model is extended to include a reconfiguration process that allows large blebs to form with small increases in area. It is observed that both geometric and biomechanical constraints are important in this process. In particular, it is shown that although blebs are driven by a pressure difference across the cellular membrane, it is not the limiting factor in determining bleb size. © 2013 Springer-Verlag Berlin Heidelberg.
Axisymmetric nonlinear waves and structures in Hall plasmas
Energy Technology Data Exchange (ETDEWEB)
Islam, Tanim [Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, California 94551-0808 (United States)
In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature-whistler drift modes that propagate along the electron drift as a Burger's shock and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral-are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.
Ideal, steady-state, axisymmetric magnetohydrodynamic equations with flow
International Nuclear Information System (INIS)
The motivation of this study is to gain additional understanding of the effect of rotation on the equilibrium of a plasma. The axisymmetric equilibria of ideal magnetohydrodynamics (MHD) with flow have been studied numerically and analytically. A general discussion is provided of previous work on plasmas with flow and comparisons are made to the static model. A variational principle has been derived for the two dimensional problem with comments as to appropriate boundary conditions. An inverse aspect ratio expansion has been used for a study of the toroidal flow equation for both low- and high-β. The inverse aspect ratio expansion has also been used for a study of equations with both poloidal and toroidal flow. An overview is provided of the adaptive finite-difference code which was developed to solve the full equations. (FI)
Three-dimensional axisymmetric flow-focusing device using stereolithography.
Morimoto, Yuya; Tan, Wei-Heong; Takeuchi, Shoji
This paper describes a three-dimensional microfluidic axisymmetric flow-focusing device (AFFD) fabricated using stereolithography. Using this method, we can fabricate AFFDs rapidly and automatically without cumbersome alignment needed in conventional methods. The AFFDs are able to be fabricated reproducibly with a micro-sized orifice of diameter around 250 mum. Using this device, we are able to produce monodisperse water-in-oil (W/O) droplets with a coefficient of variation (CV) of less than 4.5%, W/O droplets with encapsulated microbes (CV < 4.9%) and oil-in-water (O/W) droplets (CV < 3.2%) without any surface modifications. The diameter of these droplets range from 54 to 244 mum with respect to the flow rate ratio of the fluids used; these results are in good agreement with theoretical behavior. For applications of the AFFD, we demonstrate that these devices can be used to produce double emulsions and monodisperse hydrogel beads.
Cecil, Thomas E
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
Supersymmetry and noncommutative geometry
Beenakker, Wim; Suijlekom, Walter D van
In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far. The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model. This book is ...
Integral Geometry and Holography
Czech, Bartlomiej; McCandlish, Samuel; Sully, James
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we...
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Strings on Bubbling Geometries
Lin, Hai; Shock, Jonathan P
We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wavefunction.
Ochiai, T.; Nacher, J. C.
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Emergent Complex Network Geometry
Wu, Zhihao; Rahmede, Christoph; Bianconi, Ginestra
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geo...
Yale, Paul B
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Gervais, Jean-Loup; Gervais, Jean-Loup; Matsuo, Yutaka
It is shown that, classically, the W-algebras are directly related to the extrinsic geometry of the embedding of two-dimensional manifolds with chiral parametrisation (W-surfaces) into higher dimensional K\\"ahler manifolds. We study the local and the global geometries of such embeddings, and connect them to Toda equations. The additional variables of the related KP hierarchy are shown to yield a specific coordinate system of the target-manifold, and this allows us to prove that W-transformations are simply particular diffeomorphisms of this target space. The W-surfaces are shown to be instantons of the corresponding non-linear $\\sigma$-models.
Elementary differential geometry
O'Neill, Barrett
Written primarily for students who have completed the standard first courses in calculus and linear algebra, ELEMENTARY DIFFERENTIAL GEOMETRY, REVISED SECOND EDITION, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition p
Bowyer, Adrian
A Programmer's Geometry provides a guide in programming geometric shapes. The book presents formulas and examples of computer representation and coding of geometry. Each of the nine chapters of the text deals with the representation and solution of a specific geometrical problem, such as areas, vectors, and volumes. The last chapter provides a brief discussion on generating image through a computer. The codes presented in the book are written in FORTRAN 77. The text will be of great use to programmers who are working on projects that involve geometric calculations.
Gravitational wave momentum extraction in non-axisymmetric Robinson-Trautman spacetimes
Aranha, R F; Tonini, E V
We examine numerically the gravitational wave recoil in non-axisymmetric Robinson-Trautman spacetimes. We construct characteristic initial data for the Robinson-Trautman dynamics which are interpreted as corresponding to the early post-merger state of two boosted colliding black holes with a common apparent horizon. Our analysis is based on the Bondi-Sachs energy-momentum conservation laws which regulate the radiative transfer processes involved in the emission of gravitational waves. We evaluate the Bondi-Sachs momentum flux carried out by gravitational waves and the associated net kick velocity defined (in a zero-initial-Bondi-momentum frame) as proportional to the total gravitational wave impulse imparted on the system. The kick velocity distributions are obtained and analyzed for two distinct classes of initial data corresponding to the early post-merger state of (i) non-head-on collisions and (ii) head-on collisions of black holes. For the first class (i), the net gravitational wave momentum fluxes and a...
Control of supersonic axisymmetric base flows using passive splitter plates and pulsed plasma actuators
Reedy, Todd Mitchell
decreasing pressure. Implementing an array of eight electric arcs circumferentially around the base near the corner expansion, the LAFPA actuators were shown to produce significant disturbances to the separating shear layer of the base flow and cause modest influences on the base pressure when actuated over a range of high frequencies (O(kHz)), forcing modes, duty cycles, and electrical currents. To tailor the plasma actuator toward the specific flow control application of the separated base flow, several actuator geometries and energy additions were evaluated. Displaying the ability to produce disturbances in the shear layer, an open cavity actuator design outperformed the other geometries consisting of a confined cavity with an exhaust orifice. Increases in duty cycle (between 2% and 6%) and in plasma current (1/4 to 4 amps) were shown to produce large velocity disturbances causing a decrease in average base pressure. At 4 amps and a maximum duty cycle of 6%, the largest measured change in area-weighted base pressure, near -1.5%, was observed for the axisymmetric forcing mode. Positive changes in base pressure were experienced (as much as 1% increase from the no-control) for the vertical and horizontal flapping modes.
Some links between turtle geometry and analytic geometry
Rowe, Neil C.
The computer language Logo facilitates the teaching of analytic geometry and calculus from the notion of curvature, through its turtle geometry facility. The author provides some theoretical basis for finding turtle geometry equivalents of familiar curves in analytic geometry, and vice versa, by some simple methods apparently previously unnoticed. In particular, he studied turtle geometry programs where the curvature of a line is a trigonometric function of its orientation. (Author)
Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo
Pipin, V V
We explore a response of the non-linear non-axisymmetric mean-field solar dynamo model to the shallow non-axisymmetric perturbations with the strength of 1G. The amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, the depth of perturbation. It is found that perturbation which is anchored at the 0.9R have a profound effect and it produce the transient magnetic cycle of the axisymmetric magnetic field if it is initiated at the growing phase of the cycle. The non-symmetric about equator perturbation results the hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on how well the magnetic helicity is conserved. In the range of Rm=10^{4-6} the evolution returns to the normal course in the next cycle and the non-axisymmetric field is generated due to non-linear alpha-effect and the magnetic buoyancy. In the stationary state of evolution the large-scale magnetic field demonstrate, the phenomena of the "active...
Comment on the exterior solutions and their geometry in scalar-tensor theories of gravity
Tsuchida, T; Tsuchida, Tooru; Watanabe, Kazuya
We study series of the stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent with the exterior solutions in some class of the scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of the solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of the static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then show a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optica...
Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity
Tsuchida, T.; Watanabe, K.
We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.
Cooper, Brett D.; Barger, Rita
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
Spacetime and Euclidean Geometry
Brill, D R; Brill, Dieter; Jacobson, Ted
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
Diophantine geometry an introduction
Hindry, Marc
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Hartshorne, Robin
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Advanced geometries and regimes
Energy Technology Data Exchange (ETDEWEB)
Bulanov, S. S. [Univeristy of California, Berkeley, CA, 94720 (United States); Bulanov, S. V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Turchetti, G. [Dipartimento di Fisica, Università di Bologna and INFN Sezione di Bologna, Via Irnerio, 46-I-40126 Bologna (Italy); Limpouch, J.; Klimo, O.; Psikal, J. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague, Czech Republic and Czech Technical University in Prague, FNSPE, Brehova 7, 115 19 Prague (Czech Republic); Antici, P. [Dipartimento di Energetica ed INFM, Università di Roma, La Sapienza, 00165 Roma (Italy); Margarone, D.; Korn, G. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague (Czech Republic)
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
Hsü, K J; Hsü, A J
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
Teaching Geometry with Tangrams.
Russell, Dorothy S.; Bologna, Elaine M.
Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Towards relativistic quantum geometry
Directory of Open Access Journals (Sweden)
Luis Santiago Ridao
Full Text Available We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Axisymmetric whole pin life modelling of advanced gas-cooled reactor nuclear fuel
Mella, R.; Wenman, M. R.
Thermo-mechanical contributions to pellet-clad interaction (PCI) in advanced gas-cooled reactors (AGRs) are modelled in the ABAQUS finite element (FE) code. User supplied sub-routines permit the modelling of the non-linear behaviour of AGR fuel through life. Through utilisation of ABAQUS's well-developed pre- and post-processing ability, the behaviour of the axially constrained steel clad fuel was modelled. The 2D axisymmetric model includes thermo-mechanical behaviour of the fuel with time and condition dependent material properties. Pellet cladding gap dynamics and thermal behaviour are also modelled. The model treats heat up as a fully coupled temperature-displacement study. Dwell time and direct power cycling was applied to model the impact of online refuelling, a key feature of the AGR. The model includes the visco-plastic behaviour of the fuel under the stress and irradiation conditions within an AGR core and a non-linear heat transfer model. A multiscale fission gas release model is applied to compute pin pressure; this model is coupled to the PCI gap model through an explicit fission gas inventory code. Whole pin, whole life, models are able to show the impact of the fuel on all segments of cladding including weld end caps and cladding pellet locking mechanisms (unique to AGR fuel). The development of this model in a commercial FE package shows that the development of a potentially verified and future-proof fuel performance code can be created and used. The usability of a FE based fuel performance code would be an enhancement over past codes. Pre- and post-processors have lowered the entry barrier for the development of a fuel performance model to permit the ability to model complicated systems. Typical runtimes for a 5 year axisymmetric model takes less than one hour on a single core workstation. The current model has implemented: Non-linear fuel thermal behaviour, including a complex description of heat flow in the fuel. Coupled with a variety of
Averaging Analysis of Self—Excited Motion of a Quasi—Axisymmetrical Gyrostat
Institute of Scientific and Technical Information of China (English)
薛纭; 陈立群
The averaging analysis was carried out to study the motion of a quasi-axisymmetrical gyrostat under a small-magnitude self-excited control troque.The common approach to investigating the problem of rigid body rotatyion under the action of a small torque known in the body frame was described.Using this approach,the problem(Grammel's problem for the case of small torque) that is maintaining the angular velocity of a quasi-axisymmetrical gyrostat using a control torque quadratic in the angular velocity was solved.Maintaining the angular velocity of a quasi-axisymmetrical gryostat using a control torque quadratic in the angular velocity was solved.
Experimental investigation about the effect of non-axisymmetric wake impact on a low speed axial compressor
Liu, Jianyong; Lu, Yajun; Li, Zhiping
Non-axisymmetric wake impact experiments were carried out after the best exciting frequency for a low speed axial compressor had been found by axisymmetric wake impact experiments. When the number and circumferential distribution of inlet guide vanes (IGV) are logical the wakes of non-axisymmetric IGVs can exert beneficial unsteady exciting effect on their downstream rotor flow fields and improve the compressor's performance. In the present paper, four non-axisymmetric wake impact plans were found working better than the axisymmetric wake impact plan. Compared with the base plan, the best non-axisymmetric plan increased the compressor's peak efficiency, and the total pressure rise by 1.1 and 2%, and enhanced the stall margin by 4.4%. The main reason why non-axisymmetric plans worked better than the axisymmetric plan was explained as the change of the unsteady exciting signal arising from IGV wakes. Besides the high-frequency components, the non-axisymmetric plan generated a beneficial low-frequency square-wave exciting signal and other secondary frequency components. Compared with the axisymmetric plan, multi-frequency exciting wakes arising from the non-axisymmetric plans are easier to get coupling relation with complex vortices such as clearance vortices, passage vortices and shedding vortices.
An introduction to Minkowski geometries
Farnsworth, David L.
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
Approximate Methods for Analyzing and Controlling Axisymmetric Instabilities of Elongated Tokamak Plasmas.
Frantz, Eric Randall
Elongation and shaping of the tokamak plasma cross -section can allow increased beta and other favorable improvements. As the cross-section is made non-circular, however, the plasma can become unstable against axisymmetric motions, the most predominant one being a nearly uniform displacement in the direction of elongation. Without additional stabilizing mechanisms, this instability has growth rates typically (TURN)10('6)sec('-1). With passive and active feedback from external conductors, the plasma can be significantly slowed down and controlled. In this work, a mathematical formulism for analyzing the vertical instability is developed in which the external conductors are treated (or broken -up) as discrete coils. The circuit equations for the plasma induced currents can be included within the same mathematical framework. The plasma equation of motion and the circuit equations are combined and manipulated into a diagonalized form that can be graphically analyzed to determine the growth rate. An effective mode approximation (EMA) to the dispersion relation in introduced to simplify and approximate the growth rate of the more exact case. Controller voltage equations for active feedback are generalized to include position and velocity feedback and time delay. A position cut-off displacement is added to model finite spatial resolution of the position detectors or a dead-band voltage level. Stability criteria are studied for EMA and the more exact case. The time dependent responses for plasma position controller voltages, and currents are determined from the Laplace transformations. Slow responses are separated from the fast ones (dependent on plasma inertia) using a typical tokamak ordering approximation. The methods developed are applied in numerous examples for the machine geometry and plasma of TNS, an inside-D configuration plasma resembling JET, INTOR, or FED.
Numerical Calculation of Neoclassical Distribution Functions and Current Profiles in Low Collisionality, Axisymmetric Plasmas
Energy Technology Data Exchange (ETDEWEB)
B.C. Lyons, S.C. Jardin, and J.J. Ramos
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f ) in the conventional banana regime for both ions and elec trons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h ). We work in a 4D phase space in which Ψ defines a flux surface, θ is the poloidal angle, v is the total velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and λ . The Rosenbluth potentials, φ and ψ, which define the integral part of the collision operator, are expanded in Legendre series in cos χ , where χ is the pitch angle, Fourier series in cos θ , and finite elements in v . At each ψ , we solve a block tridiagonal system for hi (independent of fe ), then solve another block tridiagonal system for he (dependent on fi ). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia, et al., J. Comput. Phys. 37 , pp 183-204 (1980).] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C1 [S.C. Jardin, et al ., Computational Science & Discovery, 4 (2012).]).
Automation of Axisymmetric Drop Shape Analysis Using Digital Image Processing
Cheng, Philip Wing Ping
The Axisymmetric Drop Shape Analysis - Profile (ADSA-P) technique, as initiated by Rotenberg, is a user -oriented scheme to determine liquid-fluid interfacial tensions and contact angles from the shape of axisymmetric menisci, i.e., from sessile as well as pendant drops. The ADSA -P program requires as input several coordinate points along the drop profile, the value of the density difference between the bulk phases, and gravity. The solution yields interfacial tension and contact angle. Although the ADSA-P technique was in principle complete, it was found that it was of very limited practical use. The major difficulty with the method is the need for very precise coordinate points along the drop profile, which, up to now, could not be obtained readily. In the past, the coordinate points along the drop profile were obtained by manual digitization of photographs or negatives. From manual digitization data, the surface tension values obtained had an average error of +/-5% when compared with literature values. Another problem with the ADSA-P technique was that the computer program failed to converge for the case of very elongated pendant drops. To acquire the drop profile coordinates automatically, a technique which utilizes recent developments in digital image acquisition and analysis was developed. In order to determine the drop profile coordinates as precisely as possible, the errors due to optical distortions were eliminated. In addition, determination of drop profile coordinates to pixel and sub-pixel resolution was developed. It was found that high precision could be obtained through the use of sub-pixel resolution and a spline fitting method. The results obtained using the automatic digitization technique in conjunction with ADSA-P not only compared well with the conventional methods, but also outstripped the precision of conventional methods considerably. To solve the convergence problem of very elongated pendant drops, it was found that the reason for the
Lee, Jeongseog; Safdi, Benjamin R
Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Reny...
Chamseddine, Ali H; Mukhanov, Viatcheslav
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected manifolds with large quantized volume are then obtained as solutions. When this condition is adopted in the gravitational action it leads to the quantization of the four volume with the cosmological constant obtained as an integration constant. Restricting the condition to a three dimensional hypersurface implies quantization of the three volume and the possible appearance of mimetic dark matter. When restricting to a two dimensional hypersurface, under appropriate bounda...
Spinorial Geometry and Supergravity
Gillard, J
In the main part of this thesis, we present the foundations and initial results of the Spinorial Geometry formalism for solving Killing spinor equations. This method can be used for any supergravity theory, although we largely focus on D=11 supergravity. The D=5 case is investigated in an appendix. The exposition provides a comprehensive introduction to the formalism, and contains background material on the complex spin representations which, it is hoped, will provide a useful bridge between the mathematical literature and our methods. Many solutions to the D=11 Killing spinor equations are presented, and the consequences for the spacetime geometry are explored in each case. Also in this thesis, we consider another class of supergravity solutions, namely heterotic string backgrounds with (2,0) world-sheet supersymmetry. We investigate the consequences of taking alpha-prime corrections into account in the field equations, in order to remain consistent with anomaly cancellation, while requiring that spacetime s...
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Micro vortex generator control of axisymmetric high-speed laminar boundary layer separation
Estruch-Samper, D.; Vanstone, L.; Hillier, R.; Ganapathisubramani, B.
Interest in the development of micro vortex generators (MVGs) to control high-speed flow separation has grown in the last decade. In contrast to conventional vortex generators, MVGs are fully submerged in the boundary layer and have the potential of inducing surface flow mixing with marginal drag penalty when suitably designed. Also, they do not result in undesired reduced mass flow such as with suction methods. The flow mechanisms at the location of MVGs are not yet fully understood, and optimal designs are difficult to establish given that both numerical predictions and experiments are particularly challenged for short element heights, yet optimal MVGs are generally expected to be at least shorter than half the local boundary layer thickness. The present work aims at investigating experimentally the fundamental flow physics concerning an individual MVG element (of `canonical' or simplified geometry) at a range of near-wall heights. A fully laminar base flow is considered so as to isolate the effect of incoming turbulence as well as the more complex physics that may occur when specific and/or multiple elements are used. Tests were performed in a gun tunnel at a freestream Mach number of 8.9 and Reynolds number of /m, and the basic test model consisted of a blunt-nosed cylinder which produced an axisymmetric laminar boundary layer with an edge Mach number of 3.4 and Reynolds number of /m at the MVG location. A laminar shock-wave/boundary layer interaction with separation was induced by a flare located further downstream on the model. Measurements consisted of time-resolved surface heat transfer obtained in the axial direction immediately downstream of the MVG and along the interaction, together with simultaneous high-speed schlieren imaging. The height () of the MVG element used in a `diamond' configuration (square planform with one vertex facing the flow) was adjusted between tests ranging from = 0.03 to 0.58, where the local undisturbed boundary layer thickness
Self-consistent hybrid neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas
Lyons, Brendan Carrick
Neoclassical effects (e.g., conductivity reduction and bootstrap currents) have a profound impact on many magnetohydrodynamic (MHD) instabilities in toroidally-confined plasmas, including tearing modes, edge-localized modes, and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We review a hybrid formulation from the recent literatureAB that is appropriate for such studies. In particular, the formulation uses a set of time-dependent drift-kinetic equations (DKEs) to advance the non-Maxwellian part of the electron and ion distribution functions (fNM) with linearized Fokker-Planck-Landau collision operators. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that fNM carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by a set of MHD equations which are closed by moments of fNM . We then present two DKE solvers based upon this formulation in axisymmetric toroidal geometries. The Neoclassical Ion-Electron Solver (NIES) solves the steady-state DKEs in the low-collisionality limit. Convergence and benchmark studies are discussed, providing a proof-of-principle that this new formulation can accurately reproduce results from the literature in the limit considered. We then present the DK4D code which evolves the finite-collisionality DKEs time-dependently. Computational methods used and successful benchmarks to other neoclassical models and codes are discussed. Furthermore, we couple DK4D to a reduced, transport-timescale MHD code. The resulting hybrid code is used to simulate the evolution of the current density in a large-aspect-ratio plasma in the presence of several different time-dependent pressure profiles. These simulations demonstrate the self-consistent, dynamic formation of the ohmic and bootstrap currents. In the slowly-evolving plasmas considered
Magnetic helicity in non-axisymmetric mean-field solar dynamo
Pipin, V V
The paper address the effects of magnetic helicity conservation in a non-linear nonaxisymmetric mean-field solar dynamo model. We study the evolution of the shallow non-axisymmetric magnetic field perturbation with the strength about 10G in the solar convection zone. The dynamo evolves from the pure axisymmetric stage through the short (about 2 years) transient phase when the non-axisymmetric m=1 dynamo mode is dominant to the final stage where the axisymmetry of the dynamo is almost restored. It is found that magnetic helicity is transferred forth and back over the spectral space during the transient phase. Also our simulations shows that the non-axisymmetric distributions of magnetic helicity tend to follows the regions of the Hale polarity rule.
A Variational Principle for the Axisymmetric Stability of Rotating Relativistic Stars
Prabhu, Kartik; Wald, Robert M
It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar-Friedman-Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels th...
Non-axisymmetric vertical shear and convective instabilities as a mechanism of angular momentum transport
Volponi, Francesco
Discs with a rotation profile depending on radius and height are subject to an axisymmetric linear instability, the vertical shear instability. Here we show that non-axisymmetric perturbations, while eventually stabilized, can sustain huge exponential amplifications with growth rate close to the axisymmetric one. Transient growths are therefore to all effects genuine instabilities. The ensuing angular momentum transport is positive. These growths occur when the product of the radial times the vertical wavenumbers (both evolving with time) is positive for a positive local vertical shear, or negative for a negative local vertical shear. We studied, as well, the interaction of these vertical shear induced growths with a convective instability. The asymptotic behaviour depends on the relative strength of the axisymmetric vertical shear (s_v) and convective (s_c) growth rates. For s_v > s_c we observed the same type of behaviour described above - large growths occur with asymptotic stabilization. When s_c > s_v th...
Zupan, Karmen
Observing is an important process in learning geometry. In the first part of the thesis observing is considered from a psychological perspective: the Gestalt theory, its history, the distribution of gestalt qualities, as well as various studies and theories of templates. The observing process is considered also from the didactic point of view by means of the van Hiele's theory of levels of geometric reasoning. Since colours also influence observing, a list of advices for teachers about using ...
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
Bengtsson, Ingemar; Zyczkowski, Karol
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Inflation from quantum geometry.
Bojowald, Martin
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
Tysver, Joseph Bryce
This report presents the potential use of 3-D data at NUWES on trial runs to provide information on the geometry of two vehicles in the vicinity of intercept. Smoothing on data segments provides velocity components as well as smoothed estimates or vehicle locations. Analysis of this smoothed data can be analyzed to establish (1) distance between vehicles (2) vehicular heading directional angles (3) look angle for attack vehicle, (4) attack angle (5) projected intercept point and time, (6) p...
Krauss, L M; Krauss, Lawrence M.; Turner, Michael S.
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Simulations of ion beams for NDCX-II
Energy Technology Data Exchange (ETDEWEB)
Grote, D.P., E-mail: email@example.com [LBNL MS47-112, 1 Cyclotron Rd, Bekerley, CA 94720 (United States); Lawrence Livermore National Lab, Livermore, CA 94550 (United States); Friedman, A., E-mail: email@example.com [Lawrence Livermore National Lab, Livermore, CA 94550 (United States); Sharp, W.M. [Lawrence Livermore National Lab, Livermore, CA 94550 (United States)
NDCX-II, the second neutralized drift compression experiment, is a moderate energy, high current accelerator designed to drive targets for warm dense matter and IFE-relevant energy coupling studies, and to serve as a testbed for high current accelerator physics. As part of the design process, studies were carried out to assess the sensitivities of the accelerator to errors, and to further optimize the design in concert with the evolving pulsed power engineering. The Warp code was used to carry out detailed simulations in both axisymmetric and full 3-D geometry. Ensembles of simulations were carried out to characterize the effects of errors, such as timing jitter and noise on the accelerator waveforms, noise on the source waveform, and solenoid and source offsets. In some cases, the ensemble studies resulted in better designs, revealing operating points with improved performance and showing possible means for further improvement. These studies also revealed a new non-paraxial effect of the final focus solenoid on the beam, which must be taken into account in designing an optimal final focusing system.
Integral geometry and valuations
Solanes, Gil
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
Patch test function for axisymmetric element of conventional and couple stress theory
Institute of Scientific and Technical Information of China (English)
The enhanced patch test proposed by Chen W J(2006) can be used to assess the convergence of the problem with non-homogeneous differential equations.Based on this theory,we establish the patch test function for axisymmetric elements of conventional and couple stress theories,and reach an important conclusion that the patch test function for axisymmetric elements cannot contain non-zero constant shear.
Collapse of a non-axisymmetric, impact-created air cavity in water
Enriquez, Oscar R.; Peters, Ivo R.; Gekle, Stephan; Schmidt, Laura E.; Lohse, Detlef; van der Meer, Devaraj
The axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially-quiescent water surface and observe their subsequent grav...
Axisymmetric and 3D calculations of melt flow during VCz growth
Bänsch, E.; Davis, D.; Langmach, H.; Miller, W.; Rehse, U.; Reinhardt, G.; Uhle, M.
Axisymmetric and 3D calculations of melt flow have been performed for a configuration used at the vapour-pressure-controlled Czochalski growth of GaAs single crystals. Thermal boundary conditions were adapted from a global simulation of the temperature field. The axisymmetric calculations with the code NAVIER confirmed the ones previously perfomed with FIDAP TM. The 3D calculations showed that the flow exhibits an asymmetric transient behaviour beyond a certain critical Reynolds number.
Institute of Scientific and Technical Information of China (English)
张引科; 黄义
The Biot' s wave equations of transversely isotropic saturated poroelastic media excited by non- axisymmetrical harmonic source were solved by means of Fourier expansion and Hankel transform. Then the components of total stress in porous media are expressed with the solutions of Biot's wave equations. The method of research on non-axisymmetrical dynamic response of saturated porous media is discussed, and a numerical result is presented.
Inner complexes of Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Be(II) and dioxouranium(VI) with salicylaldehyde semicarbazone
Energy Technology Data Exchange (ETDEWEB)
Maurya, P.L.; Agarwala, B.V.; Dey, A.K. (Allahabad Univ. (India). Dept. of Chemistry)
Salicylaldehyde semicarbazone (SALSC), yields complexes, ML/sub 2/.2H/sub 2/O (M = Co(II), Ni(II), Cu(II), Zn(II) and Cd(II)) and ML/sub 2/ (M = Be(II) and UO/sub 2/(VI)). The complexes have been characterized by analytical, spectral, magnetic and thermogravimetric studies. SALSC acts as a singly negatively charged bidentate anion, and two such anions coordinate to the metal ion through the hydroxyl oxygen and nitrogen of the C = N group yielding a neutral chelate. The complexes of Co(II), Ni(II) and Cu(II) are paramagnetic with magnetic moment values 4.93, 3.35 and 1.98 BM, respectively. The magnetic and spectral data suggest octahedral geometry of Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and UO/sub 2/(VI) complexes, whereas the Be(II) complex is tetrahedral. TG study reveals the order of thermal stability as : Zn(II) approximately equal to Ni(II) >Be(II) approximately equal to Cd(II) > UO/sub 2/(VI) approximately equal to Co(II) approximately equal to Cu(II).
The shape of an axisymmetric bubble in uniform motion
Indian Academy of Sciences (India)
P N Shankkar
We consider in a frame fixed to a bubble translating with steady speed , the inviscid, axisymmetric, irrotational motion of the liquid past it. If all speeds are normalized by and lengths by $T/\\dfrac{1}{2} \\varrho U^{2}$, where is the surface tension of the liquid–bubble interface, it can be shown that the unknown bubble shape and field depend on a single parameter $ = (p_{b} − p_{∞})/\\dfrac{1}{2} \\varrho U^{2} − 1$ alone, where the pressures are the ones in the bubble and far away respectively. When is very large the bubble is almost spherical in shape while for $ ≤ ^{*} ≈ -0.315$, bubbles whose exteriors are simply connected do not exist. We solve the non-linear, free boundary problem for the whole range $^{*}$ < < ∞ by the use of an analytical representation for the bubble shape, a surface singularity method to compute potential flows and a generalized Newton's method to continue in . Apart from providing explicit representations for bubble shapes and detailed numerical values for the bubble parameters, we show that the classical linearized solution for large is a very good approximation, surprisingly, to as low values of as 2. We also show that Miksis et al [1] is inaccurate over the whole range and in serious error for large and small . These have been corrected.
Axisymmetric bifurcations of thick spherical shells under inflation and compression
deBotton, G.
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before.© 2012 Published by Elsevier Ltd.
Internal performance characteristics of vectored axisymmetric ejector nozzles
Lamb, Milton
A series of vectoring axisymmetric ejector nozzles were designed and experimentally tested for internal performance and pumping characteristics at NASA-Langley Research Center. These ejector nozzles used convergent-divergent nozzles as the primary nozzles. The model geometric variables investigated were primary nozzle throat area, primary nozzle expansion ratio, effective ejector expansion ratio (ratio of shroud exit area to primary nozzle throat area), ratio of minimum ejector area to primary nozzle throat area, ratio of ejector upper slot height to lower slot height (measured on the vertical centerline), and thrust vector angle. The primary nozzle pressure ratio was varied from 2.0 to 10.0 depending upon primary nozzle throat area. The corrected ejector-to-primary nozzle weight-flow ratio was varied from 0 (no secondary flow) to approximately 0.21 (21 percent of primary weight-flow rate) depending on ejector nozzle configuration. In addition to the internal performance and pumping characteristics, static pressures were obtained on the shroud walls.
Laboratory investigation of axisymmetric single vacuum well point
Institute of Scientific and Technical Information of China (English)
VU Van-tuan; YAO Lei-hua; WEI Ying-jie
Vacuum well point is a new but faint soft ground treatment method. This work focuses on the consolidation behavior of a reconstituted soft clayey specimen under vacuum well point combined with surcharge loading. The laboratory test was conducted through a vacuum-surcharge consolidation apparatus, and the vacuum loading scheme was adopted for vacuum pressure application to investigate the vacuum effect on soil consolidation. In the testing process, some key parameters such as vacuum pressure, pore water pressure and settlement deformation were timely recorded. Furthermore, the water content, void ratio and permeability coefficient of samples collected after loading were measured to reflect the consolidation characteristics. By comparing with the membrane system and membraneless system, something different was found for the vacuum well point method. The results indicate that the consolidation behavior of an axisymmetric single vacuum well point is almost identical to the behavior of vacuum preloading combined with prefabricated vertical drain (PVD), except for the distribution of the vacuum pressure along the well drain due to the structure of the vacuum well point. And the vacuum well point method may be useful for the improvement of soft clayey deposit in a certain depth.
Adhesion and detachment of a capsule in axisymmetric flow
Keh, M. P.; Leal, L. G.
The adhesion and detachment of a capsule on a solid boundary surface is studied via a combination of scaling theory and numerical simulation and the behavior is compared and contrasted with a vesicle. It is shown that the dominant physical property for both capsules and vesicles is the area dilation modulus Ks of the membrane. The nonzero shear modulus Gs for capsules increases the resistance to deformation and thus decreases slightly the equilibrium contact radius for an adhered capsule compared to an adhered vesicle. The detachment process in this study is due to an external axisymmetric flow. Unlike a rigid body that must be pulled away without change of shape, capsules (and vesicles) almost always detach dominantly by peeling in which the contact radius decreases but the minimum separation distance does not change until the final moments of detachment. Compared to a vesicle with the same Ks, a capsule maintains a more compact shape and is harder to elongate under a given external flow. Hence, the detachment process is slower for capsules compared to vesicles with the same Ks.
Computing Axisymmetric Jet Screech Tones using Unstructured Grids
Jorgenson, Philip C. E.; Loh, Ching Y.
The purpose of this paper is to show that computations with an aeroacoustic feedback loop, the jet screech noise, can be obtained using truly unstructured grid technology. Numerical results are presented for a nozzle with two different lip thicknesses which will be referred to in this paper as a thin and a thick lip nozzle respectively. The space-time conservation element and solution element (CE/SE) method is used to solve the conservation laws of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. Comparisons of numerical results with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.
MRI-driven Accretion onto Magnetized stars: Axisymmetric MHD Simulations
Romanova, Marina M; Koldoba, Alexander V; Lovelace, Richard V E
We present the first results of a global axisymmetric simulation of accretion onto rotating magnetized stars from a turbulent, MRI-driven disk. The angular momentum is transported outward by the magnetic stress of the turbulent flow with a rate corresponding to a Shakura-Sunyaev viscosity parameter alpha\\approx 0.01-0.04. The result of the disk-magnetosphere interaction depends on the orientation of the poloidal field in the disk relative to that of the star at the disk-magnetosphere boundary. If fields have the same polarity, then the magnetic flux is accumulated at the boundary and blocks the accretion which leads to the accumulation of matter at the boundary. Subsequently, this matter accretes to the star in outburst before accumulating again. Hence, the cycling, `bursty' accretion is observed. If the disc and stellar fields have opposite polarity, then the field reconnection enhances the penetration of the disk matter towards the deeper field lines of the magnetosphere. However, the magnetic stress at the...
Circulation Control on Axisymmetric Bodies using Synthetic Jets
Rinehart, Christopher; McMichael, James; Glezer, Ari
The capability of fluidic actuation based on synthetic jets to modify the apparent aerodynamic shape of lifting surfaces and thereby modify the aerodynamic forces and moments has been demonstrated in a number of earlier investigations of stalled two-dimensional airfoils (e.g., Amitay et al., AIAA J., 39, 2001). The present work is a study of the fundamental ability of synthetic jets to favorably modify the flow over axisymmetric bodies at subsonic speeds. Aft-facing synthetic jets oriented tangentially to a circular Coanda surface at the base produce effective flow turning and lift generation, with ratios of lift to average jet momentum approaching values typical of conventional jet-based circulation control on two-dimensional airfoils. The result is interesting in that the body is not designed to be a lifting surface, and the actuation is effected over only a portion of the body's circumference. The transient and steady global flow response to the actuation is demonstrated via phase- and time-averaged velocity measurements using particle image velocimetry (PIV).
Unsteady Aerodynamic Flow Control of a Suspended Axisymmetric Moving Platform
Lambert, Thomas; Vukasinovic, Bojan; Glezer, Ari
The aerodynamic forces on an axisymmetric wind tunnel model are altered by fluidic interaction of an azimuthal array of integrated synthetic jet actuators with the cross flow. Four-quadrant actuators are integrated into a Coanda surface on the aft section of the body, and the jets emanate from narrow, azimuthally segmented slots equally distributed around the model's perimeter. The model is suspended in the tunnel using eight wires each comprising miniature in-line force sensors and shape-memory-alloy (SMA) strands that are used to control the instantaneous forces and moments on the model and its orientation. The interaction of the actuation jets with the flow over the moving model is investigated using PIV and time-resolved force measurements to assess the transitory aerodynamic loading effected by coupling between the induced motion of the aerodynamic surface and the fluid dynamics that is driven by the actuation. It is shown that these interactions can lead to effective control of the aerodynamic forces and moments, and thereby of the model's motion. Supported by ARO.
Synthetic Jet Control of a Yawing Axisymmetric Body
Lambert, Thomas; Vukasinovic, Bojan; Glezer, Ari
The global aerodynamic forces and moments on an axisymmetric yawing body are controlled in wind tunnel experiments by exploiting the interaction of an array of synthetic jet actuators with the cross flow over the tail section of the body. The model is supported by a vertical wire through its aerodynamic center and is free to move in yaw. The baseline motion of the model is a yaw oscillation with amplitude and frequency that both monotonously increase with free stream velocity, characteristic of vortex shedding. The aft-facing control jet actuators emanate from narrow, azimuthally segmented slots around the perimeter of the tail section, and activation of the control jets effects the model's path through localized flow attachment on integrated Coanda surfaces. The control jets are used to control the yaw trajectory of the model using a closed loop PID controller. The baseline and controlled model motion is monitored using a laser vibrometer, and the flow evolution near the body and in its near wake is investigated using PIV. The coupled, time dependent response of the model to the actuation is investigated with emphasis on controlling its unstable modes. Supported by ARO.
Two-integral distribution functions for axisymmetric systems
Jiang, Zhenglu
Some formulae are presented for finding two-integral distribution functions (DFs) which depends only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known axisymmetric densities. They come from an combination of the ideas of Eddington and Fricke and they are also an extension of those shown by Jiang and Ossipkov for finding anisotropic DFs for spherical galaxies. The density of the system is required to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum about the axis of symmetry. The product of the density and its radial velocity dispersion can be also expressed as a sum of products of functions of the potential and of the radial coordinate. It can be further known that the density multipied by its rotational velocity...
Axisymmetric constant mean curvature slices in the Kerr spacetime
International Nuclear Information System (INIS)
Recently, there have been efforts to solve Einstein's equation in the context of a conformal compactification of spacetime. Of particular importance in this regard are the so-called constant mean curvature (CMC) foliations, characterized by spatial hyperboloidal hypersurfaces with a constant extrinsic mean curvature K. However, although of interest for general spacetimes, CMC slices are known explicitly only for the spherically symmetric Schwarzschild metric. This work is devoted to numerically determining axisymmetric CMC slices within the Kerr solution. We construct such slices outside the black hole horizon through an appropriate coordinate transformation in which an unknown auxiliary function A is involved. The condition K = const throughout the slice leads to a nonlinear partial differential equation for the function A, which is solved with a pseudo-spectral method. The results exhibit exponential convergence, as is to be expected in a pseudo-spectral scheme for analytic solutions. As a by-product, we identify CMC slices of the Schwarzschild solution which are not spherically symmetric. (paper)
Axisymmetric Predictions of Fluid Flow inside a Rotating Cavity System
Directory of Open Access Journals (Sweden)
Mujeebuddin Memon
Full Text Available Accurate prediction of fluid flow in the rotating cavity system is of practical interest as it is most commonly used in the gas turbine engines and compressors. This paper presents the numerical predictions of a rotating cavity flow system for Reynolds numbers of the range 1x105 < Re? < 4x105 and two different mass flow rates Cw=1092 and 2184. A finite-difference technique is employed for a Steady-state solution in the axisymmetric cylindrical polar coordinate frame of reference. The two low Reynolds number turbulence models, the low Reynolds number k-? model and the low Reynolds number second moment closure have been used to compute the basic characteristics of the flow inside the rotating cavity flow system. Different flow regions have been identified by computing flow structures and dimensions of those regions have also been studied under different flow rates. A comparison of the computed variation of moment coefficient of both the turbulence models are presented for the above mentioned parameters and the parametric effects on the moment coefficients have been discussed
Axisymmetric equilibria with pressure anisotropy and plasma flow
Evangelias, A.; Throumoulopoulos, G. N.
A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of the cases considered both the anisotropy and the flow have stronger effects on NSTX equilibria than on ITER ones.
Axisymmetrically Tropical Cyclone-like Vortices with Secondary Circulations
Sun, Liang
The secondary circulation of the tropical cyclone (TC) is related to its formation and intensification, thus becomes very important in the studies. The analytical solutions have both the primary and secondary circulation in a three-dimensionally nonhydrostatic and adiabatic model. We prove that there are three intrinsic radiuses for the axisymmetrically ideal incompressible flow. The first one is the radius of maximum primary circular velocity $r_m$. The second one is radius of the primary kernel $r_k>r_m$, across which the vorticity of the primary circulation changes sign and the vertical velocity changes direction. The last one is the radius of the maximum primary vorticity $r_d$, at which the vertical flow of the secondary circulation approaches its maximum, and across which the radius velocity changes sign. The first TC-like vortex solution has universal inflow or outflow. The relations between the intrinsic length scales are $r_k=\\sqrt{2}r_m$ and $r_d=2r_m$. The second one is a multi-planar solution, per...
Non-axisymmetric Field Effects on Alcator C-Mod
Wolfe, S.; Hutchinson, I.; Granetz, R.; Rice, J.; Hubbard, A.; Irby, J.; Vieira, R.; Cochran, W.; Gwinn, D.; Rosati, J.; Lynn, A.
A set of coils capable of producing non-axisymmetric, predominantly n=1, fields with different toroidal phase and a range of poloidal mode (m) spectra has been installed on Alcator C-Mod. This coilset has been used to suppress locked modes during low density or high current operation and also to induce locked modes in normally stable configurations in order to study error field effects. Locked modes are observed to result in braking of core toroidal rotation, modification of sawtooth activity, and significant reduction in energy and particle confinement. The inferred value of the threshold perturbation for producing a locked mode is of order B_21/B_T ˜ 10-4, where B_21 is the helically resonant m/n=2/1 field evaluated at the q=2 surface. This value is comparable to extrapolations based on experiments on JET and DIII-D, but is inconsistent with stronger BT and size scaling inferred from Compass-D results(R. J. Buttery, et al., 17th Fusion Energy Conference, Oct. 1998, Yokohama (IAEA-CN-69) EX8/5). The C-Mod result therefore has favorable implications for the locked mode threshold in ITER.
Plasma equilibria and stationary flows in axisymmetric systems. Pt. 1
International Nuclear Information System (INIS)
During discharges within a tokamak device such as JET fluctuations are observed in the plasma, of plasma density, temperature, electric potential and of the magnetic field. These fluctuations have complicated structure and are linked with different kinds of instabilities. However, it is not clear which instabilities are most important in determining the behaviour of the plasma. A comprehensive numerical theory which can predict the effect of the instabilities on the transport of plasma in axisymmetric systems has been sought using the static Grad-Shafranov-Schlueter (SGSS) equation as a basis. However, the static equation was over simplified for the situation in JET with additional heating giving rise to large toroidal flows, and an extended equation (EGSS) was developed. The results of the study include the discovery of algebraic branches of solutions to the EGSS equation even for very small poloidal flows, solutions to the inverse problem for the SGSS and EGSS equations using Fourier decomposition, classification of the boundary condition at the magnetic axis, demonstration of a visible effect of the poloidal flow on the separation of the density surface and the magnetic surface an indication of the existence of multiple branches of solutions to the EGSS and SGSS equations and their relation to stability properties. (U.K.)
The axisymmetric envelopes of RS Cnc and EP Aqr
Bertre, T Le; Nhung, P T; Winters, J M
We report on observations obtained at IRAM on two semi-regular variable Asymptotic Giant Branch (AGB) stars, RS Cnc and EP Aqr, undergoing mass loss at an intermediate rate of ~ 10^-7 solar mass per year. Interferometric data obtained with the Plateau-de-Bure interferometer (NOEMA) have been combined with On-The-Fly maps obtained with the 30-m telescope in the CO(1-0) and (2-1) rotational lines. The spectral maps of spatially resolved sources reveal an axisymmetric morphology in which matter is flowing out at a low velocity (~ 2 km/s) in the equatorial planes, and at a larger velocity (~ 8 km/s) along the polar axes. There are indications that this kind of morpho-kinematics is relatively frequent among stars at the beginning of their evolution on the Thermally-Pulsing AGB, in particular among those that show composite CO line profiles, and that it might be caused by the presence of a companion. We discuss the progress that could be expected for our understanding of the mass loss mechanisms in this kind of sou...
Arbitrary axisymmetric steady streaming: Flow, force and propulsion
Spelman, Tamsin A
A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is enhanced by inertia to induce a non-zero net flow. Building on classical work for simple geometrical forcing and motivated by the complex shape oscillations of elastic capsules and bubbles, we develop the mathematical framework to quantify the steady streaming of a spherical body with arbitrary axisymmetric time-periodic boundary conditions. We compute the flow asymptotically for small-amplitude oscillations of the boundary in the limit where the viscous penetration length scale is much smaller than the body. In that case, the flow has a boundary layer structure and the fluid motion is solved by asymptotic matching. Our results, presented in the case of no-slip boundary conditions and extended to include the motion of vibrating free surfaces, recovers classical work as parti...
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
Introductory non-Euclidean geometry
Manning, Henry Parker
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
Thermodynamic Geometry and Extremal Black Holes in String Theory
Sarkar, Tapobrata; Tiwari, Bhupendra Nath
We study a generalisation of thermodynamic geometry to degenerate quantum ground states at zero temperatures exemplified by charged extremal black holes in type II string theories. Several examples of extremal charged black holes with non degenerate thermodynamic geometries and finite but non zero state space scalar curvatures are established. These include black holes described by D1-D5-P and D2-D6-NS5-P brane systems and also two charged small black holes in Type II string theories. We also explore the modifications to the state space geometry and the scalar curvature due to the higher derivative contributions and string loop corrections as well as an exact entropy expression from quantum information theory. Our construction describes state space geometries arising out of a possible limiting thermodynamic characterisation of degenerate quantum ground states at zero temperatures.
Biologically active new Fe(II, Co(II, Ni(II, Cu(II, Zn(II and Cd(II complexes of N-(2-thienylmethylenemethanamine
Directory of Open Access Journals (Sweden)
Full Text Available Iron(II, cobalt(II, nickel (II, copper (II, zinc(II and cadmium(II complexes of the type ML2Cl2, where M is a metal and L is the Schiff base N-(2-thienylmethylenemethanamine (TNAM formed by the condensation of 2-thiophenecarboxaldehyde and methylamine, were prepared and characterized by elemental analysis as well as magnetic and spectroscopic measurements. The elemental analyses suggest the stoichiometry to be 1:2 (metal:ligand. Magnetic susceptibility data coupled with electronic, ESR and Mössbauer spectra suggest a distorted octahedral structure for the Fe(II, Co(II and Ni(II complexes, a square-planar geometry for the Cu(II compound and a tetrahedral geometry for the Zn(II and Cd(II complexes. The infrared and NMR spectra of the complexes agree with co-ordination to the central metal atom through nitrogen and sulphur atoms. Conductance measurements suggest the non-electrolytic nature of the complexes, except for the Cu(II, Zn(II and Cd(II complexes, which are 1:2 electrolytes. The Schiff base and its metal chelates were screened for their biological activity against Escherichia coli, Staphylococcus aureus and Pseudomonas aeruginosa and the metal chelates were found to possess better antibacterial activity than that of the uncomplexed Schiff base.
Editors, LearningExpress
Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day is an invaluable resource for both students and adults.
Dooner, David B
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are...... elaborated - in contrast to the familiar Newtonian mechanics and the more recent, but by now also rather well established quantum field theories. Examples are given originating from the systems biology of insulin secreting pancreatic beta-cells and the mathematical challenges of an envisioned non...
Flegg, H Graham
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Kendig, Keith
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Akopyan, A V
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
Gruber, Peter M
This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definit
REA, The Editors of
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Teaching of Geometry in Bulgaria
Bankov, Kiril
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
Theoretical issues on the spontaneous rotation of axisymmetric plasmas
International Nuclear Information System (INIS)
An extensive series of experiments have confirmed that the observed 'spontaneous rotation' phenomenon in axisymmetric plasmas is related to the confinement properties of these plasmas and connected to the excitation of collective modes associated with these properties (Coppi 2000 18th IAEA Fusion Energy Conf. (Sorrento, Italy, 2000) THP 1/17, www-pub.iaea.org/MTCD/publications/PDF/csp_008c/html/node343.htm and Coppi 2002 Nucl. Fusion 42 1). In particular, radially localized modes can extract angular momentum from the plasma column from which they grow while the background plasma has to recoil in the direction opposite to that of the mode phase velocity. In the case of the excitation of the plasma modes at the edge, the loss of their angular momentum can be connected to the directed particle ejection to the surrounding medium. The recoil angular momentum is then redistributed inside the plasma column mainly by the combination of an effective viscous diffusion and an inward angular momentum transport velocity that is connected, for instance, to ion temperature gradient (ITG) driven modes. The linear and quasi-linear theories of the collisionless trapped electron modes and of the toroidal ITG driven modes are re-examined in the context of their influence on angular momentum transport. Internal modes that produce magnetic reconnection and are electromagnetic in nature, acquire characteristic phase velocity directions in high temperature regimes and become relevant to the 'generation' of angular momentum. The drift-tearing mode, the 'complex' reconnecting mode and the m0 = 1 internal mode belong to this category, the last mode acquiring different features depending on the strength of its driving factor. Toroidal velocity profiles that reproduce the experimental observations are obtained considering a global angular momentum balance equation that includes the localized sources associated with the excited internal electrostatic and electromagnetic modes
Computer Aided Process Planning for Non-Axisymmetric Deep Drawing Products
Park, Dong Hwan; Yarlagadda, Prasad K. D. V.
In general, deep drawing products have various cross-section shapes such as cylindrical, rectangular and non-axisymmetric shapes. The application of the surface area calculation to non-axisymmetric deep drawing process has not been published yet. In this research, a surface area calculation for non-axisymmetric deep drawing products with elliptical shape was constructed for a design of blank shape of deep drawing products by using an AutoLISP function of AutoCAD software. A computer-aided process planning (CAPP) system for rotationally symmetric deep drawing products has been developed. However, the application of the system to non-axisymmetric components has not been reported yet. Thus, the CAPP system for non-axisymmetric deep drawing products with elliptical shape was constructed by using process sequence design. The system developed in this work consists of four modules. The first is recognition of shape module to recognize non-axisymmetric products. The second is a three-dimensional (3-D) modeling module to calculate the surface area for non-axisymmetric products. The third is a blank design module to create an oval-shaped blank with the identical surface area. The forth is a process planning module based on the production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing field engineers. Especially, the drawing coefficient, the punch and die radii for elliptical shape products are considered as main design parameters. The suitability of this system was verified by applying to a real deep drawing product. This CAPP system constructed would be very useful to reduce lead-time for manufacturing and improve an accuracy of products.
The Flow of Newtonian Fluids in Axisymmetric Corrugated Tubes
Sochi, Taha
This article deals with the flow of Newtonian fluids through axially-symmetric corrugated tubes. An analytical method to derive the relation between volumetric flow rate and pressure drop in laminar flow regimes is presented and applied to a number of simple tube geometries of converging-diverging nature. The method is general in terms of fluid and tube shape within the previous restrictions. Moreover, it can be used as a basis for numerical integration where analytical relations cannot be ob...
Bochnak, Jacek; Roy, Marie-Françoise
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Geometry of Periodic Monopoles
Maldonado, Rafael
BPS monopoles on $\\mathbb{R}^2\\timesS^1$ correspond, via the generalized Nahm transform, to certain solutions of the Hitchin equations on the cylinder $\\mathbb{R}\\times S^1$. The moduli space M of two monopoles with their centre-of-mass fixed is a 4-dimensional manifold with a natural hyperk\\"ahler metric, and its geodesics correspond to slow-motion monopole scattering. The purpose of this paper is to study the geometry of M in terms of the Nahm/Hitchin data, i.e. in terms of structures on $\\mathbb{R}\\times S^1$. In particular, we identify the moduli, derive the asymptotic metric on M, and discuss several geodesic surfaces and geodesics on M. The latter include novel examples of monopole dynamics.
International Nuclear Information System (INIS)
The authors address the problem of following the trajectory of a particle in simulations. It is necessary to follow the motion of the particle, and to determine its intersection with different geometric surfaces in the problem, in order to relate the stepping of the particle trajectory into real motion through the physical problem at hand. The distance a particle moves before encountering a surface is needed to compare with the actual transport distance that is about to be used in the simulation. Basic mathematical expressions are developed for the intersections of particle trajectories with plane and conic surfaces. The authors show how these are used in the EGS4 code system, which should be typical of the general problem. They also review geometry packages currently being used in electron-photon Monte Carlo programs
Geometry, Renormalization, And Supersymmetry
Berg, G M
This thesis is about understanding, applying and improving quantum field theory. We compute renormalization group flows as the evolution of a "coarse-graining" operator without the need for a Euclidean formulation. Renormalization is cast in the form of a Lie algebra of (in general infinite) matrices that generate, by exponentiation, counterterms for diagrams with subdivergences. These results may shed light on noncommutative geometry. We check our results in a scalar three-loop example. Then, we consider the renormalization of a certain supersymmetric gauge theory, the low-energy limit of a string model. We compare results to those computed directly in the string model and find agreement. Finally, we discuss the possibility of detecting quantum-mechanical phases distinguishing the two Pin groups, double covers of the full Lorentz group. Majorana fermions, if detected, would provide an important testing ground; such particles can restrict the choice of Pin group.
Subsonic Euler Flows with Large Vorticity Through an Infinitely Long Axisymmetric Nozzle
Du, Lili; Duan, Ben
This paper is a sequel to the earlier work Du and Duan (J Diff Equ 250:813-847, 2011) on well-posedness of steady subsonic Euler flows through infinitely long three-dimensional axisymmetric nozzles. In Du and Duan (J Diff Equ 250:813-847, 2011), the authors showed the existence and uniqueness of the global subsonic Euler flows through an infinitely long axisymmetric nozzle, when the variation of Bernoulli's function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value. The smallness of the variation of Bernoulli's function in the upstream prevents the attendance of the possible singularity in the nozzles, however, at the same time it also leads that the vorticity of the ideal flow is sufficiently small in the whole nozzle and the flows are indeed adjacent to axisymmetric potential flows. The purpose of this paper is to investigate the effects of the vorticity for the smooth subsonic ideal flows in infinitely long axisymmetric nozzles. We modify the formulation of the problem in the previous work Du and Duan (J Diff Equ 250:813-847, 2011) and the existence and uniqueness results on the smooth subsonic ideal polytropic flows in infinitely long axisymmetric nozzles without the restriction on the smallness of the vorticity are shown in this paper.
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model
Khavaran, A.; Krejsa, E. A.; Kim, C. M.
The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.
Generalized geometry of two-dimensional vacua
Rosa, Dario
We derive the conditions for unbroken supersymmetry for a Mink_2, (2,0) vacuum, arising from Type II supergravity on a compact eight-dimensional manifold M_8. When specialized to internal manifolds enjoying SU(4)xSU(4) structure the resulting system is elegantly rewritten in terms of generalized complex geometry. This particular class of vacua violates the correspondence between supersymmetry conditions and calibrations conditions of D branes (supersymmetry-calibrations correspondence). Our analysis includes and extends previous results about the failure of the supersymmetry-calibrations correspondence, and confirms the existence of a precise relation between such a failure and a subset of the supersymmetry conditions.
Vorticity dynamics of a bileaflet mechanical heart valve in an axisymmetric aorta
Dasi, L. P.; Ge, L.; Simon, H. A.; Sotiropoulos, F.; Yoganathan, A. P.
We present comprehensive particle image velocimetry measurements and direct numerical simulation (DNS) of physiological, pulsatile flow through a clinical quality bileaflet mechanical heart valve mounted in an idealized axisymmetric aorta geometry with a sudden expansion modeling the aortic sinus region. Instantaneous and ensemble-averaged velocity measurements as well as the associated statistics of leaflet kinematics are reported and analyzed in tandem to elucidate the structure of the velocity and vorticity fields of the ensuing flow-structure interaction. The measurements reveal that during the first half of the acceleration phase, the flow is laminar and repeatable from cycle to cycle. The valve housing shear layer rolls up into the sinus and begins to extract vorticity of opposite sign from the sinus wall. A start-up vortical structure is shed from the leaflets and is advected downstream as the leaflet shear layers become wavy and oscillatory. In the second half of flow acceleration the leaflet shear layers become unstable and break down into two von Karman-like vortex streets. The onset of vortex shedding from the valve leaflets is responsible for the growth of significant cycle-to-cycle vorticity oscillations. At peak flow, the housing and leaflet shear layers undergo secondary instabilities and break down rapidly into a chaotic, turbulent-like state with multiple small-scale vortical structures emerging in the flow. During the deceleration and closing phases all large-scale coherent flow features disappear and a chaotic small-scale vorticity field emerges, which persists even after the valve has closed. Probability density functions of the leaflet position during opening and closing phases show that the leaflet position fluctuates from cycle to cycle with larger fluctuations evident during valve closure. The DNS is carried out by prescribing the leaflet kinematics from the experimental data. The computed instantaneous vorticity fields are in very good
The geometry and origin of ultra-diffuse ghost galaxies
Burkert, Andreas
The geometry and intrinsic ellipticity distribution of ultra diffuse galaxies (UDGs) is determined from the line-of-sight distribution of axial ratios q of a large sample of UDGs, detected by Koda et al. (2015) in the Coma cluster. With high significance the data rules out an oblate, disk-like geometry, characterised by major axi a=b>c. The data is however in good agreement with prolate shapes, corresponding to a=b
Peterson, Mark A.
Cilia are motile biological appendages that are driven to bend by internal shear stresses between tubulin filaments. A continuum model of ciliary material is constructed that incorporates the essential ciliary constraints: (i) one-dimensional inextensibility of filaments, (ii) three-dimensional incompressibility, and (iii) shear strain only longitudinally along filaments. It is shown that twist of filaments about each other is not an independent degree of freedom under ciliary constraints. The constraint on twist appears in the equations of motion for cilia as a term not previously recognized. As another application of the same geometrical idea, a general approach to the polymorphism of bacterial flagella is proposed.
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
The Exact Solution for Linear Thermoelastic Axisymmetric Deformations of Generally Laminated Circular Cylindrical Shells
Nemeth, Michael P.; Schultz, Marc R.
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
A new analytical solution to axisymmetric Blot's consolidation of a finite soil layer
Institute of Scientific and Technical Information of China (English)
A new analytical method is presented to study the axisymmetric Blot's consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot's consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface (z= 0) and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.
Institute of Scientific and Technical Information of China (English)
DING Haojiang; WANG Huiming; CHEN Weiqiu
For the thermoelastic dynamic axisymmetric problem of a finite orthotropic hollow cylinder, one comes closer to reality to involve the effect of axial strain than to consider the plane strain case only. However, additional mathematical difficulties should be encountered and a different solution procedure should be developed. By the separation of variables, the thermoelastic axisymmetric dynamic problem of an orthotropic hollow cylinder taking account of the axial strain is transformed to a Volterra integral equation of the second kind for a function of time, which can be solved efficiently and quickly by the interpolation method. The solutions of displacements and stresses are obtained.It is noted that the present method is suitable for an orthotropic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical comparison is made to show the effect of the axial strain on the displacements and stresses.
Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation
Dimmelmeier, H; Font, J A; Dimmelmeier, Harald; Stergioulas, Nikolaos; Font, Jose A.
We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an extended avoided crossing between the l = 0 and l = 4 first overtones, which is important for correctly identifying mode frequencies in case of detection. For uniformly rotating stars near the mass-shedding limit, we confirm the existence of the mass-shedding-induced damping of pulsations, though the effect is not as strong as i...
Phase structures in fuzzy geometries
Govindarajan, T R; Gupta, K S; Martin, X
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of BTZ blackholes. Analysis is done analytically and through simulations. Several features like novel stripe phases as well as spontaneous symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out. Also we establish that these phases are stable due to topological obstructions.
Euclidean distance geometry and applications
Liberti, Leo; Lavor, Carlile; Maculan, Nelson; Mucherino, Antonio
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.
Linear algebra and projective geometry
Baer, Reinhold
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebra
The Geometry of Homological Triangles
Smarandache, Florentin
This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a "filter" through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles, while the last ones to their applications.
Distance Geometry for Kissing Balls
Chen, Hao
A kissing ball is a ball that is tangent to a fixed reference ball. In this paper, we will treat kissing balls with techniques from the Euclidean distance geometry. This turns out to be more general than the classical Euclidean distance geometry. We will show that the distance matrix for the kissing balls plays, at the same time, the role of Cayley-Menger matrix. Thus classical problems in Euclidean distance geometry will have new versions for kissing balls.
Virtual Monopole Geometry and Confinement
La, H S
Generalizing the geometry of the gauge covariant variables in Yang-Mills theory proposed by Johnson and Haagensen, the 4-d geometry associated with a monopole is defined for SU(2). There are three relevant geometries: AdS$_2\\times S^2$, $R^2\\times S^2$ and $H_+\\times S^2$, depending on the asymptotic behavior of the torsion. Using this geometry, the Wilson loop average is computed {\\it à la} Nambu-Goto action. In case of AdS$_2\\times S^2$, it satisfies the area law.
Digital geometry in image processing
Mukhopadhyay, Jayanta
Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing. The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Guijosa, A
This thesis explores some aspects of the recently uncovered connection between gauge theories and gravity, known as the AdS/CFT, or bulk-boundary, correspondence. This is a remarkable statement of equivalence between string or M-theory on certain backgrounds and field theories living on the boundaries of the corresponding spacetimes. Under the duality between four-dimensional N = 4 SU(N) superYang-Mills (SYM) and Type IIB string theory on AdS5 × S5, a baryon is mapped onto N fundamental strings terminating on a wrapped D5-brane. We examine the structure and energetics of this system from the vantage point of the fivebrane worldvolume action, making use of the Born-Infeld string approach. We construct supersymmetric fivebrane embeddings which correspond to gauge theory configurations with n external quarks, 0 ≤ n ≤ N. The extension of these solutions to the full asymptotically flat geometry of N D3-branes provides a detailed description of the creation of strings as the fivebrane is...
Speziale, Simone
We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is na...
Bhatia, Rajendra
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Thin accretion disks in stationary axisymmetric wormhole spacetimes
International Nuclear Information System (INIS)
In this paper, we study the physical properties and the equilibrium thermal radiation emission characteristics of matter forming thin accretion disks in stationary axially symmetric wormhole spacetimes. The thin disk models are constructed by taking different values of the wormhole's angular velocity, and the time averaged energy flux, the disk temperature, and the emission spectra of the accretion disks are obtained. Comparing the mass accretion in a rotating wormhole geometry with the one of a Kerr black hole, we verify that the intensity of the flux emerging from the disk surface is greater for wormholes than for rotating black holes with the same geometrical mass and accretion rate. We also present the conversion efficiency of the accreting mass into radiation, and show that the rotating wormholes provide a much more efficient engine for the transformation of the accreting mass into radiation than the Kerr black holes. Therefore specific signatures appear in the electromagnetic spectrum of thin disks around rotating wormholes, thus leading to the possibility of distinguishing wormhole geometries by using astrophysical observations of the emission spectra from accretion disks.
On Axisymmetric and Stationary Solutions of the Self-Gravitating Vlasov System
Ames, Ellery; Logg, Anders
Axisymmetric and stationary solutions are constructed to the Einstein--Vlasov and Vlasov--Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein--Vlasov system which contain ergoregions.
On axisymmetric and stationary solutions of the self-gravitating Vlasov system
Ames, Ellery; Andréasson, Håkan; Logg, Anders
Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.
Time-of-flight focusing in triode axisymmetric electrostatic lens up to second order (inclusive)
International Nuclear Information System (INIS)
In the problems of the space focusing of stationary charged particles fluxes, the most prevailing lenses used are the axisymmetric and electrostatic. Their electronic and optical properties in this relation are fully studied. This paper describes a method to define the conditions of the time-of-flight charged particles focusing by the energy in the triode axisymmetric electrostatic lens designed in form of the coaxial cylinders with an equal diameter. The range of electrode configuration and potential variations, that make the focusing possible, are very wide
Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems
Patrick, G W; Wulff, C
In the presence of noncompact symmetry, the stability of relative equilibria under momentum preserving perturbations does not generally imply robust stability under momentum changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev stability, and we explain the transitions between these. We apply our results to the Kirchhoff model for the motion of an axisymmetric underwater vehicle, and we numerically study dissipation induced instability of KAM stable relative equilibria for this system.
D-branes and Azumaya/matrix noncommutative differential geometry,II: Azumaya/matrix supermanifolds and differentiable maps therefrom -- with a view toward dynamical fermionic D-branes in string theory
Liu, Chien-Hao
In this Part II of D(11), we introduce new objects: super-$C^k$-schemes and Azumaya super-$C^k$-manifolds with a fundamental module (or, synonymously, matrix super-$C^k$-manifolds with a fundamental module), and extend the study in D(11.1) ([L-Y3], arXiv:1406.0929 [math.DG]) to define the notion of `differentiable maps from an Azumaya/matrix supermanifold with a fundamental module to a real manifold or supermanifold'. This allows us to introduce the notion of `fermionic D-branes' in two different styles, one parallels Ramond-Neveu-Schwarz fermionic string and the other Green-Schwarz fermionic string. A more detailed discussion on the Higgs mechanism on dynamical D-branes in our setting, taking maps from the D-brane world-volume to the space-time in question and/or sections of the Chan-Paton bundle on the D-brane world-volume as Higgs fields, is also given for the first time in the D-project. Finally note that mathematically string theory begins with the notion of a differentiable map from a string world-sheet...
A 2D boundary element method for simulating the deformation of axisymmetric compound non-Newtonian drops
Toose, E.M.; Geurts, B.J.; Kuerten, J.G.M.
The boundary integral formulation of the solution to the Stokes equations is used to describe the deformation of small compound non-Newtonian axisymmetric drops suspended in a Newtonian fluid that is subjected to an axisymmetric flow field. The non-Newtonian stress is treated as a source term in the
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
Interaction of light and matter produces the appearance of materials. To deal with the immense complexity of nature, light and matter is modelled at a macroscopic level in computer graphics. This work is the first to provide the link between the microscopic physical theories of light and matter...... of a material and determine the contents of the material. The book is in four parts. Part I provides the link between microscopic and macroscopic theories of light. Part II describes how to use the properties of microscopic particles to compute the macroscopic properties of materials. Part III illustrates...... that we can use geometrical models to handle the large number of variables which appear when we construct appearance models from microscopic theories. Finally, Part IV provides detailed appearance models for natural water, ice, and milk to demonstrate how the theory is applied....
Spectral, IR and magnetic studies of Mn(II), Co(II), Ni(II) and Cu(II) complexes with pyrrole-2-carboxyaldehyde thiosemicarbazone (L)
Chandra, Sulekh; Kumar, Anil
Mn(II), Co(II), Ni(II) and Cu(II) complexes are synthesized with thiosemicarbazone (L) derived from pyrrole-2-carboxyaldehyde. These complexes are characterized by elemental analysis, molar conductance, magnetic susceptibility measurement, mass, IR, electronic and EPR spectral studies. The molar conductance measurement of the complexes in DMSO indicates that the complexes are non-electrolyte except Co(L) 2(NO 3) 2 and Ni(L) 2(NO 3) 2 complexes which are 1:2 electrolyte. All the complexes are of high-spin type. On the basis of spectral studies an octahedral geometry may be assigned for Mn(II), Co(II) and Ni(II) complexes except Co(L) 2(NO 3) 2 and Ni(L) 2(NO 3) 2 which are of tetrahedral geometry. A tetragonal geometry may be suggested for Cu(II) complexes.
The Application of Mechanics to Geometry. Popular Lectures in Mathematics.
Kogan, B. Yu
Presented in this translation are three chapters. Chapter I discusses the composition of forces and several theorems of geometry are proved using the fundamental concepts and certain laws of statics. Chapter II discusses the perpetual motion postulate; several geometric theorems are proved using the postulate that perpetual motion is impossible.…
GPS: Geometry, Probability, and Statistics
Field, Mike
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie;
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Index Theorems on Torsional Geometries
Kimura, Tetsuji
We study various topological invariants on a differential geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH=0. By using the identification between the Clifford algebra on a geometry and the canonical quantization condition of fermion in the quantum mechanics, we construct the N=1 quantum mechanical sigma model in the Hamiltonian formalism and extend this model to N=2 system, equipped with the totally anti-symmetric tensor associated with the torsion on the target space geometry. Next we construct transition elements in the Lagrangian path integral formalism and apply them to the analyses of the Witten indices in supersymmetric systems. We improve the formulation of the Dirac index on the torsional geometry which has already been studied. We also formulate the Euler characteristic and the Hirzebruch signature on the torsional geometry.
Lobachevsky's Geometry and Research of Geometry of the Universe
Brylevskaya, L. I.
For the first time N. I. Lobachevsky gave a talk on the new geometry in 1826; three years after he had published a work "On the fundamentals of geometry", containing all fundamental theorems and methods of non-Euclidean geometry. A small part of the article was devoted to the study of geometry of the Universe. The interpretation of geometrical concepts in pure empirical way was typical for mathematicians at the beginning of the XIX century; in this connection it was important for scientists to find application of his geometry. Having the purpose to determine experimentally the properties of real physical Space, Lobachevsky decided to calculate the sum of angles in a huge triangle with two vertexes in opposite points of the terrestrial orbit and the third -- on the remote star. Investigating the possibilities of solution of the set task, Lobachevsky faced the difficulties of theoretical, technical and methodological character. More detailed research of different aspects of the problem led Lobachevsky to the comprehension of impossibility to obtain the values required for the goal achievement, and he called his geometry an imaginary geometry.
Three-dimensional vector recording in polarization sensitive liquid crystal composites by using axisymmetrically polarized beam.
Sakamoto, Moritsugu; Sasaki, Tomoyuki; Noda, Kohei; Tien, Tran Minh; Kawatsuki, Nobuhiro; Ono, Hiroshi
Three-dimensional anisotropic structures were fabricated by a recording axisymmetrically polarized beam in azobenzene (azo)-dye doped liquid crystal polymer composites. Polarization and wavefront modulation properties of fabricated anisotropic structures are investigated by experimentally and theoretically analyzing the diffraction properties. Photo-induced anisotropic structures would be utilized to generate singular light waves, such as optical and polarization vortices.
On the impact of a concave nosed axisymmetric body on a free surface
Mathai, V.; Govardhan, R.N.; Arakeri, V.H.
We report on an experimental study of the vertical impact of a concave nosed axisymmetric body on a free surface. Previous studies have shown that bodies with a convex nose, like a sphere, produce a well defined splash with a relatively large cavity behind the model. In contrast, we find that with a
On a New Formulation of Vacuum Axisymmetric Solutions of general Relativity
Witten, Louis
Axisymmetric Solutions of the vacuum Einstein equations are found in the Papapetrou-Weyl gauge. The solutions depend on two pairs of functionals, each pair of two functions depends on a different arbitrarily chosen function of one variable. Some examples are given.
Spreading of non-planar non-axisymmetric gravity and turbidity currents
Zgheib, Nadim; Bonometti, Thomas; Balachandar, Sivaramakrishnan
The dynamics of non-axisymmetric turbidity currents is considered here. The study comprises a series of experiments for which a finite volume of particle-laden solution is released into fresh water. A mixture of water and polystyrene particles of diameter 280
Non-axisymmetric reflectors concentrating radiation from an asymmetric heliostat field onto a circular absorber
Energy Technology Data Exchange (ETDEWEB)
Spirkl, W.; Timinger, A.; Muschaweck, J. [Ludwig-Maximilians-Universitaet, Munich (Germany). Sektion Physik; Ries, H. [Paul Scherrer Institute, Villigen (Switzerland); Kribus, A. [Weizmann Institute of Science, Rehovot (Israel). Environmental Sciences and Energy Research Dept.
In solar tower plants, where a rotationally symmetric field of heliostats surrounds the tower, an axisymmetric secondary concentrator such as a compound parabolic concentrator (CPC) or a tailored concentrator or a cone is the obvious choice. For locations at higher latitudes, however, the reflecting area of the heliostats may be used more efficiently if the field of heliostats is located opposite to the sun as seen from the tower. Then the field is asymmetric with regard to the tower. In the case of an asymmetric field, an axisymmetric concentrator necessarily has a concentration significantly lower than the upper limit. Furthermore, the area on the ground from which a tilted axisymmetric concentrator accepts radiation is an ellipse, including also heliostats very distant to the tower producing a large image of the sun. For these reasons we investigate asymmetric secondaries. From the shape of the edge ray reflectors constructed for rays in the central south-north plane we conclude that a skew cone reflector might be appropriate for the field, and optimize its free parameters by means of ray tracing. Asymmetric concentrators may increase the concentration by up to 25% at the same efficiency compared to optimized axisymmetric CPC or cone reflectors. (author)
The maximum optical depth toward bulge stars from axisymmetric models of the Milky Way
Kuijken, K
It has been known that recent microlensing results toward the bulge imply mass densities that are surprisingly high, given dynamical constraints on the Milky Way mass distribution. We derive the maximum optical depth toward the bulge that may be generated by axisymmetric structures in the Milky Way,
Experimental study of the structure of laminar axisymmetric H2/air diffusion flames
Toro, Vishal Vijay
This thesis presents an experimental study of the structure of laminar axisymmetric coflow hydrogen diffusion flames. The motivation behind studying these flames is the current drive towards sustainable energy and strict pollution norms. In this regard, hydrogen as a fuel is one such candidate, whic
A numerical study of two-phase Stokes flow in an axisymmetric flow-focusing device
DEFF Research Database (Denmark)
Jensen, Mads Jakob; Stone, H.A.; Bruus, Henrik
)], and predict a scaling yet to be observed: the bubble volume scales with the outlet channel radius to the power of 4 and the surface tension. Our axisymmetric simulations further show that the collapse of the gas thread before bubble snap-off is different from the recent experimental results. We suggest...
Flow of Polymer Melts in Plane- and Axi-Symmetric Converging Dies
DEFF Research Database (Denmark)
Lauridsen, Carsten Linding; Kjær, Erik Michael; Haudrum, Jan
The extensional flow has considerable influence on the pressure loss in converging flows, which are present in both extrusion and injection moulding. Both plane- and axi-symmetric converging flows have been studied with LDPE, HDPE and PS. The transient extensional viscosities are determined in al...
Chaotic oscillations in a nearly inviscid, axisymmetric capillary bridge at 2:1 parametric resonance
Mancebo, Francisco J.; Nicolás, José A.; Vega de Prada, José Manuel
We consider the 2:1 internal resonances (such that Ω1>0 and Ω2 ≃ 2Ω1 are natural frequencies) that appear in a nearly inviscid, axisymmetric capillary bridge when the slenderness Λ is such that 0
The Geometry Description Markup Language
Institute of Scientific and Technical Information of China (English)
Currently,a lot of effort is being put on designing complex detectors.A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier.A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment.However,no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files,source code (C/C++/FORTRAN),to XML and database solutions.The XML(Extensible Markup Language)has proven to provide an interesting approach for describing detector geometries,with several different but incompatible XML-based solutions existing.Therefore,interoperability and geometry data exchange among different frameworks is not possible at present.This article introduces a markup language for geometry descriptions.Its aim is to define a common approach for sharing and exchanging of geometry description data.Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML.
Linear algebra, geometry and transformation
Solomon, Bruce
Vectors, Mappings and Linearity Numeric Vectors Functions Mappings and Transformations Linearity The Matrix of a Linear Transformation Solving Linear Systems The Linear SystemThe Augmented Matrix and RRE Form Homogeneous Systems in RRE Form Inhomogeneous Systems in RRE Form The Gauss-Jordan Algorithm Two Mapping Answers Linear Geometry Geometric Vectors Geometric/Numeric Duality Dot-Product Geometry Lines, Planes, and Hyperplanes System Geometry and Row/Column Duality The Algebra of Matrices Matrix Operations Special Matrices Matrix Inversion A Logical Digression The Logic of the Inversion Alg
Quantum Consequences of Parameterizing Geometry
Wanas, M. I.
The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.
Fallow), Stray
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
Walsh, Edward T
This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl
Thermal Phase in Bubbling Geometries
Institute of Scientific and Technical Information of China (English)
LIU Chang-Yong
We use matrix model to study thermal phase in bubbling half-BPS type IIB geometries with SO(4)×SO(4) symmetry.Near the horizon limit,we find that thermal vacua of bubbling geometries have disjoint parts,and each part is one kind of phase of the thermal system.We connect the thermal dynamics of bubbling geometries with one-dimensional fermions thermal system.Finally,we try to give a new possible way to resolve information loss puzzle.
Surface pressure drag for hydrostatic two-layer flow over axisymmetric mountains
Energy Technology Data Exchange (ETDEWEB)
Leutbecher, M.
The effect of partial reflections on surface pressure drag is investigated for hydrostatic gravity waves in two-layer flow with piecewise constant buoyancy frequency. The variation of normalized surface pressure drag with interface height is analyzed for axisymmetric mountains. The results are compared with the familiar solution for infinitely long ridges. The drag for the two-layer flow is normalized with the drag of one-layer flow, which has the buoyancy frequency of the lower layer. An analytical expression for the normalized drag of axisymmetric mountains is derived from linear theory of steady flow. Additionally, two-layer flow over finite-height axisymmetric mountains is simulated numerically for flow with higher stability in the upper layer. The temporal evolution of the surface pressure drag is examined in a series of experiments with different interface and mountain heights. The focus is on the linear regime and the nonlinear regime of nonbreaking gravity waves. The dispersion of gravity waves in flow over isolated mountains prevents that the entire wave spectrum is in resonance at the same interface height, which is the case in hydrostatic flow over infinitely long ridges. In consequence, the oscillation of the normalized drag with interface height is smaller for axisymmetric mountains than for infinitely long ridges. However, even for a reflection coefficient as low as 1/3 the drag of an axisymmetric mountain can be amplified by 50% and reduced by 40%. The nonlinear drag becomes steady in the numerical experiments in which no wave breaking occurs. The steady state nonlinear drag agrees quite well with the prediction of linear theory if the linear drag is computed for a slightly lowered interface. (orig.)
Numerical simulation of the generation mechanism of axisymmetric supersonic jet screech tones
Li, X. D.; Gao, J. H.
In this paper an axisymmetric computational aeroacoustic procedure is developed to investigate the generation mechanism of axisymmetric supersonic jet screech tones. The axisymmetric Navier-Stokes equations and the two equations standard k-ɛ turbulence model modified by Turpin and Troyes ["Validation of a two-equation turbulence model for axisymmetric reacting and non-reaction flows," AIAA Paper No. 2000-3463 (2000)] are solved in the generalized curvilinear coordinate system. A generalized wall function is applied in the nozzle exit wall region. The dispersion-relation-preserving scheme is applied for space discretization. The 2N storage low-dissipation and low-dispersion Runge-Kutta scheme is employed for time integration. Much attention is paid to far-field boundary conditions and turbulence model. The underexpanded axisymmetric supersonic jet screech tones are simulated over the Mach number from 1.05 to 1.2. Numerical results are presented and compared with the experimental data by other researchers. The simulated wavelengths of A0, A1, A2, and B modes and part of simulated amplitudes agree very well with the measurement data by Ponton and Seiner ["The effects of nozzle exit lip thickness on plume resonance," J. Sound Vib. 154, 531 (1992)]. In particular, the phenomena of modes jumping have been captured correctly although the numerical procedure has to be improved to predict the amplitudes of supersonic jet screech tones more accurately. Furthermore, the phenomena of shock motions are analyzed. The predicted splitting and combination of shock cells are similar with the experimental observations of Panda ["Shock oscillation in underexpanded screeching jets," J. Fluid. Mech. 363, 173 (1998)]. Finally, the receptivity process is numerically studied and analyzed. It is shown that the receptivity zone is associated with the initial thin shear layer, and the incoming and reflected sound waves.
Large deformation and adhesive contact studies of axisymmetric membranes.
Laprade, Evan J; Long, Rong; Pham, Jonathan T; Lawrence, Jimmy; Emrick, Todd; Crosby, Alfred J; Hui, Chung-Yuen; Shull, Kenneth R
A model membrane contact system consisting of an acrylic copolymer membrane and a PDMS substrate was utilized to evaluate a recently developed nonlinear large-deformation adhesive contact analysis. Direct measurements of the local membrane apex strain during noncontact inflation indicated that the neo-Hookean model provides an accurate measure of membrane strain and supports its use as the strain energy function for the analysis. Two membrane contact geometries, exhibiting significantly different strain distributions during withdrawal, were investigated. The first examines the wet contact of an air pressurized membrane. The second looks at the dry contact of a fluid deformed membrane in which a stepper motor controls membrane-substrate separation. A time-dependent modulus emerges from the analysis, with principal tensions obtained from a comparison of predicted and experimental membrane profiles. The applicability of this numerical analysis for determining membrane tension, however, is limited by wrinkling instabilities and viscoelasticity. For this reason, a conceptually simpler method, based on the direct measurement of the membrane tension and contact angle, was also utilized. The traditional peel energy defined with this direct measurement accurately described the membrane/substrate adhesive interactions, giving well-defined peel energies that were independent of the detailed strain state of the membrane. PMID:23289644
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Siddharth Gautam; S Mitra; R Mukhopadhyay
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time scales involved in the motion and the geometry of motion can be studied using QENS. Molecular dynamics (MD) simulation not only provides insight into the details of the different types of motion possible but also does not suffer limitations of the experimental set-up. Here we report the effect of confinement on molecular dynamics in various restricted geometries as studied by QENS and MD simulations: An example where the QENS technique provided direct evidence of phase transition associated with change in the dynamical behaviour of the molecules is also discussed.
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Advances in discrete differential geometry
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Wanas, M I
In the present work, it is shown that the geometerization philosophy has not been exhausted. Some quantum roots are already built in non-symmetric geometries. Path equations in such geometries give rise to spin-gravity interaction. Some experimental evidences (the results of the COW-experiment) indicate the existence of this interaction. It is shown that the new quantum path equations could account for the results of the COW-experiment. Large scale applications, of the new path equations, admitted by such geometries, give rise to tests for the existence of this interaction on the astrophysical and cosmological scales. As a byproduct, it is shown that the quantum roots appeared explicitly, in the path equations, can be diffused in the whole geometry using a parameterization scheme.
Moment methods in extremal geometry
De Laat, D.
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
Duality principle and braided geometry
Majid, S
We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided geometry.
Geometry of the quantum universe
International Nuclear Information System (INIS)
A quantum universe with the global shape of a (Euclidean) de Sitter spacetime appears as dynamically generated background geometry in the causal dynamical triangulation (CDT) regularisation of quantum gravity. We investigate the micro- and macro-geometry of this universe, using geodesic shell decompositions of spacetime. More specifically, we focus on evidence of fractality and global anisotropy, and on how they depend on the bare coupling constants of the theory.
Higgs mass in noncommutative geometry
International Nuclear Information System (INIS)
In the noncommutative geometry approach to the standard model, an extra scalar field σ - initially suggested by particle physicist to stabilize the electroweak vacuum - makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Courant Algebroids in Parabolic Geometry
Armstrong, Stuart
To a smooth manifold $M$, a parabolic geometry associates a principal bundle, which has a parabolic subgroup of a semisimple Lie group as its structure group, and a Cartan connection. We show that the adjoint tractor bundle of a regular normal parabolic geometry can be endowed with the structure of a Courant algebroid. This gives a class of examples of transitive Courant algebroids that are not exact.
Topology and geometry for physicists
Nash, Charles
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
The Common Geometry Module (CGM).
Energy Technology Data Exchange (ETDEWEB)
Tautges, Timothy James
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
A FORTRAN code for the calculation of probe volume geometry changes in a laser anemometry system caused by window refraction
Owen, Albert K.
A computer code was written which utilizes ray tracing techniques to predict the changes in position and geometry of a laser Doppler velocimeter probe volume resulting from refraction effects. The code predicts the position change, changes in beam crossing angle, and the amount of uncrossing that occur when the beams traverse a region with a changed index of refraction, such as a glass window. The code calculates the changes for flat plate, cylinder, general axisymmetric and general surface windows and is currently operational on a VAX 8600 computer system.
Comparison of axisymmetric and three-dimensional models for gas uptake in a single bifurcation during steady expiration.
Madasu, Srinath; Ultman, James S; Borhan, Ali
Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30 deg, 70 deg, and 90 deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4-8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.
Holomorphic Cartan geometries and rational curves
Biswas, Indranil
We prove that any compact K\\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\\"ahler manifold.
Investigation of flowfields found in typical combustor geometries
Lilley, D. G.
Activities undertaken during the entire course of research are summarized. Studies were concerned with experimental and theoretical research on 2-D axisymmetric geometries under low speed nonreacting, turbulent, swirling flow conditions typical of gas turbine and ramjet combustion chambers. They included recirculation zone characterization, time-mean and turbulence simulation in swirling recirculating flow, sudden and gradual expansion flowfields, and furher complexities and parameter influences. The study included the investigation of: a complete range of swirl strengths; swirler performance; downstream contraction nozzle sizes and locations; expansion ratios; and inlet side-wall angles. Their individual and combined effects on the test section flowfield were observed, measured and characterized. Experimental methods included flow visualization (with smoke and neutrally-buoyant helium-filled soap bubbles), five-hole pitot probe time-mean velocity field measurements, and single-, double-, and triple-wire hot-wire anemometry measurements of time-mean velocities, normal and shear Reynolds sresses. Computational methods included development of the STARPIC code from the primitive-variable TEACH computer code, and its use in flowfield prediction and turbulence model development.
Realism, positivism, instrumentalism, and quantum geometry
Prugovečki, Eduard
The roles of classical realism, logical positivism, and pragmatic instrumentalism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War II developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the "schism" in twentieth century physics created by the Bohr-Einstein "disagreements" on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of "truth" in general, or its conventionalistic version in post-World War II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's "positivism" with Einstein's "realism" by emphasizing the existence of an underlying quantum reality, in which they both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by developing the conceptual and mathematical tools that are most appropriate for such a use.
Three-dimensional magnetohydrodynamics axisymmetric stagnation flow and heat transfer due to an axisymmetric shrinking/stretching sheet with viscous dissipation and heat source/sink
International Nuclear Information System (INIS)
The present work is concerned with the effects of viscous dissipation and heat source/sink on a three-dimensional magnetohydrodynamic boundary layer axisymmetric stagnation flow, and the heat transfer of an electrically conducting fluid over a sheet, which shrinks or stretches axisymmetrically in its own plane where the line of the symmetry of the stagnation flow and that of the shrinking (stretching) sheet are, in general, not aligned. The governing equations are transformed into ordinary differential equations by using suitable similarity transformations and then solved numerically by a shooting technique. This investigation explores the conditions of the non-existence, existence and uniqueness of the solutions of the similar equations numerically. It is noted that the range of the velocity ratio parameter, where the similarity solution exists, is increased with the increase of the value of the magnetic parameter. Furthermore, the study reveals that the non-alignment function affects the shrinking sheet more than the stretching sheet. In addition, the numerical results of the velocity profile, temperature profile, skin-friction coefficient, and rate of heat transfer at the sheet are discussed in detail with different parameters. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
A new method for shadow calculations: application to parameterised axisymmetric black holes
Younsi, Ziri; Rezzolla, Luciano; Konoplya, Roman; Mizuno, Yosuke
International efforts from the Black Hole Camera and Event Horizon Telescope projects, using mm and sub-mm very long baseline interferometry, are soon expected to provide the first images of the shadow cast by the candidate supermassive black hole in our Galactic center, Sagittarius A*. Observations of this shadow would provide direct evidence of the existence of astrophysical black holes. Although it is expected that astrophysical black holes are described by the axisymmetric Kerr solution, there also exist many other black hole solutions, both in general relativity and in other theories of gravity, which cannot presently be ruled out. To this end, we present calculations of black hole shadow images from various metric theories of gravity as described by our recent work on a general parameterisation of axisymmetric black holes [R. Konoplya, L. Rezzolla and A. Zhidenko, Phys. Rev. D 93, 064015 (2016)]. An algorithm to perform general ray-tracing calculations for any metric theory of gravity is first outlined ...
On axisymmetric/diamond-like mode transitions in axially compressed core-shell cylinders
Xu, Fan; Potier-Ferry, Michel
Recent interests in curvature- and stress-induced pattern formation and pattern selection motivate the present study. Surface morphological wrinkling of a cylindrical shell supported by a soft core subjected to axial compression is investigated based on a nonlinear 3D finite element model. The post-buckling behavior of core-shell cylinders beyond the first bifurcation often leads to complicated responses with surface mode transitions. The proposed finite element framework allows predicting and tracing these bifurcation portraits from a quantitative standpoint. The occurrence and evolution of 3D instability modes including sinusoidally deformed axisymmetric patterns and non-axisymmetric diamond-like modes will be highlighted according to critical dimensionless parameters. Besides, the phase diagram obtained from dimensional analyses and numerical results could be used to guide the design of core-shell cylindrical systems to achieve the desired instability patterns.
An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus.
Wirth, Benedikt; Sobey, Ian
We formulate in general terms the equations for axisymmetric and fully 3D models of a hydrocephalic brain. The model is developed using small strain poroelasticity that includes non-linear permeability. The axisymmetric model is solved for four ventricle shapes, an ellipsoid, a 'peanut' shape, a 'cross' shape and a 'bone' shape. The distribution of fluid pressure, velocity and content in the deformed parenchyma for a blocked aqueduct provides new qualitative insight into hydrocepahlus. Some observations are offered for two forms of cerebrospinal fluid flow abnormality, normal pressure hydrocephalus and idiopathic intracranial hypertension. The model is extended to include a gravitational term in the governing equations and the effect of hydrostatic pressure variation is considered. Results of a fully 3D simulations are described for two horn-like lateral ventricles and one case with two lateral ventricles and a third ventricle. PMID:16740629
Local Axisymmetric Diffusive Stability of Weakly-Magnetized, Differentially-Rotating, Stratified Fluids
Menou, K; Spruit, H C; Menou, Kristen; Balbus, Steven A.; Spruit, Henk C.
We study the local stability of stratified, differentially-rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to the magnetized and resistive, triple-diffusive case. Our fifth-order dispersion relation admits a novel branch which describes a magnetized version of multi-diffusive modes. We derive necessary conditions for axisymmetric stability in the inviscid and perfect-conductor (double-diffusive) limits. In each case, rotation must be constant on cylinders and angular velocity must not decrease with distance from the rotation axis for stability, irrespective of the relative strength of viscous, resistive and heat diffusion. Therefore, in both double-diffusive limits, solid body rotation marginally satisfies our stability criteria. The role of weak magnetic fields is essential to reach these conclusions. The triple-diffusive ...
A RANS/DES Numerical Procedure for Axisymmetric Flows with and without Strong Rotation
Energy Technology Data Exchange (ETDEWEB)
Andrade, Andrew Jacob [Univ. of California, Davis, CA (United States)
A RANS/DES numerical procedure with an extended Lax-Wendroff control-volume scheme and turbulence model is described for the accurate simulation of internal/external axisymmetric flow with and without strong rotation. This new procedure is an extension, from Cartesian to cylindrical coordinates, of (1) a second order accurate multi-grid, control-volume integration scheme, and (2) a k-ω turbulence model. This paper outlines both the axisymmetric corrections to the mentioned numerical schemes and the developments of techniques pertaining to numerical dissipation, multi-block connectivity, parallelization, etc. Furthermore, analytical and experimental case studies are presented to demonstrate accuracy and computational efficiency. Notes are also made toward numerical stability of highly rotational flows.
Fabrication and properties of axisymmetric WC/Co functionally graded hard metal via microwave sintering
Energy Technology Data Exchange (ETDEWEB)
Lin Wei; Bai Xinde; Ling Yunhan; Jiang Zuozhong; Xie Zhipeng [Dept. of Materials Science and Engineering, Tsinghua Univ., Beijing, BJ (China)
To reduce the cost of fabrication and improve the product quality, microwave sintering of axisymmetric functionally graded WC/Co hard metals was explored in this paper. WC-Co green compacts with a discontinuously axisymmetrical laying distribution of Co (3-25wt%) were first molded by cold isostatic pressure (CIP) and then sintered by microwave (2.45 GHz) irradiation in an Ar atmosphere. Microstructural changes and hardness survey have been examined through SEM analysis, etc. It was found that the densification and mechanical properties of the gradient compact were strongly dependent on the temperature and time of microwave sintering. Crystal particles remained quite small. Heat activation of WC grains and selective heating of microwave have enhanced the metallurgical and mechanical properties of cemented WC/Co functionally graded hard metals. Based on this result, preparation of nano-structural WC/Co functionally graded cemented carbides by microwave sintering is more promising. (orig.)
Impact of Impellers on the Axisymmetric Magnetic Mode in the VKS2 Dynamo Experiment
International Nuclear Information System (INIS)
In the von Karman Sodium 2 (VKS2) successful dynamo experiment of September 2006, the observed magnetic field showed a strong axisymmetric component, implying that nonaxisymmetric components of the flow field were acting. By modeling the induction effect of the spiraling flow between the blades of the impellers in a kinematic dynamo code, we find that the axisymmetric magnetic mode is excited. The control parameters are the magnetic Reynolds number of the mean flow, the coefficient measuring the induction effect α, and the type of boundary conditions. We show that using realistic values of α, the observed critical magnetic Reynolds number, Rmc≅32, can be reached easily with ferromagnetic boundary conditions. We conjecture that the dynamo action achieved in this experiment may not be related to the turbulence in the bulk of the flow, but rather to the α effect induced by the impellers
On the saturation of non-axisymmetric instabilites of magnetized spherical Couette flow
Kaplan, Elliot
We numerically investigate the saturation of the hydromagnetic instabilities of a magnetized spherical Couette flow. Previous simulations [Hollerbach, 2009] demonstrated region where the axisymmetric flow, calculated from a 2-D simulation, was linearly unstable to nonaxisymmetric perturbations. Full, nonlinear, 3d simulations [Hollerbach 2009, Travnikov 2011] showed that the saturated state would consist only of harmonics of one azimuthal wave number, though there were bifurcations and transitions as nondimensional parameters (Re, Ha) were varied. Here, the energy transfer between different aziumthal modes is formulated as a network. This demonstrates a mechanism or the saturation of one mode and for the suppression of other unstable modes. A given mode grows by extracting energy from the axisymmetric flow, and then saturates as the energy transfer to its second harmonic equals this inflow. At the same time, this mode suppresses other unstable modes by facilitating an energy transfer to linearly stable modes.
Numerical Study for Hysteresis Phenomena of Shock Wave Reflection in Overexpanded Axisymmetric Supersonic Jet
Institute of Scientific and Technical Information of China (English)
Tsuyoshi Yasunobu; Ken Matsuoka; Hideo Kashimura; Shigeru Matsuo; Toshiaki Setoguchi
When the high-pressure gas is exhausted to the vacuum chamber from the supersonic nozzle, the overexpanded supersonic jet is formed at specific condition. In two-dimensional supersonic jet, furthermore, it is known that the hysteresis phenomena for the reflection type of shock wave in the flow field is occurred under the quasi-steady flow and for instance, the transitional pressure ratio between the regular reflection (RR) and Mach reflection (MR) is affected by this phenomenon. Many papers have described the hysteresis phenomena for underexpanded supersonic jet, but this phenomenon under the overexpanded axisymmetric jet has not been detailed in the past papers. The purpose of this study is to clear the hysteresis phenomena for the reflection type of shock wave at the overexpanded axisymmetric jet using the TVD method and to discuss the characteristic of hysteresis phenomena.
Impact of axisymmetric mass models for dwarf spheroidal galaxies on indirect dark matter searches
Klop, Niki; Hayashi, Kohei; Ando, Shin'ichiro
Dwarf spheroidals are low-luminosity satellite galaxies of the Milky Way highly dominated by dark matter. Therefore, they are prime targets to search for signals from dark matter annihilation using gamma-ray observations. We analyse about 7 years of PASS8 Fermi data for seven classical dwarf galaxies, including Draco, adopting both the widely used Navarro-Frenk-White (NFW) profile and observationally motivated axisymmetric density profiles. For four of the selected dwarfs (Sextans, Carina, Sculptor and Fornax) axisymmetric mass models suggest a cored density profile rather than the commonly adopted cusped profile. We found that upper limits on the annihilation cross section for some of these dwarfs are significantly higher than the ones achieved using an NFW profile. Therefore, upper limits in the literature obtained using cusped profiles like the NFW might have been overestimated. Our results eventually show that it is extremely important to use observationally motivated density profiles going beyond the usu...
Local mechanical response in semiflexible polymer networks subjected to an axisymmetric prestress
Head, D A
Analytical and numerical calculations are presented for the mechanical response of fiber networks in a state of axisymmetric prestress, in the limit where geometric non-linearities such as fiber rotation are negligible. This allows us to focus on the anisotropy deriving purely from the non-linear force-extension curves of individual fibers. The number of independent elastic coefficients for isotropic, axisymmetric and fully anisotropic networks are enumerated, before deriving expressions for the response to a locally applied force that can be tested against e.g. microrheology experiments. Localised forces can generate anisotropy away from the point of application, so numerical integration of non-linear continuum equations is employed to determine the stress field, and induced mechanical anisotropy, at points located directly behind and in front of a force monopole. Results are presented for the wormlike chain model in normalised forms, allowing them to be easily mapped to a range of systems. Finally, the rele...
On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell
Directory of Open Access Journals (Sweden)
Rong Xiao
Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner's equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.
Institute of Scientific and Technical Information of China (English)
Guojun Nie; Zheng Zhong
Assuming the material properties varying with an exponential law both in the thickness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical numerical method is with great advantage in the computational efficiency. Moreover, study on axisymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Wave propagation on microstate geometries
Keir, Joseph
Supersymmetric microstate geometries were recently conjectured to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two and three charge supersymmetric microstate geometries, finding a number of surprising results. In both cases we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three charge microstates possess an ergoregion; these geometries therefore avoid Friedman's "ergosphere instability". In fact, in the three charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although this data must have nontrivial dependence on the Kaluza-Klein coordinate. In the two charge case we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform dec...
Geometry of black hole spacetimes
Andersson, Lars; Blue, Pieter
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.
Embedding problems in symplectic geometry
Schlenk, Felix
Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov''s famous "non-squeezing'''' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'''', and "lifting''''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.
General Construction of Tubular Geometry
Mukhopadhyay, Partha
We consider the problem of locally describing tubular geometry around a submanifold embedded in a (pseudo)Riemannian manifold in its general form. Given the geometry of ambient space in an arbitrary coordinate system and equations determining the submanifold in the same system, we compute the tubular expansion coefficients in terms of this {\\it a priori data}. This is done by using an indirect method that crucially applies the tubular expansion theorem for vielbein previously derived. With an explicit construction involving the relevant coordinate and non-coordinate frames we verify consistency of the whole method up to quadratic order in vielbein expansion. Furthermore, we perform certain (long and tedious) higher order computation which verifies the first non-trivial spin connection term in the expansion for the first time. Earlier a similar method was used to compute tubular geometry in loop space. We explain this work in the light of our general construction.
Quantum geometry and gravitational entropy
Energy Technology Data Exchange (ETDEWEB)
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Stationary axisymmetric four dimensional space-time endowed with Einstein metric
International Nuclear Information System (INIS)
In this paper, we construct Ernst equation from vacuum Einstein field equation for both zero and non-zero cosmological constant. In particular, we consider the case where the space-time admits axisymmetric using Boyer-Lindquist coordinates. This is called Kerr-Einstein solution describing a spinning black hole. Finally, we give a short discussion about the dynamics of photons on Kerr-Einstein space-time
CFD Validation Experiment of a Mach 2.5 Axisymmetric Shock-Wave/Boundary-Layer Interaction
Davis, David Owen
Preliminary results of an experimental investigation of a Mach 2.5 two-dimensional axisymmetric shock-wave/ boundary-layer interaction (SWBLI) are presented. The purpose of the investigation is to create a SWBLI dataset specifically for CFD validation purposes. Presented herein are the details of the facility and preliminary measurements characterizing the facility and interaction region. These results will serve to define the region of interest where more detailed mean and turbulence measurements will be made.
An axisymmetric finite element solution for elastic wave propagation through threaded connections
Land, J. George
An axisymmetric finite element solution method is developed for axial wave propagation through a series of threaded connections in rock drills. A piston impacts axially on a string of rods held together by threaded joints and the wave propagates through these joints before reaching the bit. The energy lost in the joints limits the maximum effective depth of the drill. Several computational techniques are used to efficiently model the problem. Non-reflecting boundaries are us...
Axisymmetric Grazing-Incidence Focusing Optics for Small-Angle Neutron Scattering
Liu, Dazhi; Gubarev, Mikhail V.; Resta, Giacomo; Ramsey, Brian D.; Moncton, David E.; Khaykovich, Boris
We propose and design novel axisymmetric focusing mirrors, known as Wolter optics, for small-angle neutron scattering instruments. Ray-tracing simulations show that using the mirrors can result in more than an order-of-magnitude increase in the neutron flux reaching detectors, while decreasing the minimum wave vector transfer. Such mirrors are made of Ni using a mature technology. They can be coated with neutron supermirror multilayers, and multiple mirrors can be nested to improve their flux...
Effect of heat transfer on magnetohydrodynamic axisymmetric flow between two stretching sheets
Energy Technology Data Exchange (ETDEWEB)
Hayat, Tasawar [Quaid-i-Azam Univ., Islamabad (Pakistan). Dept. of Mathematics; King Saud Univ., Riyadh (Saudi Arabia). Dept. of Mathematics; Nawaz, Muhammad [King Saud Univ., Riyadh (Saudi Arabia). Dept. of Mathematics
This investigation describes the effects of heat transfer on magnetohydrodynamic (MHD) axisymmetric flow of a viscous fluid between two radially stretching sheets. Navier-Stokes equations are transformed into the ordinary differential equations by utilizing similarity variables. Solution computations are presented by using the homotopy analysis method. The convergence of obtained solutions is checked. Skin friction coefficient and Nusselt number are given in tabular form. The dimensionless velocities and temperature are also analyzed for the pertinent parameters entering into the problem. (orig.)
Hydrodynamical stability of thin accretion discs: transient growth of global axisymmetric perturbations
Umurhan, O. M.; Nemirovsky, A.; Regev, O.; Shaviv, G.
The purpose of this paper is to explore how accretion discs manifest the phenomenon of transient growth on a global scale. We investigate analytically the time response of a thin accretion disc to particular axisymmetric perturbations. To facilitate an analytical treatment we replace the energy equation with a general polytropic assumption. The asymptotic expansion of Klu\\'zniak & Kita (2000), which extended the method of Regev (1983) to a full steady polytropic disc (with $n=3/2$), is furthe...
Axisymmetric buckling of a spherical shell embedded in an elastic medium under uniaxial stress at infinity
Jones, G. W.; Chapman, S. J.; Allwright, D. J.
The problem of a thin spherical linearly-elastic shell, perfectly bonded to an infinite linearly-elastic medium is considered. A constant axisymmetric stress field is applied at infinity in the matrix, and the displacement and stress fields in the shell and matrix are evaluated by means of harmonic potential functions. In order to examine the stability of this solution, the buckling problem of a shell which experiences this deformation is considered. Using Koiter's nonlinear shallow shell the...
Vortex-Nucleating Zeeman Resonance in Axisymmetric Rotating Bose-Einstein Condensates
International Nuclear Information System (INIS)
By use of the Larmor equivalence between uniform rotation and a magnetic field, we consider in the strong-interaction Thomas-Fermi regime the single centered vortex as the first Zeeman-like excited state of the axisymmetric rotating Bose-Einstein condensate. This yields a resonant-drive nucleation mechanism whose threshold is in quite good agreement with ENS, MIT, and JILA experimental results
On the shape of the fundamental sloshing mode in axisymmetric containers
Kulczycki, Tadeusz; Siudeja, Bartłomiej
In the paper we numerically study positions of high spots (extrema) of the fundamental sloshing mode of liquid in an axisymmetric tank. Our approach is based on a linear model reducing the problem to appropriate Steklov eigenvalue problem. We propose a numerical scheme for calculating sloshing modes and a novel method of making images of oscillating fluid. We also describe the relation of the high spot problem to the celebrated hot spots conjecture.
Axisymmetric modeling of ultrashort-pulse laser interactions with thin metal film
Directory of Open Access Journals (Sweden)
E. Majchrzak
Full Text Available The hyperbolic two-temperature model is used in order to describe the heat propagation in metal film subjected to an ultrashort-pulse laser heating. An axisymmetric heat soureceewith Gaussian temporeal and spatial distributions has been taken into account. At the stage of numerical computations the finite difference method is used. In the final part of the paper the examples of computations are shown.
Early bifurcation in rotating fluid flow with free surface studied by axisymmetric numerical simulations
Santos, M.B.L.; Sørensen, Jens Nørkær
Simulations of a fluid rotating inside a partially open cylindrical cavity, performed by numerical solution of the unsteady axisymmetric Navier–Stokes equations, are presented. The configuration consists of a cylindrical vessel holding the fluid, which is entrained into motion by a rotating lid. This one is a coaxial disk in contact with the fluid surface but without covering it entirely. The study focuses on the occurrence of time-dependent flow, more specifically, the first transition to un...
Dynamic Stability of Plane Free Surface of Liquid in Axisymmetric Tanks
P. Chellapandi; Siva Srinivas Kolukula
When liquid filled containers are excited vertically, it is known that, for some combinations of frequency and amplitude, the free surface undergoes unbounded motion leading to instability, called parametric instability or parametric resonance, while for other combinations the free surface remains plane. In this paper, the stability of the plane free surface is investigated theoretically when the vessel is a vertical axisymmetric container. The effect of coupled horizontal excitation on the s...
An Axi-Symmetric Segmented Composite SKA Dish Design: Performance and Production Analysis
Ivashina, M. V.; Bakker, R.; de Vaate, J. G. bij; Iupikov, O. A.; Arts, M.; Dekker, J.; van Ardenne, A.
A concept of an axi-symmetric dish as antenna reflector for the next generation radio telescope - the Square Kilometre Array (SKA) - is presented. The reflector is based on the use of novel thermoplastic composite material (reinforced with carbon fibre) in the context of the telescope design with wide band single pixel feeds. The baseline of this design represents an array of 100's to 1000's reflector antennas of 15-m diameter and covers frequencies from