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Probing deformed commutators with macroscopic harmonic oscillators
Bawaj, Mateusz; Biancofiore, Ciro; Bonaldi, Michele; Bonfigli, Federica; Borrielli, Antonio; Di Giuseppe, Giovanni; Marconi, Lorenzo; Marino, Francesco; Natali, Riccardo; Pontin, Antonio; Prodi, Giovanni A.; Serra, Enrico; Vitali, David; Marin, Francesco
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation. PMID:26088965
Solution of the Skyrme Hartree Fock Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)
NASA Astrophysics Data System (ADS)
Dobaczewski, J.; Olbratowski, P.
We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero
Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator
Paal, Eugen; Virkepu, Jueri
Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; ...
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leadingmore » order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.« less
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; Papenbrock, Thomas F.; Wendt, Kyle A.
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.
An algebraic cluster model based on the harmonic oscillator basis
NASA Technical Reports Server (NTRS)
Levai, Geza; Cseh, J.
We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.
Cooper pair of superconductivity in the coordinate representation and q-deformed harmonic oscillator
NASA Astrophysics Data System (ADS)
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
In this work we study the similarity between the wave functions of q -deformed harmonic oscillator and wave functions of Cooper pair. The wave functions of Cooper pairs in coordinate-space have an "onion-like" layered structure with exponent decay (Boltzmann) envelope modulation. The ground state wave function of q -deform harmonic oscillator has the form of oscillate functions with Gaussian decay envelope modulation. The corresponding between Boltzmann and Gaussian forms of envelope functions and their quantum similarity are discussed.
Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VII) HFODD (v2.49t): A new version of the program
Schunck, Nicolas F; McDonnell, J.; Sheikh, J. A.; Staszczak, A.; Stoitsov, Mario; Dobaczewski, J.; Toivanen, P.
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.
Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program
NASA Astrophysics Data System (ADS)
Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions
Constructing quantum logic gates using q-deformed harmonic oscillator algebras
NASA Astrophysics Data System (ADS)
Altintas, Azmi Ali; Ozaydin, Fatih; Yesilyurt, Can; Bugu, Sinan; Arik, Metin
We study two-level q-deformed angular momentum states, and using q-deformed harmonic oscillators, we provide a framework for constructing qubits and quantum gates. We also present the construction of some basic one-qubit and two-qubit quantum logic gates.
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
NASA Astrophysics Data System (ADS)
Sugawara-Tanabe, Kazuko
We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters δ and γ. The special cases with tan γ = 1/√3 (γ = 30°) and √3 /5(γ˜19°) are discussed.
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
Sugawara-Tanabe, Kazuko
We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters {delta} and {gamma}. The special cases with tan {gamma} = 1/{radical}(3)({gamma} = 30 deg.) and {radical}(3)/5({gamma}{approx}19 deg.) are discussed.
Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VI) HFODD (v2.40h): A new version of the program
NASA Astrophysics Data System (ADS)
Dobaczewski, J.; Satuła, W.; Carlsson, B. G.; Engel, J.; Olbratowski, P.; Powałowski, P.; Sadziak, M.; Sarich, J.; Schunck, N.; Staszczak, A.; Stoitsov, M.; Zalewski, M.; Zduńczuk, H.
We describe the new version (v2.40h) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the DT2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected three insignificant errors. New version program summaryProgram title: HFODD (v2.40h) Catalogue identifier: ADFL_v2_2 Program summary URL:
Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VII) HFODD (v2.49t): A new version of the program
NASA Astrophysics Data System (ADS)
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (IV) HFODD (v2.08i): a new version of the program
NASA Astrophysics Data System (ADS)
Dobaczewski, J.; Olbratowski, P.
We describe the new version (v2.08i) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. The new version contains an interface to the LAPACK subroutine ZHPEVX. Program summaryTitle of the program:HFODD (v2.08i) Catalogue number: ADTO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTO Reference in CPC for earlier version of program: J. Dobaczewski and J. Dudek, Comput. Phys. Commun. 131 (2000) 164 (v1.75r) Catalogue number of previous version: ADML Licensing provisions: none Does the new version supersede the previous one: yes Computers on which the program has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems: UNIX, LINUX, Windows-2000 Programming language used: FORTRAN-77 and FORTRAN-90 Memory required to execute with typical data: 10 Mwords No. of bits in a word: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Has the code been vectorised?: Yes No. of bytes in distributed program, including test data, etc.: 265352 No. of lines in distributed program: 52656 Distribution format: tar gzip file Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for
Four-body continuum-discretized coupled-channels calculations using a transformed harmonic oscillator basis
Rodriguez-Gallardo, M.; Arias, J. M.; Gomez-Camacho, J.; Moro, A. M.; Johnson, R. C.; Tostevin, J. A.; Thompson, I. J.
The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, {sup 6}He+{sup 12}C at 229.8 MeV, {sup 6}He+{sup 64}Zn at 10 and 13.6 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV, induced by the Borromean nucleus {sup 6}He. Both the Coulomb and nuclear interactions with a target are taken into account.
Some properties of an infinite family of deformations of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Quesne, Christiane
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians Hk on the plane, depending on a positive real parameter k. Two algebraic extensions of Hk are described. The first one, based on the elements of the dihedral group D2k and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of Hk for odd integer k. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of Hk of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.
The q-DEFORMED SCHRÖDINGER Equation of the Harmonic Oscillator on the Quantum Euclidean Space
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Watamura, Satoshi
We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.
Analytical transformed harmonic oscillator basis for continuum discretized coupled channels calculations
Moro, A. M.; Arias, J. M.; Gomez-Camacho, J.; Perez-Bernal, F.
A new method for continuum discretization in continuum-discretized coupled-channels calculations is proposed. The method is based on an analytic local-scale transformation of the harmonic-oscillator wave functions proposed for other purposes in a recent work [Karatagladis et al., Phys. Rev. C 71, 064601 (2005)]. The new approach is compared with the standard method of continuum discretization in terms of energy bins for the reactions d+{sup 58}Ni at 80 MeV, {sup 6}Li+{sup 40}Ca at 156 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV and 240 MeV/nucleon. In all cases very good agreement between both approaches is found.
Workshop on Harmonic Oscillators
NASA Technical Reports Server (NTRS)
Han, D. (Editor); Kim, Y. S. (Editor); Zachary, W. W. (Editor)
Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics.
Covariant harmonic oscillators: 1973 revisited
NASA Technical Reports Server (NTRS)
Noz, M. E.
Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.
Covariant harmonic oscillators and coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
On the moment of inertia of a quantum harmonic oscillator
Khamzin, A. A. Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.
An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.
The Quantum Group as a Symmetry ---The Schrödinger Equation of the N-Dimensional q-Deformed Harmonic Oscillator---
NASA Astrophysics Data System (ADS)
Carow-Watamura, U.; Watamura, S.
With the aim to construct a dynamical model with quantum group symmetry, the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidian space is investigated. After reviewing the differential calculus on the q-Euclidian space, the q-analog of the creation-annihilation operator is constructed. It is shown that it produces systematically all eigenfunctions of the Schrödinger equation and eigenvalues. We also present an alternative way to solve the Schrödinger equation which is based on the q-analysis. We represent the Schrödinger equation by the q-difference equation and solve it by using q-polynomials and q-exponential functions. The problem of the involution corresponding to the reality condition is discussed.
Scaling properties of the harmonic oscillator basis calculations for N = Z nuclei in the infrared limit with the JISP16 potential
NASA Astrophysics Data System (ADS)
Constantinou, Chrysovalantis; Caprio, Mark A.; Vary, James P.; Maris, Pieter
It has recently been found that when no-core configuration interaction (NCCI) calculations of low-mass nuclei are plotted against an infrared momentum cutoff λsc (scaling cutoff), a universal curve is obtained for the energy and the RMS radius. The plotted results must have an ultraviolet (UV) cutoff ΛUV greater than or equal to the intrinsic cutoff ΛNN of the interaction. This assures that UV convergence is reached. The scaling property then allows for the performance of extrapolations in the IR limit. Here we conduct NCCI calculations in the harmonic oscillator basis with the JISP16 potential. In the IR limit we obtain universal curves for N = Z nuclei up to and including 8Be . An extrapolation in the IR limit for the ground state energy and the RMS radius is performed, and extrapolated results are obtained. Supported by US DOE (DE-FG02-95ER-40934, DESC0008485 SciDAC/NUCLEI, DE-FG02-87ER40371), US NSF (0904782), and Research Corporation for Science Advancement (Cottrell Scholar Award). Computational resources provided by NERSC (US DOE DE-AC02-05CH11231).
Galilean covariant harmonic oscillator
NASA Technical Reports Server (NTRS)
Horzela, Andrzej; Kapuscik, Edward
A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Synchronous Discrete Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Antippa, Adel F.; Dubois, Daniel M.
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2π in phase space, is an integral multiple N of the discrete time step Δt. It is fully synchronous when N is even. It is pseudo-synchronous when T/Δt is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is "blue shifted" relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval Δt. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Relativistic harmonic oscillator revisited
Bars, Itzhak
The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.
Symmetry Based No Core Shell Model in a Deformed Basis
NASA Astrophysics Data System (ADS)
Kekejian, David; Draayer, Jerry; Launey, Kristina
To address current limitations of shell-model descriptions of large spatial deformation and cluster structures, we adopt a no-core shell model with a deformed harmonic oscillator basis and implement an angular momentum projection in a symmetry-adapted scheme. This approach allows us to reach larger model spaces as a result of computational memory savings for calculations of highly deformed states, such as the Hoyle state in C-12. The method is first tested with schematic interactions, but the ultimate goal is to carry forward calculations with realistic nucleon-nucleon interactions in future work. Supported by the U.S. NSF (OCI-0904874, ACI-1516338) and the U.S. DOE (DE-SC0005248), and benefitted from computing resources provided by Blue Waters and LSU's Center for Computation & Technology.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Coherent states for the relativistic harmonic oscillator
NASA Technical Reports Server (NTRS)
Aldaya, Victor; Guerrero, J.
Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.
Quantum wormholes and harmonic oscillators
NASA Technical Reports Server (NTRS)
Garay, Luis J.
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.
Harmonic Oscillators as Bridges between Theories
NASA Astrophysics Data System (ADS)
Kim, Y. S.; Noz, Marilyn E.
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. It is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called SL(2, c). Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.
The harmonic oscillator and nuclear physics
NASA Technical Reports Server (NTRS)
Rowe, D. J.
The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.
Second International Workshop on Harmonic Oscillators
NASA Technical Reports Server (NTRS)
Han, Daesoo (Editor); Wolf, Kurt Bernardo (Editor)
The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.
Kraus representation of a damped harmonic oscillator and its application
Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki
By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity.
Pisot q-coherent states quantization of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Gazeau, J. P.; del Olmo, M. A.
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0
deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories.
Markovian evolution of strongly coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Joshi, Chaitanya; Öhberg, Patrik; Cresser, James D.; Andersson, Erika
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.
Quantum nondemolition measurements of harmonic oscillators
NASA Technical Reports Server (NTRS)
Thorne, K. S.; Caves, C. M.; Zimmermann, M.; Sandberg, V. D.; Drever, R. W. P.
Measuring systems to determine the real component of the complex amplitude of a harmonic oscillator are described. This amplitude is constant in the absence of driving forces, and the uncertainty principle accounts for the fact that only the real component can be measured precisely and continuously ('quantum nondemolition measurement'). Application of the measuring systems to the detection of gravitational waves is considered.
Group Theory of Covariant Harmonic Oscillators
ERIC Educational Resources Information Center
Kim, Y. S.; Noz, Marilyn E.
A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…
Quantum harmonic oscillator in a thermal bath
NASA Technical Reports Server (NTRS)
Zhang, Yuhong
The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.
Pisot q-coherent states quantization of the harmonic oscillator
Gazeau, J.P.; Olmo, M.A. del
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0
deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0
Deformed numbers are Fibonacci-like integer sequences (1/q a quadratic unit Pisot number). Black-Right-Pointing-Pointer We examine the main physical characteristics of the corresponding quantum oscillator.
Quantum harmonic oscillator with superoscillating initial datum
Buniy, R. V.; Struppa, D. C.; Colombo, F.; Sabadini, I.
In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.
Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Plyushchay, Mikhail S.
Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized osp (1 |2 ) superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via nonphysical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator.
Information theories for time-dependent harmonic oscillator
Choi, Jeong Ryeol; Kim, Min-Soo; Kim, Daeyeoul; Maamache, Mustapha; Menouar, Salah; Nahm, In Hyun
Highlights: > Information theories for the general time-dependent harmonic oscillator based on invariant operator method. > Time dependence of entropies and entropic uncertainty relation. > Characteristics of Shannon information and Fisher information. > Application of information theories to particular systems that have time-dependent behavior. - Abstract: Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville-von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.
Classical and revival time periods of confined harmonic oscillator
NASA Astrophysics Data System (ADS)
Ghosh, P.; Ghosh, S.; Bera, N.
We have used perturbation theory to compute energy eigenvalues, classical and the revival time periods for a one-dimensional harmonic oscillator confined in a box. First we have considered a simple harmonic oscillator as the unperturbed problem and boundary as perturbation. In next case, free particle in a box is considered as unperturbed problem that has been perturbed by a parabolic potential. We have used Fourier Grid Hamiltonian method to estimate classical and revival time period for the confined harmonic oscillator, which crosses smoothly from free particle in a box to a simple harmonic oscillator.
Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations
Gevorkyan, A. S.; Burdik, C.; Oganesyan, K. B.
Spontaneous transitions between bound states of an atomic system, 'Lamb Shift' of energy level, as well as many other phenomena in real nonrelativistic quantum systems are connected with the influence of quantum vacuum fluctuations which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system 'quantum harmonic oscillator (QHO)+ environment' is described in terms of complex probabilistic processes (CPP) which satisfies a stochastic differential equation (SDE) of Langevin-Schroedinger (L-Sch) type. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. The energy spectrum of QHO and a possibility of infringement of detailed balance of transitions between quantum levels including spontaneous decay of <
Chiral potential renormalized in harmonic-oscillator space
NASA Astrophysics Data System (ADS)
Yang, C.-J.
We renormalize the chiral effective field theory potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultraviolet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J -matrix method to reproduce the nucleon-nucleon scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy Tlab=100 MeV with number of HO basis nmax as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. This work serves as the input to perform ab initio calculations.
A possible generalization of the harmonic oscillator potential
NASA Technical Reports Server (NTRS)
Levai, Geza
A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.
Finite quantum kinematics of the harmonic oscillator
Shiri-Garakani, Mohsen; Finkelstein, David Ritz
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the time-independent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zero-point energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators, and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.
Finite quantum theory of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shiri-Garakani, Mohsen
We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants h, h', h″ instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N = l(l + 1) ˜ 1/(h ' h″) states and Hamiltonian H = A(Lx)2 + B(Ly)2, and the physically interesting case has N ≫ 1. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N ≫ 1 there are three broad classes of FLHO: soft, medium, and hard, with B/A ≪ 1, B/A ˜ 1, and B/A ≫ 1 respectively. The field oscillators responsible for infra-red and ultraviolet divergences are soft and hard respectively. Medium oscillators have B/A ˜ 1 and approximate the QLHO. They have ˜ N low-lying states with nearly the same zero-point energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z axis with Lz ˜ +/-l. The soft and hard FLHO's have infinitesimal 0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators with Lx ˜ 0 or Ly ˜ 0 instead of Lz ˜ +/-l. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
Harmonic oscillator interaction with squeezed radiation
NASA Technical Reports Server (NTRS)
Dodonov, V. V.; Nikonov, D. E.
Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.
Improving Density Functionals with Quantum Harmonic Oscillators
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).
Harmonic oscillator in quantum rotational spectra: Molecules and nuclei
NASA Technical Reports Server (NTRS)
Pavlichenkov, Igor M.
The mapping of a rotational dynamics on a harmonic oscillator is considered. The method used for studying the stabilization of the rigid top rotation around the intermediate moment of inertial axix by orbiting particle is described.
Driven harmonic oscillator as a quantum simulator for open systems
Piilo, Jyrki; Maniscalco, Sabrina
We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored electric field pulses. The non-Markovian dynamics of the damped harmonic oscillator is obtained by using the information about the spectral density of the open system when averaging over the drives of the closed oscillator. We consider single trapped ions as a specific physical implementation of the simulator, and we show how the simulator approach reveals physical insight into the open system dynamics, e.g., the characteristic quantum mechanical non-Markovian oscillatory behavior of the energy of the damped oscillator, usually obtained by the non-Lindblad-type master equation, can have a simple semiclassical interpretation.
A harmonic oscillator having "volleyball damping"
NASA Astrophysics Data System (ADS)
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.
Relation of squeezed states between damped harmonic and simple harmonic oscillators
NASA Technical Reports Server (NTRS)
Um, Chung-In; Yeon, Kyu-Hwang; George, Thomas F.; Pandey, Lakshmi N.
The minimum uncertainty and other relations are evaluated in the framework of the coherent states of the damped harmonic oscillator. It is shown that the coherent states of the damped harmonic oscillator are the squeezed coherent states of the simple harmonic oscillator. The unitary operator is also constructed, and this connects coherent states with damped harmonic and simple harmonic oscillators.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
NASA Technical Reports Server (NTRS)
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
Violation of smooth observable macroscopic realism in a harmonic oscillator.
Leshem, Amir; Gat, Omri
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.
Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
NASA Astrophysics Data System (ADS)
Mahdifar, A.; Roknizadeh, R.; Naderi, M. H.
In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using the nonlinear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs model. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface appears as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
Symmetry algebra of a generalized anisotropic harmonic oscillator
NASA Technical Reports Server (NTRS)
Castanos, O.; Lopez-Pena, R.
It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.
The Study of Damped Harmonic Oscillations Using an Electronic Counter
ERIC Educational Resources Information Center
Wadhwa, Ajay
We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…
The One-Dimensional Damped Forced Harmonic Oscillator Revisited
ERIC Educational Resources Information Center
Flores-Hidalgo, G.; Barone, F. A.
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.
A Look at Damped Harmonic Oscillators through the Phase Plane
ERIC Educational Resources Information Center
Daneshbod, Yousef; Latulippe, Joe
Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
ERIC Educational Resources Information Center
Pendrill, Ann-Marie; Eager, David
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
ERIC Educational Resources Information Center
Nita, Gelu M.
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data.
Song, Qiang; Yu, Wenwu; Cao, Jinde; Liu, Fang
This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis.
Equity prices as a simple harmonic oscillator with noise
NASA Astrophysics Data System (ADS)
Ataullah, Ali; Tippett, Mark
The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.
Quantum kicked harmonic oscillator in contact with a heat bath
NASA Astrophysics Data System (ADS)
Prado Reynoso, M. Á.; López Vázquez, P. C.; Gorin, T.
We consider the quantum harmonic oscillator in contact with a finite-temperature bath, modeled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos, on the one hand, and ballistic or diffusive energy absorption, on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase-space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high-resolution Wigner functions at long times, where the system approaches a quasistationary cyclic evolution. Thereby, we perform an accurate study of the thermodynamic properties of a nonintegrable, quantum chaotic system in contact with a heat bath at finite temperature. In particular, we find that the heat transfer between harmonic oscillator and heat bath is governed by Fourier's law.
An analogue of the Berry phase for simple harmonic oscillators
NASA Astrophysics Data System (ADS)
Suslov, S. K.
We evaluate a variant of Berry's phase for a 'missing' family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.
Coherent and squeezed states for the 3D harmonic oscillator
NASA Astrophysics Data System (ADS)
Mazouz, Amel; Bentaiba, Mustapha; Mahieddine, Ali
A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.
Collision-induced squeezing in a harmonic oscillator
NASA Technical Reports Server (NTRS)
Lee, Hai-Woong
The concept of squeezing has so far been applied mainly to light, as is evidenced by the number of research works on the subject of squeezed light. Since, in quantum mechanics, both light and the simple harmonic oscillator are described within the same mathematical framework, there is of course no difficulty in applying the concept to the simple harmonic oscillator as well. In fact, the theoretical development of squeezed states and squeezed light owes much to the physical insights that one obtains as the analogy between light and the harmonic oscillator is exploited. The example presented shows clearly that two states with different phases in general have different degrees of squeezing, even if they have the same state distribution. This means that, even if one considers collision processes that produce the same state distribution, the degree of squeezing obtained during and after the collisions can be quite different, depending on how the phases phi(sub n) of the probability amplitudes develop in time as the collisions proceed. It is therefore evident that, for a detailed study of collision-induced squeezing, further study on the time development of the phases in collisions and its relation to collision parameters such as potential energy surfaces and collision energy is needed.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
NASA Astrophysics Data System (ADS)
Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber
This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.
Observations of Harmonic Oscillations and ELM Magnetic Precursors in NSTX
NASA Astrophysics Data System (ADS)
Kelly, F.; Fredrickson, E.; Bell, R.; Tritz, K.; Maingi, R.; Takahashi, H.
Recent experiments in the National Spherical Torus Experiment (NSTX) demonstrated the progressive suppression of edge localized modes (ELMs) with increasing lithium deposition. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n harmonics more frequent. Signatures of these harmonic oscillations with a significant edge component were observed in both the high-n Mirnov magnetic and soft X-ray diagnostics of NSTX. Two distinct sets of harmonic oscillations can be observed during some ELM-free periods. The harmonic oscillations are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. NSTX magnetic diagnostics also observe distinctive signatures of ELMs. Transient n = 1 and n = 2 mode bursts and occasional higher n modes with frequency in the 30 to 90 kHz range occurred simultaneous with the increase in fast Da signal. These bursts of n = 1 and n = 2 modes resemble a model simulation of ELMs by T. Evans in which a bifurcation of magnetic topology is driven by nonlinear feedback amplification of thermoelectric currents from linear peeling-ballooning modes.
Quantum harmonic oscillator: an elementary derivation of the energy spectrum
NASA Astrophysics Data System (ADS)
Borghi, Riccardo
An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of linear differential equation theory or Fourier analysis are required, but rather only a few basics of elementary calculus. The pivotal role in our analysis is played by the sole particle localization constraint, which implies square integrability of stationary-state wavefunctions. The oscillator ground-state characterization is then achieved in a way that could be grasped, in principle, even by first-year undergraduates. A very elementary approach to build up and to characterize all higher-level energy eigenstates completes our analysis.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
NASA Astrophysics Data System (ADS)
Sheehan, D. P.; Wright, J. H.
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
Sheehan, D. P.; Wright, J. H.
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.
Elementary derivation of the quantum propagator for the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shao, Jiushu
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
Analysis of transonic flow about harmonically oscillating airfoils and wings
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.
A finite difference method for analyzing the unsteady transonic flow about harmonically oscillating wings is discussed. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting partial differential equations for small disturbances. Initial solutions were obtained using relaxation procedures, but the solution range proved to be limited in terms of Mach number and reduced frequency. Recent two-dimensional results are presented which have been obtained with direct solution procedures in which the difference equations are solved 'all at once' and these provide reasonable correlation for practical values of Mach number and reduced frequency.
Random reverse-cyclic matrices and screened harmonic oscillator
NASA Astrophysics Data System (ADS)
Srivastava, Shashi C. L.; Jain, Sudhir R.
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner.
Brownian motion with adhesion: harmonic oscillator with fluctuating mass.
Gitterman, M; Klyatskin, V I
In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Tang, J.
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process
NASA Astrophysics Data System (ADS)
Ma, Shan; Woolley, Matthew J.; Petersen, Ian R.; Yamamoto, Naoki
We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2\\aleph +1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2\\aleph +1) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
NASA Astrophysics Data System (ADS)
Chou, Chia-Chun
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
ERIC Educational Resources Information Center
Lee, Keeyung
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
Exact solution of a quantum forced time-dependent harmonic oscillator
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
The Harmonic Oscillator with a Gaussian Perturbation: Evaluation of the Integrals and Example Applications
ERIC Educational Resources Information Center
Earl, Boyd L.
A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…
The Acoustic Simple Harmonic Oscillator: Experimental Verification and Applications
NASA Astrophysics Data System (ADS)
Matteson, Sam
In his famous volume, The Sensations of Tone, published in 1877, Hermann Helmholtz introduced a resonator that was central to his investigations of acoustics. This talk revisits the device that Helmholtz described and examines it as a manifestation of an acoustic simple harmonic oscillator (SHO). The presentation demonstrates that an enclosed volume which communicates with the outside world via a narrow tube exhibits a single strong frequency response in analogy to a mechanical SHO, along with weaker resonances of the air in the short pipe that comprises the ``neck.'' The investigations, furthermore, report results of a straightforward experiment that confirms the SHO model (with damping) and that is very accessible to undergraduate students using inexpensive equipment and internet-obtainable freeware. The current work also extends the analysis to include applications of the Helmholtz Resonator to several folk instruments, namely, the ocarina, whistling, and the ``bottle band.''
Free fall and harmonic oscillations: analyzing trampoline jumps
NASA Astrophysics Data System (ADS)
Pendrill, Ann-Marie; Eager, David
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is obtained in terms of maximum normalized force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained on a larger garden trampoline, and even larger accelerations have been measured for gymnastic trampolines.
Phase-space treatment of the driven quantum harmonic oscillator
NASA Astrophysics Data System (ADS)
Campos, Diógenes
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.
A Perturbation of the Dunkl Harmonic Oscillator on the Line
NASA Astrophysics Data System (ADS)
Álvarez López, Jesús A.; Calaza, Manuel
Let J_σ be the Dunkl harmonic oscillator on R (σ>-1/2). For 00, it is proved that, if σ>u-1/2, then the operator U=J_σ+ξ|x|^{-2u}, with appropriate domain, is essentially self-adjoint in L^2({R},|x|^{2σ} dx), the Schwartz space S is a core of overline U^{1/2}, and overline U has a discrete spectrum, which is estimated in terms of the spectrum of overline{J_σ}. A generalization J_{σ,τ} of J_σ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for J_{σ,τ}, where the perturbation has an additional term involving, either the factor x^{-1} on odd functions, or the factor x on even functions. Versions of these results on R_+ are derived.
A method of solving simple harmonic oscillator Schroedinger equation
NASA Technical Reports Server (NTRS)
Maury, Juan Carlos F.
A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.
Excitation with quantum light. I. Exciting a harmonic oscillator
NASA Astrophysics Data System (ADS)
Carreño, J. C. López; Laussy, F. P.
We present a two-part study of the excitation of an optical target by quantum light. In this first part, we introduce the problematic and address the first case of interest, that of exciting the quantum harmonic oscillator, corresponding to, e.g., a single-mode passive cavity or a noninteracting bosonic field. We introduce a mapping of the Hilbert space that allows to chart usefully the accessible regions. We then consider the quantum excitation from single-photon sources in the form of a two-level system under various regimes of (classical) pumping: incoherent, coherent, and in the Mollow triplet regime. We close this first part with an overview of the material to be covered in the subsequent work.
Arregui, I.; Asensio Ramos, A.; Diaz, A. J.
The detection of multiple mode harmonic kink oscillations in coronal loops enables us to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic flux tube expansion under each of the hypotheses. The two models are then compared using a Bayesian model comparison scheme to assess how plausible each one is given our current state of knowledge.
Avoiding dissipation in a system of three quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Manzano, Gonzalo; Galve, Fernando; Zambrini, Roberta
We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as to have several degrees of freedom unaffected by decoherence, irrespective of the specific spectral density or initial state of the bath. This partial thermalization allows observing asymptotic entanglement at moderate temperatures, even in the nonresonant case. This latter feature cannot be seen in the simpler situation of only two oscillators, highlighting the richer structural variety of the three-body case. When departing from the strict conditions for partial thermalization, a hierarchical structure of dissipation rates for the normal modes is observed, leading to a long transient where quantum correlations such as the quantum discord are largely preserved, as well as to synchronous dynamics of the oscillators quadratures.
Ecological optimization of an irreversible harmonic oscillators Carnot heat engine
NASA Astrophysics Data System (ADS)
Liu, Xiaowei; Chen, Lingen; Wu, Feng; Sun, Fengrui
A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.
Revised calculation of four-particle harmonic-oscillator transformation brackets matrix
NASA Astrophysics Data System (ADS)
Mickevičius, S.; Germanas, D.; Kalinauskas, R. K.
In this article we present a new, considerably enhanced and more rapid method for calculation of the matrix of four-particle harmonic-oscillator transformation brackets (4HOB). The new method is an improved version of 4HOB matrix calculations which facilitates the matrix calculation by finding the eigenvectors of the 4HOB matrix explicitly. Using this idea the new Fortran code for fast and 4HOB matrix calculation is presented. The calculation time decreases more than a few hundred times for large matrices. As many problems of nuclear and hadron physics structure are modeled on the harmonic oscillator (HO) basis our presented method can be useful for large-scale nuclear structure and many-particle identical fermion systems calculations. Program summaryTitle of program: HOTB_M Catalogue identifier: AEFQ_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 2149 No. of bytes in distributed program, including test data, etc.: 17576 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any computer with Fortran 90 compiler. Operating system: Windows, Linux, FreeBSD, True64 Unix. RAM: Up to a few Gigabytes (see Tables 1 and 2 included in the distribution package) Classification: 17.16, 17.17. Catalogue identifier of previous version: AEFQ_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1377 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the matrix of the 4HOB in a more effective way, which allows us to calculate the matrix of the brackets up to a few hundred times more rapidly than in a previous version. Solution method: The method is based on compact expressions of 4HOB, presented in [1] and its simplifications presented in this paper. Reasons for new version
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Singh, Manu Pratap; Rajput, B. S.
Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.
Feinberg-Horodecki states of a time-dependent mass distribution harmonic oscillator
NASA Astrophysics Data System (ADS)
Eshghi, M.; Sever, R.; Ikhdair, S. M.
The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass m(t) to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential V(t) acting on the TDM m(t) oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent mass reduces to m0.
Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation
NASA Astrophysics Data System (ADS)
Hassan, S. S.; Joshi, A.; Frege, O. M.; Emam, W.
A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity-intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator.
Edge Event-Triggered Synchronization in Networks of Coupled Harmonic Oscillators.
Wei, Bo; Xiao, Feng; Dai, Ming-Zhe
The synchronization problems of networks of coupled harmonic oscillators are addressed by the edge event-triggered approach in this paper. The network dynamics with respect to edge states are presented and a new edge event-triggered control protocol is designed. Combined with the periodic event-detecting and edge event-triggered approach, sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented. Two event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption. Finally, simulations are conducted to illustrate the effectiveness of the edge event-triggered control algorithm.
Calorimetric measurement of work for a driven harmonic oscillator
NASA Astrophysics Data System (ADS)
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
On quantum harmonic oscillator being subjected to absolute potential state
NASA Astrophysics Data System (ADS)
Nityayogananda, Swami
In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as `like-potential' energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remains dormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity - this needs further research. The more the QOE, the greater will be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.
Heat and work fluctuations for a harmonic oscillator.
Sabhapandit, Sanjib
The formalism of Kundu et al. [J. Stat. Mech. P03007 (2011)], for computing the large deviations of heat flow in harmonic systems, is applied to the case of single Brownian particle in a harmonic trap and coupled to two heat baths at different temperatures. The large-τ form of the moment generating function
Entanglement prethermalization in an interaction quench between two harmonic oscillators
NASA Astrophysics Data System (ADS)
Ikeda, Tatsuhiko N.; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito
Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.
Observations of ELM Magnetic Precursors and Harmonic Oscillations in NSTX
NASA Astrophysics Data System (ADS)
Kelly, F.; Frederickson, E.; Bell, R.; Tritz, K.; Takahashi, H.; Maingi, R.; NSTX Collaboration
Recent experiments on NSTX have shown n=1 dominant and n=2 mode ELM magnetic precursors with mode frequency in the 30 to 90 kHz range. The growing magnetic oscillations measured with the NSTX high-n Mirnov diagnostic occurred simultaneous with the onset of the increase in fast D α signal. These bursts of dominantly n=1, some n=2 and fewer higher modes resemble the predictions of a model simulation of ELMs by T. Evans in which a feedback amplification mechanism causes explosive growth of the separatrix topology driven by thermoelectric currents in flux tubes connecting the divertor plates. The n=1 mode remained dominant as wall recycling was reduced with lithium conditioning and n=3 RMP was applied, suggesting the trigger mechanism remained the same. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n Harmonics Oscillations (HOs) more frequent. The HOs are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. Work supported in part by US DOE contract no. DE-AC02-09CH11466.
Calorimetric measurement of work for a driven harmonic oscillator.
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
Entanglement prethermalization in an interaction quench between two harmonic oscillators.
Ikeda, Tatsuhiko N; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito
Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.
Entanglement dynamics for a conditionally kicked harmonic oscillator
NASA Astrophysics Data System (ADS)
Arrais, Eric G.; Sales, J. S.; de Almeida, N. G.
The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0, the so-called Lamb-Dicke parameter η whose square is proportional to the effective Planck constant {{\\hslash }}{{eff}}, and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting {{\\hslash }}{{eff}} become negligible. In this paper we investigate how the ratio T, considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or {{\\hslash }}{{eff}} parameters.
Coherent states and uncertainty relations for the damped harmonic oscillator with time-dependent frequency
NASA Technical Reports Server (NTRS)
Yeon, Kyu-Hwang; Um, Chung-In; George, Thomas F.; Pandey, Lakshmi N.
Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have.
Phase of the quantum harmonic oscillator with applications to optical polarization
NASA Technical Reports Server (NTRS)
Shepard, Scott R.
The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.
Amplitude and phase representation of quantum invariants for the time-dependent harmonic oscillator
Fernandez Guasti, M.; Moya-Cessa, H.
The correspondence between classical and quantum invariants is established. The Ermakov-Lewis quantum invariant of the time-dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase operators. In doing so, Turski's phase operator as well as Susskind-Glogower operators are generalized to the time-dependent harmonic-oscillator case. A quantum derivation of the Manley-Rowe relations is shown as an example.
Brownian motion of a harmonic oscillator in a noninertial reference frame.
Jiménez-Aquino, J I; Romero-Bastida, M
The Brownian motion of a charged harmonic oscillator in the presence of additional force fields, such as a constant magnetic field and arbitrary time-dependent electric and mechanical forces, is studied in a rotational reference frame under uniform motion. By assuming an isotropic surrounding medium (a scalar friction constant), we solve explicitly the Smoluchowski equation associated with the Langevin equation for the charged harmonic oscillator and calculate the mean square displacements along and orthogonal to the rotation axis.
Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties
NASA Astrophysics Data System (ADS)
Mojaveri, B.; Dehghani, A.
In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the su(1,1) Lie algebra. This is why we call them the generalized su(1,1) CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.
Time-dependent Hartree approximation and time-dependent harmonic oscillator model
NASA Astrophysics Data System (ADS)
Blaizot, J. P.; Schulz, H.
We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schrödinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory.
Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium
NASA Astrophysics Data System (ADS)
Jafari, Marjan; Kheirandish, Fardin
The quantum dynamics of a damped harmonic oscillator is investigated in the presence of an anisotropic heat bath. The medium is modeled by a continuum of three dimensional harmonic oscillators and anisotropic coupling is treated by introducing tensor coupling functions. Starting from a classical Lagrangian, the total system is quantized in the framework of the canonical quantization. Following the Fano technique, the Hamiltonian of the system is diagonalized in terms of creation and annihilation operators that are linear combinations of the basic dynamical variables. Using the diagonalized Hamiltonian, the mean force internal energy, free energy and entropy of the damped oscillator are calculated.
On the effects of a screw dislocation and a linear potential on the harmonic oscillator
NASA Astrophysics Data System (ADS)
Bueno, M. J.; Furtado, C.; Bakke, K.
Quantum effects on the harmonic oscillator due to the presence of a linear scalar potential and a screw dislocation are investigated. By searching for bound states solutions, it is shown that an Aharonov-Bohm-type effect for bound states and a restriction of the values of the angular frequency of the harmonic oscillator can be obtained, where the allowed values are determined by the topology of the screw dislocation and the quantum numbers associated with the radial modes and the angular momentum. As particular cases, the angular frequency and the energy levels associated with the ground state and the first excited state of the system are obtained.
Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator: An Undergraduate Vibrational Spectroscopy Laboratory Exercise
ERIC Educational Resources Information Center
Parnis, J. Mark; Thompson, Matthew G. K.
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
On the damping of the angular momentum of a spherical harmonic oscillator as a model for heavy ion collisions
Isar, A.; Sandulescu, A. ); Scheid, W. )
In the frame of the Lindblad theory of open quantum systems, the spherical harmonic oscillator with opening operators linear in the coordinates and the momenta of the considered system is analyzed. Explicit expressions for the damping of the energy, angular momentum and its projection, including the coupling of the harmonic oscillator due to the environment, are obtained.
Adaptive radial basis function mesh deformation using data reduction
NASA Astrophysics Data System (ADS)
Gillebaart, T.; Blom, D. S.; van Zuijlen, A. H.; Bijl, H.
Radial Basis Function (RBF) mesh deformation is one of the most robust mesh deformation methods available. Using the greedy (data reduction) method in combination with an explicit boundary correction, results in an efficient method as shown in literature. However, to ensure the method remains robust, two issues are addressed: 1) how to ensure that the set of control points remains an accurate representation of the geometry in time and 2) how to use/automate the explicit boundary correction, while ensuring a high mesh quality. In this paper, we propose an adaptive RBF mesh deformation method, which ensures the set of control points always represents the geometry/displacement up to a certain (user-specified) criteria, by keeping track of the boundary error throughout the simulation and re-selecting when needed. Opposed to the unit displacement and prescribed displacement selection methods, the adaptive method is more robust, user-independent and efficient, for the cases considered. Secondly, the analysis of a single high aspect ratio cell is used to formulate an equation for the correction radius needed, depending on the characteristics of the correction function used, maximum aspect ratio, minimum first cell height and boundary error. Based on the analysis two new radial basis correction functions are derived and proposed. This proposed automated procedure is verified while varying the correction function, Reynolds number (and thus first cell height and aspect ratio) and boundary error. Finally, the parallel efficiency is studied for the two adaptive methods, unit displacement and prescribed displacement for both the CPU as well as the memory formulation with a 2D oscillating and translating airfoil with oscillating flap, a 3D flexible locally deforming tube and deforming wind turbine blade. Generally, the memory formulation requires less work (due to the large amount of work required for evaluating RBF's), but the parallel efficiency reduces due to the limited
Generalized uncertainty principle corrections to the simple harmonic oscillator in phase space
NASA Astrophysics Data System (ADS)
Das, Saurya; Robbins, Matthew P. G.; Walton, Mark A.
We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.
The Adiabatic Invariant of the n-Degree-of-Freedom Harmonic Oscillator
ERIC Educational Resources Information Center
Devaud, M.; Leroy, V.; Bacri, J.-C.; Hocquet, T.
In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with…
Convergence for Fourier Series Solutions of the Forced Harmonic Oscillator II
ERIC Educational Resources Information Center
Fay, Temple H.
This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…
Note on the Time-Dependent Damped and Forced Harmonic Oscillator.
ERIC Educational Resources Information Center
Leach, P. G. L.
A Hamiltonian for the time-dependent damped and forced harmonic oscillator is derived. A simple time-dependent linear canonical transformation transforms the Hamiltonian to one whose solution is readily obtained. The wave function for the corresponding quantum mechanical problem is given. (Author/GA)
The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators
Morales, J.; Ovando, G.; Pena, J. J.
One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.
Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes
ERIC Educational Resources Information Center
Gauthier, N.
An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…
Discrete Excitation Spectrum of a Classical Harmonic Oscillator in Zero-Point Radiation
NASA Astrophysics Data System (ADS)
Huang, Wayne Cheng-Wei; Batelaan, Herman
We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.
Nonsingular parametric oscillators Darboux-related to the classical harmonic oscillator
NASA Astrophysics Data System (ADS)
Rosu, H. C.; Cornejo-Pérez, O.; Chen, P.
Interesting nonsingular parametric oscillators which are Darboux-related to the classical harmonic oscillator and have periodic dissipative/gain features are identified through a modified factorization method. The same method is applied to the upside-down (hyperbolic) "oscillator" for which the obtained Darboux partners show transient underdamped features.
Experimental demonstration of a technique for generation of arbitrary harmonic oscillator states.
NASA Astrophysics Data System (ADS)
Ben-Kish, A.; Demarco, B.; Rowe, M.; Meyer, V.; Britton, J.; Itano, W. M.; Jelenković, B. M.; Langer, C.; Leibfried, D.; Rosenband, T.; Wineland, D. J.
Synthesizing arbitrary quantum states is at the heart of such diverse fields as quantum computation and reaction control in chemistry. For harmonic oscillator states, particular interactions (in general, non-linear) can be used to generate special states such as squeezed states. However, it is usually intractable to realize the interactions required to create arbitrary states. Law and Eberly [1] have devised a technique for arbitrary harmonic oscillator state generation that couples the oscillator to a two-level atomic or spin system and applies a sequence of operations that use simple interactions. We demonstrate the general features of this technique on the harmonic motion of a single trapped ^9Be^+ ion and extend it to the generation of arbitrary spin-oscillator states [2]. [1] C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055 (1996). [2] B. Kneer and C. K. Law, Phys. Rev. A 57, 2096 (1998).
Equilibrium and stationary nonequilibrium states in a chain of colliding harmonic oscillators
Equilibrium and nonequilibrium properties of a chain of colliding harmonic oscillators (ding-dong model) are investigated. Our chain is modeled as harmonically bounded particles that can only interact with neighboring particles by hard-core interaction. Between the collisions, particles are just independent harmonic oscillators. We are especially interested in the stationary nonequilibrium state of the ding-dong model coupled with two stochastic heat reservoirs (not thermostated) at the ends, whose temperature is different. We check the Gallavotti-Cohen fluctuation theorem [G. Gallavoti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)] and also the Evans-Searles identity [D. Evans and D. Searles, Phys. Rev. E. 50, 1994 (1994)] numerically. It is verified that the former theorem is satisfied for this system, although the system is not a thermostated system.
Damped harmonic oscillator model for analyzing the dynamic characteristics of STM system
NASA Astrophysics Data System (ADS)
Liu, A. P.; Yao, X. X.; Wang, X.; Yang, D. X.; Zhang, X. M.
Recognizing and distinguishing the dynamic characteristics of scanning tunneling microscopy (STM) system is fatal for studying STM image. In this paper, a method for analyzing system's characteristics by using a damped harmonic oscillator model is presented. The model is driven by random force and all of its properties are described by damping and periodic. For the general solution of such harmonic oscillator's Langevin equation is deduced and the auto-correlation function (ACF) is obtained for fitting curve. It is shown that damping and periodic property of the two curves have a good agreement by comparing the fitting curve with the auto-correlation curve of time series dates which are acquired by STM. It could be concluded that the damped harmonic oscillator model and auto-correlation method are feasible for analyzing the dynamic characteristics of STM system.
Transformations of the perturbed two-body problem to unperturbed harmonic oscillators
NASA Technical Reports Server (NTRS)
Szebehely, V.; Bond, V.
Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.
Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions
NASA Astrophysics Data System (ADS)
Ferkous, N.; Boudjedaa, T.
We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green's function techniques using both momentum and position space representations. The even and odd solutions of the problem are discussed. The corresponding limiting cases are recovered. For the harmonic oscillator with a point interaction in more than one dimension, divergent series appear. We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states. The results obtained here are consistent with other investigations using different methods. Supported by the Algerian Ministry of Higher Education and Scientific Research under the CNEPRU project No. D01720140001
A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
NASA Astrophysics Data System (ADS)
Vignat, C.; Lamberti, P. W.
Recently, Cariñena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator
Chen Xi; Muga, J. G.
We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes ('shortcuts to adiabaticity') designed to reproduce the initial populations at some predetermined final frequency and time. We provide lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.
Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice
NASA Astrophysics Data System (ADS)
Deymier, P. A.; Runge, K.; Vasseur, J. O.
We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise
NASA Astrophysics Data System (ADS)
Jara, Milton; Komorowski, Tomasz; Olla, Stefano
We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to the solution of the fractional diffusion equation . For a pinned system we prove that its energy evolves diffusively, generalizing some results of Basile and Olla (J. Stat. Phys. 155(6):1126-1142, 2014).
Dynamics of SU(1,1) coherent states for the damped harmonic oscillator
Choi, Jeong Ryeol; Yeon, Kyu Hwang
Gerry, Ma, and Vrscay [Phys. Rev. A 39, 668 (1989)] studied the time evolution of SU(1,1) coherent states for the damped harmonic oscillator by introducing the Kanai-Caldirola Hamiltonian. The purposes of this Brief Report are to demonstrate that there are somewhat serious errors on their results and to correct them. Most of the figures given in their work are reproduced with correction in order to facilitate our explanation of results.
Quantum optics. Quantum harmonic oscillator state synthesis by reservoir engineering.
Kienzler, D; Lo, H-Y; Keitch, B; de Clercq, L; Leupold, F; Lindenfelser, F; Marinelli, M; Negnevitsky, V; Home, J P
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
Containment control for coupled harmonic oscillators with multiple leaders under directed topology
NASA Astrophysics Data System (ADS)
Xu, Chengjie; Zheng, Ying; Su, Housheng; Wang, Hua O.
This paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology. Using tools from matrix, graph and stability theories, necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous-time and sampled-data-based protocols, respectively. When the continuous-time protocol is used, it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time. When the sampled-data-based protocol is used, it is shown that the containment can be achieved if and only if: (1) an appropriate sampling period is chosen and (2) for every follower, there exists at least one leader that has a directed path to that follower at any time. And we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case. Finally, numerical simulations are presented to illustrate the theoretical findings.
Brownian motion of a classical harmonic oscillator in a magnetic field.
Jiménez-Aquino, J I; Velasco, R M; Uribe, F J
In this paper, the stochastic diffusion process of a charged classical harmonic oscillator in a constant magnetic field is exactly described through the analytical solution of the associated Langevin equation. Due to the presence of the magnetic field, stochastic diffusion takes place across and along the magnetic field. Along the magnetic field, the Brownian motion is exactly the same as that of the ordinary one-dimensional classical harmonic oscillator, which was very well described in Chandrasekhar's celebrated paper [Rev. Mod. Phys. 15, 1 (1943)]. Across the magnetic field, the stochastic process takes place on a plane, perpendicular to the magnetic field. For internally Gaussian white noise, this planar-diffusion process is exactly described through the first two moments of the positions and velocities and their corresponding cross correlations. In the absence of the magnetic field, our analytical results are the same as those calculated by Chandrasekhar for the ordinary harmonic oscillator. The stochastic planar diffusion is also well characterized in the overdamped approximation, through the solutions of the Langevin equation.
Steady-state entanglement of harmonic oscillators via dissipation in a single superconducting artificial atom
NASA Astrophysics Data System (ADS)
Wang, Fei; Nie, Wei; Feng, Xunli; Oh, C. H.
The correlated emission lasing (CEL) is experimentally demonstrated in harmonic oscillators coupled via a single three-level artificial atom [Phys. Rev. Lett. 115, 223603 (2015), 10.1103/PhysRevLett.115.223603] in which two-mode entanglement only exists in a certain time period when the harmonic oscillators are resonant with the atomic transitions. Here we examine this system and show that it is possible to obtain the steady-state entanglement when the two harmonic oscillators are resonant with Rabi sidebands. Applying dressed atomic states and Bogoliubov-mode transformation, we obtain the analytical results of the variance sum of a pair of Einstein-Podolsky-Rosen (EPR)-like operators. The stable entanglement originates from the dissipation process of the Bogoliubov modes because the atomic system can act as a reservoir in dressed state representation. We also show that the entanglement is robust against the dephasing rates of the superconducing atom, which is expected to have important applications in quantum information processing.
The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano
The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these "curved" harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK)-type approach, with two free parameters κ1,κ2 which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere S2, hyperbolic plane H2, AntiDeSitter sphere AdS1+1, and DeSitter sphere dS1+1) appear in this family, with Euclidean and Minkowski spaces as flat particular cases. We solve the equations of motion for the curved harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: by direct integration, by obtaining the general CK version of Binet's equation, and finally as a consequence of its superintegrable character. The orbits are conics with center at the potential origin on any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents pertinent results of the theory of conics on spaces of constant curvature.
HOTB: High precision parallel code for calculation of four-particle harmonic oscillator transformation brackets
NASA Astrophysics Data System (ADS)
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more
Condition for equivalence of q-deformed and anharmonic oscillators
NASA Technical Reports Server (NTRS)
Artoni, M.; Zang, Jun; Birman, Joseph L.
The equivalence between the q-deformed harmonic oscillator and a specific anharmonic oscillator model, by which some new insight into the problem of the physical meaning of the parameter q can be attained, are discussed.
Resonant behavior of a harmonic oscillator with fluctuating mass driven by a Mittag-Leffler noise
NASA Astrophysics Data System (ADS)
Zhong, Suchuan; Yang, Jianqiang; Zhang, Lu; Ma, Hong; Luo, Maokang
The resonant behavior of a generalized Langevin equation (GLE) in the presence of a Mittag-Leffler noise is studied analytically in this paper. Considering that a GLE with a Mittag-Leffler friction kernel is very useful for modeling anomalous diffusion processes with long-memory and long-range dependence, and the surrounding molecules do not only collide with the Brownian particle but also adhere to the Brownian particle for random time. Thus, we consider the Brownian particle with fluctuating mass, and the fluctuations of the mass are modelled as a dichotomous noise. Applying the stochastic averaging method, we obtain the exact expression of the output amplitude gain of the system. By studying the impact of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude gain. The results indicate that the bona fide SR, the wide sense SR and the conventional SR phenomena occur in the proposed harmonic oscillator with fluctuating mass driven by Mittag-Leffler noise. It is found that when we consider the output amplitude gain versus the driving frequency, the phenomena of stochastic multi-resonance (SMR) with two, three and four peaks are observed, and the quadruple-peaks SR phenomenon had never been observed in previous literature. Besides, when we investigate the dependence of output amplitude gain on the memory exponent, the inverse stochastic resonance (ISR) phenomenon takes place, in contrast to the well-known phenomenon of stochastic resonance. Furthermore, we compare the corresponding ordinary harmonic oscillator without memory to our generalized model, and found that the properties of long-memory and long-range dependence endows our generalized model with more abundant dynamic behaviors than the ordinary harmonic oscillator without memory.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Menikoff, Ralph
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.
Even and odd coherent states of supersymmetric harmonic oscillators and their nonclassical properties
NASA Astrophysics Data System (ADS)
Afshar, Davood; Motamedinasab, Amin; Anbaraki, Azam; Jafarpour, Mojtaba
In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.
Step potential problem and harmonic oscillator problem in the minimum length quantum mechanics
NASA Astrophysics Data System (ADS)
Park, Soyeon; Woo, Byeong Hyo; Jung, Min; Jang, Eun Ji; Chung, Won Sang
In this paper, we use the quasi-position representation of the minimum length quantum mechanics (MLQM) to study the effects of minimum length uncertainty principle (MLUP) on the quantum mechanical system up to a first-order in β. We introduce the probability density and the probability flux to discuss two problems such as particle in a box and step potential problem. For the step potential, we compute the transmission coefficient and the reflection coefficient and compare them with those of the ordinary quantum mechanics. We also discuss the harmonic oscillator problem in MLQM.
Coherent states for nonlinear harmonic oscillator and some of its properties
Amir, Naila E-mail: firstname.lastname@example.com; Iqbal, Shahid E-mail: email@example.com
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Comment on 'Wave functions of a time-dependent harmonic oscillator in a static magnetic field'
Maamache, M.; Bounames, A.; Ferkous, N.
We show that the procedure used by Ferreira et al. [Phys. Rev. A 66, 024103 (2002)] is not correct for the following reasons: (i) the invariant I(t) they derived does not satisfy the Liouville-Von Neuman equation. (ii) They found that the eigenvalues of I(t) are time dependent which should not be the case according to the Lewis-Riesenfeld theory. We give a correct procedure to find the solution of the system they considered, i.e., the Schroedinger equation for a two-dimensional harmonic oscillator with time-dependent mass and frequency in the presence of a static magnetic field.
Stochastic resonance in a fractional harmonic oscillator subject to random mass and signal-modulated noise
NASA Astrophysics Data System (ADS)
Guo, Feng; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Li, Heng
Stochastic resonance in a fractional harmonic oscillator with random mass and signal-modulated noise is investigated. Applying linear system theory and the characteristics of the noises, the analysis expression of the mean output-amplitude-gain (OAG) is obtained. It is shown that the OAG varies non-monotonically with the increase of the intensity of the multiplicative dichotomous noise, with the increase of the frequency of the driving force, as well as with the increase of the system frequency. In addition, the OAG is a non-monotonic function of the system friction coefficient, as a function of the viscous damping coefficient, as a function of the fractional exponent.
Dressed Photons Induced Resistance Oscillation and Zero Resistance in Arrayed Simple Harmonic Oscillators with No Impurity
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies. PMID:27886252
Harmonic oscillators and resonance series generated by a periodic unstable classical orbit
NASA Technical Reports Server (NTRS)
Kazansky, A. K.; Ostrovsky, Valentin N.
The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.
Fourth-order master equation for a charged harmonic oscillator interacting with the electromagnetic field
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one.
Dressed Photons Induced Resistance Oscillation and Zero Resistance in Arrayed Simple Harmonic Oscillators with No Impurity
NASA Astrophysics Data System (ADS)
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
Dressed Photons Induced Resistance Oscillation and Zero Resistance in Arrayed Simple Harmonic Oscillators with No Impurity.
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
Use of quantum self-friction potentials and forces in standard convention for study of harmonic oscillator
NASA Astrophysics Data System (ADS)
Guseinov, I. I.; Mamedov, B. A.
In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the L^{{(pl^{ * } )}}-SF Laguerre polynomials (L^{{(pl^{ * } )}}-SFLPs) and L^{{(α^{*} )}}-modified SFLPs (L^{{(α^{*} )}}-MSFLPs) in standard convention, the V^{{(pl^{ * } )}}-SF potentials (V^{{(pl^{ * } )}}-SFPs), V^{{(α^{*} )}}-modified SFPs (V^{{(α^{*} )}}-MSFPs), F^{{(pl^{ * } )}}-SF forces (F^{{(pl^{ * } )}}-SFFs) and F^{{(α^{*} )}}-modified SFFs (F^{{(α^{*} )}}-MSFFs) are investigated, where pl^{ * } = 2l + 2 - α^{*} and α^{*} is the integer (α^{*} = α, - ∞ < α ≤ 2) or non-integer (α^{*} ≠ α, - ∞ < α < 3) SF quantum number. We note that the potentials (V^{{(pl^{ * } )}}-SFPs and V^{{(α^{*} )}}-MSFPs), and forces (F^{{(pl^{ * } )}}-SFFs and F^{{(α^{*} )}}-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., V_{num}^{{(pl^{ * } )}} = V_{num}^{{(α^{*} )}} and F_{num}^{{(pl^{ * } )}} = F_{num}^{{(α^{*} )}}. The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.
Information Theoretic Study of the Confined Harmonic Oscillator in Position, Momentum and Phase-Space
NASA Astrophysics Data System (ADS)
Laguna, Humberto; Sagar, Robin
The confined quantum harmonic oscillator (CHO) is an intermediate model which lies between the particle-in-a-box (PIAB), where the free particle is confined, and the quantum harmonic oscillator (HO) where the particle is not confined but is under the influence of a harmonic potential. Position and momentum space densities, and phase-space Wigner functions, are obtained for this system and analyzed using tools from information theory. Shannon entropies are used to gain insights into the localization of the particle in position, momentum and phase-space. The statistical correlation between the position and momentum of the particle is examined using the Wigner function and its mutual information. The analysis is performed as a function of the quantum number and of the box length, and the calculated quantities are compared to those of the PIAB and HO models. Our interests lie in determining similarities or differences among the different models and if there are regimes where the behavior of the CHO model more closely resembles either that of the PIAB or HO model. Departamento de Quimica
Use of videos for students to see the effect of changing gravity on harmonic oscillators
NASA Astrophysics Data System (ADS)
Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber
In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.
Harmonic oscillations of laminae in non-Newtonian fluids: A lattice Boltzmann-Immersed Boundary approach
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.
Reducibility of 1D quantum harmonic oscillator perturbed by a quasiperiodic potential with logarithmic decay
NASA Astrophysics Data System (ADS)
Wang, Zhiguo; Liang, Zhenguo
In this paper we prove an infinite dimensional KAM theorem, in which the assumptions on the derivatives of the perturbation in [24] are weakened from polynomial decay to logarithmic decay. As a consequence, we can apply it to 1D quantum harmonic oscillators and prove the reducibility of the linear harmonic oscillator, T=-\\frac{{{\\text{d}}2}}{\\text{d}{{x}2}}+{{x}2} , on {{L}2}≤ft({R}\\right) perturbed by the quasi-periodic in the time potential V(x,ω t;ω ) with logarithmic decay. This proves the pure-point nature of the spectrum of the Floquet operator K, where K:=‑i∑k=1nωk∂∂θk‑d2dx2+x2+εV(x,θω) is defined on {{L}2}≤ft({R}\\right)\\otimes {{L}2}≤ft({{{T}}n}\\right) , and the potential V(x,θ ;ω ) has logarithmic decay as well as its gradient in ω.
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
Bocko, M.F.; Onofrio, R.
Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves {ital et} {ital al}., 1980, Rev. Mod. Phys. {bold 52}, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. {copyright} {ital 1996 The American Physical Society.}
Double simple-harmonic-oscillator formulation of the thermal equilibrium of a fluid interacting with a coherent source of phonons
NASA Technical Reports Server (NTRS)
Defacio, B.; Vannevel, Alan; Brander, O.
A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ
NASA Astrophysics Data System (ADS)
Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.
Solution of the Quantum Harmonic Oscillator Plus a Delta-Function Potential at the Origin: The "Oddness" of Its Even-Parity Solutions
ERIC Educational Resources Information Center
Viana-Gomes, J.; Peres, N. M. R.
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
Generalized power-spectrum Larmor formula for an extended charged particle embedded in a harmonic oscillator
NASA Astrophysics Data System (ADS)
Marengo, Edwin A.; Khodja, Mohamed R.
The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor's familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.
Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity.
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.
Study of the harmonic oscillation on EAST by an eight-channel Doppler Backscattering (DBS) system
NASA Astrophysics Data System (ADS)
Zhou, C.; Liu, A. D.; Wang, M. Y.; Hu, J. Q.; Zhang, J.; Li, H.; Lan, T.; Xie, J. L.; Liu, W. D.; Yu, C. X.; Doyle, E. J.; University of California, Los Angeles Collaboration; University of Science; Technology of China Team
The eight-channel DBS system has been installed for turbulence measurements in such plasmas. The frequency range is 55 to 75 GHz, covering the entire H-mode pedestal, with a turbulence wavenumber range of 4-12/cm. A harmonic oscillation has been observed by DBS on EAST during ELMy-free H mode. The fundamental frequency of the coherent oscillation is 12-20 kHz and 2nd-8th harmonic are observed, and the radial coverage is from the edge to rho 0.85. Work supported by the Natural Science Foundation of China (NSFC) under 11475173, 11505184, National Magnetic Confinement Fusion Energy Development Program of China under 2013GB106002 and 2014GB109002, and DOE Grants DE- SC0010424 and DE-SC0010469.
Alternative descriptions of wave and particle aspects of the harmonic oscillator
NASA Technical Reports Server (NTRS)
Schuch, Dieter
The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators.
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO.
Relation between the extended time-delayed feedback control algorithm and the method of harmonic oscillators.
Pyragas, Viktoras; Pyragas, Kestutis
In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
Relation between the extended time-delayed feedback control algorithm and the method of harmonic oscillators
NASA Astrophysics Data System (ADS)
Pyragas, Viktoras; Pyragas, Kestutis
In a recent paper [Phys. Rev. E 91, 012920 (2015), 10.1103/PhysRevE.91.012920] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator
NASA Astrophysics Data System (ADS)
Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen
Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.
A time-discrete harmonic oscillator model of human car-following
NASA Astrophysics Data System (ADS)
Wagner, P.
A time-discrete stochastic harmonic oscillator is presented as a model of human car-following behaviour. This describes especially the non-continuous control of a human driver - acceleration changes from time to time at so called action-points and is kept constant in between. Analytical results can be derived which allow to classify the different types of motion possible within this approach. These results show that with weaker control by the human, unstable behaviour of the oscillator becomes more likely. This is in line with common understanding about the causes of accidents. Finally, since even the stochastic behaviour of this model is in parts analytically tractable, the width of the speed-difference and distance fluctuations can be expressed as function of the model's parameter. This allows a fresh view on empirical car-following data and the identification of parameters from real data in the context of the theory presented here.
The quantum fidelity for the time-periodic singular harmonic oscillator
NASA Astrophysics Data System (ADS)
Combescure, Monique
In this paper we perform an exact study of "quantum fidelity" (also called Loschmidt echo) for the time-periodic quantum harmonic oscillator of the following Hamiltonian: Ĥg(t)≔(P2/2)+f(t)(Q2/2)+(g2/Q2), when compared with the quantum evolution induced by Ĥ0(t) (g=0), in the case where f is a T-periodic function and g a real constant. The reference (initial) state is taken to be an arbitrary "generalized coherent state" in the sense of Perelomov. We show that, starting with a quadratic decrease in time in the neighborhood of t =0, this quantum fidelity may recur to its initial value 1 at an infinite sequence of times tk. We discuss the result when the classical motion induced by Hamiltonian Ĥ0(t) is assumed to be stable versus unstable.
Semiclassical analysis of long-wavelength multiphoton processes: The periodically driven harmonic oscillator
Fox, Ronald F.; Vela-Arevalo, Luz V.
The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances.
Entanglement in a continuously measured two-level system coupled to a harmonic oscillator
Hernandez-Concepcion, E.; Alonso, D.; Brouard, S.
The dynamics of a two-level system (TLS) coupled to a harmonic oscillator (HO) is studied under the combined effect of a thermal bath acting on the HO and of a detector continuously measuring one of the components of the spinlike TLS. The analysis focuses on the dynamics of the 'relative entropy of entanglement' (REE) in the one-energy-excitation manifold of the reduced TLS+HO system. For this model system, a stationary state is shown to be reached for which the relative entropy of entanglement is in general nonzero, even though, under certain approximations, the separate effects of bath and detector would be to remove any trace of this resource from the system. Analytical as well as numerical results are obtained for the REE as a function of the different parameters involved in the model definition.
Harmonic oscillator representation in the theory of scattering and nuclear reactions
NASA Technical Reports Server (NTRS)
Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.
The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962
Attractors and Spectral Characteristics of Neural Structures Based on the Model of the Quantum Harmonic Oscillator
Rigatos, Gerasimos G.
Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of importance for the realization of quantum computing machines. To this end, this paper studies neural structures with weights that follow the model of the quantum harmonic oscillator. These weights correspond to diffusing particles, which interact to each other as the theory of Brownian motion predicts. The learning of the stochastic weights (convergence of the diffusing particles to an equilibrium) is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of the number of attractors. Spectral analysis shows that the stochastic weights satisfy an equation which is analogous to the principle of uncertainty.
Manipulating Fock states of a harmonic oscillator while preserving its linearity
NASA Astrophysics Data System (ADS)
Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.
We present a scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first- to second-excited-state transition on resonance with the oscillator. In this scheme, which we call ef-resonant, the spurious oscillator Kerr nonlinearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave three-dimensional cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2 ×106 ) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr nonlinearity below 350 Hz. At times much longer than the transmon coherence times, a nonlinear cavity response with driving power is also observed and explained.
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
NASA Astrophysics Data System (ADS)
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
In this work, we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore, the motion is periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.
Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System
Jolma, Ingunn W.; Ni, Xiao Yu; Rensing, Ludger; Ruoff, Peter
Abstract Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks. PMID:20197027
Research and fabrication of harmonic oscillator with high quality in Si-based MOEMS acceleration seismic geophone
NASA Astrophysics Data System (ADS)
Tong, Zhengrong; Wang, Zhiyong; En, De; Chen, Caihe; Li, Xuejiao; Xie, Xiaofang
A kind of photo-electronic integrated acceleration seismic detecting technology, which is novel and precise based on waveguide M-Z interference, is presented. It provieds modern geologic prospect with a novel detection technology. The principle of the photo-electronic integrated acceleration seismic geophone is introduced in this paper. The core of the photo-electronic integrated acceleration is the silicon harmonic oscillator, which is supported by four silicon beams and integrated on the signal beam of the M-Z interferometer. When the seismic mass is subjected to a normal acceleration a z, the acceleration a z, will result in an inertial force F z, causing the mass to move up or down like the piston, until the counter force of the beam suspension equals this inertial force. The principle of the harmonic oscillator is briefly introduced, the factors influencing the anisotropic etching quality of the harmonic oscillator are analyzed in detail. In experiment, the fabrication technology was studied and improved. The high quality harmonic oscillator has been successfully fabricated. It has been applied in the integrated optical chip of "the theory and experiment research of photoelectric integrated acceleration seismic geophone technology".
A Back-to-Front Derivation: The Equal Spacing of Quantum Levels Is a Proof of Simple Harmonic Oscillator Physics
ERIC Educational Resources Information Center
Andrews, David L.; Romero, Luciana C. Davila
The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…
Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure
NASA Astrophysics Data System (ADS)
Zhao, Liyun; Zhou, Jin; Wu, Quanjun
This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.
Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach
Cari, C. Suparmi, A.
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
Quantization and instability of the damped harmonic oscillator subject to a time-dependent force
Majima, H. Suzuki, A.
We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity (-{gamma}x) and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: L=mxy-U(x+1/2 y)+U(x-1/2 y)+({gamma})/2 (xy-yx)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x{+-}y/2)=1/2 k(x{+-}y/2){sup 2} specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian H. The Heisenberg equations of motion utilizing the quantized Hamiltonian H surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force. - Highlights: > A method of quantizing dissipative systems is presented. > In order to obtain the method, we apply Bateman's dual system approach. > A formula for a transition amplitude is derived. > We use the formula to study the instability of the dissipative systems.
Retrieval of aerosol refractive index from extinction spectra with a damped harmonic-oscillator band model.
Thomas, Gareth E; Bass, Stephen F; Grainger, Roy G; Lambert, Alyn
A new method for the retrieval of the spectral refractive indices of micrometer-sized particles from infrared aerosol extinction spectra has been developed. With this method we use a classical damped harmonic-oscillator model of molecular absorption in conjunction with Mie scattering to model extinction spectra, which we then fit to the measurements using a numerical optimal estimation algorithm. The main advantage of this method over the more traditional Kramers-Kronig approach is that it allows the full complex refractive-index spectra, along with the parameters of the particle size distribution, to be retrieved from a single extinction spectrum. The retrieval scheme has been extensively characterized and has been found to provide refractive indices with a maximum uncertainty of approximately 10% (with a minimum of approximately 0.1%). Comparison of refractive indices calculated from measurements of a ternary solution of HNO3, H2SO4, and H2O with those published in J. Phys. Chem. A 104, 783 (2000) show similar differences as found by other authors.
Are There Signatures of Harmonic Oscillator Shells Far from Stability? First Spectroscopy of 110Zr
NASA Astrophysics Data System (ADS)
Paul, N.; Corsi, A.; Obertelli, A.; Doornenbal, P.; Authelet, G.; Baba, H.; Bally, B.; Bender, M.; Calvet, D.; Château, F.; Chen, S.; Delaroche, J.-P.; Delbart, A.; Gheller, J.-M.; Giganon, A.; Gillibert, A.; Girod, M.; Heenen, P.-H.; Lapoux, V.; Libert, J.; Motobayashi, T.; Niikura, M.; Otsuka, T.; Rodríguez, T. R.; Roussé, J.-Y.; Sakurai, H.; Santamaria, C.; Shimizu, N.; Steppenbeck, D.; Taniuchi, R.; Togashi, T.; Tsunoda, Y.; Uesaka, T.; Ando, T.; Arici, T.; Blazhev, A.; Browne, F.; Bruce, A. M.; Carroll, R.; Chung, L. X.; Cortés, M. L.; Dewald, M.; Ding, B.; Flavigny, F.; Franchoo, S.; Górska, M.; Gottardo, A.; Jungclaus, A.; Lee, J.; Lettmann, M.; Linh, B. D.; Liu, J.; Liu, Z.; Lizarazo, C.; Momiyama, S.; Moschner, K.; Nagamine, S.; Nakatsuka, N.; Nita, C.; Nobs, C. R.; Olivier, L.; Patel, Z.; Podolyák, Zs.; Rudigier, M.; Saito, T.; Shand, C.; Söderström, P.-A.; Stefan, I.; Orlandi, R.; Vaquero, V.; Werner, V.; Wimmer, K.; Xu, Z.
The first measurement of the low-lying states of the neutron-rich 110Zr and 112Mo was performed via in-beam γ -ray spectroscopy after one proton removal on hydrogen at ˜200 MeV /nucleon . The 21+ excitation energies were found at 185(11) keV in 110Zr, and 235(7) keV in 112Mo, while the R42=E (41+)/E (21+) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of 110Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z =40 and N =70 . The present data also invalidate predictions for a tetrahedral ground state symmetry in 110Zr.
Nonlinear spectroscopic theory of displaced harmonic oscillators with differing curvatures: a correlation function approach.
Fidler, Andrew F; Engel, Gregory S
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high-frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency modulation of the different oscillators. We illustrate how the topologically protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally, we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators
NASA Astrophysics Data System (ADS)
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.
A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.
The stochastic electrodynamic solution of the charged harmonic oscillator in a constant uniform magnetic field
NASA Astrophysics Data System (ADS)
Davis, Brian Thompson
An isotropic three-dimensional non-relativistic charged harmonic oscillator immersed in the stochastic zero point field, an applied classical radiation field, and a constant uniform magnetic field is treated. The method followed is that of previous work [1, 2, 3, 4] with no static magnetic field present. Starting from a non-runaway classical stochastic motion equation, an appropriate conjugate momentum is derived. The classical position/conjugate momentum phase space distribution, a product of Dirac delta distributions, is ensemble averaged. The Liouville equation for this ensemble averaged phase space distribution, along with a separate independent equation that the distribution must satisfy, are derived in dipole approximation. The Weyl transformed Liouville, equation is used to derive a stochastic Schroedinger equation valid to first order in the Larmor frequency. The stochastic equation is the same as the quantum one to this order, except for the presence of radiation reaction vector potentials that produce spontaneous emission without quantization of the applied radiation field. The ensemble averaged Weyl transformed phase space distribution is also shown to be separable into a product of Schroedinger eigenfunctions, in general. Electric dipole spectra and transition probabilities for spontaneous emission and resonant absorption are calculated using the stochastic Schroedinger equation and its exact solutions. The results are compared to the corresponding predictions of quantum electrodynamics and found to be in agreement.
Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.
In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ⩽ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended magentoohydrodynamics (MHD) code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by rotation and/or rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHOs can be destabilized in principle with rotation in either direction. The modeling results are consistent with observations of EHO, support the proposed theory of the EHO as a low-n kink/peeling mode destabilized by edge E × B rotational shear, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.
Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, Wm.; Tobias, B. J.; Yan, Z.
In quiescent H-mode (QH) regime, the edge harmonic oscillations (EHO) play an important role in avoiding the transient ELM power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n <= 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-I and MIR diagnostics, as well as the kink/peeling mode properties of the ideal MHD code ELITE. The numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the toroidal rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that the low-n EHO can be destabilized in principle with rotation in both directions. These modeling results are consistent with experimental observations of the EHO and support the proposed theory of the EHO as a rotational shear driven kink/peeling mode.
Are There Signatures of Harmonic Oscillator Shells Far from Stability? First Spectroscopy of ^{110}Zr.
Paul, N; Corsi, A; Obertelli, A; Doornenbal, P; Authelet, G; Baba, H; Bally, B; Bender, M; Calvet, D; Château, F; Chen, S; Delaroche, J-P; Delbart, A; Gheller, J-M; Giganon, A; Gillibert, A; Girod, M; Heenen, P-H; Lapoux, V; Libert, J; Motobayashi, T; Niikura, M; Otsuka, T; Rodríguez, T R; Roussé, J-Y; Sakurai, H; Santamaria, C; Shimizu, N; Steppenbeck, D; Taniuchi, R; Togashi, T; Tsunoda, Y; Uesaka, T; Ando, T; Arici, T; Blazhev, A; Browne, F; Bruce, A M; Carroll, R; Chung, L X; Cortés, M L; Dewald, M; Ding, B; Flavigny, F; Franchoo, S; Górska, M; Gottardo, A; Jungclaus, A; Lee, J; Lettmann, M; Linh, B D; Liu, J; Liu, Z; Lizarazo, C; Momiyama, S; Moschner, K; Nagamine, S; Nakatsuka, N; Nita, C; Nobs, C R; Olivier, L; Patel, Z; Podolyák, Zs; Rudigier, M; Saito, T; Shand, C; Söderström, P-A; Stefan, I; Orlandi, R; Vaquero, V; Werner, V; Wimmer, K; Xu, Z
The first measurement of the low-lying states of the neutron-rich ^{110}Zr and ^{112}Mo was performed via in-beam γ-ray spectroscopy after one proton removal on hydrogen at ∼200 MeV/nucleon. The 2_{1}^{+} excitation energies were found at 185(11) keV in ^{110}Zr, and 235(7) keV in ^{112}Mo, while the R_{42}=E(4_{1}^{+})/E(2_{1}^{+}) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of ^{110}Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z=40 and N=70. The present data also invalidate predictions for a tetrahedral ground state symmetry in ^{110}Zr.
Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards
NASA Astrophysics Data System (ADS)
Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards.
Chen, Y F; Tung, J C; Tuan, P H; Yu, Y T; Liang, H C; Huang, K F
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
Variational study of a two-level system coupled to a harmonic oscillator in an ultrastrong-coupling regime
Hwang, Myung-Joong; Choi, Mahn-Soo
The nonclassical behavior of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solutions do not account accurately for nonclassical effects such as squeezing. We suggest a trial wave function and demonstrate that it has an excellent accuracy for the quantum correlation effects as well as for the energy.
Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic
NASA Astrophysics Data System (ADS)
Hanin, Boris; Zelditch, Steve; Zhou, Peng
We study the scaling asymptotics of the eigenspace projection kernels Π_{hbar, E}(x,y) of the isotropic Harmonic Oscillator {hat{H}_{hbar} = - hbar^2 Δ +|x|^2} of eigenvalue {E = hbar(N + d/2)} in the semi-classical limit {hbar to 0} . The principal result is an explicit formula for the scaling asymptotics of Π_{hbar, E}(x,y) for x, y in a {hbar^{2/3}} neighborhood of the caustic C_E as {hbar → 0.} The scaling asymptotics are applied to the distribution of nodal sets of Gaussian random eigenfunctions around the caustic as {hbar to 0} . In previous work we proved that the density of zeros of Gaussian random eigenfunctions of {hat{H}_{hbar}} have different orders in the Planck constant {hbar} in the allowed and forbidden regions: In the allowed region the density is of order {hbar^{-1}} while it is {hbar^{-1/2}} in the forbidden region. Our main result on nodal sets is that the density of zeros is of order {hbar^{-2/3}} in an {hbar^{2/3}} -tube around the caustic. This tube radius is the `critical radius'. For annuli of larger inner and outer radii {hbar^{α}} with {0 < α < 2/3} we obtain density results that interpolate between this critical radius result and our prior ones in the allowed and forbidden region. We also show that the Hausdorff ( d-2)-dimensional measure of the intersection of the nodal set with the caustic is of order {hbar^{- 2/3}}.
Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential
NASA Astrophysics Data System (ADS)
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D
NASA Astrophysics Data System (ADS)
Ren, X.; Chen, M.; Chen, X.; Domier, C. W.; Ferraro, N. M.; Kramer, G. J.; Luhmann, N. C., Jr.; Muscatello, C. M.; Nazikian, R.; Shi, L.; Tobias, B. J.; Valeo, E.
Quiescent H-mode (QH-mode) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation, which can help to explain the physics behind EHO modes. MIR data sometimes indicate a counter-propagation between dominant (n=1) and higher harmonic modes of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical mis-alignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-linear structure of the EHO modes, which induces multiple harmonics that are properly charaterized in the synthetic diagnostic. By excluding mis-alignments of optics as well as patially eliminating non-linearity of EHO mode structure as possible explanation for the data, counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. The identification of a non-ideal structure motivates further exploration of nonlinear models of this instability. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
Single particle calculations for a Woods-Saxon potential with triaxial deformations, and large Cartesian oscillator basis (TRIAXIAL 2014, Third version of the code Triaxial)
NASA Astrophysics Data System (ADS)
Mohammed-Azizi, B.; Medjadi, D. E.
, WINDOWS 7, LINUX. RAM: 256 Mb (depending on nmax). Swap file: 4Gb (depending on nmax) Classification: 17.7. Does the new version supersede the previous version?: Yes Catalogue identifier of previous version: ADSK_v2_0 Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 634 Nature of problem: The Single particle energies and the single particle wave functions are calculated from one-body Hamiltonian including a central field of Woods-Saxon type, a spin-orbit interaction, and the Coulomb potential for the protons. We consider only ellipsoidal (triaxial) shapes. The deformation of the nuclear shape is fixed by the usual Bohr parameters (β,γ). Solution method: The representative matrix of the Hamiltonian is built by means of the Cartesian basis of the anisotropic harmonic oscillator, and then diagonalized by a set of subroutines of the EISPACK library. Two quadrature methods of Gauss are employed to calculate respectively the integrals of the matrix elements of the Hamiltonian, and the integral defining the Coulomb potential. Two quantum numbers are conserved: the parity and the signature. Due to the Kramers degeneracy, only positive signature is considered. Therefore, calculations are made for positive and negative parity separately (with positive signature only). Reasons for new version: Now, there are several ways to obtain the eigenvalues and the eigenfunctions. The eigenvalues can be obtained from the subroutine 'eigvals' or from the array 'energies' or also from the formatted files 'valuu.dat', 'eigenvalo.dat', 'eigenva.dat' or better from the unformatted file 'eigenvaunf.dat'. The eigenfunctions can be obtained straightforwardly in configuration space from the subroutine 'eigfunc' or by their components on the oscillator basis from the subroutine 'compnts'. The latter are also recorded on a formatted file 'componento.dat' or on an unformatted file 'componentounf.dat'. Summary of revisions: This version is
Form of the effective interaction in harmonic-oscillator-based effective theory
NASA Astrophysics Data System (ADS)
Haxton, W. C.
I explore the form of the effective interaction in harmonic-oscillator-based effective theory (HOBET) in leading order (LO) through next-to-next-to-next-to-leading order (NLO3). Because the included space in a HOBET (as in the shell model) is defined by the oscillator energy, both long-distance (low-momentum) and short-distance (high-momentum) degrees of freedom reside in the high-energy excluded space. A HOBET effective interaction is developed in which a short-range contact-gradient expansion, free of operator mixing and corresponding to a systematic expansion in nodal quantum numbers, is combined with an exact summation of the relative kinetic energy. By this means the very strong coupling of the included (P) and excluded (Q) spaces by the kinetic energy is removed. One finds a simple and rather surprising result, that the interplay of QT and QV is governed by a single parameter κ, the ratio of an observable, the binding energy |E|, to a parameter in the effective theory, the oscillator energy ℏω. Once the functional dependence on κ is identified, the remaining order-by-order subtraction of the short-range physics residing in Q becomes systematic and rapidly converging. Numerical calculations are used to demonstrate how well the resulting expansion reproduces the running of Heff from high scales to a typical shell-model scale of 8ℏω. At NLO3 various global properties of Heff are reproduced to a typical accuracy of 0.01%, or about 1 keV, at 8ℏω. Channel-by-channel variations in convergence rates are similar to those found in effective field theory approaches. The state dependence of the effective interaction has been a troubling problem in nuclear physics and is embodied in the energy dependence of Heff(|E|) in the Bloch-Horowitz formalism. It is shown that almost all of this state dependence is also extracted in the procedures followed here, isolated in the analytic dependence of Heff on κ. Thus there exists a simple, Hermitian Heff that can be use
Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems
NASA Technical Reports Server (NTRS)
Isar, Aurelian
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
Deformation quantization and boundary value problems
NASA Astrophysics Data System (ADS)
Tarkhanov, Nikolai
We describe a natural construction of deformation quantization on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.
Research on the Dynamic Problems of 3D Cross Coupling Quantum Harmonic Oscillator by Virtue of Intermediate Representation | x> λ, ν
NASA Astrophysics Data System (ADS)
Xu, Shi-Min; Xu, Xing-Lei; Li, Hong-Qi
The intermediate representation (namely intermediate coordinate-momentum representation) | x> λ, ν are introduced and employed to research the expression of the operator tauhat{p}+σhat{x} in intermediate representation | x> λ, ν . The systematic Hamilton operator hat{H} of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ, ν, τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator | x> λ, ν λ, ν < x|, and the Radon transformation of Wigner function is just a margin distribution.
Chaos in axially symmetric potentials with octupole deformation
Heiss, W.D.; Nazmitdinov, R.G.; Radu, S. Departamento de Fisica Teorica C-XI, Universidad Autonoma de Madrid, E-28049, Madrid )
Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the motion is strongly dependent on the quadrupole deformation in that for a prolate deformation virtually no chaos is discernible while for the oblate case the motion shows strong chaos when the octupole term is turned on.
Realization of quantum gates based on three-dimensional harmonic oscillator in a time-varying electromagnetic field
NASA Astrophysics Data System (ADS)
Gautam, Kumar; Chauhan, Garv; Rawat, Tarun Kumar; Parthasarathy, Harish; Sharma, Navneet
This paper presents the design of a given quantum unitary gate by perturbing a three-dimensional (3-D) quantum harmonic oscillator with a time-varying but spatially constant electromagnetic field. The idea is based on expressing the radiation- perturbed Hamiltonian as the sum of the unperturbed Hamiltonian and O( e) and perturbations and then solving the Schrödinger equation to obtain the evolution operator at time T up to , and this is a linear-quadratic function of the perturbing electromagnetic field values over the time interval [0, T]. Setting the variational derivative of the error energy with respect to the electromagnetic field values with an average electromagnetic field energy constraint leads to the optimal electromagnetic field solution, a linear integral equation. The reliability of such a gate design procedure in the presence of heat bath coupling is analysed, and finally, an example illustrating how atoms and molecules can be approximated using oscillators is presented.
Perelomov and Barut-Girardello SU(1, 1) Coherent States for Harmonic Oscillator in One-Dimensional Half Space
NASA Astrophysics Data System (ADS)
Liu, Q. H.; Zhuo, H.
The Perelomov and the Barut-Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below √ {9/4-6/π } that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut-Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.
An Efficient Radial Basis Function Mesh Deformation Scheme within an Adjoint-Based Aerodynamic Optimization Framework
NASA Astrophysics Data System (ADS)
Poirier, Vincent
Mesh deformation schemes play an important role in numerical aerodynamic optimization. As the aerodynamic shape changes, the computational mesh must adapt to conform to the deformed geometry. In this work, an extension to an existing fast and robust Radial Basis Function (RBF) mesh movement scheme is presented. Using a reduced set of surface points to define the mesh deformation increases the efficiency of the RBF method; however, at the cost of introducing errors into the parameterization by not recovering the exact displacement of all surface points. A secondary mesh movement is implemented, within an adjoint-based optimization framework, to eliminate these errors. The proposed scheme is tested within a 3D Euler flow by reducing the pressure drag while maintaining lift of a wing-body configured Boeing-747 and an Onera-M6 wing. As well, an inverse pressure design is executed on the Onera-M6 wing and an inverse span loading case is presented for a wing-body configured DLR-F6 aircraft.
Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation.
Braun, J; Buntkowsky, G; Bernarding, J; Tolxdorff, T; Sack, I
New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.
Using Monte Carlo ray tracing simulations to model the quantum harmonic oscillator modes observed in uranium nitride
Lin, J. Y. Y.; Aczel, Adam A; Abernathy, Douglas L; Nagler, Stephen E; Buyers, W. J. L.; Granroth, Garrett E
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of- flight chopper spectrometers [A.A. Aczel et al, Nature Communications 3, 1124 (2012)]. These modes are well described by 3D isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for the nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states (PDOS), and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T-dependence of the scattering from these modes is strongly influenced by the uranium lattice.
Using Monte Carlo ray tracing simulations to model the quantum harmonic oscillator modes observed in uranium nitride
NASA Astrophysics Data System (ADS)
Lin, J. Y. Y.; Aczel, A. A.; Abernathy, D. L.; Nagler, S. E.; Buyers, W. J. L.; Granroth, G. E.
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of-flight chopper spectrometers [A. A. Aczel et al., Nat. Commun. 3, 1124 (2012), 10.1038/ncomms2117]. These modes are well described by three-dimensional isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states, and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature-dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T dependence of the scattering from these modes is strongly influenced by the uranium lattice.
Computer-simulation calculations of the electronic stopping of fast heavy charges by a classical harmonic oscillator
Jakas, M. M.; Perez de la Rosa, F. J.; Custidiano, E. R.
The accuracy of Bohr's and more recent analytical calculations of the electronic stopping of heavy charges by a classical harmonic oscillator is analyzed. According to results in this paper, for |{xi}|{>=}100 ({xi} being the Bohr stopping parameter) the present simulations agree with previous theoretical calculations, whereas for smaller |{xi}| values, discrepancies are evident. In fact, for |{xi}|<100 the stopping cross section seems to be sensitive to the sign of the ion charge. The so-called Barkas effect is unambiguously observed and positively charged projectiles appear to have a larger stopping compared to that of negative ones at the same {xi}. Bohr's calculations, however, seem to reproduce the stopping of negative charges relatively well, but those of positive ions are consequently underestimated. By giving the electron an initial velocity, the so-called inner-shell effect on the stopping can be readily studied. The present simulations show that previous analytical predictions of this effect do not account for the present results.
Harmonic oscillations of a lamina in a viscous fluid near a solid surface: A lattice Boltzmann-immersed boundary approach
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
In this paper, a rigid thickless lamina is immersed in a quiescent viscous fluid and it undergoes transverse finite amplitude harmonic oscillations near a solid surface. The surrounding flow physics is computed through the lattice Boltzmann method. In order to account for the presence of the lamina in the lattice fluid background, the Immersed Boundary method is adopted. Several scenarios are investigated by varying the distance between the initial position of the lamina and the solid wall. For a given lamina-solid surface distance, the effect of the Reynolds number is investigated, together with the influence of the Keulegan-Carpenter number. Findings in terms of drag coefficient show that the force exerted by the encompassing fluid upon the lamina is remarkably influenced by the distance from the solid surface, especially for low values of the Reynolds number. Moreover, such results are confirmed by the computation of the hydrodynamic function. In fact, it highlights that the added mass effect and the non-linear damping experienced by the oscillating lamina grow as the above mentioned distance and the Reynolds number reduce.
Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics
NASA Astrophysics Data System (ADS)
Ivanovich Aptekarev, Alexander; Nikolaevich Tulyakov, Dmitry; Valero Toranzo, Irene; Sanchez Dehesa, Jesús
The Rényi entropies Rp [ ρ ], p> 0, ≠ 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρn(r) density of the Rydberg wavefunctions Ψn,l, { μ }(r); so, to the ℒp-norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n,l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.
Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics
NASA Astrophysics Data System (ADS)
Aptekarev, Alexander Ivanovich; Tulyakov, Dmitry Nikolaevich; Toranzo, Irene Valero; Dehesa, Jesús Sanchez
The Rényi entropies R p [ ρ ], p> 0, ≠ 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρ n (r) density of the Rydberg wavefunctions Ψ n,l, { μ }(r); so, to the ℒ p -norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n,l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.
Sampled-data-based consensus and containment control of multiple harmonic oscillators: A motion-planning approach
NASA Astrophysics Data System (ADS)
Liu, Yongfang; Zhao, Yu; Chen, Guanrong
This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.
Sampled-data-based consensus and containment control of multiple harmonic oscillators: A motion-planning approach.
Liu, Yongfang; Zhao, Yu; Chen, Guanrong
This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.
Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.
Classical and quantum harmonic oscillators with time dependent mass and frequency: A new class of exactly solvable model
NASA Astrophysics Data System (ADS)
Mandal, Swapan
The classical harmonic oscillator with time dependent mass and frequency is investigated to obtain a closed form exact analytical solution. It is found that the closed form analytical solutions are indeed possible if the time dependent mass of the oscillator is inversely proportional to the time dependent frequency. The scaled wronskian obtained from the linearly independent solutions of the equation of motion of the classical oscillator is used to obtain the solution corresponding to its quantum mechanical counterpart. The analytical solution of the present oscillator is used to obtain the squeezing effects of the input coherent light. In addition to the possibilities of getting the squeezed states, the present solution will be of use for investigating various quantum statistical properties of the radiation fields. As an example, we investigate the antibunching of the input thermal (chaotic) light coupled to the oscillator. Therefore, the appearance of the photon antibunching does not warrant the squeezing and vice-versa. The exact solution is obtained at the cost of the stringent condition where the product of time dependent mass and frequency of the oscillator is time invariant.
On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces
Noguera, Norman; Rózga, Krzysztof
In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
Adaptive Runge-Kutta integration for stiff systems: Comparing Nosé and Nosé-Hoover dynamics for the harmonic oscillator
NASA Astrophysics Data System (ADS)
Graham Hoover, William; Clinton Sprott, Julien; Griswold Hoover, Carol
We describe the application of adaptive (variable time step) integrators to stiff differential equations encountered in many applications. Linear harmonic oscillators subject to nonlinear thermal constraints can exhibit either stiff or smooth dynamics. Two closely related examples, Nosé's dynamics and Nosé-Hoover dynamics, are both based on Hamiltonian mechanics and generate microstates consistent with Gibbs' canonical ensemble. Nosé's dynamics is stiff and can present severe numerical difficulties. Nosé-Hoover dynamics, although it follows exactly the same trajectory, is smooth and relatively trouble-free. We emphasize the power of adaptive integrators to resolve stiff problems such as the Nosé dynamics for the harmonic oscillator. The solutions also illustrate the power of computer graphics to enrich numerical solutions.
NASA Technical Reports Server (NTRS)
Stenholm, Stig
A single mode cavity is deformed smoothly to change its electromagnetic eigenfrequency. The system is modeled as a simple harmonic oscillator with a varying period. The Wigner function of the problem is obtained exactly by starting with a squeezed initial state. The result is evaluated for a linear change of the cavity length. The approach to the adiabatic limit is investigated. The maximum squeezing is found to occur for smooth change lasting only a fraction of the oscillational period. However, only a factor of two improvement over the adiabatic result proves to be possible. The sudden limit cannot be investigated meaningfully within the model.
Structural basis of inter-protofilament interaction and lateral deformation of microtubules
Sui, Haixin; Downing, Kenneth H.
Summary The diverse functions of microtubules require stiff structures possessing sufficient lateral flexibility to enable bending with high curvature. We used cryo-electron microscopy to investigate the molecular basis for these critical mechanical properties. High-quality structural maps were used to build pseudo-atomic models of microtubules containing 11 to 16 protofilaments, representing a wide range of lateral curvature. Protofilaments in all these microtubules were connected primarily via inter-protofilament interactions between the M loops, and the H1′-S2 and H2-S3 loops. We postulate that the tolerance of the loop-loop interactions to lateral deformation provides the capacity for high-curvature bending without breaking. On the other hand, the local molecular architecture that surrounds these connecting loops contributes to the overall rigidity. Inter-protofilament interactions in the seam region are similar to those in the normal helical regions, suggesting that the existence of the seam does not significantly affect the mechanical properties of microtubules. PMID:20696402
Addendum to "An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates" [Phys. Lett. A 379 (26-27) (2015) 1589-1593
NASA Astrophysics Data System (ADS)
Quesne, C.
The classical and quantum solutions of a nonlinear model describing harmonic oscillators on the sphere and the hyperbolic plane, derived in polar coordinates in a recent paper (Quesne, 2015) [1], are extended by the inclusion of an isotonic term.
Investigation of Bohr Hamiltonian in the presence of time-dependent Manning-Rosen, harmonic oscillator and double ring shaped potentials
NASA Astrophysics Data System (ADS)
Sobhani, Hadi; Hassanabadi, Hassan
This paper contains study of Bohr Hamiltonian considering time-dependent form of two important and famous nuclear potentials and harmonic oscillator. Dependence on time in interactions is considered in general form. In order to investigate this system, a powerful mathematical method has been employed, so-called Lewis-Riesenfeld dynamical invariant method. Appropriate dynamical invariant for considered system has been constructed. Then its eigen functions and the wave function are derived. At the end, we discussed about physical meaning of the results.
A dynamical basis for crustal deformation and seismotectonic block movements in central Europe
NASA Technical Reports Server (NTRS)
Liu, H.-S.
The stress field in the earth's crust as inferred from satellite gravity data causes crustal deformation and seismotectonic block movements in central Europe. The satellite-determined stresses in the crust of central Europe are consistent with earthquake focal mechanisms, joint-orientation and in situ stress measurements.
Franck-Condon factors perturbed by damped harmonic oscillators: Solvent enhanced X 1Ag ↔ A1B1u absorption and fluorescence spectra of perylene
NASA Astrophysics Data System (ADS)
Wang, Chen-Wen; Yang, Ling; Zhu, Chaoyuan; Yu, Jian-Guo; Lin, Sheng-Hsien
Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang-Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X 1Ag ↔ A1B1u absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v10 is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases.
Probing deformed quantum commutators
NASA Astrophysics Data System (ADS)
Rossi, Matteo A. C.; Giani, Tommaso; Paris, Matteo G. A.
Several quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose their physical meaning. In quantum mechanics, the insurgence of such a minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on position measurements has a lower bound. The value of the minimal length is not predicted by theories and must be estimated experimentally. In this paper, we address the quantum bound to the estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra induced by the deformed commutation relations.
Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial
NASA Astrophysics Data System (ADS)
Marquette, Ian; Quesne, Christiane
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent PIV, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed Xm1,m2,…,mk Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.
Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective
NASA Astrophysics Data System (ADS)
Ayvaz, Muzaffer; Demiralp, Metin
In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.
Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective
Ayvaz, Muzaffer; Demiralp, Metin
In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.
Comment on 'Solving the two-mode squeezed harmonic oscillator and the kth-order harmonic generation in Bargmann-Hilbert spaces'
NASA Astrophysics Data System (ADS)
Lo, C. F.
Recently Zhang (2013 J. Phys. A: Math. Theor. 46 455302) proposed an analytical approach to solve the time-independent Schrödinger equation for the single-mode and two-mode squeezed harmonic oscillators in the Bargmann space of entire functions. In this comment we show that the eigenfunctions of these two systems exist in closed form and are expressed in terms of the Hermite polynomials. Moreover, since both oscillators exhibit the SU(1,1) dynamical symmetry, the eigenvalue problem can be tackled in a unified manner. In the Hilbert space of analytic functions of a complex variable in the unit disc, the energy eigenvalue equations involve first-order ordinary differential equations only, so we can easily solve these equations to obtain simple closed-form solutions.
Coherence and decoherence processes of a harmonic oscillator coupled with finite temperature field: Exact eigenbasis solution of Kossakowski-Linblad's equation
NASA Astrophysics Data System (ADS)
Tay, Buang Ann
The eigenvalue problem of Kossakowski-Linblad's kinetic equation associated with the reduced density matrix of a harmonic oscillator interacting with a thermal bath in equilibrium is solved. The solution gives rise to a complete orthogonal eigenbasis endowed with Hilbert space structure that has a weighted norm. We find that the eigenfunctions at finite temperature can be obtained from the eigenfunction at zero temperature through a hyperbolic rotation on the position variables. This transformation enables the extension of the simple harmonic oscillator density matrix to that of a finite temperature. We further investigate the decay of these extended states under our dissipative kinetic equation. Furthermore, the Hilbert space structure enables the proof of a H -theorem in this system. We apply the eigenbasis expansion of an initial state to analyze decoherence as well as coherence processes. We find that coherence process occurs at a longer time scale compared to decoherence process. The time scales of both processes are estimated with the eigenbasis expansion. In the same way we analyze the evolution of the coherent state. We show that in addition to the ordinary decay time, we found another time scale which is defined by the time when the motion of the peak of the coherent state become comparative to the width of the coherent state. In contrast to the ordinary decay time this new relaxation time depends on the initial value of the momentum of the oscillator. We also find that our eigenbasis is applicable to a class of non-linear interactions, with a slight extension of the form of transport coefficients due to the non-linear interactions.
A remarkable spectral feature of the Schrödinger Hamiltonian of the harmonic oscillator perturbed by an attractive δ‧-interaction centred at the origin: double degeneracy and level crossing
NASA Astrophysics Data System (ADS)
Albeverio, Sergio; Fassari, Silvestro; Rinaldi, Fabio
We rigorously define the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive δ‧-interaction, of strength β, centred at 0 (the bottom of the confining parabolic potential), by explicitly providing its resolvent. Our approach is based on a 'coupling constant renormalization', related to a technique originated in quantum field theory and implemented in the rigorous mathematical construction of the self-adjoint operator representing the negative Laplacian perturbed by the δ-interaction in two and three dimensions. The way the δ‧-interaction enters in our Hamiltonian corresponds to the one originally discussed for the free Hamiltonian (instead of the harmonic oscillator one) by P Sěba. It should not be confused with the δ‧-potential perturbation of the harmonic oscillator discussed, e.g., in a recent paper by Gadella, Glasser and Nieto (also introduced by P Sěba as a perturbation of the one-dimensional free Laplacian and recently investigated in that context by Golovaty, Hryniv and Zolotaryuk). We investigate in detail the spectrum of our perturbed harmonic oscillator. The spectral structure differs from that of the one-dimensional harmonic oscillator perturbed by an attractive δ-interaction centred at the origin: the even eigenvalues are not modified at all by the δ‧-interaction. Moreover, all the odd eigenvalues, regarded as functions of β, exhibit the rather remarkable phenomenon called 'level crossing' after first producing the double degeneracy of all the even eigenvalues for the value \\beta = \\beta _0 = \\frac{{2\\sqrt \\pi }}{{B\\left( {\\frac{3}{4},\\frac{1}{2}} \\right)}} \\cong 1.47934(B( ·, ·) being the beta function). Dedicated to Professor Gianfausto Dell'Antonio on the occasion of his 80th birthday.
A novel model of interaction between high frequency electromagnetic non-ionizing fields and microtubules viewed as coupled two-degrees of freedom harmonic oscillators.
Caligiuri, Luigi Maxmilian
The question regarding the potential biological and adverse health effects of non-ionizing electromagnetic fields on living organisms is of primary importance in biophysics and medicine. Despite the several experimental evidences showing such occurrence in a wide frequency range from extremely low frequency to microwaves, a definitive theoretical model able to explain a possible mechanism of interaction between electromagnetic fields and living matter, especially in the case of weak and very weak intensities, is still missing. In this paper it has been suggested a possible mechanism of interaction involving the resonant absorption of electromagnetic radiation by microtubules. To this aim these have been modeled as non-dissipative forced harmonic oscillators characterized by two coupled "macroscopic" degrees of freedom, respectively describing longitudinal and transversal vibrations induced by the electromagnetic field. We have shown that the proposed model, although at a preliminary stage, is able to explain the ability of even weak electromagnetic radiating electromagnetic fields to transfer high quantities of energy to living systems by means of a resonant mechanism, so capable to easily damage microtubules structure.
UF-CHERS Measurements of Ion Temperature and Toroidal Rotation Fluctuations Associated with the Edge Harmonic Oscillation in Quiescent H-mode Plasmas
NASA Astrophysics Data System (ADS)
Truong, D. D.; Fonck, R. J.; McKee, G. R.; Yan, Z.; Grierson, B. A.
The UF-CHERS (Ultra Fast CHarge Exchange Recombination Spectroscopy) diagnostic at DIII-D measures local, long-wavelength ion temperature and toroidal velocity fluctuations at turbulence-relevant spatiotemporal scales from emission of the CVI n=8 ->7 transition. During Quiescent H-mode (QH-mode) plasmas, which offer ELM-free improved confinement, UF-CHERS measurements observed coherent, low frequency (fo 10kHz) pedestal oscillations in Ti and vtor at the Edge Harmonic Oscillation (EHO) frequency while several modes between 35-75 kHz are suppressed when the EHO appears. Although broadband ion temperature and density fluctuations were reduced by the EHO, the toroidal rotation showed increased fluctuation amplitude. Investigating ion temperature and toroidal fluctuations associated with the EHO may provide insights into the saturated instability driving the EHO. Supported by DOE Grants DE-FG02-08ER54999, DE-FC02-04ER54698, and NSF GRFP Grant DGE-1256259.
An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.
Comparison between the Morse eigenfunctions and deformed oscillator wavefunctions
Recamier, J.; Mochan, W. L.; Gorayeb, M.; Paz, J. L.
In this work we introduce deformed creation and annihilation operators which differ from the usual harmonic oscillator operators a, a{sup {dagger}} by a number operator function A circumflex = a circumflex f(n circumflex ), A circumflex {sup {dagger}} = f(n circumflex )a circumflex {sup {dagger}}. We construct the deformed coordinate and momentum in terms of the deformed operators and maintain only up to first order terms in the deformed operators. By application of the deformed annihilation operator upon the vacuum state we get the ground state wavefunction in the configuration space and the wavefunctions for excited states are obtained by repeated application of the deformed creation operator. Finally, we compare the wavefunctions obtained with the deformed operators with the corresponding Morse eigenfunctions.
Relation of deformed nonlinear algebras with linear ones
NASA Astrophysics Data System (ADS)
Nowicki, A.; Tkachuk, V. M.
The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator.
Evaluation of high-resolution sea ice models on the basis of statistical and scaling properties of Arctic sea ice drift and deformation
NASA Astrophysics Data System (ADS)
Girard, L.; Weiss, J.; Molines, J. M.; Barnier, B.; Bouillon, S.
Sea ice drift and deformation from models are evaluated on the basis of statistical and scaling properties. These properties are derived from two observation data sets: the RADARSAT Geophysical Processor System (RGPS) and buoy trajectories from the International Arctic Buoy Program (IABP). Two simulations obtained with the Louvain-la-Neuve Ice Model (LIM) coupled to a high-resolution ocean model and a simulation obtained with the Los Alamos Sea Ice Model (CICE) were analyzed. Model ice drift compares well with observations in terms of large-scale velocity field and distributions of velocity fluctuations although a significant bias on the mean ice speed is noted. On the other hand, the statistical properties of ice deformation are not well simulated by the models: (1) The distributions of strain rates are incorrect: RGPS distributions of strain rates are power law tailed, i.e., exhibit "wild randomness," whereas models distributions remain in the Gaussian attraction basin, i.e., exhibit "mild randomness." (2) The models are unable to reproduce the spatial and temporal correlations of the deformation fields: In the observations, ice deformation follows spatial and temporal scaling laws that express the heterogeneity and the intermittency of deformation. These relations do not appear in simulated ice deformation. Mean deformation in models is almost scale independent. The statistical properties of ice deformation are a signature of the ice mechanical behavior. The present work therefore suggests that the mechanical framework currently used by models is inappropriate. A different modeling framework based on elastic interactions could improve the representation of the statistical and scaling properties of ice deformation.
Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a
Decoherence of spin-deformed bosonic model
Dehdashti, Sh.; Mahdifar, A.; Bagheri Harouni, M.; Roknizadeh, R.
The decoherence rate and some parameters affecting it are investigated for the generalized spin-boson model. We consider the spin-bosonic model when the bosonic environment is modeled by the deformed harmonic oscillators. We show that the state of the environment approaches a non-linear coherent state. Then, we obtain the decoherence rate of a two-level system which is in contact with a deformed bosonic environment which is either in thermal equilibrium or in the ground state. By using some recent realization of f-deformed oscillators, we show that some physical parameters strongly affect the decoherence rate of a two-level system. -- Highlights: •Decoherence of the generalized spin-boson model is considered. •In this model the environment consists of f-oscillators. •Via the interaction, the state of the environment approaches non-linear coherent states. •Effective parameters on decoherence are considered.
The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle
NASA Astrophysics Data System (ADS)
Masood, Syed; Faizal, Mir; Zaz, Zaid; Ali, Ahmed Farag; Raza, Jamil; Shah, Mushtaq B.
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
Franck-Condon factors perturbed by damped harmonic oscillators: Solvent enhanced X {sup 1}A{sub g} ↔ A{sup 1}B{sub 1u} absorption and fluorescence spectra of perylene
Wang, Chen-Wen; Zhu, Chaoyuan Lin, Sheng-Hsien; Yang, Ling; Yu, Jian-Guo
Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang–Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X {sup 1}A{sub g} ↔ A{sup 1}B{sub 1u} absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v{sub 10} is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases.
Deformation of supersymmetric and conformal quantum mechanics through affine transformations
NASA Technical Reports Server (NTRS)
Spiridonov, Vyacheslav
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.
Exploring continuum structures with a pseudo-state basis
Lay, J. A.; Moro, A. M.; Arias, J. M.; Gomez-Camacho, J.
The ability of a recently developed square-integrable discrete basis to represent the properties of the continuum of a two-body system is investigated. The basis is obtained performing a simple analytic local scale transformation to the harmonic oscillator basis. Scattering phase-shifts and the electric transition probabilities B(E1) and B(E2) have been evaluated for several potentials using the proposed basis. Both quantities are found to be in excellent agreement with the exact values calculated from the true scattering states. The basis has been applied to describe the projectile continuum in the {sup 6}He scattering by {sup 12}C and {sup 208}Pb targets at 240 MeV/nucleon and the {sup 11}Be scattering by {sup 12}C at 67 MeV/nucleon. The calculated breakup differential cross sections are found to be in very good agreement with the available experimental data for these reactions.
Core excitation effects in halo nuclei using a transformed oscillator basis
Lay, J. A.; Arias, J. M.; Moro, A. M.; Gomez-Camacho, J.
A recent generalization of the Transformed Harmonic Oscillator basis, intended to consider core excitations in the structure of one nucleon halo nuclei, is applied to the break up of {sup 11}Be. The reaction studied is {sup 11}Be+{sup 208}Pb at 69 MeV/nucleon. The experimental set up is designed to ensure pure dipole Coulomb excitations. Making use of the Equivalent Photon Method and the electromagnetic transition probabilities obtained with the transformed oscillator basis, a relevant contribution of the quadrupole excitations of the core is found. The inclusion of core excitations is, therefore, necessary for the correct extraction of the dipole electromagnetic transition probability of halo nuclei.
Time-dependent q-deformed bi-coherent states for generalized uncertainty relations
NASA Astrophysics Data System (ADS)
Gouba, Laure
We consider the time-dependent bi-coherent states that are essentially the Gazeau-Klauder coherent states for the two dimensional noncommutative harmonic oscillator. Starting from some q-deformations of the oscillator algebra for which the entire deformed Fock space can be constructed explicitly, we define the q-deformed bi-coherent states. We verify the generalized Heisenberg's uncertainty relations projected onto these states. For the initial value in time, the states are shown to satisfy a generalized version of Heisenberg's uncertainty relations. For the initial value in time and for the parameter of noncommutativity θ = 0, the inequalities are saturated for the simultaneous measurement of the position-momentum observables. When the time evolves, the uncertainty products are different from their values at the initial time and do not always respect the generalized uncertainty relations.
Spectral gaps of spin-orbit coupled particles in deformed traps
NASA Astrophysics Data System (ADS)
Marchukov, O. V.; Volosniev, A. G.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.
We consider a spin-orbit coupled system of particles in an external trap that is represented by a deformed harmonic oscillator potential. The spin-orbit interaction is a Rashba interaction that does not commute with the trapping potential and requires a full numerical treatment in order to obtain the spectrum. The effect of a Zeeman term is also considered. Our results demonstrate that variable spectral gaps occur as a function of strength of the Rashba interaction and deformation of the harmonic trapping potential. The single-particle density of states and the critical strength for superfluidity vary tremendously with the interaction parameter. The strong variations with Rashba coupling and deformation imply that the few- and many-body physics of spin-orbit coupled systems can be manipulated by variation of these parameters.
Solution of the Self-consistent Skyrme Hartree-Fock-Bogoliubov Equations in the Cartesian Deformed Harmonic Oscillator Bssis (VII_HFODD (v.2.73y): a new version of the jprogram
Schunck, N.; Dobaczewski, J.; Satula, W.; Baczyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.
HFODD is a physics computer code that is used to model the structure of the nucleus. It is an implimentation of the nuclear energy Density Functional Theory (DFT), where the energy of the nucleus is obtained by intergration over space of some phenomenological energy density, which is itself a functional of the neutron and proton densities. In HFODD, the energy density derives from either the Skyre or the Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated a the Hartree-Fock-Boboliubov (HFB) approximation. This version is the 8th release of the code; the 7 previous versions have been published in Computer Physics Communications (see references). Version 2.49p was partly developed at LLNL and was released under a GPL License and IM number LLNL-CODE-470611. The currect version 2.73y is the second version that has been partly developed a LLNL.
Nuclear shape phase transition within a conjunction of γ-rigid and γ-stable collective behaviors in deformation-dependent mass formalism
NASA Astrophysics Data System (ADS)
Chabab, M.; El Batoul, A.; Lahbas, A.; Oulne, M.
In this paper, we present a theoretical study of a conjunction of γ-rigid and γ-stable collective motions in critical point symmetries of the phase transitions from spherical to deformed shapes of nuclei using an exactly separable version of the Bohr Hamiltonian with a deformation-dependent mass term. The deformation-dependent mass is applied simultaneously to γ-rigid and γ-stable parts of this famous collective Hamiltonian. Moreover, the β part of the problem is described by means of Davidson potential, while the γ-angular part corresponding to axially symmetric shapes is treated by a harmonic oscillator potential. The energy eigenvalues and normalized eigenfunctions of the problem are obtained in compact forms by making use of the asymptotic iteration method. The combined effect of the deformation-dependent mass and rigidity as well as harmonic oscillator stiffness parameters on the energy spectrum and wave functions is duly investigated. Also, the electric quadrupole transition ratios and energy spectrum of some γ-stable and prolate nuclei are calculated and compared with the experimental data as well as with other theoretical models.
Modification of the malus law for the torsional deformation of lyotropic nematics in magnetic field on the basis of statistical approach
NASA Astrophysics Data System (ADS)
Golovanov, A. V.; Shapovalov, V. I.
A method based on the statistical approach is proposed to calculate the light intensity for the torsional deformation of lyotropic nematic liquid crystals at violated Mauguin adiabatic approximation. Theoretical dependences of the light intensity on the magnetic field strength are obtained for two limiting cases of lyotropic nematic anchoring with bearing surfaces: infinite and low anchoring energies.
Hamiltonian Light-Front Ffield Theory in a Basis Function Approach
Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Sternberg, P.; Ng, E.G.; Yang, C.
Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here, we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. We outline our approach, present illustrative features of some non-interacting systems in a cavity and discuss the computational challenges.
(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation
Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert
Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translates into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.
How to spoil a good basis set for Rayleigh-Ritz calculations
Pupyshev, Vladimir I.; Montgomery, H. E. Jr.
For model quantum mechanical systems such as the harmonic oscillator and a particle in an impenetrable box, we consider the set of exact discrete spectrum functions and define the modified basis set by subtraction of the ground state wavefunction from all the other wavefunctions with some real weights. It is demonstrated that the modified set of functions is complete in the space of square integrable functions if and only if the series of the squared weights diverges. A similar, but nonequivalent criterion is derived for convergence of Rayleigh-Ritz ground state energy calculations to the exact ground state energy value with the basis set extension. Some numerical illustrations are provided which demonstrate a wide variety of possible situations for model systems.
Parity Deformed Jaynes-Cummings Model: "Robust Maximally Entangled States"
Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, S. Amiri
The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement. PMID:27917882
Parity Deformed Jaynes-Cummings Model: "Robust Maximally Entangled States"
NASA Astrophysics Data System (ADS)
Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, S. Amiri
The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement.
Applications of Basis Light-Front Quantization to QED
NASA Astrophysics Data System (ADS)
Vary, James P.; Zhao, Xingbo; Ilderton, Anton; Honkanen, Heli; Maris, Pieter; Brodsky, Stanley J.
Hamiltonian light-front quantum field theory provides a framework for calculating both static and dynamic properties of strongly interacting relativistic systems. Invariant masses, correlated parton amplitudes and time-dependent scattering amplitudes, possibly with strong external time-dependent fields, represent a few of the important applications. By choosing the light-front gauge and adopting an orthonormal basis function representation, we obtain a large, sparse, Hamiltonian matrix eigenvalue problem for mass eigenstates that we solve by adapting ab initio no-core methods of nuclear many-body theory. In the continuum limit, the infinite matrix limit, we recover full covariance. Guided by the symmetries of light-front quantized theory, we adopt a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present results for non-linear Compton scattering, evaluated non-perturbatively, where a strong and time-dependent laser field accelerates the electron and produces states of higher invariant mass i.e. final states with photon emission.
Solutions to Kuessner's integral equation in unsteady flow using local basis functions
NASA Technical Reports Server (NTRS)
Fromme, J. A.; Halstead, D. W.
The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.
Bunnell, W P
Spinal deformity is a relatively common disorder, particularly in teenage girls. Early detection is possible by a simple, quick visual inspection that should be a standard part of the routine examination of all preteen and teenage patients. Follow-up observation will reveal those curvatures that are progressive and permit orthotic treatment to prevent further increase in the deformity. Spinal fusion offers correction and stabilization of more severe degrees of scoliosis.
Normal ordering for nonlinear deformed ladder operators and the f-generalization of the Stirling and Bell numbers
NASA Astrophysics Data System (ADS)
Aleixo, A. N. F.; Balantekin, A. B.
We resolve the normal ordering problem for symmetric ( D ˆ + D ˆ - ) n and asymmetric ( Dˆ + r D ˆ - ) n strings of the nonlinear deformed ladder operators D ˆ ± for supersymmetric and shape-invariant potential systems, where r and n are positive integers. We provide exact and explicit expressions for their normal forms N { ( D ˆ + D ˆ - ) n } and N { ( Dˆ + r D ˆ - ) n } , where in N { . . . } all D ˆ - are at the right side. We find that the solutions involve sequence of expansion coefficients which, for r, n > 1, corresponds to the f-deformed generalization of the classical Stirling and Bell numbers of the second kind. We apply the general formalism for the translational shape-invariant potential systems as well as for the particular case of the harmonic oscillator potential system. We show that these numbers are obtained for families of polynomial expressions generated with the deformations parameters and the parameters related to the forms of the supersymmetric partner potentials.
The impact damped harmonic oscillator in free decay
NASA Technical Reports Server (NTRS)
Brown, G. V.; North, C. M.
The impact-damped oscillator in free decay is studied by using time history solutions. A large range of oscillator amplitude is covered. The amount of damping is correlated with the behavior of the impacting mass. There are three behavior regimes: (1) a low amplitude range with less than one impact per cycle and very low damping, (2) a useful middle amplitude range with a finite number of impacts per cycle, and (3) a high amplitude range with an infinite number of impacts per cycle and progressively decreasing damping. For light damping the impact damping in the middle range is: (1) proportional to impactor mass, (2) additive to proportional damping, (3) a unique function of vibration amplitude, (4) proportional to 1-epsilon, where epsilon is the coefficient of restitution, and (5) very roughly inversely proportional to amplitude. The system exhibits jump phenomena and period doublings. An impactor with 2 percent of the oscillator's mass can produce a loss factor near 0.1.
Intuitive Solution to Quantum Harmonic Oscillator at Infinity
ERIC Educational Resources Information Center
Pye, Cory C.
The attempt to develop the laboratory component of a one-semester quantum chemistry course at Saint Mary's University has led to allowing the students to solve a big problem in quantum chemistry. It is done by subdivision into smaller problems that can be independently tackled by a student with a two-year calculus background.
Generalized Energy Equipartition in Harmonic Oscillators Driven by Active Baths
NASA Astrophysics Data System (ADS)
Maggi, Claudio; Paoluzzi, Matteo; Pellicciotta, Nicola; Lepore, Alessia; Angelani, Luca; Di Leonardo, Roberto
We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.
On harmonic oscillators and their Kemmer relativistic forms
NASA Technical Reports Server (NTRS)
Debergh, Nathalie; Beckers, Jules
It is shown that Dirac (Kemmer) equations are intimately connected with (para)supercharges coming from (para)supersymmetric quantum mechanics, a nonrelativistic theory. The dimensions of the irreducible representations of Clifford (Kemmer) algebras play a fundamental role in such an analysis. These considerations are illustrated through oscillator like interactions, leading to (para)relativistic oscillators.
Non-Heisenberg states of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Dechoum, K.; França, H. M.
The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0) within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic equation with a free parameter h' with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h'>0. The exact solutions for which h'
On the measurement of time for the quantum harmonic oscillator
NASA Technical Reports Server (NTRS)
Shepard, Scott R.
A generalization of previous treatments of quantum phase is presented. Restrictions on the class of realizable phase statistics are thereby removed; thus, permitting 'phase wavefunction collapse' (and other advantages). This is accomplished by exciting the auxiliary mode of the measurement apparatus in a time-reversed fashion. The mathematical properties of this auxiliary mode are studied in the hope that they will lead to an identification of a physical apparatus which can realize the quantum phase measurement.
The finite harmonic oscillator and its associated sequences
Gurevich, Shamgar; Hadani, Ronny; Sochen, Nir
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. PMID:18635684
Laser cooling of a harmonic oscillator's bath with optomechanics
NASA Astrophysics Data System (ADS)
Xu, Xunnong; Taylor, Jacob
Thermal noise reduction in mechanical systems is a topic both of fundamental interest for studying quantum physics at the macroscopic level and for application of interest, such as building high sensitivity mechanics based sensors. Similar to laser cooling of neutral atoms and trapped ions, the cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an efficient scheme for reducing the thermal load on a mechanical resonator while improving its quality factor. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.
Entangling Qubits in a One-Dimensional Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Owen, Edmund; Dean, Matthew; Barnes, Crispin
We present a method for generating entanglement between qubits associated with a pair of particles interacting in a one-dimensional harmonic potential. By considering the effect of the interaction on the energy spectrum of the system, we show that, under certain approximations, a ``power-of-SWAP" operation is performed on the initial two-qubit quantum state without requiring any time-dependent control. Initialization errors and deviations from our approximation are shown to have a negligible effect on the final state. Using a GPU-accelerated iteration scheme to find numerical solutions to the two-particle time-dependent Schr"odinger equation, we demonstrate that it is possible to generate maximally entangled Bell states between the two qubits with high fidelity for a range of possible interaction potentials.
[Neurogenic foot deformities].
Senst, S
There is a multitude of neurological diseases which may lead to neuro-orthopaedic problems and subsequently to neurogenic foot deformities. For this reason the diagnostician will be consistently surprised that there is a great multitude of different foot abnormalities and that not only the typical spastic talipes equines dominates. Of particular significance here is that these deformities almost always develop progressively, whereas most diseases persist per se, cerebral palsy being a typical case in point. However, in MMC (myelomeningocele) patients, there is also the danger of a worsening of the basic problem in the case of tethered cord syndrome. Unlike congenital talipes equinovarus, neuro-orthopaedic talipes equinovarus often shows over- or undercorrection postoperatively due to a shift in muscle imbalance. It is important, therefore, that the basis of conservative therapy include regular physiotherapy and orthoses during the day and, if necessary, at night. Botulinum toxin has been established as an additional measure for spasticity; however, this cannot always prevent surgical intervention, but is able to delay this to a better point in the development of the child/patient. The present article describes the diversity of neurological deformities and presents conservative as well as surgical therapeutic approaches.
Cohen, Bruce E; Nicholson, Christopher W
The bunionette, or tailor's bunion, is a lateral prominence of the fifth metatarsal head. Most commonly, bunionettes are the result of a widened 4-5 intermetatarsal angle with associated varus of the metatarsophalangeal joint. When symptomatic, these deformities often respond to nonsurgical treatment methods, such as wider shoes and padding techniques. When these methods are unsuccessful, surgical treatment is based on preoperative radiographs and associated lesions, such as hyperkeratoses. In rare situations, a simple lateral eminence resection is appropriate; however, the risk of recurrence or overresection is high with this technique. Patients with a lateral bow to the fifth metatarsal are treated with a distal chevron-type osteotomy. A widened 4-5 intermetatarsal angle often requires a diaphyseal osteotomy for correction.
Deform PF-MT: Particle Filter With Mode Tracker for Tracking Nonaffine Contour Deformations
Vaswani, Namrata; Rathi, Yogesh; Yezzi, Anthony; Tannenbaum, Allen
We propose algorithms for tracking the boundary contour of a deforming object from an image sequence, when the nonaffine (local) deformation over consecutive frames is large and there is overlapping clutter, occlusions, low contrast, or outlier imagery. When the object is arbitrarily deforming, each, or at least most, contour points can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters (PF) for large dimensional problems is impractically expensive. However, in most real problems, at any given time, most of the contour deformation occurs in a small number of dimensions ("effective basis space") while the residual deformation in the rest of the state space ("residual space") is small. This property enables us to apply the particle filtering with mode tracking (PF-MT) idea that was proposed for such large dimensional problems in recent work. Since most contour deformation is low spatial frequency, we propose to use the space of deformation at a subsampled set of locations as the effective basis space. The resulting algorithm is called deform PF-MT. It requires significant modifications compared to the original PF-MT because the space of contours is a non-Euclidean infinite dimensional space. PMID:19933014
Dislocations: 75 years of Deformation Mechanisms
NASA Technical Reports Server (NTRS)
Schneider, Judy
The selection of papers presented in this section reflect on themes to be explored at the "Dislocations: 75 years of Deformation Mechanisms" Symposium to be held at the Annual 2009 TMS meeting. The symposium was sponsored by the Mechanical Behavior of Materials Committee to give tribute to the evolution of a concept that has formed the basis of our mechanistic understanding of how crystalline solids plastically deform and how they fail.
NASA Technical Reports Server (NTRS)
Clark, T. A.; Thomsen, P.
A study is presented of deformations in antennas with the emphasis on their influence on VLBI measurements. The GIFTS structural analysis program has been used to model the VLBI antenna in Fairbanks (Alaska). The report identifies key deformations and studies the effect of gravity, wind, and temperature. Estimates of expected deformations are given.
Correlated states and transparency of a barrier for low-energy particles at monotonic deformation of a potential well with dissipation and a stochastic force
NASA Astrophysics Data System (ADS)
Vysotskii, V. I.; Vysotskyy, M. V.
The features of the formation of correlated coherent states of a particle in a parabolic potential well at its monotonic deformation (expansion or compression) in finite limits have been considered in the presence of dissipation and a stochastic force. It has been shown that, in both deformation regimes, a correlated coherent state is rapidly formed with a large correlation coefficient | r| → 1, which corresponds at a low energy of the particle to a very significant (by a factor of 1050-10100 or larger) increase in the transparency of the potential barrier at its interaction with atoms (nuclei) forming the "walls" of the potential well or other atoms located in the same well. The efficiency of the formation of correlated coherent states, as well as | r|, increases with an increase in the deformation interval and with a decrease in the deformation time. The presence of the stochastic force acting on the particle can significantly reduce the maximum | r| value and result in the fast relaxation of correlated coherent states with | r| → 0. The effect of dissipation in real systems is weaker than the action of the stochastic force. It has been shown that the formation of correlated coherent states at the fast expansion of the well can underlie the mechanism of nuclear reactions at a low energy, e.g., in microcracks developing in the bulk of metal hydrides loaded with hydrogen or deuterium, as well as in a low-pressure plasma in a variable magnetic field in which the motion of ions is similar to a harmonic oscillator with a variable frequency.
Study of resonant structures in a deformed mean field by the contour deformation method in momentum space
NASA Astrophysics Data System (ADS)
Hagen, G.; Vaagen, J. S.
Solution of the momentum space Schrödinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single-particle states that includes bound, resonant, and complex continuum states may be obtained by the contour deformation method. This generalized basis in the complex energy plane is known as a Berggren basis. The momentum space Schrödinger equation is an integral equation that is easily solved by matrix diagonalization routines even for the case of deformed fields. The method is demonstrated for axial symmetry and a fictitious "deformed He5" but may be extended to more general deformation and applied to truly deformed halo nuclei.
Finite deformation of elasto-plastic solids
NASA Technical Reports Server (NTRS)
Osias, J. R.
A theoretical basis is established for analysis of finite deformation of metals. The observation that finite deformation of such elastoplastic materials may be viewed as a process rather than an event leads to derivation of a complete initial and boundary value problem distinguished by its quasilinear nature. This feature of the formulation motivates adoption of an incremental approach to numerical problem solving. Numerical solution capability is established for problems of plane stress and plane strain. The validity of the theory and numerical analysis is demonstrated by consideration of a number of problems of homogeneous finite deformation for which analytic solutions are available. Subsequently the analysis is employed for the investigation of necking in flat metal tensile bars. The results of this investigation provide the first full numerical solutions for tensile necking in plane stress and plane strain. In addition a basis is provided for assessment of the validity of stress-strain relations inferred from tensile test data.
Deformations of superconformal theories
NASA Astrophysics Data System (ADS)
Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in d ≥ 3 dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and non-central charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.
Deformation mechanisms in experimentally deformed Boom Clay
NASA Astrophysics Data System (ADS)
Desbois, Guillaume; Schuck, Bernhard; Urai, Janos
Bulk mechanical and transport properties of reference claystones for deep disposal of radioactive waste have been investigated since many years but little is known about microscale deformation mechanisms because accessing the relevant microstructure in these soft, very fine-grained, low permeable and low porous materials remains difficult. Recent development of ion beam polishing methods to prepare high quality damage free surfaces for scanning electron microscope (SEM) is opening new fields of microstructural investigation in claystones towards a better understanding of the deformation behavior transitional between rocks and soils. We present results of Boom Clay deformed in a triaxial cell in a consolidated - undrained test at a confining pressure of 0.375 MPa (i.e. close to natural value), with σ1 perpendicular to the bedding. Experiments stopped at 20 % strain. As a first approximation, the plasticity of the sample can be described by a Mohr-Coulomb type failure envelope with a coefficient of cohesion C = 0.117 MPa and an internal friction angle ϕ = 18.7°. After deformation test, the bulk sample shows a shear zone at an angle of about 35° from the vertical with an offset of about 5 mm. We used the "Lamipeel" method that allows producing a permanent absolutely plane and large size etched micro relief-replica in order to localize and to document the shear zone at the scale of the deformed core. High-resolution imaging of microstructures was mostly done by using the BIB-SEM method on key-regions identified after the "Lamipeel" method. Detailed BIB-SEM investigations of shear zones show the following: the boundaries between the shear zone and the host rock are sharp, clay aggregates and clastic grains are strongly reoriented parallel to the shear direction, and the porosity is significantly reduced in the shear zone and the grain size is smaller in the shear zone than in the host rock but there is no evidence for broken grains. Comparison of microstructures
Evans, D
A discussion of the essential deformity in calcaneo-valgus feet develops a theme originally put forward in 1961 on the relapsed club foot (Evans 1961). Whereas in the normal foot the medial and lateral columns are about equal in length, in talipes equino-varus the lateral column is longer and in calcaneo-valgus shorter than the medial column. The suggestion is that in the treatment of both deformities the length of the columns be made equal. A method is described of treating calcaneo-valgus deformity by inserting cortical bone grafts taken from the tibia to elongate the anterior end of the calcaneus.
Large-scale deformed quasiparticle random-phase approximation calculations of the γ -ray strength function using the Gogny force
NASA Astrophysics Data System (ADS)
Martini, M.; Péru, S.; Hilaire, S.; Goriely, S.; Lechaftois, F.
Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we present large-scale calculations of the E 1 γ -ray strength function obtained in the framework of the axially symmetric deformed quasiparticle random-phase approximation based on the finite-range Gogny force. This approach is applied to even-even nuclei, the strength function for odd nuclei being derived by interpolation. The convergence with respect to the adopted number of harmonic oscillator shells and the cutoff energy introduced in the 2-quasiparticle (2 -q p ) excitation space is analyzed. The calculations performed with two different Gogny interactions, namely D1S and D1M, are compared. A systematic energy shift of the E 1 strength is found for D1M relative to D1S, leading to a lower energy centroid and a smaller energy-weighted sum rule for D1M. When comparing with experimental photoabsorption data, the Gogny-QRPA predictions are found to overestimate the giant dipole energy by typically ˜2 MeV. Despite the microscopic nature of our self-consistent Hartree-Fock-Bogoliubov plus QRPA calculation, some phenomenological corrections need to be included to take into account the effects beyond the standard 2 -q p QRPA excitations and the coupling between the single-particle and low-lying collective phonon degrees of freedom. For this purpose, three prescriptions of folding procedure are considered and adjusted to reproduce experimental photoabsorption data at best. All of them are shown to lead to somewhat similar predictions of the E 1 strength, both at low energies and for exotic neutron-rich nuclei. Predictions of γ -ray strength functions and Maxwellian-averaged neutron capture rates for the whole Sn isotopic chain are also discussed and compared with previous theoretical calculations.
NASA Astrophysics Data System (ADS)
Green, Harry
The Third Rock Deformation Colloquium was held December 4, 1989, at the AGU Fall Meeting in San Francisco. Steve Kirby of the U.S. Geological Survey, Menlo Park, Calif., reported on actions taken by the rock deformation steering committee. Brian Wernicke of Harvard University, Cambridge, Mass., talked on the structural geology of the Great Basin.The steering committee voted for "Committee on Deformation of Earth Materials" as the name for the AGU technical committee on rock deformation, Kirby said. Considerable discussion has occurred in the steering committee over our relationship to the AGU Mineral Physics Committee. Indeed, Kirby will become chairman of that committee in 1990, underlining the overlap of the two groups. It was agreed that we will pursue closer association with Mineral Physics.
Wrist deformities after fracture.
Vanheest, Ann
Wrist deformities can occur after fracture because of malunion of the fracture or injury to the growth plate leading to imbalance of growth. Prevention of malunion is paramount by early recognition with proper reduction and casting or fixation with casting. If a mal-union occurs, an osteotomy may be necessary if anticipated growth will not correct the deformity. Injury of the growth plate may lead to wrist deformity in two ways: angular growth or growth arrest. Angular growth deformities are corrected most commonly by osteotomy. Growth arrest of the radius or the ulna leads to an ulnar-positive or an ulnar-negative variance at the wrist. If the ulnar variance is symptomatic, treatment is centered on achieving a level joint. Options for joint leveling procedures include epiphysiodesis or physeal stapling of the longer bone, lengthening osteotomy of the shorter bone, or shortening osteotomy of the longer bone.
An improved choice of oscillator basis for banana shaped nuclides
Chasman, R.R.
The question of the appropriate choice of oscillator basis functions for studying exotic nuclear shapes is raised. Difficulties with the conventional choice of oscillator basis states are noted for shapes having a large banana component. A prescription for an improved oscillator basis to study these shapes is given. It can be applied in a more general context. New calculations with this improved basis are presented for the banana deformation mode. The change of basis gives results that improve the prospects of finding states in the banana minimum for many isotopes of Tl, Pb and Bi.
Principles of rock deformation
Nicolas, A.
This text focuses on the recent achievements in the analysis of rock deformation. It gives an analytical presentation of the essential structures in terms of kinetic and dynamic interpretation. The physical properties underlying the interpretation of rock structures are exposed in simple terms. Emphasized in the book are: the role of fluids in rock fracturing; the kinematic analysis of magnetic flow structures; the application of crystalline plasticity to the kinematic and dynamic analysis of the large deformation imprinted in many metamorphic rocks.
NASA Astrophysics Data System (ADS)
Antonellini, Marco; Mollema, Pauline Nella
We report for the first time the occurrence of polygonal faults in sandstone, which is compelling given that layer-bound polygonal fault systems have been observed so far only in fine-grained sediments such as clay and chalk. The polygonal faults are shear deformation bands that developed under shallow burial conditions via strain hardening in dm-wide zones. The edges of the polygons are 1-5 m long. The shear deformation bands are organized as conjugate faults along each edge of the polygon and form characteristic horst-like structures. The individual deformation bands have slip magnitudes ranging from a few mm to 1.5 cm; the cumulative average slip magnitude in a zone is up to 10 cm. The deformation bands heaves, in aggregate form, accommodate a small isotropic horizontal extension (strain <0.005). The individual shear deformation bands show abutting T-junctions, veering, curving, and merging where they mechanically interact. Crosscutting relationships are rare. The interactions of the deformation bands are similar to those of mode I opening fractures. The documented fault networks have important implications for evaluating the geometry of km-scale polygonal fault systems in the subsurface, top seal integrity, as well as constraining paleo-tectonic stress regimes.
Experimental Deformation of Magnetite
NASA Astrophysics Data System (ADS)
Till, J. L.; Rybacki, E.; Morales, L. F. G.
Magnetite is an important iron ore mineral and the most prominent Fe-oxide phase in the Earth's crust. The systematic occurrence of magnetite in zones of intense deformation in oceanic core complexes suggests that it may play a role in strain localization in some silicate rocks. We performed a series of high-temperature deformation experiments on synthetic magnetite aggregates and natural single crystals to characterize the rheological behavior of magnetite. As starting material, we used fine-grained magnetite powder that was hot isostatically pressed at 1100°C for several hours, resulting in polycrystalline material with a mean grain size of around 40 μm and containing 3-5% porosity. Samples were deformed to 15-20% axial strain under constant load (approximating constant stress) conditions in a Paterson-type gas apparatus for triaxial deformation at temperatures between 900 and 1100°C and 300 MPa confining pressure. The aggregates exhibit typical power-law creep behavior. At high stresses, samples deformed by dislocation creep exhibit stress exponents close to 3, revealing a transition to near-Newtonian creep with stress exponents around 1.3 at lower stresses. Natural magnetite single crystals deformed at 1 atm pressure and temperatures between 950°C and 1150 °C also exhibit stress exponents close to 3, but with lower flow stresses and a lower apparent activation energy than the aggregates. Such behavior may result from the different oxygen fugacity buffers used. Crystallographic-preferred orientations in all polycrystalline samples are very weak and corroborate numerical models of CPO development, suggesting that texture development in magnetite may be inherently slow compared with lower symmetry phases. Comparison of our results with experimental deformation data for various silicate minerals suggests that magnetite should be weaker than most silicates during ductile creep in dry igneous rocks.
Molecular basis for erythrocyte shape
NASA Astrophysics Data System (ADS)
Elgsaeter, A.; Mikkelsen, A.
The isolated plasma membrane of the human erythrocytes displays the same shape and shape transformations as the intact cells. It is therefore generally believed that the plasma membrane plays a dominant role in determining erythrocyte shape. The plasma membrane consists of a fluid lipid bilayer to the surface of which is attached a protein skeleton. The two halves of the lipid bilayer and the protein network (gel) are tighly coupled, but at the same time elastically deformable and can slide relative to one another in the plane of the cell membrane. The equilibrium shape of such a structure is determined by the combined mechano-chemical properties of the individual layers and equals the cell shape that for the given cell volume corresponds to the lowest total elastic free energy. The elastic free energy of the lipid bilayer is mainly associated with bending and change in surface area for each of the two lipid monolayer. For the protein membrane skeleton the elastic free energy mainly equals the sum of the local contributions due to shear deformation and surface change. When the mechano-chemical properties of each of the layers are known, calculation of the equilibrium shape is in principle just an exercise in standard continuum mechanics. The elastic properties of pure lipid monolayers have long been qualitatively fairly well known. The changes in lipid bilayer elastic properties resulting from the presence of integral membrane proteins have just recently become better understood. The detailed molecular basis for the elastic properties of the protein membrane skeleton remains unresolved despite many attempts to elucidate the problem. It is widely agreed that the elastic properties are largely accounted for by the highly elongated spectrin molecules, but whether the membrane skelton elasticity is mainly of entropic or entalphic origin is still unsettled.
Infinitesimal deformations of naturally graded filiform Leibniz algebras
NASA Astrophysics Data System (ADS)
Khudoyberdiyev, A. Kh.; Omirov, B. A.
In the present paper we describe infinitesimal deformations of complex naturally graded filiform Leibniz algebras. It is known that any n-dimensional filiform Lie algebra can be obtained by a linear integrable deformation of the naturally graded algebra Fn3(0) . We establish that in the same way any n-dimensional filiform Leibniz algebra can be obtained by an infinitesimal deformation of the filiform Leibniz algebras Fn1,Fn2and Fn3(α) . Moreover, we describe the linear integrable deformations of the above-mentioned algebras with a fixed basis of HL2 in the set of all n-dimensional Leibniz algebras. Among these deformations one new rigid algebra has been found.
Dubois, P.F.
This paper discusses the basis system. Basis is a program development system for scientific programs. It has been developed over the last five years at Lawrence Livermore National Laboratory (LLNL), where it is now used in about twenty major programming efforts. The Basis System includes two major components, a program development system and a run-time package. The run-time package provides the Basis Language interpreter, through which the user does input, output, plotting, and control of the program's subroutines and functions. Variables in the scientific packages are known to this interpreter, so that the user may arbitrarily print, plot, and calculate with, any major program variables. Also provided are facilities for dynamic memory management, terminal logs, error recovery, text-file i/o, and the attachment of non-Basis-developed packages.
Deformation behavior and microstructure evolution of wrought magnesium alloys
NASA Astrophysics Data System (ADS)
Wang, Shouren; Song, Linghui; Kang, Sukbong; Cho, Jaehyung; Wang, Yingzi
There are many researches on the deformation behavior of wrought magnesium alloys, such as AZ31, AZ80, AZ91, and ZK60 magnesium alloys at different temperatures and strain rates, but few of them focuses on the deformation behavior of AZ41M and ZK60M alloys, especially under the twin-roll casting (TRC) state. Meanwhile, the existing researches only focus on the grain refinement law of the magnesium alloys under deformation conditions, the deformation mechanism has not been revealed yet. The hot compression behavior of AZ41M and ZK60M magnesium alloys under the temperature and strain rate ranges of 250-400 °C and 0.001-1 s-1 are studied by thermal simulation methods using Gleeble 1500 machine and virtual simulation using finite element analysis software. Simulation results show that sine hyperbolic law is the most suitable flow stress model for wider deformation conditions. The most reasonable selected deformation conditions of ZK60M alloy is 350 °C/0.1 s-1 for TRC and 350 °C/1 s-1 for conventional casting (CC), while AZ41M alloy is 300 °C/0.01 s-1 for TRC and 350 °C/0.1 s-1 for CC. Deformation behavior and dynamic recrystallization (DRX) mechanism of them are analyzed at the same deformation conditions. The microstructures of AZ41M and ZK60M alloys are observed at different deformed conditions by optical microscopy (OM) and electron back scatter diffraction (EBSD) and it reveals the flow behavior and deformation mechanism of them. Working harden and work soften contribute to the activation of basal, non-basal slip systems which promote DRX. The proposed research reveals the deformation behavior and mechanism of the AZ41M and ZK 60M magnesium alloys and concludes their optimized deformation parameters and processes and provides a theory basis for their manufacturing and application.
Crustal deformation and earthquakes
NASA Technical Reports Server (NTRS)
Cohen, S. C.
The manner in which the Earth's surface deforms during the cycle of stress accumulation and release along major faults is investigated. In an investigation of the crustal deformation associated with a thin channel asthenosphere displacements are reduced from those computed for a half space asthenosphere. A previous finding by other workers that displacements are enhanced when flow is confined to a thin channel is based on several invalid approximations. The major predictions of the finite element model are that the near field postseismic displacements and strain rates are less than those for a half space asthenosphere and that the postseismic strain rates at intermediate distances are greater (in magnitude). The finite width of the asthenosphere ceases to have a significant impact on the crustal deformation pattern when its magnitude exceeds about three lithosphere thicknesses.
Interfacial Bubble Deformations
NASA Astrophysics Data System (ADS)
Seymour, Brian; Shabane, Parvis; Cypull, Olivia; Cheng, Shengfeng; Feitosa, Klebert
Soap bubbles floating at an air-water experience deformations as a result of surface tension and hydrostatic forces. In this experiment, we investigate the nature of such deformations by taking cross-sectional images of bubbles of different volumes. The results show that as their volume increases, bubbles transition from spherical to hemispherical shape. The deformation of the interface also changes with bubble volume with the capillary rise converging to the capillary length as volume increases. The profile of the top and bottom of the bubble and the capillary rise are completely determined by the volume and pressure differences. James Madison University Department of Physics and Astronomy, 4VA Consortium, Research Corporation for Advancement of Science.
Minster, B.; Prescott, W.; Royden, L.
Our goal is to understand the motions of the plates, the deformation along their boundaries and within their interiors, and the processes that control these tectonic phenomena. In the broadest terms, we must strive to understand the relationships of regional and local deformation to flow in the upper mantle and the rheological, thermal and density structure of the lithosphere. The essential data sets which we require to reach our goal consist of maps of current strain rates at the earth's surface and the distribution of integrated deformation through time as recorded in the geologic record. Our success will depend on the effective synthesis of crustal kinematics with a variety of other geological and geophysical data, within a quantitative theoretical framework describing processes in the earth's interior. Only in this way can we relate the snapshot of current motions and earth structure provided by geodetic and geophysical data with long-term processes operating on the time scales relevant to most geological processes. The wide-spread use of space-based techniques, coupled with traditional geological and geophysical data, promises a revolution in our understanding of the kinematics and dynamics of plate motions over a broad range of spatial and temporal scales and in a variety of geologic settings. The space-based techniques that best address problems in plate motion and deformation are precise space-geodetic positioning -- on land and on the seafloor -- and satellite acquisition of detailed altimetric and remote sensing data in oceanic and continental areas. The overall science objectives for the NASA Solid Earth Science plan for the 1990's, are to Understand the motion and deformation of the lithosphere within and across plate boundaries'', and to understand the dynamics of the mantle, the structure and evolution of the lithosphere, and the landforms that result from local and regional deformation. 57 refs., 7 figs., 2 tabs.
Nanolaminate deformable mirrors
Papavasiliou, Alexandros P.; Olivier, Scot S.
A deformable mirror formed out of two layers of a nanolaminate foil attached to a stiff substrate is introduced. Deformation is provided by an electrostatic force between two of the layers. The internal stiffness of the structure allows for high-spatial-frequency shapes. The nanolaminate foil of the present invention allows for a high-quality mirror surface. The device achieves high precision in the vertical direction by using foils with accurately controlled thicknesses, but does not require high precision in the lateral dimensions, allowing such mirrors to be fabricated using crude lithography techniques. Such techniques allow structures up to about the meter scale to be fabricated.
Nanolaminate deformable mirrors
Papavasiliou, Alexandros P.; Olivier, Scot S.
A deformable mirror formed out of two layers of a nanolaminate foil attached to a stiff substrate is introduced. Deformation is provided by an electrostatic force between two of the layers. The internal stiffness of the structure allows for high-spatial-frequency shapes. The nanolaminate foil of the present invention allows for a high-quality mirror surface. The device achieves high precision in the vertical direction by using foils with accurately controlled thicknesses, but does not require high precision in the lateral dimensions, allowing such mirrors to be fabricated using crude lithography techniques. Such techniques allow structures up to about the meter scale to be fabricated.
Micromachined, Electrostatically Deformable Reflectors
NASA Technical Reports Server (NTRS)
Bartman, Randall K.; Wang, Paul K. C.; Miller, Linda M.; Kenny, Thomas W.; Kaiser, William J.; Hadaegh, Fred Y.; Agronin, Michael L.
Micromachined, closed-loop, electrostatically actuated reflectors (microCLEARs) provide relatively simple and inexpensive alternatives to large, complex, expensive adaptive optics used to control wavefronts of beams of light in astronomy and in experimental laser weapons. Micromachining used to make deformable mirror, supporting structure, and actuation circuitry. Development of microCLEARs may not only overcome some of disadvantages and limitations of older adaptive optics but may also satisfy demands of potential market for small, inexpensive deformable mirrors in electronically controlled film cameras, video cameras, and other commercial optoelectronic instruments.
R.J. Garrett
As part of the internal Integrated Safety Management Assessment verification process, it was determined that there was a lack of documentation that summarizes the safety basis of the current Yucca Mountain Project (YMP) site characterization activities. It was noted that a safety basis would make it possible to establish a technically justifiable graded approach to the implementation of the requirements identified in the Standards/Requirements Identification Document. The Standards/Requirements Identification Documents commit a facility to compliance with specific requirements and, together with the hazard baseline documentation, provide a technical basis for ensuring that the public and workers are protected. This Safety Basis Report has been developed to establish and document the safety basis of the current site characterization activities, establish and document the hazard baseline, and provide the technical basis for identifying structures, systems, and components (SSCs) that perform functions necessary to protect the public, the worker, and the environment from hazards unique to the YMP site characterization activities. This technical basis for identifying SSCs serves as a grading process for the implementation of programs such as Conduct of Operations (DOE Order 5480.19) and the Suspect/Counterfeit Items Program. In addition, this report provides a consolidated summary of the hazards analyses processes developed to support the design, construction, and operation of the YMP site characterization facilities and, therefore, provides a tool for evaluating the safety impacts of changes to the design and operation of the YMP site characterization activities.
Determination of stable points in deformation analysis
NASA Astrophysics Data System (ADS)
Vodopivec, F.; Savsek-Safic, S.
Determination of displacements of natural and man-made objects is one of the more demanding tasks of the surveying profession. The underlying problem is in the identification of stability and potential hazards of man-made objects in the time of building and later on, as well as earth movements brought about by natural forces or unsupervised land consumption. Due to a constant emergence of displacements, the identification of size, velocity and periodicity of displacements plays an important role especially in civil engineering, mining and related geosciences. The preliminary condition for the deformation analysis is to measure and process the data of respective epochs carefully in the sense of estimating the quality of a given network. In observations, a special emphasis should be given to detecting and eliminating the gross errors. The characteristic point displacements are identified on the basis of at least two epochs and solely on identical network points. This paper aims at presenting the implementation of the Hannover, Asanin and Mihailovic deformation analysis approaches. For the purpose of testing the approaches a trigonometric network in the shape of a sexangle with a centre point was used. The observations and displacements were simulated, accordingly, for pattern generation of normally distributed random variables the Box and Mueller polar generation method was used. On the basis of geodetic observations and with the use of statistical methods the displacements of a given object are determined. Additionally, a comparison regarding the efficiency of stable point identification according to the deformation analysis approaches has been made.
Nanoscale deformation mechanisms in bone.
Gupta, Himadri S; Wagermaier, Wolfgang; Zickler, Gerald A; Raz-Ben Aroush, D; Funari, Sérgio S; Roschger, Paul; Wagner, H Daniel; Fratzl, Peter
Deformation mechanisms in bone matrix at the nanoscale control its exceptional mechanical properties, but the detailed nature of these processes is as yet unknown. In situ tensile testing with synchrotron X-ray scattering allowed us to study directly and quantitatively the deformation mechanisms at the nanometer level. We find that bone deformation is not homogeneous but distributed between a tensile deformation of the fibrils and a shearing in the interfibrillar matrix between them.
[Babies with cranial deformity].
Feijen, Michelle M W; Claessens, Edith A W M Habets; Dovens, Anke J Leenders; Vles, Johannes S; van der Hulst, Rene R W J
Plagiocephaly was diagnosed in a baby aged 4 months and brachycephaly in a baby aged 5 months. Positional or deformational plagio- or brachycephaly is characterized by changes in shape and symmetry of the cranial vault. Treatment options are conservative and may include physiotherapy and helmet therapy. During the last two decades the incidence of positional plagiocephaly has increased in the Netherlands. This increase is due to the recommendation that babies be laid on their backs in order to reduce the risk of sudden infant death syndrome. We suggest the following: in cases of positional preference of the infant, referral to a physiotherapist is indicated. In cases of unacceptable deformity of the cranium at the age 5 months, moulding helmet therapy is a possible treatment option.
Partially segmented deformable mirror
Bliss, Erlan S.; Smith, James R.; Salmon, J. Thaddeus; Monjes, Julio A.
A partially segmented deformable mirror is formed with a mirror plate having a smooth and continuous front surface and a plurality of actuators to its back surface. The back surface is divided into triangular areas which are mutually separated by grooves. The grooves are deep enough to make the plate deformable and the actuators for displacing the mirror plate in the direction normal to its surface are inserted in the grooves at the vertices of the triangular areas. Each actuator includes a transducer supported by a receptacle with outer shells having outer surfaces. The vertices have inner walls which are approximately perpendicular to the mirror surface and make planar contacts with the outer surfaces of the outer shells. The adhesive which is used on these contact surfaces tends to contract when it dries but the outer shells can bend and serve to minimize the tendency of the mirror to warp.
Partially segmented deformable mirror
Bliss, E.S.; Smith, J.R.; Salmon, J.T.; Monjes, J.A.
A partially segmented deformable mirror is formed with a mirror plate having a smooth and continuous front surface and a plurality of actuators to its back surface. The back surface is divided into triangular areas which are mutually separated by grooves. The grooves are deep enough to make the plate deformable and the actuators for displacing the mirror plate in the direction normal to its surface are inserted in the grooves at the vertices of the triangular areas. Each actuator includes a transducer supported by a receptacle with outer shells having outer surfaces. The vertices have inner walls which are approximately perpendicular to the mirror surface and make planar contacts with the outer surfaces of the outer shells. The adhesive which is used on these contact surfaces tends to contract when it dries but the outer shells can bend and serve to minimize the tendency of the mirror to warp. 5 figures.
Osteotomies for bunionette deformity.
Weil, Lowell; Weil, Lowell Scott
A variety of surgical osteotomy procedures have been described for the bunionette deformity.Metatarsal osteotomies narrow the forefoot, maintain the length of the metatarsal, and preserve function of the metatarsophalangeal joint. Distal metatarsal osteotomies produce less correction and reduce postoperative disability; however, they pose a risk of inadequate correction because of the small width of the fifth metatarsal head and transfer lesions if shortened or dorsiflexed excessively. The sliding oblique metaphyseal osteotomy described by Smith and Weil (without fixation) and later by Steinke (with fixation) is easy to perform and provides good cancellous bone contact. Fixation is sometimes difficult and bone healing can take a few months owing to the unstable construct of this osteotomy. Kitaoka described a distal chevron osteotomy, which provides lateral pressure relief and reduced plantar pressure. This osteotomy is currently the most common procedure used; however, it may prove difficult to perform if the deformity is large and the bone is narrow. Diaphyseal osteotomies are indicated when greater correction is needed; however, they require more dissection and there is greater postoperative convalescence with non–weight bearing for several weeks. Proximal base osteotomies may be used to address significantly increased 4–5 IMAs or when a large degree of sagittal plane correction is required. Approaches that have been described include opening and closing base wedges and basal chevrons. Advantages to this approach are the ability to avoid epiphyseal plates in pediatric patients and maintain function of the MTPJ, while disadvantages include inherent instability of the location of the osteotomy, embarrassment of intraosseous and extraosseus blood supply of the metatarsal, and technical demand. Non–weight bearing is essential for several weeks. The Scarfette procedure is a combination head–shaft procedure, which is indicated to treat mild to moderate
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
Advanced Curvature Deformable Mirrors
designs using just a glass wafer and a wafer of Carbon Fiber Reinforced Polymer ( CFRP ). In both cases minimum bend radius decreases and the resonant... matrix is consequently nearly diagonal. The long actuators at the outer edge of the deformable mirror are largely outside the working pupil so their...formal reconstruction of the wave front either explicitly or implicitly in the control matrix . The WFS-DM combination is acting like an analog computer
Deformation of Wrinkled Graphene
The deformation of monolayer graphene, produced by chemical vapor deposition (CVD), on a polyester film substrate has been investigated through the use of Raman spectroscopy. It has been found that the microstructure of the CVD graphene consists of a hexagonal array of islands of flat monolayer graphene separated by wrinkled material. During deformation, it was found that the rate of shift of the Raman 2D band wavenumber per unit strain was less than 25% of that of flat flakes of mechanically exfoliated graphene, whereas the rate of band broadening per unit strain was about 75% of that of the exfoliated material. This unusual deformation behavior has been modeled in terms of mechanically isolated graphene islands separated by the graphene wrinkles, with the strain distribution in each graphene island determined using shear lag analysis. The effect of the size and position of the Raman laser beam spot has also been incorporated in the model. The predictions fit well with the behavior observed experimentally for the Raman band shifts and broadening of the wrinkled CVD graphene. The effect of wrinkles upon the efficiency of graphene to reinforce nanocomposites is also discussed. PMID:25765609
Deformable micro torque swimmer
NASA Astrophysics Data System (ADS)
Ishikawa, Takuji; Tanaka, Tomoyuki; Omori, Toshihiro; Imai, Yohsuke
We investigated the deformation of a ciliate swimming freely in a fluid otherwise at rest. The cell body was modeled as a capsule with a hyper elastic membrane enclosing Newtonian fluid. Thrust forces due to the ciliary beat were modeled as torques distributed above the cell body. Effects of the membrane elasticity, the aspect ratio of cell's reference shape and the density difference between the cell and the surrounding fluid were investigated. The results showed that the cell deformed like heart shape when Capillary number (Ca) was sufficiently large, and the swimming velocity decreased as Ca was increased. The gravity effect on the membrane tension suggested that the upwards and downwards swimming velocities of Paramecium might be reglated by the calcium ion channels distributed locally around the anterior end. Moreover, the gravity induced deformation made a cell directed vertically downwards, which resulted in a positive geotaxis like behavior with physical origin. These results are important to understand physiology of ciliate's biological responses to mechanical stimuli.
NASA Technical Reports Server (NTRS)
Strauss, Karl F.; Sheldon, Douglas J.
Several missions and instruments in the conceptual design phase rely on the technique of interferometry to create detectable fringe patterns. The intimate emplacement of reflective material upon electron device cells based upon chalcogenide material technology permits high-speed, predictable deformation of the reflective surface to a subnanometer or finer resolution with a very high degree of accuracy. In this innovation, a layer of reflective material is deposited upon a wafer containing (perhaps in the millions) chalcogenic memory cells with the reflective material becoming the front surface of a mirror and the chalcogenic material becoming a means of selectively deforming the mirror by the application of heat to the chalcogenic material. By doing so, the mirror surface can deform anywhere from nil to nanometers in spots the size of a modern day memory cell, thereby permitting realtime tuning of mirror focus and reflectivity to mitigate aberrations caused elsewhere in the optical system. Modern foundry methods permit the design and manufacture of individual memory cells having an area of or equal to the Feature (F) size of the design (assume 65 nm). Fabrication rules and restraints generally require the instantiation of one memory cell to another no closer than 1.5 F, or, for this innovation, 90 nm from its neighbor in any direction. Chalcogenide is a semiconducting glass compound consisting of a combination of chalcogen ions, the ratios of which vary according to properties desired. It has been shown that the application of heat to cells of chalcogenic material cause a large alteration in resistance to the range of 4 orders of magnitude. It is this effect upon which chalcogenidebased commercial memories rely. Upon removal of the heat source, the chalcogenide rapidly cools and remains frozen in the excited state. It has also been shown that the chalcogenide expands in volume because of the applied heat, meaning that the coefficient of expansion of chalcogenic
Neuromechanical Basis of Kinesiology.
ERIC Educational Resources Information Center
Enoka, Roger M.
This textbook provides a scientific basis for the study of human motion. The eight chapters are organized under three major sections. Part One--The Force-Motion Relationship--contains chapters on (1) motion; (2) force; (3) types of movement analysis. In Part Two--The Simple Joint System--chapters concern (4) simple joint system components; (5)…
Diverse deformation patterns of Aleutian volcanoes from InSAR
Lu, Zhiming; Dzurisin, D.; Wicks, C.; Power, J.
Interferometric synthetic aperture radar (InSAR) is capable of measuring ground-surface deformation with centimeter-to-subcentimeter precision at a spatial resolution of tens of meters over an area of hundreds to thousands of square kilometers. With its global coverage and all-weather imaging capability, InSAR has become an increasingly important measurement technique for constraining magma dynamics of volcanoes over remote regions such as the Aleutian Islands. The spatial pattern of surface deformation data derived from InSAR images enables the construction of detailed mechanical models to enhance the study of magmatic processes. This paper summarizes the diverse deformation patterns of the Aleutian volcanoes observed with InSAR and demonstrates that deformation patterns and associated magma supply mechanisms in the Aleutians are diverse and vary between volcanoes. These findings provide a basis for improved models and better understanding of magmatic plumbing systems.
Fréchet-algebraic deformation quantizations
NASA Astrophysics Data System (ADS)
Waldmann, S.
In this review I present some recent results on the convergence properties of formal star products. Based on a general construction of a Fréchet topology for an algebra with countable vector space basis I discuss several examples from deformation quantization: the Wick star product on the flat phase space m2n gives a first example of a Fréchet algebraic framework for the canonical commutation relations. More interesting, the star product on the Poincare disk can be treated along the same lines, leading to a non-trivial example of a convergent star product on a curved Kahler manifold.
Creep deformation of TD-nickel chromium
NASA Technical Reports Server (NTRS)
Kane, R. D.; Ebert, L. J.
An investigation was conducted of the mechanical behavioral characteristics of thoria-dispersed (TD) NiCr materials at elevated temperatures. The experimental procedure used is discussed along with the significance of the obtained results. Attention is given to basic creep behavior and creep thermal activation parameter measurements. It is found that the overall creep behavior of TD-NiCr can be explained on the basis of the relative contributions of two parallel-concurrent deformation mechanisms, including diffusion controlled grain boundary sliding and dislocation motion.
Demonstration of Double EIT Using Coupled Harmonic Oscillators and RLC Circuits
ERIC Educational Resources Information Center
Harden, Joshua; Joshi, Amitabh; Serna, Juan D.
Single and double electromagnetically induced transparencies (EIT) in a medium, consisting of four-level atoms in the inverted-Y configuration, are discussed using mechanical and electrical analogies. A three-coupled spring-mass system subject to damping and driven by an external force is used to represent the four-level atom mechanically. The…
Exact Solution of a Quantum Forced Time-Dependent Harmonic Oscillator
has met with limited success because of analytical difficulties, although progress has been made during the past three decades. 1 -5 Camiz et al6 have...M. R. Felx, E. Fijalkow and A. Munier, Phys. Lett. A 74, 11 (1979). 5. J. G. Hartly and J. R. Ray, Phys. Rev. A 2_4, 2873 (1981). 6. P. Camiz , A
Propagator for the general time-dependent harmonic oscillator with application to an ion trap
Harari, Gal; Ben-Aryeh, Yacob; Mann, Ady
We present the simplest possible formula for the propagator of the general time-dependent quadratic Hamiltonian, including linear terms. The method is based on the use of a linear time-dependent invariant and requires only the solution of a linear homogeneous second-order ordinary differential equation corresponding to the classical quadratic Hamiltonian. We give an example for the case of the Paul trap.
Decoherence of a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Brouard, S.; Alonso, D.; Sokolovski, D.
We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double-well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a ''coherent'' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power-law) or rapid (Gaussian) decoherence of the mean values themselves.
Time-Independent Variational Approach to Inelastic Collisions of a Particle with a Harmonic Oscillator
could. The criterion for the validity of semiclassical calculation is that, for given initial oscillator and incident energies, the ;% possible...This is an expression of the correspondence principle. As is well known, suitable semiclassical calculations may give rather accurate results even when...follows: I "> - Ikot> + Co +' VKT >, (6) where ;o,> is the normalized eigen function of Ho and Go is the Green s function, defined by ',.4 G lim (7) -oE-Ho
Differential invariants of feedback transformations for quasi-harmonic oscillation equations
NASA Astrophysics Data System (ADS)
Gritsenko, Dmitry S.; Kiriukhin, Oleg M.
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie pseudo-group of local feedback transformations. In particular, considered class describes behavior of conservative mechanical systems. We construct the class of rational differential invariants that separate regular orbits. It is well known that differential invariants form algebra with respect to the operation of addition and multiplication (Alekseevskij et al. 1991) [20]. In our case, constructed rational differential operators form a field (in algebraic sense). Rational differential invariants were studied by Rosenlicht (1956, 1963) [25,26], Kruglikov and Lychagin (2011) [24].
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
ERIC Educational Resources Information Center
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
Exact Wave Functions and Coherent States of a Damped Driven Harmonic Oscillator
result of Pedrosa ( 1 7 ) and is somewhat different in form from that of Korsch. (18) Here, we point out that for a given equation of motion there can be...Eq. (32) in Ref. 8 should be corrected such as (27ruu ) - (21ru ) 16. C. C. Gerry, Phys. Rev. A 31, 2721 (1985). 17. I. A. Pedrosa , J. Math. Phys. 28
Sessile drop deformations under an impinging jet
NASA Astrophysics Data System (ADS)
Feng, James Q.
The problem of steady axisymmetric deformations of a liquid sessile drop on a flat solid surface under an impinging gas jet is of interest for understanding the fundamental behavior of free surface flows as well as for establishing the theoretical basis in process design for the Aerosol direct-write technology. It is studied here numerically using a Galerkin finite-element method, by computing solutions of Navier-Stokes equations. For effective material deposition in Aerosol printing, the desired value of Reynolds number for the laminar gas jet is found to be greater than ~500. The sessile drop can be severely deformed by an impinging gas jet when the capillary number is approaching a critical value beyond which no steady axisymmetric free surface deformation can exist. Solution branches in a parameter space show turning points at the critical values of capillary number, which typically indicate the onset of free surface shape instability. By tracking solution branches around turning points with an arc-length continuation algorithm, critical values of capillary number can be accurately determined. Near turning points, all the free surface profiles in various parameter settings take a common shape with a dimple at the center and bulge near the contact line. An empirical formula for the critical capillary number for sessile drops with contact angle is derived for typical ranges of jet Reynolds number and relative drop sizes especially pertinent to Aerosol printing.
A generalized anisotropic deformation formulation for geomaterials
NASA Astrophysics Data System (ADS)
Lei, Z.; Rougier, Esteban; Knight, E. E.; Munjiza, A.; Viswanathan, H.
In this paper, the combined finite-discrete element method (FDEM) has been applied to analyze the deformation of anisotropic geomaterials. In the most general case geomaterials are both non-homogeneous and non-isotropic. With the aim of addressing anisotropic material problems, improved 2D FDEM formulations have been developed. These formulations feature the unified hypo-hyper elastic approach combined with a multiplicative decomposition-based selective integration for volumetric and shear deformation modes. This approach is significantly different from the co-rotational formulations typically encountered in finite element codes. Unlike the co-rotational formulation, the multiplicative decomposition-based formulation naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. This approach can be implemented for a whole family of finite elements from solids to shells and membranes. This novel 2D FDEM based material formulation was designed in such a way that the anisotropic properties of the solid can be specified in a cell by cell basis, therefore enabling the user to seed these anisotropic properties following any type of spatial variation, for example, following a curvilinear path. In addition, due to the selective integration, there are no problems with volumetric or shear locking with any type of finite element employed.
Algorithmic deformation of matrix factorisations
NASA Astrophysics Data System (ADS)
Carqueville, Nils; Dowdy, Laura; Recknagel, Andreas
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these algorithms and apply them to several examples. Apart from explicit results in concrete cases, this leads to a novel way to generate new matrix factorisations via nilpotent substitutions, and to criteria whether boundary obstructions can be lifted by bulk deformations.
Radioactive Waste Management Basis
Perkins, B K
The purpose of this Radioactive Waste Management Basis is to describe the systematic approach for planning, executing, and evaluating the management of radioactive waste at LLNL. The implementation of this document will ensure that waste management activities at LLNL are conducted in compliance with the requirements of DOE Order 435.1, Radioactive Waste Management, and the Implementation Guide for DOE Manual 435.1-1, Radioactive Waste Management Manual. Technical justification is provided where methods for meeting the requirements of DOE Order 435.1 deviate from the DOE Manual 435.1-1 and Implementation Guide.
NASA Astrophysics Data System (ADS)
Price, C. E.; Shepard, J. R.
We compute properties of the nucleon in a hybrid chiral model based on the linear σ-model with quark degrees of freedom treated explicity. In contrast to previous calculations, we do not use the hedgehog ansatz. Instead we solve self-consistently for a state with well defined spin and isospin projections. We allow this state to be deformed and find that, although d- and g-state admixtures in the predominantly s-state single quark wave functions are not large, they have profound effects on many nucleon properties including magnetic moments and gA. Our best fit parameters provide excellent agreement with experiment but are much different from those determined in hedgehog calculations.
[Rheumatic forefoot deformities].
Fuhrmann, R
The frequency and extent of rheumatic forefoot deformities have been greatly reduced since the introduction of disease-modifying antirheumatic drugs (DMARD). The accompanying reduction in arthritic destruction of joints opens up new treatment options whereby priority is given to joint preservation. This is true for the first middle foot ray as well as for the small toe rays. Whereas resection arthroplasty of the metatarsophalangeal joints II-V was previously considered the gold standard treatment, joint-preserving operative procedures (e.g. metatarsal osteotomy and periarticular soft tissue interventions) are now being increasingly more propagated. Resection arthroplasty of the first midfoot ray has major biomechanical disadvantages so that it is not surprising that reconstructive procedures are given priority. In patients with severe arthritic destruction of the first metatarsophalangeal joint, arthrodesis has substantial biomechanical advantages compared to resection arthroplasty. Nevertheless, it has not yet been confirmed that fusion leads to superior clinical results.
[Spectrum research on metamorphic and deformation of tectonically deformed coals].
Li, Xiao-Shi; Ju, Yi-Wen; Hou, Quan-Lin; Lin, Hong
The structural and compositive evolution of tectonically deformed coals (TDCs) and their influencing factors were investigated and analyzed in detail through Fourier transform infrared spectroscopy (FTIR) and laser Raman spectra analysis. The TDC samples (0.7% < Ro,max <3.1%) were collected from Huaibei coalfield with different deformation mechanisms and intensity. The FTIR of TDCs shows that the metamorphism and the deformation affect the degradation and polycondensation process of macromolecular structure to different degree. The Raman spectra analysis indicates that secondary structure defects can be produced mainly by structural deformation, also the metamorphism influences the secondary structure defects and aromatic structure. Through comprehensive analysis, it was discussed that the ductile deformation could change to strain energy through the increase and accumulation of dislocation in molecular structure units of TDC, and it could make an obvious influence on degradation and polycondensation. While the brittle deformation could change to frictional heat energy and promote the metamorphism and degradation of TDC structure, but has less effect on polycondensation. Furthermore, degradation is the main reason for affecting the structural evolution of coal in lower metamorphic stage, and polycondensation is the most important controlling factor in higher metamorphic stage. Under metamorphism and deformation, the small molecules which break and fall off from the macromolecular tructure of TDC are preferentially replenished and embedded into the secondary structure defects or the residual aromatic rings were formed into aromatic structure by polycondensation. This process improved the stability of coal structure. It is easier for ductile deformation of coal to induce the secondary structure defects than brittle deformation.
Perceptual transparency from image deformation
Kawabe, Takahiro; Maruya, Kazushi; Nishida, Shin'ya
Human vision has a remarkable ability to perceive two layers at the same retinal locations, a transparent layer in front of a background surface. Critical image cues to perceptual transparency, studied extensively in the past, are changes in luminance or color that could be caused by light absorptions and reflections by the front layer, but such image changes may not be clearly visible when the front layer consists of a pure transparent material such as water. Our daily experiences with transparent materials of this kind suggest that an alternative potential cue of visual transparency is image deformations of a background pattern caused by light refraction. Although previous studies have indicated that these image deformations, at least static ones, play little role in perceptual transparency, here we show that dynamic image deformations of the background pattern, which could be produced by light refraction on a moving liquid's surface, can produce a vivid impression of a transparent liquid layer without the aid of any other visual cues as to the presence of a transparent layer. Furthermore, a transparent liquid layer perceptually emerges even from a randomly generated dynamic image deformation as long as it is similar to real liquid deformations in its spatiotemporal frequency profile. Our findings indicate that the brain can perceptually infer the presence of "invisible" transparent liquids by analyzing the spatiotemporal structure of dynamic image deformation, for which it uses a relatively simple computation that does not require high-level knowledge about the detailed physics of liquid deformation. PMID:26240313
A simulation study of planar swaging deformation
NASA Astrophysics Data System (ADS)
Zhang, Cheng-Gen; Jen, Gwang-Shen; Su, Gwang-Huei
Planar swaging deformation was studied with a photoplastic method. The domestic polycarbonate was used as a simulation material. The full-field strain distribution for planar swaging deformation was obtained. The average error of the calculated strain was less than 7 percent. The deformation area and the effect of friction on deformation area were studied with the characteristics of photoplasticity. This paper points out the special features of planar swaging deformation and the effect of lubrication on deformation flow.
Femoral deformity planning: intentional placement of the apex of deformity.
Fabricant, Peter D; Camara, James M; Rozbruch, S Robert
Traditionally, correction of femoral deformity has been performed with osteotomies through the center of rotation of angulation (CORA), but the CORA location is not always practical. If the osteotomy is created at a site adjacent to the CORA, an additional translation must be performed to accurately correct the deformity. However, at times, the ideal osteotomy site may require an unfeasible amount of translation. Multiple osteotomies may also be problematic, and when overcorrection of the mechanical axis is planned, the CORA method is not practical.This article describes a novel method by which the surgeon may choose the location of the osteotomy regardless of the location of the CORA and may consolidate a multiapical deformity into a single corrective osteotomy. Furthermore, intentional mechanical axis overcorrection may be performed to unload knee joint arthritis. Simple, complex, and multiapical deformities may now be corrected via a single familiar surgical procedure, such as a distal femoral osteotomy, and the need for translation is eliminated.
Videogrammetric Model Deformation Measurement Technique
NASA Technical Reports Server (NTRS)
Burner, A. W.; Liu, Tian-Shu
The theory, methods, and applications of the videogrammetric model deformation (VMD) measurement technique used at NASA for wind tunnel testing are presented. The VMD technique, based on non-topographic photogrammetry, can determine static and dynamic aeroelastic deformation and attitude of a wind-tunnel model. Hardware of the system includes a video-rate CCD camera, a computer with an image acquisition frame grabber board, illumination lights, and retroreflective or painted targets on a wind tunnel model. Custom software includes routines for image acquisition, target-tracking/identification, target centroid calculation, camera calibration, and deformation calculations. Applications of the VMD technique at five large NASA wind tunnels are discussed.
Control of micromachined deformable mirrors
NASA Technical Reports Server (NTRS)
Agronin, M. L.; Bartman, R.; Hadaegh, F. Y.; Kaiser, W.; Wang, P. K. C.
A micromachined deformable mirror with pixelated electrostatic actuators is proposed. The paper begins with a physical description of the proposed mirror. Then a mathematical model in the form of a nonlinear partial differential equation describing the mirror surface deformations is derived. This model is used to derive the required voltages for the actuators to achieve a specified static deformation of the mirror surface. This is followed by the derivation of a static nonlinear feedback controller for achieving noninteracting actuation. Then the structure for a complete control system for wavefront correction is proposed. The paper concludes with a discussion of the physical implementation of the proposed control system.
Dynamic soft tissue deformation estimation based on energy analysis
NASA Astrophysics Data System (ADS)
Gao, Dedong; Lei, Yong; Yao, Bin
The needle placement accuracy of millimeters is required in many needle-based surgeries. The tissue deformation, especially that occurring on the surface of organ tissue, affects the needle-targeting accuracy of both manual and robotic needle insertions. It is necessary to understand the mechanism of tissue deformation during needle insertion into soft tissue. In this paper, soft tissue surface deformation is investigated on the basis of continuum mechanics, where a geometry model is presented to quantitatively approximate the volume of tissue deformation. The energy-based method is presented to the dynamic process of needle insertion into soft tissue based on continuum mechanics, and the volume of the cone is exploited to quantitatively approximate the deformation on the surface of soft tissue. The external work is converted into potential, kinetic, dissipated, and strain energies during the dynamic rigid needle-tissue interactive process. The needle insertion experimental setup, consisting of a linear actuator, force sensor, needle, tissue container, and a light, is constructed while an image-based method for measuring the depth and radius of the soft tissue surface deformations is introduced to obtain the experimental data. The relationship between the changed volume of tissue deformation and the insertion parameters is created based on the law of conservation of energy, with the volume of tissue deformation having been obtained using image-based measurements. The experiments are performed on phantom specimens, and an energy-based analytical fitted model is presented to estimate the volume of tissue deformation. The experimental results show that the energy-based analytical fitted model can predict the volume of soft tissue deformation, and the root mean squared errors of the fitting model and experimental data are 0.61 and 0.25 at the velocities 2.50 mm/s and 5.00 mm/s. The estimating parameters of the soft tissue surface deformations are proven to be useful
Deformation Detection of Potential Landslide with InSAR Observation
NASA Astrophysics Data System (ADS)
Liu, Yuzhou; Liao, Mingsheng; Shi, Xuguo; Zhang, Lu
Influenced by geological and climate conditions, Guide County has been identified as a landslide prone area. Multi-temporal InSAR technique can implement continuous earth surface deformation detection with long time scale and wide geography coverage. In this research, we employ the SBAS method to survey potential landslide in Guide County. Two anomalous deformation regions have been detected by L-band PALSAR stacks. Preliminary correlation between the time series deformation and triggering factors is analyzed to explore the driving mechanism for landslide movement. As a consequence, L-band SAR has a good application potential in landslide monitoring and the results can be the basis for landslide recognizing and early warning.
Deformed Calogero-Sutherland model and fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Atai, Farrokh; Langmann, Edwin
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.
Variable focal length deformable mirror
Headley, Daniel; Ramsey, Marc; Schwarz, Jens
A variable focal length deformable mirror has an inner ring and an outer ring that simply support and push axially on opposite sides of a mirror plate. The resulting variable clamping force deforms the mirror plate to provide a parabolic mirror shape. The rings are parallel planar sections of a single paraboloid and can provide an on-axis focus, if the rings are circular, or an off-axis focus, if the rings are elliptical. The focal length of the deformable mirror can be varied by changing the variable clamping force. The deformable mirror can generally be used in any application requiring the focusing or defocusing of light, including with both coherent and incoherent light sources.
ROCK DEFORMATION. Final Progress Report
The Gordon Research Conference (GRC) on ROCK DEFORMATION was held at II Ciocco from 5/19/02 thru 5/24/02. Emphasis was placed on current unpublished research and discussion of the future target areas in this field.
Taylor, W. C.
Ten children with gross deformity of the external ear were observed. In six the facial bones were underdeveloped on the same side as the deformed ear. In all six there was a congenital abnormality of the kidney or upper urinary tract, usually on the same side as the deformed ear. In addition there were usually other associated congenital defects in each case. In the remaining four children the facial bones appeared normal, and pyelography showed no abnormality of the urinary tract. In these four children there were no other associated defects. These observations emphasize the importance of investigating the urinary tract in children with gross deformity of the external ear, especially where there is an associated underdevelopment of the facial bones. PMID:14317453
Anisotropic ripple deformation in phosphorene
Kou, Liangzhi; Ma, Yandong; Smith, Sean C.; ...
Here, two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticitymore » theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.« less
Anisotropic ripple deformation in phosphorene
Kou, Liangzhi; Ma, Yandong; Smith, Sean C.; Chen, Changfeng
Here, two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.
Anisotropic Ripple Deformation in Phosphorene.
Kou, Liangzhi; Ma, Yandong; Smith, Sean C; Chen, Changfeng
Two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.
Plastic Deformation of Granular Materials
discontinuities. These result will be important in our granular flow work, when considering viscoplastic constitutive relations (i.e. relaxation systems...5 CUNDN( NUMRES Plastic Deformation of Granular Materials (U) 61102F 6. AUTHOR(S) 2304/A4 Dr. E. Bruce Pitman 7 PERFORMING ORGANIZATION NA .h • 8...lose hyperbolicity. 98 3 81 061! SUBJECT TERMS 15. NUMBER OF PAGES granular material ; plastic deformation; hyperbolic 12 equations 16. PRICE CODE 17
Cleft Nasal Deformity and Rhinoplasty
Kaufman, Yoav; Buchanan, Edward P.; Wolfswinkel, Erik M.; Weathers, William M.; Stal, Samuel
The cleft nasal deformity is a complex challenge in plastic surgery involving the skin, cartilage, mucosa, and skeletal platform. Ever since Blair and Brown first described the intricacies of the cleft pathology in 1931, the appropriate approach has been extensively debated in the literature with respect to timing, technique, and extent of surgical intervention. In this article, the authors review the literature and summarize the various modalities for achieving a successful rhinoplasty in the patient with a cleft nasal deformity. PMID:24179452
Time-Dependent Deformation Modelling for a Chopped-Glass Fiber Composite for Automotive Durability Design Criteria
Ren, W
Time-dependent deformation behavior of a polymeric composite with chopped-glass-fiber reinforcement was investigated for automotive applications, The material under stress was exposed to representative automobile service environments. Results show that environment has substantial effects on time-dependent deformation behavior of the material. The data were analyzed and experimentally-based models developed for the time-dependent deformation behavior as a basis for automotive structural durability design criteria.
Two-temperature continuum thermomechanics of deforming amorphous solids
NASA Astrophysics Data System (ADS)
Kamrin, Ken; Bouchbinder, Eran
There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent, finite-deformation, continuum framework for deforming amorphous solids. The basic premise is that the configurational degrees of freedom of the material - the part of the internal energy/entropy that corresponds to mechanically stable microscopic configurations - are characterized by a configurational temperature that might differ from that of the vibrational degrees of freedom, which equilibrate rapidly with an external heat bath. This results in an approximate internal energy decomposition into weakly interacting configurational and vibrational subsystems, which exchange energy following a Fourier-like law, leading to a thermomechanical framework permitting two well-defined temperatures. In this framework, internal variables, that carry information about the state of the material equilibrate with the configurational subsystem, are explicitly associated with energy and entropy of their own, and couple to a viscoplastic flow rule. The coefficients that determine the rate of flow of entropy and heat between different internal systems are proposed to explicitly depend on the rate of irreversible deformation. As an application of this framework, we discuss two constitutive models for the response of glassy materials, a simple phenomenological model and a model related to the concept of Shear-Transformation-Zones as the basis for internal variables. The models account for several salient features of glassy deformation phenomenology. Directions for future investigation are briefly discussed.
Using surface deformation to infer reservoir dilation induced by injection
NASA Astrophysics Data System (ADS)
Nanayakkara, Asanga Sanjeewee
Reservoir dilations occur due to variety of subsurface injection operations including waste disposal, waterflooding, steam injection, CO 2 sequestration and aquifer storage recovery. These reservoir dilations propagate to the surrounding formations and extend up to the ground surface resulting in surface deformations. The surface deformations can be measured by using various technologies such as tiltmeters and interferometric synthetic aperture radar (InSAR) and they can be inverted to infer reservoir dilations by solving an ill-posed inverse problem. This concept forms the basis of the research work presented in this thesis. Initially, the characteristics of the surface and subsurface deformations (induced by the injection operations) and correlations between them were investigated in detail by applying both analytical (based on center of dilatation approach) and numerical methods (fully coupled finite element method). Then, a simple set of guidelines to obtain quick estimates for the surface heave characteristics were proposed. The guidelines are in the form of simple analytical equations or charts and thereby they could be very useful in obtaining preliminary assessment for the surface deformation characteristics induced by the subsurface injection operations. Next, the mathematical aspects of the inverse problem were discussed in detail and the factors affecting the accuracy of the inverse solution were investigated through an extensive parametric study including both two-dimensional and three-dimensional problems. Then, a method was developed to infer reservoir dilation (with high accuracy and high spatial resolution) using a limited number of surface deformation measurements. The proposed method was applied to infer the reservoir dilation induced by a waste disposal operation conducted at Frog Lake, Alberta and the practical issues pertaining to the proposed method were discussed. Finally, guidelines for tiltmeter array design were proposed and
Analysis of Mining Terrain Deformation Characteristics with Deformation Information System
NASA Astrophysics Data System (ADS)
Blachowski, Jan; Milczarek, Wojciech; Grzempowski, Piotr
Mapping and prediction of mining related deformations of the earth surface is an important measure for minimising threat to surface infrastructure, human population, the environment and safety of the mining operation itself arising from underground extraction of useful minerals. The number of methods and techniques used for monitoring and analysis of mining terrain deformations is wide and increasing with the development of geographical information technologies. These include for example: terrestrial geodetic measurements, global positioning systems, remote sensing, spatial interpolation, finite element method modelling, GIS based modelling, geological modelling, empirical modelling using the Knothe theory, artificial neural networks, fuzzy logic calculations and other. The aim of this paper is to introduce the concept of an integrated Deformation Information System (DIS) developed in geographic information systems environment for analysis and modelling of various spatial data related to mining activity and demonstrate its applications for mapping and visualising, as well as identifying possible mining terrain deformation areas with various spatial modelling methods. The DIS concept is based on connected modules that include: the spatial database - the core of the system, the spatial data collection module formed by: terrestrial, satellite and remote sensing measurements of the ground changes, the spatial data mining module for data discovery and extraction, the geological modelling module, the spatial data modeling module with data processing algorithms for spatio-temporal analysis and mapping of mining deformations and their characteristics (e.g. deformation parameters: tilt, curvature and horizontal strain), the multivariate spatial data classification module and the visualization module allowing two-dimensional interactive and static mapping and three-dimensional visualizations of mining ground characteristics. The Systems's functionality has been presented on
Possible future directions for understanding transpressional deformation and oblique tectonics
NASA Astrophysics Data System (ADS)
Tikoff, Basil; Davis, Joshua; Titus, Sarah
In some sense, it was unlikely that transpression (+- transtension) should become the avenue for discussion about three-dimensional deformations generally, including - in roughly chronological order - strain partitioning, non-steady state deformation, triclinic deformation, and emphasis on flow apophyses (vs stress or strain). We speculate that there were two reasons for this path. First, as highlighted by the work of Sanderson and Marchini (1984), a mathematically very simple deformation can give rise to a variety of complicated effects. The implications of the partitioning of the stretching and vorticity of a deforming system are still not fully appreciated in structural geology or, particularly, in allied fields (experimental deformation, geophysics). There is still significant understanding yet to be gained in the response of real rocks to simple, three-dimensional boundary conditions. Second, transpression is a widely applicable deformation style, especially at the plate boundary scale. Any area of oblique convergence or divergence that has straight and parallel flow lines, which are not strictly normal or tangential to a straight plate boundary, will undergo transpressional or transtensional deformation. Shear zones can also exhibit transpressional deformation, but may exhibit slight variations from end-member models. There are a variety of ways in which mathematical advances may further our understanding of transpressional systems. We present a framework for our ongoing work, which involves statistical analysis of various geologic quantities, such as lineation-foliation pairs, ellipsoids, and homogeneous deformations. At its core, our approach consists of transferring standard multivariate statistical techniques to geologic sample spaces, using exponential mappings. Analyses include normality tests, estimates of mean and variance, and hypothesis testing. These tools can inform a variety of geologic modeling questions in more mathematically rigorous ways. For
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
NASA Astrophysics Data System (ADS)
Kaercher, P. M.; Zepeda-Alarcon, E.; Prakapenka, V.; Kanitpanyacharoen, W.; Smith, J.; Sinogeikin, S. V.; Wenk, H. R.
The crystal structure of the high pressure SiO2 polymorph stishovite has been studied in detail, yet little is known about its deformation mechanisms. Information about how stishovite deforms under stress is important for understanding subduction of quartz-bearing crustal rocks into the mantle. Particularly, stishovite is elastically anisotropic and thus development of crystallographic preferred orientation (CPO) during deformation may contribute to seismic anomalies in the mantle. We converted a natural sample of flint to stishovite in a laser heated diamond anvil cell and compressed the stishovite aggregate up to 38 GPa. Diffraction patterns were collected in situ in radial geometry at the Advanced Light Source (ALS) and the Advanced Photon Source (APS) to examine development of CPO during deformation. We find that (001) poles preferentially align with the compression direction and infer deformation mechanisms leading to the observed CPO with visco-plastic self consistent (VPSC) polycrystal plasticity models. Our results show pyramidal and basal slip are most likely active at high pressure and ambient temperature, in agreement with transmission electron microscopy (TEM) studies of rutile (TiO2) and paratellurite (TeO2), which are isostructural to stishovite. Conversely other TEM studies of stishovite done at higher temperature suggest dominant prismatic slip. This indicates that a variety of slip systems may be active in stishovite, depending on conditions. As a result, stishovite's contribution to the seismic signature in the mantle may vary as a function of pressure and temperature and thus depth.
Finite deformation analysis of geomaterials
NASA Astrophysics Data System (ADS)
Jeremi, Boris; Runesson, Kenneth; Sture, Stein
The mathematical structure and numerical analysis of classical small deformation elasto-plasticity is generally well established. However, development of large deformation elastic-plastic numerical formulation for dilatant, pressure sensitive material models is still a research area.In this paper we present development of the finite element formulation and implementation for large deformation, elastic-plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process.The algorithm is tested in conjunction with the novel hyperelasto-plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto-plastic problems in geomechanics.We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS-89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching.
Bilateral cleft lip nasal deformity
Singh, Arun Kumar; Nandini, R.
Bilateral cleft lip nose deformity is a multi-factorial and complex deformity which tends to aggravate with growth of the child, if not attended surgically. The goals of primary bilateral cleft lip nose surgery are, closure of the nasal floor and sill, lengthening of the columella, repositioning of the alar base, achieving nasal tip projection, repositioning of the lower lateral cartilages, and reorienting the nares from horizontal to oblique position. The multiplicity of procedures in the literature for correction of this deformity alludes to the fact that no single procedure is entirely effective. The timing for surgical intervention and its extent varies considerably. Early surgery on cartilage may adversely affect growth and development; at the same time, allowing the cartilage to grow in an abnormal position and contributing to aggravation of deformity. Some surgeons advocate correction of deformity at an early age. However, others like the cartilages to grow and mature before going in for surgery. With peer pressure also becoming an important consideration during the teens, the current trend is towards early intervention. There is no unanimity in the extent of nasal dissection to be done at the time of primary lip repair. While many perform limited nasal dissection for the fear of growth retardation, others opt for full cartilage correction at the time of primary surgery itself. The value of naso-alveolar moulding (NAM) too is not universally accepted and has now more opponents than proponents. Also most centres in the developing world have neither the personnel nor the facilities for the same. The secondary cleft nasal deformity is variable and is affected by the extent of the original abnormality, any prior surgeries performed and alteration due to nasal growth. This article reviews the currently popular methods for correction of nasal deformity associated with bilateral cleft lip, it's management both at the time of cleft lip repair and also secondarily
Deformation of second and third quantization
NASA Astrophysics Data System (ADS)
Faizal, Mir
In this paper, we will deform the second and third quantized theories by deforming the canonical commutation relations in such a way that they become consistent with the generalized uncertainty principle. Thus, we will first deform the second quantized commutator and obtain a deformed version of the Wheeler-DeWitt equation. Then we will further deform the third quantized theory by deforming the third quantized canonical commutation relation. This way we will obtain a deformed version of the third quantized theory for the multiverse.
CMAC with General Basis Functions.
Chun-Shin, Lin; Ching-Tsan, Chiang
The cerebellar model articulation controller (CMAC) is often used in learning control. It can be viewed as a basis function network (BFN). The conventional CMAC uses local constant basis functions. A disadvantage is that its output is constant within each quantized state and the derivative information is not preserved. If the constant basis functions are replaced by non-constant differentiable basis functions, the derivative information will be able to be stored into the structure as well. In this paper, the generalized scheme that uses general basis functions is investigated. The conventional CMAC is a special case of the generalized technique. The mathematical foundation for the modified scheme is derived and the convergence of learning is proved. Simulations for the CMAC with Gaussian basis functions (GBFs) are performed to demonstrate the improvement of accuracy in modeling, and the capability in providing derivative information. Copyright 1996 Elsevier Science Ltd
Transverse deformations of extreme horizons
NASA Astrophysics Data System (ADS)
Li, Carmen; Lucietti, James
We consider the inverse problem of determining all extreme black hole solutions to the Einstein equations with a prescribed near-horizon geometry. We investigate this problem by considering infinitesimal deformations of the near-horizon geometry along transverse null geodesics. We show that, up to a gauge transformation, the linearised Einstein equations reduce to an elliptic PDE for the extrinsic curvature of a cross-section of the horizon. We deduce that for a given near-horizon geometry there exists a finite dimensional moduli space of infinitesimal transverse deformations. We then establish a uniqueness theorem for transverse deformations of the extreme Kerr horizon. In particular, we prove that the only smooth axisymmetric transverse deformation of the near-horizon geometry of extreme Kerr, such that cross-sections of the horizon are marginally trapped surfaces, corresponds to that of the extreme Kerr black hole. Furthermore, we determine all smooth and biaxisymmetric transverse deformations of the near-horizon geometry of the five-dimensional extreme Myers-Perry black hole with equal angular momenta. We find a three parameter family of solutions such that cross-sections of the horizon are marginally trapped, which is more general than the known black hole solutions. We discuss the possibility that they correspond to new five-dimensional vacuum black holes.
Chaetal deformities in aquatic oligochaeta
Brinkhurst, R.O.; Wetzel, M.J.
Gross deformities in the chaetae of specimens of the tubificid Potamothrix hammoniensis were described by Milbrink from Lake Vaenern, Sweden. This lake is one of the most mercury-polluted major lakes of the world. Statistical tests showed a highly significant correlation between the incidence of deformities and the mercury concentration in the sediments. Changes in the pulp and paper mill process led to marked reduction in specimens with deformities. Similarly modified specimens of various species have been observed at a number of sites contaminated with heavy metals or oil residues in North America. Experimental work on chaetal form has demonstrated changes due to conductivity which have also been observed in saline inland waters. These experiments suggest that chaetae may be shed and replaced by worms every few days. EDX observation of chaetae indicated that metals may accumulate in them, and so provide a potential depuration mechanism. Independent physiological studies suggest that worms may be capable of regulating their metal levels.
Finite Deformation of Magnetoelastic Film
Barham, Matthew Ian
A nonlinear two-dimensional theory is developed for thin magnetoelastic lms capable of large deformations. This is derived directly from three-dimensional theory. Signi cant simpli cations emerge in the descent from three dimensions to two, permitting the self eld generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers with two material models. First weak magnetization is investigated leading to a free energy where magnetization and deformation are un-coupled. The second closely couples the magnetization and deformation. Numerical solutions are obtained to equilibrium boundary-value problems in which the membrane is subjected to lateral pressure and an applied magnetic eld. An instability is inferred and investigated for the weak magnetization material model.
Deformed Richardson-Gaudin model
NASA Astrophysics Data System (ADS)
Kulish, P.; Stolin, A.; Johannesson, L. H.
The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows the algebraic construction of its eigenstates. In this work we show that the quantum group theory provides a possibility to deform the Hamiltonian preserving integrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term into the auxiliary L-operator which generates integrals of motion of the system. Moreover, the quantum inverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These states have a highly complex entanglement structure which require further investigation.
Deformation of Unentangled Swollen Gels
NASA Astrophysics Data System (ADS)
Sariyer, Ozan; Panyukov, Sergey; Rubinstein, Michael
We study the deformation characteristics (Poisson's ratios and stress-strain relations) of unentangled gels swollen and uniaxially or biaxially deformed in excess solvent by considering the balance of osmotic pressure and elastic stress in unconstrained dimensions. Our scaling theory predicts a crossover from theta solvent behavior to marginal solvent behavior upon stretching gels that are in concentrated regime at swelling equilibrium - a phenomenon that was experimentally observed long ago, but not understood theoretically. For gels that are in the semidilute good solvent regime at swelling equilibrium, we predict a crossover to theta solvent behavior upon compression and a crossover to marginal solvent behavior upon stretching. Our theory reproduces the previously known results for equilibrium swelling degree as well as known deformation characteristics in theta and athermal solvents.
Shock metamorphism of deformed quartz
NASA Technical Reports Server (NTRS)
Gratz, Andrew J.; Christie, John; Tyburczy, James; Ahrens, Thomas; Pongratz, Peter
The effect produced by shock loading (to peak pressures of 12 and 24) on deformed synthetic quartz containing a dislocation and abundant bubbles and small inclusions was investigated, and the relationships between preexisting dislocation density shock lamellae in the target material were examined. The resultant material was found to be inhomogeneously deformed and extremely fractured. Results of TEM examinations indicate that no change in dislocation density was caused by shock loading except in regions containing shock lamellae, where the dislocation density was lowered. The shock-induced defects tend to nucleate on and be controlled by preexisting stress concentrators; shock lamellae, glassy veins, and most curviplanar defects form in tension, presumably during release. An extremely mobile silica fluid is formed and injected into fractures during release, which forcibly removes crystalline fragments from vein walls. It is concluded that shock deformation in quartz is dominated by fracture and melting.
Deformation processes in forging ceramics
NASA Technical Reports Server (NTRS)
Cannon, R. M.; Rhodes, W. H.
The deformation processes involved in the forging of refractory ceramic oxides were investigated. A combination of mechanical testing and forging was utilized to investigate both the flow and fracture processes involved. Deformation studies of very fine grain Al203 revealed an apparent transition in behavior, characterized by a shift in the strain rate sensitivity from 0.5 at low stresses to near unity at higher stresses. The behavior is indicative of a shift in control between two dependent mechanisms, one of which is indicated to be cation limited diffusional creep with significant boundary enhancement. The possible contributions of slip, indicated by crystallographic texture, interface control of the diffusional creep and inhomogeneous boundary sliding are also discussed. Additional experiments indicated an independence of deformation behavior on MgO doping and retained hot pressing impurities, at least for ultrafine grained material, and also an independence of test atmosphere.
Dislocation structure and deformation hardening alloy fcc single crystals at the mesolevel
NASA Astrophysics Data System (ADS)
Teplyakova, L. A.; Kunitsyna, T. S.; Koneva, N. A.; Kozlov, E. V.; Kondratyuk, A. A.; Zboikova, N. A.; Kakushkin, Yu A.; Iakhin, A. A.
The article presents the evaluation results of impacts of various strengthening mechanisms to flow stress. Such evaluations were made on the basis of the measured parameters of the dislocation substructure formed in monocrystals of [001]-Ni3Fe alloy deformed by compression within the stage II. It was found that the main impact to deformation resistance in the alloys with net substructure is made by the mechanism of dislocation impediment, which is caused by contact interaction between moving dislocations and forest dislocations.
Microstructure of deformed graywacke sandstones
Dengler, L.A.
Microsctures in low-permeability graywacke sandstones were studied by optical and scanning electron microscopy (SEM). SEM specimens were prepared by ion-bombardment of thick polished samples. The undeformed rock contains grains in a matrix composed primarily of authigenic chlorite and kaolinite. Chlorite platelets are randomly arranged in face-to-edge relation to one another. Kaolinite occurs as pseudohexagonal crystals stacked face-to-face in pore filling books. Uniaxial-stress experiments covered a range of confining pressures from .1 to 600 MPa. Below 50 MPa confining pressure, intergranular fracturing occurs within the fault zone and near the sample's cylindrical surface. Between 100 and 300 MPa confining pressure, fault zones contain highly fractured grains, gauge and slickensides on grain surfaces. At 600 MPa, the sample contains a diffuse shear zone of highly fractured grains and no well-defined fault. In all samples, the distribution of microcracks is heterogeneous. Different clay minerals exhibit different modes of deformation. Chlorite structure responds to applied stress by compaction, reducing both pore size and volume. Chlorite platelets are plastically deformed in even the least strained samples. Kaolinite does not deform plastically in any of the samples examined. Deformation of kaolinite is restricted to toppling of the book structure. Dilatant crack growth was studied in two samples unloaded prior to failure. Uniaxially-strained samples deform primarily along grain boundaries, producing intergranular cracks and realignment of chlorite platelets. Intragranular crack density is linearly related to axial-strain, although grains are less fractured than in uniaxially-stressed samples tested at equivalent mean pressures. Cracks are rarely longer than a grain diameter. Nuclear-explosively deformed samples were recovered after the Rio Blanco gas stimulation experiment. (JGB)
Switching deformation mode during natural faulting in Carrara marbles.
NASA Astrophysics Data System (ADS)
Molli, Giancarlo
A study on meso- and microstructural features of a high angle normal fault observed in the Alpi Apuane NW Tuscany (Italy) is presented to document switching in the deformation mode during different evolutionary stages of a fault zone growth in naturally deformed Carrara marble. The studied fault was formed at c.3 Km of depth and belongs to structures related to the most recent deformation history of the Alpi Apuane metamorphic core (from c.4 Ma until now, Fellin et al. 2007; Molli, 2008). On the basis of deformation mechanisms and their chronology interpreted from cross-cutting relationships, different stages of the fault zone evolution have been recognized. An early stage of deformation (stage 1) was associated with extensional and shear veins now observable in both hangingwall and footwall blocks as part of the deformation zone developed at decameter-scale. Geochemical data indicate vein-development in a locally closed system where a "stationary" fluid phase migrates over meter scale distances (Molli et al., in press). During stage 2, a localization of the deformation, possibly in precursory coarse grained calcite/quartz shear veins of stage 1, took place. During this second stage crystal-plastic deformation affected areas at the head and along the hanging wall rim of fractures accommodating fault tip distorsions in a way recalling the mode-II geometry of stable crack propagation (Atkinson, 1987; Vermilye and Scholtz, 1993; Kim et al., 2004). Following pervasive cataclasis (stage 3) characterizes a plurimeter-wide dilational jog between two non-parallel main slip surfaces with brecciation and far-derived fluids channelling leading to significant geochemical alteration of the fault rocks with respect to the protolith (Molli et al., in press). Cataclastic deformation produced a grain size refinement and a decimetric thick fault core asymmetrically bounded by the upper main slip surface. Deformation was then localized within ultracataclasite of the fault core where
Controllable objective with deformable mirrors
Agafonov, V V; Safronov, A G
A new optical device - an objective with deformable mirrors and parameters controlled in the dynamic regime is proposed. The computer simulation of the objective is performed. The dependences of some parameters of the objective on the control voltage are determined. The simulation showed that the ranges of control of the rear focal segment and the focal distance for the objective with the focal distance 602 mm were 1057 and 340 mm, respectively, which is substantially greater than in the control of an equivalent deformable mirror. (laser applications and other topics in quantum electronics)
Analytical volcano deformation source models
Lisowski, Michael; Dzurisin, Daniel
Primary volcanic landforms are created by the ascent and eruption of magma. The ascending magma displaces and interacts with surrounding rock and fluids as it creates new pathways, flows through cracks or conduits, vesiculates, and accumulates in underground reservoirs. The formation of new pathways and pressure changes within existing conduits and reservoirs stress and deform the surrounding rock. Eruption products load the crust. The pattern and rate of surface deformation around volcanoes reflect the tectonic and volcanic processes transmitted to the surface through the mechanical properties of the crust.
Ilizarov principles of deformity correction.
Spiegelberg, B; Parratt, T; Dheerendra, S K; Khan, W S; Jennings, R; Marsh, D R
Ilizarov frames provide a versatile fixation system for the management of bony deformities, fractures and their complications. The frames give stability, soft tissue preservation, adjustability and functionality allowing bone to realise its full osteogenic potential. It is important that we have a clear and concise understanding of the Ilizarov principles of deformity correction to best make use of this fixation system. In this review article, the history of Ilizarov frame, the basic sciences behind it, the mechanical principles governing its use and the clinical use of the fixation system are discussed.
Ilizarov principles of deformity correction
Spiegelberg, B; Parratt, T; Dheerendra, SK; Khan, WS; Jennings, R; Marsh, DR
Ilizarov frames provide a versatile fixation system for the management of bony deformities, fractures and their complications. The frames give stability, soft tissue preservation, adjustability and functionality allowing bone to realise its full osteogenic potential. It is important that we have a clear and concise understanding of the Ilizarov principles of deformity correction to best make use of this fixation system. In this review article, the history of Ilizarov frame, the basic sciences behind it, the mechanical principles governing its use and the clinical use of the fixation system are discussed. PMID:20353638
Cavity coalescence in superplastic deformation
Stowell, M.J.; Livesey, D.W.; Ridley, N.
An analysis of the probability distribution function of particles randomly dispersed in a solid has been applied to cavitation during superplastic deformation and a method of predicting cavity coalescence developed. Cavity size distribution data were obtained from two microduplex nickel-silver alloys deformed superplastically to various extents at elevated temperature, and compared to theoretical predictions. Excellent agreement occurred for small void sizes but the model underestimated the number of voids in the largest size groups. It is argued that the discrepancy results from a combination of effects due to non-random cavity distributions and to enhanced growth rates and incomplete spheroidization of the largest cavities.
A mesh deformation technique based on two-step solution of the elasticity equations
NASA Astrophysics Data System (ADS)
Huang, Guo; Huang, Haiming; Guo, Jin
In the computation of fluid mechanics problems with moving boundaries, including fluid-structure interaction, fluid mesh deformation is a common problem to be solved. An automatic mesh deformation technique for large deformations of the fluid mesh is presented on the basis of a pseudo-solid method in which the fluid mesh motion is governed by the equations of elasticity. A two-dimensional mathematical model of a linear elastic body is built by using the finite element method. The numerical result shows that the proposed method has a better performance in moving the fluid mesh without producing distorted elements than that of the classic one-step methods.
A mesh deformation technique based on two-step solution of the elasticity equations
NASA Astrophysics Data System (ADS)
Huang, Guo; Huang, Haiming; Guo, Jin
In the computation of fluid mechanics problems with moving boundaries, including fluid-structure interaction, fluid mesh deformation is a common problem to be solved. An automatic mesh deformation technique for large deformations of the fluid mesh is presented on the basis of a pseudo-solid method in which the fluid mesh motion is governed by the equations of elasticity. A two-dimensional mathematical model of a linear elastic body is built by using the finite element method. The numerical result shows that the proposed method has a better performance in moving the fluid mesh without producing distorted elements than that of the classic one-step methods.
An automated deformable image registration evaluation of confidence tool
NASA Astrophysics Data System (ADS)
Kirby, Neil; Chen, Josephine; Kim, Hojin; Morin, Olivier; Nie, Ke; Pouliot, Jean
Deformable image registration (DIR) is a powerful tool for radiation oncology, but it can produce errors. Beyond this, DIR accuracy is not a fixed quantity and varies on a case-by-case basis. The purpose of this study is to explore the possibility of an automated program to create a patient- and voxel-specific evaluation of DIR accuracy. AUTODIRECT is a software tool that was developed to perform this evaluation for the application of a clinical DIR algorithm to a set of patient images. In brief, AUTODIRECT uses algorithms to generate deformations and applies them to these images (along with processing) to generate sets of test images, with known deformations that are similar to the actual ones and with realistic noise properties. The clinical DIR algorithm is applied to these test image sets (currently 4). From these tests, AUTODIRECT generates spatial and dose uncertainty estimates for each image voxel based on a Student's t distribution. In this study, four commercially available DIR algorithms were used to deform a dose distribution associated with a virtual pelvic phantom image set, and AUTODIRECT was used to generate dose uncertainty estimates for each deformation. The virtual phantom image set has a known ground-truth deformation, so the true dose-warping errors of the DIR algorithms were also known. AUTODIRECT predicted error patterns that closely matched the actual error spatial distribution. On average AUTODIRECT overestimated the magnitude of the dose errors, but tuning the AUTODIRECT algorithms should improve agreement. This proof-of-principle test demonstrates the potential for the AUTODIRECT algorithm as an empirical method to predict DIR errors.
Hydromechanical Normal Deformation Experiments and Coupling to Fracture Surface Geometry
NASA Astrophysics Data System (ADS)
Thörn, J.; Fransson, A. M.
Civil engineering structures founded in fractured crystalline rock, such as the Fennoscandian Shield (Norway-Sweden-Finland) requires allowance for both stability and/or deformations of the rock mass and groundwater ingress and groundwater pressure changes. Coupling these issues could be the key to solving the challenges that arise from construction of e.g. hydropower dams, road and railroad tunnels, and most certainly the construction of nuclear waste repositories within fractured crystalline rock, all of which are currently planned in Sweden. Excavation related deformation in fractures may cause groundwater leakage even from the most elaborate pre-excavation grouting works. A better understanding on hydraulically (or grouting) induced deformations in the near-field of tunnels, where the stress field is re-distributed due to the opening may both provide a basis for more accurate numerical modelling and grouting or excavation procedures that minimize the damage on the completed grouting fans. Subjects of this study were experiments conducted as measurement of deformations in boreholes close to tunnels due to stepwise injection tests, and laboratory hydromechanical experiments conducted as flow and normal deformation measurements in a permeameter during cycles of up to 2.5 MPa confining pressure, and subsequent surface scanning of the samples for coupling of HM-results to geometric appearance, aperture and contact geometry. When expressed in terms of hydraulic aperture (b) and fracture normal stiffness (kn) the results of both in situ and lab experiments support a previously suggested relationship based on field data where kn is inversely proportional to roughly b2. The relationship was assumed to be valid for low compressive stress across fractures with limited previous deformation. One important data set used to establish the relationship was transmissivity and storage coefficients from hydraulic interference tests previously performed at Äspö Hard Rock
Highly deformable nanofilaments in flow
NASA Astrophysics Data System (ADS)
Pawłowska, S.
Experimental analysis of hydrogel nanofilaments conveyed by flow is conducted to help in understanding physical phenomena responsible for transport properties and shape deformations of long bio-objects, like DNA or proteins. Investigated hydrogel nanofilaments exhibit typical macromolecules-like behavior, as spontaneous conformational changes and cross-flow migration. Results of the experiments indicate critical role of thermal fluctuations behavior of single filaments.
Beak deformities in Northwestern Crows: evidence of a multispecies epizootic
Van Hemert, Caroline; Handel, Colleen M.
Beak abnormalities are rare among adult birds and, typically, are not widespread in a given population, within a region, or across multiple species. A high concentration of beak deformities was recently documented in Black-capped Chickadees (Poecile atricapillus) and other resident avian species in Alaska. We describe a parallel condition in Northwestern Crows (Corvus caurinus) that signals the emergence of a multispecies epizootic. On the basis of 186 Northwestern Crows captured at six sites in Alaska during 2007 and 2008, we estimated the prevalence of beak deformities in adults to be 16.9 ± 5.3%, the highest rate of gross deformities ever recorded in a wild bird population. Prevalence varied among sites and was as high as 36% on the Kenai Peninsula, which suggests possible epizootic clusters. We also documented beak abnormalities in an additional 148 Northwestern Crows in south-central and southeastern Alaska and in 64 crows near Vancouver, British Columbia, and Puget Sound, Washington, a region where both Northwestern Crows and American Crows (C. brachyrhynchos) occur. The increase in frequency and distribution of crows observed with abnormal beaks throughout the Pacific Northwest since the late 1990s indicates a geographic expansion of this problem. Affected crows exhibited elongated and often crossed beaks that were morphologically similar to deformities documented in Black-capped Chickadees and other species in Alaska over approximately the same period. Additional research is needed to determine the etiology and potential adverse effects on bird populations affected by this disorder.
Finite deformations of an electroelastic circular cylindrical tube
NASA Astrophysics Data System (ADS)
Melnikov, Andrey; Ogden, Ray W.
In this paper the theory of nonlinear electroelasticity is used to examine deformations of a pressurized thick-walled circular cylindrical tube of soft dielectric material with closed ends and compliant electrodes on its curved boundaries. Expressions for the dependence of the pressure and reduced axial load on the deformation and a potential difference between, or uniform surface charge distributions on, the electrodes are obtained in respect of a general isotropic electroelastic energy function. To illustrate the behaviour of the tube, specific forms of energy functions accounting for different mechanical properties coupled with a deformation independent quadratic dependence on the electric field are used for numerical purposes, for a given potential difference and separately for a given charge distribution. Numerical dependences of the non-dimensional pressure and reduced axial load on the deformation are obtained for the considered energy functions. Results are then given for the thin-walled approximation as a limiting case of a thick-walled cylindrical tube without restriction on the energy function. The theory described herein provides a general basis for the detailed analysis of the electroelastic response of tubular dielectric elastomer actuators, which is illustrated for a fixed axial load in the absence of internal pressure and fixed internal pressure in the absence of an applied axial load.
PLATFORM DEFORMATION PHASE CORRECTION FOR THE AMiBA-13 COPLANAR INTERFEROMETER
Liao, Yu-Wei; Lin, Kai-Yang; Huang, Yau-De; Ho, Paul T. P.; Chen, Ming-Tang; Locutus Huang, Chih-Wei; Koch, Patrick M.; Nishioka, Hiroaki; Umetsu, Keiichi; Han, Chih-Chiang; Li, Chao-Te; Martin-Cocher, Pierre; Oshiro, Peter; Proty Wu, Jiun-Huei; Cheng, Tai-An; Fu, Szu-Yuan; Wang, Fu-Cheng; Liu, Guo-Chin; Molnar, Sandor M.; Chang, Yu-Yen E-mail: email@example.com
We present a new way to solve the platform deformation problem of coplanar interferometers. The platform of a coplanar interferometer can be deformed due to driving forces and gravity. A deformed platform will induce extra components into the geometric delay of each baseline and change the phases of observed visibilities. The reconstructed images will also be diluted due to the errors of the phases. The platform deformations of The Yuan-Tseh Lee Array for Microwave Background Anisotropy (AMiBA) were modeled based on photogrammetry data with about 20 mount pointing positions. We then used the differential optical pointing error between two optical telescopes to fit the model parameters in the entire horizontal coordinate space. With the platform deformation model, we can predict the errors of the geometric phase delays due to platform deformation with a given azimuth and elevation of the targets and calibrators. After correcting the phases of the radio point sources in the AMiBA interferometric data, we recover 50%-70% flux loss due to phase errors. This allows us to restore more than 90% of a source flux. The method outlined in this work is not only applicable to the correction of deformation for other coplanar telescopes but also to single-dish telescopes with deformation problems. This work also forms the basis of the upcoming science results of AMiBA-13.
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
Kaercher, Pamela M.; Zepeda-Alarcon, Eloisa; Prakapenka, Vitali B.; ...
Although the crystal structure of the high pressure SiO2 polymorph stishovite has been studied in detail, little is known about the development of crystallographic preferred orientation (CPO) during deformation in stishovite. Insight into CPO and associated deformation mechanics of stishovite would provide important information for understanding subduction of quartz-bearing crustal rocks into the mantle. To study CPO development, we converted a natural sample of flint to stishovite in a laser heated diamond anvil cell and compressed the stishovite aggregate up to 38 GPa. We collected diffraction patterns in radial geometry to examine in situ development of crystallographic preferred orientation andmore » find that (001) poles preferentially align with the compression direction. Viscoplastic self-consistent modeling suggests the most likely slip systems at high pressure and ambient temperature are pyramidal and basal slip.« less
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
NASA Astrophysics Data System (ADS)
Kaercher, Pamela M.; Zepeda-Alarcon, Eloisa; Prakapenka, Vitali B.; Kanitpanyacharoen, Waruntorn; Smith, Jesse S.; Sinogeikin, Stanislav; Wenk, Hans-Rudolf
Although the crystal structure of the high-pressure SiO2 polymorph stishovite has been studied in detail, little is known about the development of crystallographic preferred orientation (CPO) during deformation in stishovite. Insight into CPO and associated deformation mechanics of stishovite would provide important information for understanding subduction of quartz-bearing crustal rocks into the mantle. To study CPO development, we converted a natural sample of flint to stishovite in a laser-heated diamond anvil cell and compressed the stishovite aggregate up to 38 GPa. We collected diffraction patterns in radial geometry to examine in situ development of crystallographic preferred orientation and find that (001) poles preferentially align with the compression direction. Viscoplastic self-consistent modeling suggests the most likely slip systems at high pressure and ambient temperature are pyramidal and basal slip.
Highly deformable bones: unusual deformation mechanisms of seahorse armor.
Porter, Michael M; Novitskaya, Ekaterina; Castro-Ceseña, Ana Bertha; Meyers, Marc A; McKittrick, Joanna
Multifunctional materials and devices found in nature serve as inspiration for advanced synthetic materials, structures and robotics. Here, we elucidate the architecture and unusual deformation mechanisms of seahorse tails that provide prehension as well as protection against predators. The seahorse tail is composed of subdermal bony plates arranged in articulating ring-like segments that overlap for controlled ventral bending and twisting. The bony plates are highly deformable materials designed to slide past one another and buckle when compressed. This complex plate and segment motion, along with the unique hardness distribution and structural hierarchy of each plate, provide seahorses with joint flexibility while shielding them against impact and crushing. Mimicking seahorse armor may lead to novel bio-inspired technologies, such as flexible armor, fracture-resistant structures or prehensile robotics.
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
Kaercher, Pamela M.; Zepeda-Alarcon, Eloisa; Prakapenka, Vitali B.; Kanitpanyacharoen, Waruntorn; Smith, Jesse S.; Sinogeikin, Stanislav; Wenk, Hans-Rudolf
Although the crystal structure of the high pressure SiO2 polymorph stishovite has been studied in detail, little is known about the development of crystallographic preferred orientation (CPO) during deformation in stishovite. Insight into CPO and associated deformation mechanics of stishovite would provide important information for understanding subduction of quartz-bearing crustal rocks into the mantle. To study CPO development, we converted a natural sample of flint to stishovite in a laser heated diamond anvil cell and compressed the stishovite aggregate up to 38 GPa. We collected diffraction patterns in radial geometry to examine in situ development of crystallographic preferred orientation and find that (001) poles preferentially align with the compression direction. Viscoplastic self-consistent modeling suggests the most likely slip systems at high pressure and ambient temperature are pyramidal and basal slip.
Clusterization and quadrupole deformation in nuclei
Cseh, J.; Algora, A.; Antonenko, N. V.; Jolos, R. V.; Scheid, W.; Darai, J.; Hess, P. O.
We study the interrelation of the clusterization and quadrupole deformation of atomic nuclei, by applying cluster models. Both the energetic stability and the exclusion principle is investigated. Special attention is paid to the relative orientations of deformed clusters.
Development of mathematical models and methods for calculation of rail steel deformation resistance of various chemical composition
NASA Astrophysics Data System (ADS)
Umansky, A. A.; Golovatenko, A. V.; Kadykov, V. N.; Dumova, L. V.
Using the device of the complex "Gleeble System 3800" the physical experimental studies of deformation resistance of chrome rail steel at different thermo-mechanical deformation parameters were carried out. On the basis of mathematical processing of experimental data the statistical model of dependence of the rail steel deformation resistance on the simultaneous influence of deformation degree, rate and temperature, as well as the steel chemical composition, was developed. The nature of influence of deformation parameters and the content of chemical elements in steel on its resistance to plastic deformation is scientifically substantiated. Verification of the adequacy of the proposed model by the comparative analysis of the calculated and actual rolling forces during passes in the universal rail-and-structural steel mill JSC "EVRAZ Consolidated West Siberian Metallurgical Plant" ("EVRAZ ZSMK") showed the possibility of its use for development and improvement of new modes of rails rolling.
Deformed special relativity and deformed symmetries in a canonical framework
Ghosh, Subir; Pal, Probir
In this paper we have studied the nature of kinematical and dynamical laws in {kappa}-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of {kappa}-Minkowski phase space algebra that yields the {kappa}-extended finite Lorentz transformations derived in [D. Kimberly, J. Magueijo, and J. Medeiros, Phys. Rev. D 70, 084007 (2004).]. This is a particular form of a deformed special relativity model that admits a modified energy-momentum dispersion law as well as noncommutative {kappa}-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and not {kappa}-Minkowski) phase space algebra and special relativity Lorentz transformation (and not {kappa}-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical {kappa}-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the {kappa}-particle.
3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization.
Noblet, Vincent; Heinrich, Christian; Heitz, Fabrice; Armspach, Jean-Paul
This paper deals with topology preservation in three-dimensional (3-D) deformable image registration. This work is a nontrivial extension of, which addresses the case of two-dimensional (2-D) topology preserving mappings. In both cases, the deformation map is modeled as a hierarchical displacement field, decomposed on a multiresolution B-spline basis. Topology preservation is enforced by controlling the Jacobian of the transformation. Finding the optimal displacement parameters amounts to solving a constrained optimization problem: The residual energy between the target image and the deformed source image is minimized under constraints on the Jacobian. Unlike the 2-D case, in which simple linear constraints are derived, the 3-D B-spline-based deformable mapping yields a difficult (until now, unsolved) optimization problem. In this paper, we tackle the problem by resorting to interval analysis optimization techniques. Care is taken to keep the computational burden as low as possible. Results on multipatient 3-D MRI registration illustrate the ability of the method to preserve topology on the continuous image domain.
Free vibrations and buckling analysis of laminated plates by oscillatory radial basis functions
NASA Astrophysics Data System (ADS)
Neves, A. M. A.; Ferreira, A. J. M.
In this paper the free vibrations and buckling analysis of laminated plates is performed using a global meshless method. A refined version of Kant's theorie which accounts for transverse normal stress and through-the-thickness deformation is used. The innovation is the use of oscillatory radial basis functions. Numerical examples are performed and results are presented and compared to available references. Such functions proved to be an alternative to the tradicional nonoscillatory radial basis functions.
Symmetries and deformations in the spherical shell model
NASA Astrophysics Data System (ADS)
Van Isacker, P.; Pittel, S.
We discuss symmetries of the spherical shell model that make contact with the geometric collective model of Bohr and Mottelson. The most celebrated symmetry of this kind is SU(3), which is the basis of Elliott's model of rotation. It corresponds to a deformed mean field induced by a quadrupole interaction in a single major oscillator shell N and can be generalized to include several major shells. As such, Elliott's SU(3) model establishes the link between the spherical shell model and the (quadrupole component of the) geometric collective model. We introduce the analogue symmetry induced by an octupole interaction in two major oscillator shells N-1 and N, leading to an octupole-deformed solution of the spherical shell model. We show that in the limit of large oscillator shells, N\\to ∞ , the algebraic octupole interaction tends to that of the geometric collective model.
Disorder-Driven Metal-Insulator Transitions in Deformable Lattices
NASA Astrophysics Data System (ADS)
Di Sante, Domenico; Fratini, Simone; Dobrosavljević, Vladimir; Ciuchi, Sergio
We show that, in the presence of a deformable lattice potential, the nature of the disorder-driven metal-insulator transition is fundamentally changed with respect to the noninteracting (Anderson) scenario. For strong disorder, even a modest electron-phonon interaction is found to dramatically renormalize the random potential, opening a mobility gap at the Fermi energy. This process, which reflects disorder-enhanced polaron formation, is here given a microscopic basis by treating the lattice deformations and Anderson localization effects on the same footing. We identify an intermediate "bad insulator" transport regime which displays resistivity values exceeding the Mott-Ioffe-Regel limit and with a negative temperature coefficient, as often observed in strongly disordered metals. Our calculations reveal that this behavior originates from significant temperature-induced rearrangements of electronic states due to enhanced interaction effects close to the disorder-driven metal-insulator transition.
Deformation of noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan
In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .
Variational approach and deformed derivatives
NASA Astrophysics Data System (ADS)
Weberszpil, J.; Helayël-Neto, J. A.
Recently, we have demonstrated that there exists a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis' scenario, with a local form of fractional-derivative operators for fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. Here, in this paper, we present an extension of the traditional calculus of variations for systems containing deformed-derivatives embedded into the Lagrangian and the Lagrangian densities for classical and field systems. The results extend the classical Euler-Lagrange equations and the Hamiltonian formalism. The resulting dynamical equations seem to be compatible with those found in the literature, specially with mass-dependent and with nonlinear equations for systems in classical and quantum mechanics. Examples are presented to illustrate applications of the formulation. Also, the conserved Noether current is worked out.
Deformation processes in forging ceramics
NASA Technical Reports Server (NTRS)
Cannon, R. M.; Rhodes, W. H.
The deformation processes involved in the forging of refractory ceramic oxides were investigated. A combination of mechanical testing and forging are utilized to investigate both the flow and fracture processes involved. An additional hemisphere forging was done which failed prematurely. Analysis and comparison with available fracture data for AL2O3 indicated possible causes of the failure. Examination of previous forgings indicated an increase in grain boundary cavitation with increasing strain.
Graviton resonances on deformed branes
NASA Astrophysics Data System (ADS)
Cruz, W. T.; Gomes, A. R.; Almeida, C. A. S.
Plane-wave solutions of Schrödinger-like equations obtained from the metric perturbations in 5D braneworld scenarios can present resonant modes. The search for those structures is important because they can provide us with massive modes with not suppressed couplings with the membrane. We propose in this paper the study of graviton Kaluza-Klein spectrum in a special kind of membrane that possesses internal structure. The interest in the study of these deformed defects is due to the fact that they have a richer internal structure that has implications in the matter energy density along the extra dimensions and this produces a space-time background whose curvature has a splitting, if compared to the usual kink-like models. Such models arise from (4, 1)-branes constructed with one scalar field coupled with gravity where we find two-kink solutions from deformations of a phi4 potential. The main objective of this work is to observe the effects of deformation process in the resonant modes as well as in the coupling between the graviton massive modes and the brane.
Integrable Deformations of T -Dual σ Models
NASA Astrophysics Data System (ADS)
Borsato, Riccardo; Wulff, Linus
We present a method to deform (generically non-Abelian) T duals of two-dimensional σ models, which preserves classical integrability. The deformed models are identified by a linear operator ω on the dualized subalgebra, which satisfies the 2-cocycle condition. We prove that the so-called homogeneous Yang-Baxter deformations are equivalent, via a field redefinition, to our deformed models when ω is invertible. We explain the details for deformations of T duals of principal chiral models, and present the corresponding generalization to the case of supercoset models.
Accidental degeneracies in nonlinear quantum deformed systems
NASA Astrophysics Data System (ADS)
Aleixo, A. N. F.; Balantekin, A. B.
We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.
Exploring Means of Determining Surface Deformation at Augustine Volcano
NASA Astrophysics Data System (ADS)
Lovick, J. T.; Lawlor, O.; Dean, K.; Dehn, J.; Freymueller, J.; Atwood, D.
The recent January 2006 eruption of Augustine Volcano followed a nearly a year of increased seismic activity, that has been actively monitored by the Alaska Volcano Observatory (AVO). The eruption has generated a topographical signal that GPS ground stations were able to monitor. This work addresses the question as to which other techniques are able to see this deformation. While we primarily use remotely sensed data, with SAR derived products and techniques as a focus, we also explore the use of ICESAT data. Deformation started in the summer of 2005, with a period of inflation leading up to the January 2006 eruption and which was then followed by a period deflation. The deformation of the flanks of Augustine island was subtle, and GPS stations at the perimeter of the island generally show less that 2cm of total deformation. The summit GPS stations show significantly greater inflation, however these stations were destroyed during the eruption. Traditional INSAR has difficulties when applied to a volcano like Augustine, due to the small area of the island, its large topographic relief, the deposition of ash over the large areas of the island and the long orbital repeat interval of current SAR satellites, all work against the technique. This does not mean however that the outlook is bleak, Permanent Scatterer (PS) INSAR related techniques show great potential. The scientific basis of each technique examined is explained along with the challenges, and limitations that are inherent therein. Deformation results obtained from each method are also presented, and compared with the GPS measurements. The following techniques are examined, 1) INSAR/DINSAR, 2) Permanent Scatterers, 3) Delta K interferometry, 4) ICESAT LIDAR integration, 5) SAR layover/shadow mapping and geometric techniques. Because eruptions at small island volcanoes are common throughout the Aleutian chain, techniques developed for the analysis of this eruption will have great applicability to these and
Occurrence of oral deformities in larval anurans
Drake, D.L.; Altig, R.; Grace, J.B.; Walls, S.C.
We quantified deformities in the marginal papillae, tooth rows, and jaw sheaths of tadpoles from 13 population samples representing three families and 11 sites in the southeastern United States. Oral deformities were observed in all samples and in 13.5-98% of the specimens per sample. Batrachochytrium dendrobatidis (chytrid) infections were detected in three samples. There was high variability among samples in the pattern and number of discovered deformities. Pairwise associations between oral structures containing deformities were nonrandom for several populations, especially those with B. dendrobatidis infections or high total numbers of deformities. Comparisons of deformities among samples using multivariate analyses revealed that tadpole samples grouped together by family. Analyses of ordination indicated that three variables, the number of deformities, the number of significant associations among deformity types within populations, and whether populations were infected with B. dendrobatidis, were significantly correlated with the pattern of deformities. Our data indicate that the incidence of oral deformities can be high in natural populations and that phylogeny and B. dendrobatidis infection exert a strong influence on the occurrence and type of oral deformities in tadpoles. ?? by the American Society of Ichthyologists and Herperologists.
Mesh deformation based on artificial neural networks
NASA Astrophysics Data System (ADS)
Stadler, Domen; Kosel, Franc; Čelič, Damjan; Lipej, Andrej
In the article a new mesh deformation algorithm based on artificial neural networks is introduced. This method is a point-to-point method, meaning that it does not use connectivity information for calculation of the mesh deformation. Two already known point-to-point methods, based on interpolation techniques, are also presented. In contrast to the two known interpolation methods, the new method does not require a summation over all boundary nodes for one displacement calculation. The consequence of this fact is a shorter computational time of mesh deformation, which is proven by different deformation tests. The quality of the deformed meshes with all three deformation methods was also compared. Finally, the generated and the deformed three-dimensional meshes were used in the computational fluid dynamics numerical analysis of a Francis water turbine. A comparison of the analysis results was made to prove the applicability of the new method in every day computation.
Helium release during shale deformation: Experimental validation
NASA Astrophysics Data System (ADS)
Bauer, Stephen J.; Gardner, W. Payton; Heath, Jason E.
This work describes initial experimental results of helium tracer release monitoring during deformation of shale. Naturally occurring radiogenic 4He is present in high concentration in most shales. During rock deformation, accumulated helium could be released as fractures are created and new transport pathways are created. We present the results of an experimental study in which confined reservoir shale samples, cored parallel and perpendicular to bedding, which were initially saturated with helium to simulate reservoir conditions, are subjected to triaxial compressive deformation. During the deformation experiment, differential stress, axial, and radial strains are systematically tracked. Release of helium is dynamically measured using a helium mass spectrometer leak detector. Helium released during deformation is observable at the laboratory scale and the release is tightly coupled to the shale deformation. These first measurements of dynamic helium release from rocks undergoing deformation show that helium provides information on the evolution of microstructure as a function of changes in stress and strain.
Identification of genes related to beak deformity of chickens using digital gene expression profiling.
Bai, Hao; Zhu, Jing; Sun, Yanyan; Liu, Ranran; Liu, Nian; Li, Dongli; Wen, Jie; Chen, Jilan
Frequencies of up to 3% of beak deformity (normally a crossed beak) occur in some indigenous chickens in China, such as and Beijing-You. Chickens with deformed beaks have reduced feed intake, growth rate, and abnormal behaviors. Beak deformity represents an economic as well as an animal welfare problem in the poultry industry. Because the genetic basis of beak deformity remains incompletely understood, the present study sought to identify important genes and metabolic pathways involved in this phenotype. Digital gene expression analysis was performed on deformed and normal beaks collected from Beijing-You chickens to detect global gene expression differences. A total of >11 million cDNA tags were sequenced, and 5,864,499 and 5,648,877 clean tags were obtained in the libraries of deformed and normal beaks, respectively. In total, 1,156 differentially expressed genes (DEG) were identified in the deformed beak with 409 being up-regulated and 747 down-regulated in the deformed beaks. qRT-PCR using eight genes was performed to verify the results of DGE profiling. Gene ontology (GO) analysis highlighted that genes of the keratin family on GGA25 were abundant among the DEGs. Pathway analysis showed that many DEGs were linked to the biosynthesis of unsaturated fatty acids and glycerolipid metabolism. Combining the analyses, 11 genes (MUC, LOC426217, BMP4, ACAA1, LPL, ALDH7A1, GLA, RETSAT, SDR16C5, WWOX, and MOGAT1) were highlighted as potential candidate genes for beak deformity in chickens. Some of these genes have been identified previously, while others have unknown function with respect to thus phenotype. To the best of our knowledge, this is the first genome-wide study to investigate the transcriptome differences in the deformed and normal beaks of chickens. The DEGs identified here are worthy of further functional characterization.
Innovative design of composite structures: Axisymmetric deformations of unsymmetrically laminated cylinders loaded in axial compression
NASA Technical Reports Server (NTRS)
Hyer, M. W.; Paraska, P. J.
The study focuses on the axisymmetric deformation response of unsymmetrically laminate cylinders loaded in axial compression by known loads. A geometrically nonlinear analysis is used. Though buckling is not studied, the deformations can be considered to be the prebuckling response. Attention is directed at three 16 layer laminates: a (90 sub 8/0 sub 8) sub T; a (0 sub 8/90 sub 8) sub T and a (0/90) sub 4s. The symmetric laminate is used as a basis for comparison, while the two unsymmetric laminates were chosen because they have equal but opposite bending-stretching effects. Particular attention is given to the influence of the thermally-induced preloading deformations that accompany the cool-down of any unsymmetric laminate from the consolidation temperature. Simple support and clamped boundary conditions are considered. It is concluded that: (1) The radial deformations of an unsymmetric laminate are significantly larger than the radial deformations of a symmetric laminate, although for both symmetric and unsymmetric laminates the large deformations are confined to a boundary layer near the ends of the cylinder; (2) For this nonlinear problem the length of the boundary layer is a function of the applied load; (3) The sign of the radial deformations near the supported end of the cylinder depends strongly on the sense (sign) of the laminate asymmetry; (4) For unsymmetric laminates, ignoring the thermally-induced preloading deformations that accompany cool-down results in load-induced deformations that are under predicted; and (5) The support conditions strongly influence the response but the influence of the sense of asymmetry and the influence of the thermally-induced preloading deformations are independent of the support conditions.
Identification of Genes Related to Beak Deformity of Chickens Using Digital Gene Expression Profiling
Sun, Yanyan; Liu, Ranran; Liu, Nian; Li, Dongli; Wen, Jie; Chen, Jilan
Frequencies of up to 3% of beak deformity (normally a crossed beak) occur in some indigenous chickens in China, such as and Beijing-You. Chickens with deformed beaks have reduced feed intake, growth rate, and abnormal behaviors. Beak deformity represents an economic as well as an animal welfare problem in the poultry industry. Because the genetic basis of beak deformity remains incompletely understood, the present study sought to identify important genes and metabolic pathways involved in this phenotype. Digital gene expression analysis was performed on deformed and normal beaks collected from Beijing-You chickens to detect global gene expression differences. A total of >11 million cDNA tags were sequenced, and 5,864,499 and 5,648,877 clean tags were obtained in the libraries of deformed and normal beaks, respectively. In total, 1,156 differentially expressed genes (DEG) were identified in the deformed beak with 409 being up-regulated and 747 down-regulated in the deformed beaks. qRT-PCR using eight genes was performed to verify the results of DGE profiling. Gene ontology (GO) analysis highlighted that genes of the keratin family on GGA25 were abundant among the DEGs. Pathway analysis showed that many DEGs were linked to the biosynthesis of unsaturated fatty acids and glycerolipid metabolism. Combining the analyses, 11 genes (MUC, LOC426217, BMP4, ACAA1, LPL, ALDH7A1, GLA, RETSAT, SDR16C5, WWOX, and MOGAT1) were highlighted as potential candidate genes for beak deformity in chickens. Some of these genes have been identified previously, while others have unknown function with respect to thus phenotype. To the best of our knowledge, this is the first genome-wide study to investigate the transcriptome differences in the deformed and normal beaks of chickens. The DEGs identified here are worthy of further functional characterization. PMID:25198128
ERIC Educational Resources Information Center
Weinberg, Robert A.
Discusses the molecular basis of cancer, focusing on genetics of the disease. Indicates that human cancers are initiated by oncogenes (altered versions of normal genes) and that in one case the critical alteration is a single point mutation that changes one amino acid in the protein encoded by the gene. (JN)
GASB's Basis of Accounting Project.
ERIC Educational Resources Information Center
Kovlak, Daniel L.
In July 1984, the Governmental Accounting Standards Board began its "Measurement Focus/Basis of Accounting" project, which addresses measurement issues and revenue and expenditure recognition problems involving governmental funds. This article explains the project's background, alternatives discussed by the board, and tentative…
Complete Basis Set Model Chemistries
NASA Astrophysics Data System (ADS)
Ochterski, Joseph Wallace
The major source of error in most ab initio calculations of molecular energies is the truncation of the one-electron basis set. Extrapolation to the complete basis set second -order (CBS2) limit using the N^{-1 } asymptotic convergence of N-configuration pair natural orbital (PNO) expansions can be combined with the use of relatively small basis sets for the higher-order correlation energy to develop cost effective computational models. Following this strategy, four new computational models denoted CBS-4, CBS-q, CBS-Q, and CBS-QCI/APNO are introduced. The mean absolute deviations (MAD) from experiment for the 125 energies of the G2 test set are 2.0, 1.7, 1.0 and 0.5 kcal/mol, respectively. The error distributions for all six models are indistinguishable from Gaussian distribution functions. Calculations on the cyclopropenyl radical and cyclopropenylidene provide new dissociation energies which are in accord with an interpretation of the thermochemistry emphasizing aromaticity. Several levels of theory are examined as candidates for the routine calculation of molecular geometries. The very simple UHF/3-21G* model gives bond lengths to an accuracy of +/-0.027 A compared with experiment for a test set of 69 small molecules. The commonly used MP2/6-31G* model (RMS error 0.025 A) offers virtually no improvement and use of the considerably more expensive QCISD calculations with the same basis set provides only a modest reduction to 0.020 A. However, spin projected MP3 calculations with a modified basis set including f -functions on Si, P, S, and Cl, reduce the RMS error to 0.010 A. This PMP3/6-31Gdf* model is recommended as a general scheme of geometry optimization for small molecules. The equilibrium structure and binding energy of the water dimer have been determined for several levels of ab initio theory. The basis set convergence of the SCF energy, the intramolecular and intermolecular MP2 energy, and higher-order effects, are examined separately and realistic error
Augmented Reality Marker Hiding with Texture Deformation.
Kawai, Norihiko; Sato, Tomokazu; Nakashima, Yuta; Yokoya, Naokazu
Augmented reality (AR) marker hiding is a technique to visually remove AR markers in a real-time video stream. A conventional approach transforms a background image with a homography matrix calculated on the basis of a camera pose and overlays the transformed image on an AR marker region in a real-time frame, assuming that the AR marker is on a planar surface. However, this approach may cause discontinuities in textures around the boundary between the marker and its surrounding area when the planar surface assumption is not satisfied. This paper proposes a method for AR marker hiding without discontinuities around texture boundaries even under nonplanar background geometry without measuring it. For doing this, our method estimates the dense motion in the marker's background by analyzing the motion of sparse feature points around it, together with a smooth motion assumption, and deforms the background image according to it. Our experiments demonstrate the effectiveness of the proposed method in various environments with different background geometries and textures.
Theory of the deformation of aligned polyethylene
Hammad, A.; Swinburne, T. D.; Hasan, H.; Del Rosso, S.; Iannucci, L.; Sutton, A. P.
Solitons are proposed as the agents of plastic and viscoelastic deformation in aligned polyethylene. Interactions between straight, parallel molecules are mapped rigorously onto the Frenkel–Kontorova model. It is shown that these molecular interactions distribute an applied load between molecules, with a characteristic transfer length equal to the soliton width. Load transfer leads to the introduction of tensile and compressive solitons at the chain ends to mark the onset of plasticity at a well-defined yield stress, which is much less than the theoretical pull-out stress. Interaction energies between solitons and an equation of motion for solitons are derived. The equation of motion is based on Langevin dynamics and the fluctuation–dissipation theorem and it leads to the rigorous definition of an effective mass for solitons. It forms the basis of a soliton dynamics in direct analogy to dislocation dynamics. Close parallels are drawn between solitons in aligned polymers and dislocations in crystals, including the configurational force on a soliton. The origins of the strain rate and temperature dependencies of the viscoelastic behaviour are discussed in terms of the formation energy of solitons. A failure mechanism is proposed involving soliton condensation under a tensile load. PMID:26339196
Incremental Carcass Theory of Polycrystalline Media at Large Elastic and Plastic Deformations
NASA Astrophysics Data System (ADS)
Akhundov, V. M.
A two-level carcass theory as applied to media with a polycrystalline structure at large elastic and plastic deformation of crystals (crystal grains) is presented. The theory is incremental, in accordance with the incremental nature of governing equations of a crystal, which take into account the prehistory of its deformation in the medium. The theory is based on the field of carcass (macroscopic) displacements, which determines the material displacements of carcass points and carcass (macroscopic) deformations of the medium. At the macromechanical level, the equations of macroscopic deformation and motion are given in an incremental form. At the micromechanical (locally structural) level, incremental microboundary-value problems for nodal presentation blocks of the polycrystalline material are solved on the basis of carcass displacements and their increments. From the internal fields of nodal blocks and their increments found, the incremental macroscopic stresses are determined, which allow one to close the system of equations of the macromechanical level of analysis.
Inflation-predictable behavior and co-eruption deformation at Axial Seamount
NASA Astrophysics Data System (ADS)
Nooner, Scott L.; Chadwick, William W.
Deformation of the ground surface at active volcanoes provides information about magma movements at depth. Improved seafloor deformation measurements between 2011 and 2015 documented a fourfold increase in magma supply and confirmed that Axial Seamount's eruptive behavior is inflation-predictable, probably triggered by a critical level of magmatic pressure. A 2015 eruption was successfully forecast on the basis of this deformation pattern and marked the first time that deflation and tilt were captured in real time by a new seafloor cabled observatory, revealing the timing, location, and volume of eruption-related magma movements. Improved modeling of the deformation suggests a steeply dipping prolate-spheroid pressure source beneath the eastern caldera that is consistent with the location of the zone of highest melt within the subcaldera magma reservoir determined from multichannel seismic results.
[Calculation of the strain-deformation condition of the spinal motor segment during loading].
Chumachenko, E N; Logashina, I V
A mathematical model is proposed to analyze the spinal strain-deformation condition resulting from axial and lateral g-loads generated by changes in the gravity field and/or pilot's maneuvering high-performance aircraft. The solution algorithm takes into account changes in the intervertebral disk pressure and the fibrous ring shape at the time of close-to-critical g values. Calculation of the spinal strain-deformation condition was implemented by the instrumentality of computer system SPLEN (KOMMEK ltd., Russia). Analysis of the spinal strain-deformation condition was made for 2 types of external loads, i.e. normal and unilateral with a bending moment. Maximum permissible loads on a spinal segment were evaluated, as well as distribution of strain intensity, mean strains, spinal deformation and destruction field was described. The constructed computer models could be used as a basis for developing a technique of predicting characteristic spinal injuries in consequence of specific extreme loads and pathologies.
Deformation and recrystallization mechanisms in naturally deformed sillimanites
NASA Astrophysics Data System (ADS)
Lambregts, P. J.; van Roermund, H. L. M.
Prismatic sillimanite (Al 2SiO 5), with a length between 0.3 and 2.5 mm, was obtained from a garnet migmatite. The sillimanite, naturally deformed at a temperature of 750 ° C and a confining pressure of 6 kbar, has been studied using optical and transmission electron microscopy techniques. Optical and universal stage measurements reveal undulatory extinction, "sharp" deformation-induced subgrain boundaries (subparallel to (001) and (010)) and minor recrystallization. Transmission electron microscopy shows free dislocations, dislocation loops, (110) planar defects and tiltwalls parallel to (001). Dislocations have Burgers vectors of [001] and [100]. All isolated
Leukocyte deformability: finite element modeling of large viscoelastic deformation.
Dong, C; Skalak, R
An axisymmetric deformation of a viscoelastic sphere bounded by a prestressed elastic thin shell in response to external pressure is studied by a finite element method. The research is motivated by the need for understanding the passive behavior of human leukocytes (white blood cells) and interpreting extensive experimental data in terms of the mechanical properties. The cell at rest is modeled as a sphere consisting of a cortical prestressed shell with incompressible Maxwell fluid interior. A large-strain deformation theory is developed based on the proposed model. General non-linear, large strain constitutive relations for the cortical shell are derived by neglecting the bending stiffness. A representation of the constitutive equations in the form of an integral of strain history for the incompressible Maxwell interior is used in the formulation of numerical scheme. A finite element program is developed, in which a sliding boundary condition is imposed on all contact surfaces. The mathematical model developed is applied to evaluate experimental data of pipette tests and observations of blood flow.
Advanced materials characterization based on full field deformation measurements
NASA Astrophysics Data System (ADS)
Carpentier, A. Paige
approximation must be independent of the deformation measurements, independent of the material properties (geometric stress approximation), and be simple for use in the industry. A remarkable benefit of the full-field deformation measurement is that it lets us observe the physical phenomena of the deformation which enables the derivation of simple and accurate geometric stress approximations. In particular, linear axial through the thickness strain distributions consistently measured in composite short-beam specimens allow a rigorous derivation of extremely simple stress approximations. The observation of linear through the thickness axial strain distributions has become the basis for eliminating the need of using Bernoulli-Euler kinematic assumptions of the rigid cross sections remaining perpendicular to the beam neutral axis throughout the deformation. Such assumptions are not consistent with the deformation mechanisms and therefore are arguable as a rigorous basis for stress approximation. Simple stress approximations are derived in this work based on the observations from the full-field deformation measurements; accuracy of such approximations are verified; and their limitations determined.
Plastic Deformation of Accreted Planetesimals
NASA Astrophysics Data System (ADS)
Kadish, J.
The early stages of planetesimal growth follow an accretion model (Weidenschilling, Icarus 2000), which influences the intrinsic strength of a body and may control how its shape evolves after growth. In previous work we have determined the stress field of an accreted planetesimal accounting for possible variation in the object's spin as it accretes (Kadish et al., IJSS In Press) At the end of growth, these objects are subject to transport mechanisms that can distribute them throughout the solar system. As they are transported these objects can be spun-up by tidal forces (Scheeres et al, Icarus 2000), YORP (Bottke et al., Asteroids III 2002), and collisions (Binzel et al., Asteroids II 1989). Such an increase of spin will cause perturbations to the initial stress field and may lead to failure. We are able to show analytically that failure is initiated on the object's surface and a plastic zone propagates inward as the object's spin is increased. If we model an accreted body as a conglomeration of rocks similar to a gravel or sand, the deformation in the region of failure is characterized using a Mohr-Coulomb failure criterion with negligible cohesion and zero hardening(e.g. Holsapple, Icarus 2001). Such a response is highly non-linear and must be solved using finite elements and iterative methods (Simo and Hughes, Computational Inelasticity 1998). Using the commercial finite element code ABAQUS, we present the shape deformation resulting from an elasto-plastic analysis of a spinning, self-gravitating accreted sphere that is spun-up after growth is complete. The methodology can be extended to model plastic deformation due to local failure for more complex planetesimal shapes, such as for the asteroid Kleopatra. This work has implications for the evolution of planetesimal shapes, the creation of binary and contact binary asteroids, and for the maximum spin rate of small planetary bodies.
Formation Flying and Deformable Instruments
NASA Astrophysics Data System (ADS)
Rio, Yvon
Astronomers have always attempted to build very stable instruments. They fight all that can cause mechanical deformation or image motion. This has led to well established technologies (autoguide, active optics, thermal control, tip/tilt correction), as well as observing methods based on the use of controlled motion (scanning, micro scanning, shift and add, chopping and nodding). Formation flying disturbs this practice. It is neither possible to reduce the relative motion to very small amplitudes, nor to control it at will. Some impacts on Simbol-X instrument design, and operation are presented.
Formation Flying and Deformable Instruments
Rio, Yvon
Astronomers have always attempted to build very stable instruments. They fight all that can cause mechanical deformation or image motion. This has led to well established technologies (autoguide, active optics, thermal control, tip/tilt correction), as well as observing methods based on the use of controlled motion (scanning, micro scanning, shift and add, chopping and nodding). Formation flying disturbs this practice. It is neither possible to reduce the relative motion to very small amplitudes, nor to control it at will. Some impacts on Simbol-X instrument design, and operation are presented.
Dissipation in deforming chaotic billiards
NASA Astrophysics Data System (ADS)
Barnett, Alexander Harvey
Chaotic billiards (hard-walled cavities) in two or more dimensions are paradigm systems in the fields of classical and quantum chaos. We study the dissipation (irreversible heating) rate in such billiard systems due to general shape deformations which are periodic in time. We are motivated by older studies of one-body nuclear dissipation and by anticipated mesoscopic applications. We review the classical and quantum linear response theories of dissipation rate and demonstrate their correspondence in the semiclassical limit. In both pictures, heating is a result of stochastic energy spreading. The heating rate can be expressed as a frequency-dependent friction coefficient μ(ω), which depends on billiard shape and deformation choice. We show that there is a special class of deformations for which μ vanishes as like a power law in the small- ω limit. Namely, for deformations which cause translations and dilations μ ~ ω4 whereas for those which cause rotations μ ~ ω2. This contrasts the generic case for which μ ~ ω4 We show how a systematic treatment of this special class leads to an improved version of the `wall formula' estimate for μ(0). We show that the special nature of dilation (a new result) is semiclassically equivalent to a quasi- orthogonality relation between the (undeformed) billiard quantum eigenstates on the boundary. This quasi- orthogonality forms the heart of a `scaling method' for the numerical calculation of quantum eigenstates, invented recently by Vergini and Saraceno. The scaling method is orders of magnitude more efficient than any other known billiard quantization method, however an adequate explanation for its success has been lacking until now. We explain the scaling method, its errors, and applications. We also present improvements to Heller's plane wave method. Two smaller projects conclude the thesis. Firstly, we give a new formalism for quantum point contact (QPC) conductance in terms of scattering cross-section in the half
Deformational characteristics of thermoplastic elastomers
NASA Astrophysics Data System (ADS)
Indukuri, Kishore K.
This thesis focuses primarily on the structure-property relationships of poly (styrene-ethylene-butylene-styrene) triblock copolymer TPEs. First evidence for strain-induced crystallization occurring in certain SEBS block copolymers has been established using unique techniques like deformation calorimetry, combined in-situ small angle X-ray and wide angle X-ray diffraction (SAXD/WAXD). Also the ramifications of such strain-induced crystallization on the mechanical properties like cyclic hysteresis, stress relaxation/creep retention of these SEBS systems have been studied. In addition, the structural changes in the morphology of these systems on deformation have been investigated using combined SAXD/WAXD setup. Small angle X-ray diffraction probed the changes at the nano-scale of polystyrene (PS) cylinders, while wide angle X-ray diffraction probed the changes at molecular length scales of the amorphous/crystalline domains of the elastomeric mid-block in these systems. New structural features at both these length scales have been observed and incorporated into the overall deformation mechanisms of the material. Continuous processing techniques like extrusion have been used to obtain ultra long-range order and orientation in these SEBS systems. Thus well ordered crystal like hexagonal packing of cylinders, where in each element in this hexagonal lattice can be individually addressed without any grain boundaries can be realized using these robust techniques. The effect of long-range order/orientation on the mechanical properties has been studied. In addition, these well ordered systems serve as model systems for evaluating deformation mechanisms of these SEBS systems, where the relative contributions of each of the phases can be estimated. EPDM/i-PP thermoplastic vulcanizates (TPVs) have micron size scale phase separated morphologies of EPDM rubber dispersed in a semicrystalline i-PP matrix as a result of the dynamic vulcanization process. Confocal microscopy studies
Tectonic deformation in southern California
NASA Technical Reports Server (NTRS)
Jackson, David D.
Our objectives were to use modem geodetic data, especially those derived from space techniques like Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), and the Global Positioning System (GPS) to infer crustal deformation in southern California and relate it to plate tectonics and earthquake hazard. To do this, we needed to collect some original data, write computer programs to determine positions of survey markers from geodetic observables, interpret time dependent positions in terms of velocity and earthquake caused episodic displacements, and construct a model to explain these velocities and displacements in terms of fault slip and plate movements.
Deformable Mirrors Correct Optical Distortions
NASA Technical Reports Server (NTRS)
By combining the high sensitivity of space telescopes with revolutionary imaging technologies consisting primarily of adaptive optics, the Terrestrial Planet Finder is slated to have imaging power 100 times greater than the Hubble Space Telescope. To this end, Boston Micromachines Corporation, of Cambridge, Massachusetts, received Small Business Innovation Research (SBIR) contracts from the Jet Propulsion Laboratory for space-based adaptive optical technology. The work resulted in a microelectromechanical systems (MEMS) deformable mirror (DM) called the Kilo-DM. The company now offers a full line of MEMS DMs, which are being used in observatories across the world, in laser communication, and microscopy.
A two-dimensional deformable phantom for quantitatively verifying deformation algorithms
Kirby, Neil; Chuang, Cynthia; Pouliot, Jean
Purpose: The incorporation of deformable image registration into the treatment planning process is rapidly advancing. For this reason, the methods used to verify the underlying deformation algorithms must evolve equally fast. This manuscript proposes a two-dimensional deformable phantom, which can objectively verify the accuracy of deformation algorithms, as the next step for improving these techniques. Methods: The phantom represents a single plane of the anatomy for a head and neck patient. Inflation of a balloon catheter inside the phantom simulates tumor growth. CT and camera images of the phantom are acquired before and after its deformation. Nonradiopaque markers reside on the surface of the deformable anatomy and are visible through an acrylic plate, which enables an optical camera to measure their positions; thus, establishing the ground-truth deformation. This measured deformation is directly compared to the predictions of deformation algorithms, using several similarity metrics. The ratio of the number of points with more than a 3 mm deformation error over the number that are deformed by more than 3 mm is used for an error metric to evaluate algorithm accuracy. Results: An optical method of characterizing deformation has been successfully demonstrated. For the tests of this method, the balloon catheter deforms 32 out of the 54 surface markers by more than 3 mm. Different deformation errors result from the different similarity metrics. The most accurate deformation predictions had an error of 75%. Conclusions: The results presented here demonstrate the utility of the phantom for objectively verifying deformation algorithms and determining which is the most accurate. They also indicate that the phantom would benefit from more electron density heterogeneity. The reduction of the deformable anatomy to a two-dimensional system allows for the use of nonradiopaque markers, which do not influence deformation algorithms. This is the fundamental advantage of this
Perceptual basis for reactive teleoperation.
Park, Y. S.; Ewing, T. F.; Boyle, J. M.; Yule, T. J.
To enhance task performance in partially structured environment, enhancement of teleoperation was proposed by introducing autonomous behaviors. Such autonomy is implemented based on reactive robotic architecture, where reactive motor agents that directly couples sensory inputs and motor actions become the building blocks. To this end, presented in this paper is a perceptual basis for the motor agents. The perceptual basis consists of perceptual agents that extracts environmental information from a structured light vision system and provide action oriented perception for the corresponding motor agents. Rather than performing general scene reconstruction, a perceptual agent directly provides the motion reference for the motor behavior. Various sensory mechanisms--sensor fission, fusion, and fashion--becomes basic building blocks of the perception process. Since perception is a process deeply intertwined with the motor actions, active perception may also incorporate motor behaviors as an integral perceptual process.
Authorization basis requirements comparison report
Brantley, W.M.
The TWRS Authorization Basis (AB) consists of a set of documents identified by TWRS management with the concurrence of DOE-RL. Upon implementation of the TWRS Basis for Interim Operation (BIO) and Technical Safety Requirements (TSRs), the AB list will be revised to include the BIO and TSRs. Some documents that currently form part of the AB will be removed from the list. This SD identifies each - requirement from those documents, and recommends a disposition for each to ensure that necessary requirements are retained when the AB is revised to incorporate the BIO and TSRs. This SD also identifies documents that will remain part of the AB after the BIO and TSRs are implemented. This document does not change the AB, but provides guidance for the preparation of change documentation.
Perceptual basis for reactive teleoperation
NASA Astrophysics Data System (ADS)
Park, Young S.; Ewing, Thomas F.; Boyle, James M.; Yule, Thomas J.
To improve task performance in partially structured environments, enhancements to teleoperation have been proposed by introducing autonomous behaviors. Such autonomy is implemented based on a reactive robotic architecture, where reactive motor agents that directly couple sensory inputs and motor actions become the building blocks. To this end, a perceptual basis for the motor agents is presented in this paper. The perceptual basis consists of perceptual agents that extract environmental information from a structured light vision system and provide action-oriented perception for the corresponding motor agents. Rather than performing general scene reconstruction, a perceptual agent directly provides the motion reference for the motor behavior. Various sensory mechanisms - sensor fission, fusion, and fashion - become basic building blocks of the perception process. Since perception is a process deeply intertwined with the motor actions, active perception may also incorporate motor behaviors as an integral perceptual process.
TCAP Aluminium Dissolution Flowsheet Basis
The Actinide Technology Section has proposed the use of an nitric acid HNO3 and potassium fluoride KF flowsheet for stripping palladium Pd from palladium-coated kieselguhr Pd/K and removing aluminum (Al) metal foam from the TCAP coils. The basis for the HNO3-KF flowsheet is drawn from many sources. A brief review of the sources will be presented. The basic flowsheet involves three process steps, each with its own chemistry.
Hanford Generic Interim Safety Basis
Lavender, J.C.
The purpose of this document is to identify WHC programs and requirements that are an integral part of the authorization basis for nuclear facilities that are generic to all WHC-managed facilities. The purpose of these programs is to implement the DOE Orders, as WHC becomes contractually obligated to implement them. The Hanford Generic ISB focuses on the institutional controls and safety requirements identified in DOE Order 5480.23, Nuclear Safety Analysis Reports.
Performance Basis for Airborne Separation
NASA Technical Reports Server (NTRS)
Wing, David J.
Emerging applications of Airborne Separation Assistance System (ASAS) technologies make possible new and powerful methods in Air Traffic Management (ATM) that may significantly improve the system-level performance of operations in the future ATM system. These applications typically involve the aircraft managing certain components of its Four Dimensional (4D) trajectory within the degrees of freedom defined by a set of operational constraints negotiated with the Air Navigation Service Provider. It is hypothesized that reliable individual performance by many aircraft will translate into higher total system-level performance. To actually realize this improvement, the new capabilities must be attracted to high demand and complexity regions where high ATM performance is critical. Operational approval for use in such environments will require participating aircraft to be certified to rigorous and appropriate performance standards. Currently, no formal basis exists for defining these standards. This paper provides a context for defining the performance basis for 4D-ASAS operations. The trajectory constraints to be met by the aircraft are defined, categorized, and assessed for performance requirements. A proposed extension of the existing Required Navigation Performance (RNP) construct into a dynamic standard (Dynamic RNP) is outlined. Sample data is presented from an ongoing high-fidelity batch simulation series that is characterizing the performance of an advanced 4D-ASAS application. Data of this type will contribute to the evaluation and validation of the proposed performance basis.
Deformation During Friction Stir Welding
NASA Technical Reports Server (NTRS)
White, Henry J.
Friction Stir Welding (FSW) is a solid state welding process that exhibits characteristics similar to traditional metal cutting processes. The plastic deformation that occurs during friction stir welding is due to the superposition of three flow fields: a primary rotation of a radially symmetric solid plug of metal surrounding the pin tool, a secondary uniform translation, and a tertiary ring vortex flow (smoke rings) surrounding the tool. If the metal sticks to the tool, the plug surface extends down into the metal from the outer edge of the tool shoulder, decreases in diameter like a funnel, and closes up beneath the pin. Since its invention, ten years have gone by and still very little is known about the physics of the friction stir welding process. In this experiment, an H13 steel weld tool (shoulder diameter, 0.797 in; pin diameter, 0.312 in; and pin length, 0.2506 in) was used to weld three 0.255 in thick plates. The deformation behavior during friction stir welding was investigated by metallographically preparing a plan view sections of the weldment and taking Vickers hardness test in the key-hole region.
Thermocapillary motion of deformable drops
NASA Astrophysics Data System (ADS)
Haj-Hariri, Hossein; Shi, Qingping; Borhan, Ali
The thermocapillary motion of initially spherical drops/bubbles driven by a constant temperature gradient in an unbounded liquid medium is simulated numerically. Effects of convection of momentum and energy, as well as shape deformations, are addressed. The method used is based on interface tracking on a base cartesian grid, and uses a smeared color or indicator function for the determination of the surface topology. Quad-tree adaptive refinement of the cartesian grid is implemented to enhance the fidelity of the surface tracking. It is shown that convection of energy results in a slowing of the drop, as the isotherms get wrapped around the front of the drop. Shape deformation resulting from inertial effects affect the migration velocity. The physical results obtained are in agreement with the existing literature. Furthermore, remarks are made on the sensitivity of the calculated solutions to the smearing of the fluid properties. Analysis and simulations show that the migration velocity depends very strongly on the smearing of the interfacial force whereas it is rather insensitive to the smearing of other properties, hence the adaptive grid.
Deformable human body model development
Wray, W.O.; Aida, T.
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). A Deformable Human Body Model (DHBM) capable of simulating a wide variety of deformation interactions between man and his environment has been developed. The model was intended to have applications in automobile safety analysis, soldier survivability studies and assistive technology development for the disabled. To date, we have demonstrated the utility of the DHBM in automobile safety analysis and are currently engaged in discussions with the U.S. military involving two additional applications. More specifically, the DHBM has been incorporated into a Virtual Safety Lab (VSL) for automobile design under contract to General Motors Corporation. Furthermore, we have won $1.8M in funding from the U.S. Army Medical Research and Material Command for development of a noninvasive intracranial pressure measurement system. The proposed research makes use of the detailed head model that is a component of the DHBM; the project duration is three years. In addition, we have been contacted by the Air Force Armstrong Aerospace Medical Research Laboratory concerning possible use of the DHBM in analyzing the loads and injury potential to pilots upon ejection from military aircraft. Current discussions with Armstrong involve possible LANL participation in a comparison between DHBM and the Air Force Articulated Total Body (ATB) model that is the current military standard.
Deformation parameters influencing prepreg tack
Ahn, K.J.; Seferis, J.C. ); Pelton, T.; Wilhelm, M. )
A compression to tension apparatus and a methodology capable of measuring prepreg tack have been analyzed in detail in order to establish fundamental material and operating characteristics. Both intrinsic and extrinsic parameters influencing prepreg tack were identified and analyzed using commercially available carbon fiber/epoxy prepregs and mechanical testing equipment. Two different factors, (1) contact (or wetting) area of adjacent prepreg plies and (2) viscoelastic properties of the prepreg, were found to control prepreg tack. At low temperatures, contact area was the main deformation controlling step, while at high temperatures, the viscoelastic property of the prepreg was found to be dominant. Both interlaminar and intralaminar deformations were observed depending on the prepreg systems examined as well as the operating conditions of the test. In addition, hold time, hold pressure, loading rate, resin content, and out-time were also found to affect prepreg tack. Energy of separation, which may be viewed as a descriptor of prepreg tack, was observed to increase with increasing hold time, hold pressure, and loading rate. Energy of separation also showed a maximum value at a specific resin content for a specific prepreg system, while it decreased with increasing prepreg out-time due to prepreg surface characteristic change rather than bulk physical aging. Conclusively, it was observed that prepreg tack must be viewed as an extrinsic, bulk, but surface-sensitive, viscoelastic property which depends on material as well as operating conditions.
Protein transfer to membranes upon shape deformation
NASA Astrophysics Data System (ADS)
Sagis, L. M. C.; Bijl, E.; Antono, L.; de Ruijter, N. C. A.; van Valenberg, H.
Red blood cells, milk fat droplets, or liposomes all have interfaces consisting of lipid membranes. These particles show significant shape deformations as a result of flow. Here we show that these shape deformations can induce adsorption of proteins to the membrane. Red blood cell deformability is an important factor in several diseases involving obstructions of the microcirculatory system, and deformation induced protein adsorption will alter the rigidity of their membranes. Deformation induced protein transfer will also affect adsorption of cells onto implant surfaces, and the performance of liposome based controlled release systems. Quantitative models describing this phenomenon in biomaterials do not exist. Using a simple quantitative model, we provide new insight in this phenomenon. We present data that show convincingly that for cells or droplets with diameters upwards of a few micrometers, shape deformations induce adsorption of proteins at their interface even at moderate flow rates.
Deformable mirrors development program at ESO
NASA Astrophysics Data System (ADS)
Stroebele, Stefan; Vernet, Elise; Brinkmann, Martin; Jakob, Gerd; Lilley, Paul; Casali, Mark; Madec, Pierre-Yves; Kasper, Markus
Over the last decade, adaptive optics has become essential in different fields of research including medicine and industrial applications. With this new need, the market of deformable mirrors has expanded a lot allowing new technologies and actuation principles to be developed. Several E-ELT instruments have identified the need for post focal deformable mirrors but with the increasing size of the telescopes the requirements on the deformable mirrors become more demanding. A simple scaling up of existing technologies from few hundred actuators to thousands of actuators will not be sufficient to satisfy the future needs of ESO. To bridge the gap between available deformable mirrors and the future needs for the E-ELT, ESO started a development program for deformable mirror technologies. The requirements and the path to get the deformable mirrors for post focal adaptive optics systems for the E-ELT is presented.
Realistic haptic rendering of interacting deformable objects in virtual environments.
Duriez, Christian; Dubois, Frédéric; Kheddar, Abderrahmane; Andriot, Claude
A new computer haptics algorithm to be used in general interactive manipulations of deformable virtual objects is presented. In multimodal interactive simulations, haptic feedback computation often comes from contact forces. Subsequently, the fidelity of haptic rendering depends significantly on contact space modeling. Contact and friction laws between deformable models are often simplified in up to date methods. They do not allow a "realistic" rendering of the subtleties of contact space physical phenomena (such as slip and stick effects due to friction or mechanical coupling between contacts). In this paper, we use Signorini's contact law and Coulomb's friction law as a computer haptics basis. Real-time performance is made possible thanks to a linearization of the behavior in the contact space, formulated as the so-called Delassus operator, and iteratively solved by a Gauss-Seidel type algorithm. Dynamic deformation uses corotational global formulation to obtain the Delassus operator in which the mass and stiffness ratio are dissociated from the simulation time step. This last point is crucial to keep stable haptic feedback. This global approach has been packaged, implemented, and tested. Stable and realistic 6D haptic feedback is demonstrated through a clipping task experiment.
Self-adjointness of deformed unbounded operators
Much, Albert
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
Regularities of bainitic steel deformation transition
NASA Astrophysics Data System (ADS)
Gromov, V. E.; Nikitina, E. N.; Ivanov, Yu F.; Aksenova, K. V.
Quantitative analysis of defect and carbide subsystems evolution in medium-carbon bainitic steel subjected to compressive strain up to 36% was performed by means of transmission electron diffraction microscopy. Dislocation substructure and carbide phase parameters dependence on degree of deformation are identified, possible reasons of staging in their changes are discussed. It is suggested that the reason for bainitic steel softening at high (over 15%) degrees of deformation is activation of deformation microtwinning process.
Learning a hierarchical deformable template for rapid deformable object parsing.
Zhu, Long Leo; Chen, Yuanhao; Yuille, Alan
In this paper, we address the tasks of detecting, segmenting, parsing, and matching deformable objects. We use a novel probabilistic object model that we call a hierarchical deformable template (HDT). The HDT represents the object by state variables defined over a hierarchy (with typically five levels). The hierarchy is built recursively by composing elementary structures to form more complex structures. A probability distribution--a parameterized exponential model--is defined over the hierarchy to quantify the variability in shape and appearance of the object at multiple scales. To perform inference--to estimate the most probable states of the hierarchy for an input image--we use a bottom-up algorithm called compositional inference. This algorithm is an approximate version of dynamic programming where approximations are made (e.g., pruning) to ensure that the algorithm is fast while maintaining high performance. We adapt the structure-perceptron algorithm to estimate the parameters of the HDT in a discriminative manner (simultaneously estimating the appearance and shape parameters). More precisely, we specify an exponential distribution for the HDT using a dictionary of potentials, which capture the appearance and shape cues. This dictionary can be large and so does not require handcrafting the potentials. Instead, structure-perceptron assigns weights to the potentials so that less important potentials receive small weights (this is like a "soft" form of feature selection). Finally, we provide experimental evaluation of HDTs on different visual tasks, including detection, segmentation, matching (alignment), and parsing. We show that HDTs achieve state-of-the-art performance for these different tasks when evaluated on data sets with groundtruth (and when compared to alternative algorithms, which are typically specialized to each task).
Consecutive Rosochatius deformations of the Neumann system
NASA Astrophysics Data System (ADS)
Xia, Baoqiang; Zhou, Ruguang
Consecutive Rosochatius deformations of the Neumann system are investigated. It is first shown that different realizations of a classical sl(2) Gaudin magnet model yield different integrable Hamiltonian systems. Then an algorithm of constructing infinitely many symplectic realizations of sl(2) algebra from a known one is presented and thus the Neumann system can be deformed consecutively. The second Rosochatius deformation of the Neumann system is taken as an illustrative example to show that the deformed systems admit separations of variables and may be linearized on the Jacobi variety.
Origami-enabled deformable silicon solar cells
Tang, Rui; Huang, Hai; Liang, Hanshuang; Liang, Mengbing; Tu, Hongen; Xu, Yong; Song, Zeming; Jiang, Hanqing; Yu, Hongyu
Deformable electronics have found various applications and elastomeric materials have been widely used to reach flexibility and stretchability. In this Letter, we report an alternative approach to enable deformability through origami. In this approach, the deformability is achieved through folding and unfolding at the creases while the functional devices do not experience strain. We have demonstrated an example of origami-enabled silicon solar cells and showed that this solar cell can reach up to 644% areal compactness while maintaining reasonable good performance upon cyclic folding/unfolding. This approach opens an alternative direction of producing flexible, stretchable, and deformable electronics.
Deformation twinning: Influence of strain rate
Gray, G.T. III
Twins in most crystal structures, including advanced materials such as intermetallics, form more readily as the temperature of deformation is decreased or the rate of deformation is increased. Both parameters lead to the suppression of thermally-activated dislocation processes which can result in stresses high enough to nucleate and grow deformation twins. Under high-strain rate or shock-loading/impact conditions deformation twinning is observed to be promoted even in high stacking fault energy FCC metals and alloys, composites, and ordered intermetallics which normally do not readily deform via twinning. Under such conditions and in particular under the extreme loading rates typical of shock wave deformation the competition between slip and deformation twinning can be examined in detail. In this paper, examples of deformation twinning in the intermetallics TiAl, Ti-48Al-lV and Ni{sub 3}A as well in the cermet Al-B{sub 4}C as a function of strain rate will be presented. Discussion includes: (1) the microstructural and experimental variables influencing twin formation in these systems and twinning topics related to high-strain-rate loading, (2) the high velocity of twin formation, and (3) the influence of deformation twinning on the constitutive response of advanced materials.
Matching Rules for Collective Behaviors on Complex Networks: Optimal Configurations for Vibration Frequencies of Networked Harmonic Oscillators
Zhan, Meng; Liu, Shuai; He, Zhiwei
The structure-dynamics-function has become one of central problems in modern sciences, and it is a great challenge to unveil the organization rules for different dynamical processes on networks. In this work, we study the vibration spectra of the classical mass spring model with different masses on complex networks, and pay our attention to how the mass spatial configuration influences the second-smallest vibrational frequency () and the largest one (). For random networks, we find that becomes maximal and becomes minimal if the node degrees are point-to-point-positively correlated with the masses. In these cases, we call it point-to-point matching. Moreover, becomes minimal under the condition that the heaviest mass is placed on the lowest-degree vertex, and is maximal as long as the lightest mass is placed on the highest-degree vertex, and in both cases all other masses can be arbitrarily settled. Correspondingly, we call it single-point matching. These findings indicate that the matchings between the node dynamics (parameter) and the node position rule the global systems dynamics, and sometimes only one node is enough to control the collective behaviors of the whole system. Therefore, the matching rules might be the common organization rules for collective behaviors on networks. PMID:24386088
Realization of a quantum gate using gravitational search algorithm by perturbing three-dimensional harmonic oscillator with an electromagnetic field
NASA Astrophysics Data System (ADS)
Sharma, Navneet; Rawat, Tarun Kumar; Parthasarathy, Harish; Gautam, Kumar
The aim of this paper is to design a current source obtained as a representation of p information symbols \\{I_k\\} so that the electromagnetic (EM) field generated interacts with a quantum atomic system producing after a fixed duration T a unitary gate U( T) that is as close as possible to a given unitary gate U_g. The design procedure involves calculating the EM field produced by \\{I_k\\} and hence the perturbing Hamiltonian produced by \\{I_k\\} finally resulting in the evolution operator produced by \\{I_k\\} up to cubic order based on the Dyson series expansion. The gate error energy is thus obtained as a cubic polynomial in \\{I_k\\} which is minimized using gravitational search algorithm. The signal to noise ratio (SNR) in the designed gate is higher as compared to that using quadratic Dyson series expansion. The SNR is calculated as the ratio of the Frobenius norm square of the desired gate to that of the desired gate error.
Matching rules for collective behaviors on complex networks: optimal configurations for vibration frequencies of networked harmonic oscillators.
Zhan, Meng; Liu, Shuai; He, Zhiwei
The structure-dynamics-function has become one of central problems in modern sciences, and it is a great challenge to unveil the organization rules for different dynamical processes on networks. In this work, we study the vibration spectra of the classical mass spring model with different masses on complex networks, and pay our attention to how the mass spatial configuration influences the second-smallest vibrational frequency (ω2) and the largest one (ωN). For random networks, we find that ω2 becomes maximal and ωN becomes minimal if the node degrees are point-to-point-positively correlated with the masses. In these cases, we call it point-to-point matching. Moreover, ω2 becomes minimal under the condition that the heaviest mass is placed on the lowest-degree vertex, and ωN is maximal as long as the lightest mass is placed on the highest-degree vertex, and in both cases all other masses can be arbitrarily settled. Correspondingly, we call it single-point matching. These findings indicate that the matchings between the node dynamics (parameter) and the node position rule the global systems dynamics, and sometimes only one node is enough to control the collective behaviors of the whole system. Therefore, the matching rules might be the common organization rules for collective behaviors on networks.
Compound dislocation models (CDMs) for volcano deformation analyses
NASA Astrophysics Data System (ADS)
Nikkhoo, Mehdi; Walter, Thomas R.; Lundgren, Paul R.; Prats-Iraola, Pau
Volcanic crises are often preceded and accompanied by volcano deformation caused by magmatic and hydrothermal processes. Fast and efficient model identification and parameter estimation techniques for various sources of deformation are crucial for process understanding, volcano hazard assessment and early warning purposes. As a simple model that can be a basis for rapid inversion techniques, we present a compound dislocation model (CDM) that is composed of three mutually orthogonal rectangular dislocations (RDs). We present new RD solutions, which are free of artefact singularities and that also possess full rotational degrees of freedom. The CDM can represent both planar intrusions in the near field and volumetric sources of inflation and deflation in the far field. Therefore, this source model can be applied to shallow dikes and sills, as well as to deep planar and equidimensional sources of any geometry, including oblate, prolate and other triaxial ellipsoidal shapes. In either case the sources may possess any arbitrary orientation in space. After systematically evaluating the CDM, we apply it to the co-eruptive displacements of the 2015 Calbuco eruption observed by the Sentinel-1A satellite in both ascending and descending orbits. The results show that the deformation source is a deflating vertical lens-shaped source at an approximate depth of 8 km centred beneath Calbuco volcano. The parameters of the optimal source model clearly show that it is significantly different from an isotropic point source or a single dislocation model. The Calbuco example reflects the convenience of using the CDM for a rapid interpretation of deformation data.
Deformed ellipsoidal diffraction grating blank
NASA Technical Reports Server (NTRS)
Decew, Alan E., Jr.
The Deformed Ellipsoidal Grating Blank (DEGB) is the primary component in an ultraviolet spectrometer. Since one of the major concerns for these instruments is throughput, significant efforts are made to reduce the number of components and subsequently reflections. Each reflection results in losses through absorption and scattering. It is these two sources of photon loss that dictated the requirements for the DEGB. The first goal is to shape the DEGB in such a way that the energy at the entrance slit is focused as well as possible on the exit slit. The second goal is to produce a surface smooth enough to minimize the photon loss due to scattering. The program was accomplished in three phases. The first phase was the fabrication planning. The second phase was the actual fabrication and initial testing. The last phase was the final testing of the completed DEGB.
Deformation in the continental lithosphere
NASA Astrophysics Data System (ADS)
The Physical Properties of Earth Materials Committee, a technical committee of AGU's Tectonophysics Section, is organizing a dinner/colloquium as part of the Fall Meeting in San Francisco, Calif. This event will be held Monday, December 3rd, in the Gold Rush Room of the Holiday Inn Golden Gateway Hotel at 1500 Van Ness St. There will be a no-host bar from 6:30 to 7:30 P.M., followed by dinner from 7:30 to 8:30 P.M. Paul Tapponnier will deliver the after-dinner talk, "Large-Scale Deformation Mechanisms in the Continental Lithosphere: Where Do We Stand?" It will start at 8:30 P.M. and a business meeting will follow at 9:30 P.M.
Deformation quantization of fermi fields
Galaviz, I. Garcia-Compean, H. Przanowski, M. Turrubiates, F.J.
Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal *-product and the Wigner functional are obtained by extending the formalism proposed recently in [I. Galaviz, H. Garcia-Compean, M. Przanowski, F.J. Turrubiates, Weyl-Wigner-Moyal Formalism for Fermi Classical Systems, arXiv:hep-th/0612245] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal *-product, the Wigner functional, the normal ordering operator, and finally, the Dirac propagator have been found with the use of these variables.
Deformation and seismicity of Taiwan.
Vita-Finzi, C
14C-dated Holocene coastal uplift, conventional and satellite geodetic measurements, and coseismic and aseismic fault slip reveal the pattern of distributed deformation at Taiwan resulting from convergence between the Philippine Sea plate and Eurasia; as in other subduction orogenic settings, the locus of strain release and accumulation is strongly influenced by changes in fault geometry across strike. Uplift evidence from the islands of Lutao and Lanhsu is consistent with progressive oblique collision between the Luzon arc and the Chinese continental margin. In the Coastal Range, geodetic and seismic records show that shortening is taken up serially by discontinuous slip on imbricate faults. The geodetic data point to net extension across the Central Range, but deformed Holocene shorelines in the Hengchun Peninsula at its southern extremity suggest that the extension is a superficial effect partly caused by blind reverse faulting. The fastest shortening rates indicated by geodesy are recorded on the Longitudinal Valley fault and across the Chukou fault within the fold-and-thrust belt. In the former, the strain is dissipated mainly as aseismic reverse and strike-slip displacement. In contrast, the fold-and-thrust belt has witnessed five earthquakes with magnitudes of 6.5 or above in the 20th century, including the 1999.9.21 Chi-Chi earthquake (magnitude approximately 7.6) on a branch of the Chukou fault. The neotectonic and geodetic data for Taiwan as a whole suggest that the fold-and-thrust belt will continue to host the majority of great earthquakes on the island.
Computer-assisted surgery patterns of ligamentous deformity of the knee: a clinical and cadaveric study.
Schwarzkopf, Ran; Hadley, Scott; Abbasi, Mohammed; Meere, Patrick A
Knee malalignment during total knee arthroplasty (TKA) is commonly classified as either varus or valgus on the basis of a standing anteroposterior radiograph. Computer-assisted surgery (CAS) navigation TKA provides precise dynamic evaluation of knee alignment throughout the full range of motion (FROM). The goal of this study was to classify patterns of CAS-generated knee deformity curves that match specific soft tissue contracture combinations. This can then be applied as an algorithm for soft tissue balancing on the basis of the preoperative knee deformity curve. Computer navigation-generated graphs from 65 consecutive TKA procedures performed by a single surgeon were analyzed. A stress-strain curve of the coronal alignment of the knee was recorded throughout FROM before bony resection. All graphs were classified into groups according to their pattern. Cadaveric knee models were then used to test the correlation between isolated and combined ligamentous contractures and identified CAS deformity curves. An analysis of the intraoperative knee alignment graphs revealed four distinct patterns of coronal deformity on the basis of intraoperative data: 13% diagonal, 18.5% C-shaped, 43.5% comma shaped, and 25% S-shaped. Each represents the change in varus and valgus alignment during FROM. All patterns were reproduced with cadaveric knees by recreating specific contracture constellations. A tight posterior capsule gave an S-shaped curve, a tight lateral collateral ligament gave a C-shaped curve, tight medial collateral ligament gave a diagonal curve, and a tight posterior lateral corner gave a comma-shaped curve. Release of the specific contractures resulted in correction of all patterns of deformity as measured by CAS. We propose a new classification system for coronal plane knee deformity throughout FROM. This system intends to match individual and combined soft tissue pathological contractures to specific stress-strain curves obtained through routine knee CAS
Code of Federal Regulations, 2010 CFR
... 14 Aeronautics and Space 4 2010-01-01 2010-01-01 false Basis. 400.1 Section 400.1 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION GENERAL BASIS AND SCOPE § 400.1 Basis. The basis for the regulations in this chapter is the...
Code of Federal Regulations, 2014 CFR
... 14 Aeronautics and Space 4 2014-01-01 2014-01-01 false Basis. 400.1 Section 400.1 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION GENERAL BASIS AND SCOPE § 400.1 Basis. The basis for the regulations in this chapter is the...
Code of Federal Regulations, 2013 CFR
... 14 Aeronautics and Space 4 2013-01-01 2013-01-01 false Basis. 400.1 Section 400.1 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION GENERAL BASIS AND SCOPE § 400.1 Basis. The basis for the regulations in this chapter is the...
Code of Federal Regulations, 2012 CFR
... 14 Aeronautics and Space 4 2012-01-01 2012-01-01 false Basis. 400.1 Section 400.1 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION GENERAL BASIS AND SCOPE § 400.1 Basis. The basis for the regulations in this chapter is the...
Code of Federal Regulations, 2011 CFR
... 14 Aeronautics and Space 4 2011-01-01 2011-01-01 false Basis. 400.1 Section 400.1 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION GENERAL BASIS AND SCOPE § 400.1 Basis. The basis for the regulations in this chapter is the...
10 CFR 830.202 - Safety basis.
Code of Federal Regulations, 2012 CFR
... 10 Energy 4 2012-01-01 2012-01-01 false Safety basis. 830.202 Section 830.202 Energy DEPARTMENT OF ENERGY NUCLEAR SAFETY MANAGEMENT Safety Basis Requirements § 830.202 Safety basis. (a) The contractor... in the safety basis any changes, conditions, or hazard controls directed by DOE....
10 CFR 830.202 - Safety basis.
Code of Federal Regulations, 2013 CFR
... 10 Energy 4 2013-01-01 2013-01-01 false Safety basis. 830.202 Section 830.202 Energy DEPARTMENT OF ENERGY NUCLEAR SAFETY MANAGEMENT Safety Basis Requirements § 830.202 Safety basis. (a) The contractor... in the safety basis any changes, conditions, or hazard controls directed by DOE....
10 CFR 830.202 - Safety basis.
Code of Federal Regulations, 2011 CFR
... 10 Energy 4 2011-01-01 2011-01-01 false Safety basis. 830.202 Section 830.202 Energy DEPARTMENT OF ENERGY NUCLEAR SAFETY MANAGEMENT Safety Basis Requirements § 830.202 Safety basis. (a) The contractor... in the safety basis any changes, conditions, or hazard controls directed by DOE....
10 CFR 830.202 - Safety basis.
Code of Federal Regulations, 2014 CFR
... 10 Energy 4 2014-01-01 2014-01-01 false Safety basis. 830.202 Section 830.202 Energy DEPARTMENT OF ENERGY NUCLEAR SAFETY MANAGEMENT Safety Basis Requirements § 830.202 Safety basis. (a) The contractor... in the safety basis any changes, conditions, or hazard controls directed by DOE....
Solute transport through a deforming porous medium
NASA Astrophysics Data System (ADS)
Peters, Glen P.; Smith, David W.
Solute transport through a porous medium is typically modelled assuming the porous medium is rigid. However, many applications exist where the porous medium is deforming, including, municipal landfill liners, mine tailings dams, and land subsidence. In this paper, mass balance laws are used to derive the flow and transport equations for a deforming porous medium. The equations are derived in both spatial and material co-ordinate systems. Solute transport through an engineered landfill liner is used as an illustrative example to show the differences between the theory for a rigid porous medium, and small and large deformation analysis of a deforming porous medium. It is found that the large deformation model produces shorter solute breakthrough times, followed by the small deformation model, and then the rigid porous medium model. It is also found that it is important to include spatial and temporal void ratio variations in the large deformation analysis. It is shown that a non-linear large deformation model may greatly reduce the solute breakthrough time, compared to a standard transport analysis typically employed by environmental engineers.
Measuring Viscoelastic Deformation with an Optical Mouse
ERIC Educational Resources Information Center
Ng, T. W.
The feasibility of using an optical mouse to track the viscoelastic deformation of low-density polyethylene films that have a fixed attached load is presented. It is seen that using an optical mouse and with rudimentary experiment paraphernalia and arrangement, it is possible to get good measurements of viscoelastic deformation.
Plastic deformation mechanisms in nanocrystalline metallic materials
NASA Astrophysics Data System (ADS)
Ovid'ko, Ilya A.
This article discusses the experiments, computer simulations, and theoretical models addressing the conventional and specific mechanisms of plastic deformation in nanocrystalline metallic materials. Particular attention is devoted to the competition between lattice dislocation slip and specific deformation mechanisms mediated by grain boundaries as well as its sensitivity to grain size and other parameters of nanocrystalline metallic structures.
Acquired nasal deformities in fighter pilots.
Schreinemakers, Joyce R C; van Amerongen, Pieter; Kon, Moshe
Fighter pilots may develop slowly progressive deformities of their noses during their flying careers. The spectrum of deformities that may be acquired ranges from soft tissue to osseous changes. The main cause is the varying pressure exerted by the oxygen mask on the skin and bony pyramid of the nose during flying.
Quantification of abdominal aortic deformation after EVAR
NASA Astrophysics Data System (ADS)
Demirci, Stefanie; Manstad-Hulaas, Frode; Navab, Nassir
Quantification of abdominal aortic deformation is an important requirement for the evaluation of endovascular stenting procedures and the further refinement of stent graft design. During endovascular aortic repair (EVAR) treatment, the aortic shape is subject to severe deformation that is imposed by medical instruments such as guide wires, catheters, and, the stent graft. This deformation can affect the flow characteristics and morphology of the aorta which have been shown to be elicitors for stent graft failures and be reason for reappearance of aneurysms. We present a method for quantifying the deformation of an aneurysmatic aorta imposed by an inserted stent graft device. The outline of the procedure includes initial rigid alignment of the two abdominal scans, segmentation of abdominal vessel trees, and automatic reduction of their centerline structures to one specified region of interest around the aorta. This is accomplished by preprocessing and remodeling of the pre- and postoperative aortic shapes before performing a non-rigid registration. We further narrow the resulting displacement fields to only include local non-rigid deformation and therefore, eliminate all remaining global rigid transformations. Finally, deformations for specified locations can be calculated from the resulting displacement fields. In order to evaluate our method, experiments for the extraction of aortic deformation fields are conducted on 15 patient datasets from endovascular aortic repair (EVAR) treatment. A visual assessment of the registration results and evaluation of the usage of deformation quantification were performed by two vascular surgeons and one interventional radiologist who are all experts in EVAR procedures.
Umbral Deformations on Discrete SPACE TIME
NASA Astrophysics Data System (ADS)
Zachos, Cosmas K.
Given a minimum measurable length underlying spacetime, the latter may be effectively regarded as discrete, at scales of order the Planck length. A systematic discretization of continuum physics may be effected most efficiently through the umbral deformation. General functionals yielding such deformations at the level of solutions are furnished and illustrated, and broad features of discrete oscillations and wave propagation are outlined.
Exploiting Adaptive Optics with Deformable Secondary Mirrors
progress in tomographic wavefront sensing and altitude conjugated adaptive correction, and is a critical step forward for adaptive optics for future large...geostationary satellites, captured at the 6.5 m MMT telescope, using the deformable secondary adaptive optics system....new technology to the unique development of deformable secondary mirrors pioneered at the University of Arizona's Center for Astronomical Adaptive
7 CFR 51.1013 - Badly deformed.
Code of Federal Regulations, 2010 CFR
... Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE REGULATIONS AND STANDARDS UNDER THE AGRICULTURAL MARKETING ACT OF 1946... Standards for Persian (Tahiti) Limes Definitions § 51.1013 Badly deformed. Badly deformed means that...
Influence of thermal deformation of a multilayer dielectric grating on a spectrally combined beam.
Yang, Lei; Wu, Zhen; Zhang, Bin
In spectral beam combining (SBC) systems, temperature rise inevitably happens to the multilayer dielectric grating (MDG) due to irradiation of the high-power continuous-wave (CW) laser, resulting in thermal deformation of the MDG and degradation of the characteristics of the combined beam due to thermal deformation of the grating. The calculation model of thermal deformation of the MDG has been proposed, and the distributions of temperature field and thermal deformation of the grating have been analyzed. On this basis, a propagation model of a SBC system has further been built up. By utilizing the diffraction integral method and the principle of incoherent superposition, the intensity distribution and the beam quality of the combined beam with different power densities based on the MDG have been numerically calculated and analyzed in detail. The results show that both the maximum temperature rise and the thermal deformation of the MDG increase dramatically with the increasing power density of the incident laser beam. Side lobes appear in the intensity distribution of the combined beam due to thermal deformation of the MDG. Furthermore, the side lobes of the combined beam become increasingly obvious with increasing power density. Additionally, the beam quality of the combined beam degrades significantly with increasing power density of the incident laser beam.
An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.
Internal dosimetry technical basis manual
Not Available
The internal dosimetry program at the Savannah River Site (SRS) consists of radiation protection programs and activities used to detect and evaluate intakes of radioactive material by radiation workers. Examples of such programs are: air monitoring; surface contamination monitoring; personal contamination surveys; radiobioassay; and dose assessment. The objectives of the internal dosimetry program are to demonstrate that the workplace is under control and that workers are not being exposed to radioactive material, and to detect and assess inadvertent intakes in the workplace. The Savannah River Site Internal Dosimetry Technical Basis Manual (TBM) is intended to provide a technical and philosophical discussion of the radiobioassay and dose assessment aspects of the internal dosimetry program. Detailed information on air, surface, and personal contamination surveillance programs is not given in this manual except for how these programs interface with routine and special bioassay programs.
Holographic study of conventional and negative Poisson's ratio metallic foams - Elasticity, yield and micro-deformation
NASA Technical Reports Server (NTRS)
Chen, C. P.; Lakes, R. S.
An experimental study by holographic interferometry is reported of the following material properties of conventional and negative Poisson's ratio copper foams: Young's moduli, Poisson's ratios, yield strengths and characteristic lengths associated with inhomogeneous deformation. The Young's modulus and yield strength of the conventional copper foam were comparable to those predicted by microstructural modeling on the basis of cellular rib bending. The reentrant copper foam exhibited a negative Poisson's ratio, as indicated by the elliptical contour fringes on the specimen surface in the bending tests. Inhomogeneous, non-affine deformation was observed holographically in both foam materials.
Deformation measurements of smart aerodynamic surfaces
NASA Astrophysics Data System (ADS)
Fleming, Gary A.; Burner, Alpheus W.
Video Model Deformation (VMD) and Projection Moire Interferometry (PMI) were used to acquire wind tunnel model deformation measurements of the Northrop Grumman-built Smart Wing tested in the NASA Langley Transonic Dynamics Tunnel. The F18-E/F platform Smart Wing was outfitted with embedded shape memory alloys to actuate a seamless trailing edge aileron and flat, and an embedded torque tube to generate wing twist. The VMD system was used to obtain highly accurate deformation measurements at three spanwise locations along the main body of the wing, and at spanwise locations on the flap and aileron. The PMI system was used to obtain full-field wing shape and deformation measurements over the entire wing lower surface. Although less accurate than the VMD system, the PMI system revealed deformations occurring between VMD target rows indistinguishable by VMD. This paper presents the VMD and PMI techniques and discusses their application in the Smart Wing test.
Deformation Measurements of Smart Aerodynamic Surfaces
NASA Technical Reports Server (NTRS)
Fleming, Gary A.; Burner, Alpheus
Video Model Deformation (VMD) and Projection Moire Interferometry (PMI) were used to acquire wind tunnel model deformation measurements of the Northrop Grumman-built Smart Wing tested in the NASA Langley Transonic Dynamics Tunnel. The F18-E/F planform Smart Wing was outfitted with embedded shape memory alloys to actuate a seamless trailing edge aileron and flap, and an embedded torque tube to generate wing twist. The VMD system was used to obtain highly accurate deformation measurements at three spanwise locations along the main body of the wing, and at spanwise locations on the flap and aileron. The PMI system was used to obtain full-field wing shape and deformation measurements over the entire wing lower surface. Although less accurate than the VMD system, the PMI system revealed deformations occurring between VMD target rows indistinguishable by VMD. This paper presents the VMD and PMI techniques and discusses their application in the Smart Wing test.
Nilpotent deformations of N = 2 superspace
NASA Astrophysics Data System (ADS)
Ivanov, Evgeny; Zupnik, Boris; Lechtenfeld, Olaf
We investigate deformations of four-dimensional N = (1,1) euclidean superspace induced by nonanticommuting fermionic coordinates. We essentially use the harmonic superspace approach and consider nilpotent bi-differential Poisson operators only. One variant of such deformations (termed chiral nilpotent) directly generalizes the recently studied chiral deformation of N = (1/2,1/2) superspace. It preserves chirality and harmonic analyticity but generically breaks N = (1,1) to N = (1,0) supersymmetry. Yet, for degenerate choices of the constant deformation matrix N = (1,1/2) supersymmetry can be retained, i.e. a fraction of 3/4. An alternative version (termed analytic nilpotent) imposes minimal nonanticommutativity on the analytic coordinates of harmonic superspace. It does not affect the analytic subspace and respects all supersymmetries, at the expense of chirality however. For a chiral nilpotent deformation, we present non(anti)commutative euclidean analogs of N = 2 Maxwell and hypermultiplet off-shell actions.
The properties of Q-deformed hyperbolic and trigonometric functions in quantum deformation
Deta, U. A. E-mail: firstname.lastname@example.com; Suparmi
Quantum deformation has been studied due to its relation with applications in nuclear physics, conformal field theory, and statistical-quantum theory. The q-deformation of hyperbolic function was introduced by Arai. The application of q-deformed functions has been widely used in quantum mechanics. The properties of this two kinds of system explained in this paper including their derivative. The graph of q-deformed functions presented using Matlab. The special case is given for modified Poschl-Teller plus q-deformed Scarf II trigonometry potentials.
Inelastic deformation and dislocation structure of a nickel alloy - Effects of deformation and thermal histories
NASA Technical Reports Server (NTRS)
Chan, K. S.; Page, R. A.
Inelastic deformation behavior of the cast Ni-base alloy, B1900 + Hf, was investigated using data from step-temperature tensile tests and thermomechanical cyclic tests in the temperature ranges 538-760 C and 760-982 C. The deformation results were correlated with the dislocation structures of deformed specimens, identified by TEM. It was found that, in the 760-982 C temperature range, there are no thermal history effects in the inelastic deformation behavior of B1900 + Hf. In the 538-760 range, anomalous cyclic hardening and, possibly, thermal history effects were observed in thermomechanically deformed alloy, caused by sessile (010) dislocations in the gamma-prime phase.
Large Deformations of a Soft Porous Material
NASA Astrophysics Data System (ADS)
MacMinn, Christopher W.; Dufresne, Eric R.; Wettlaufer, John S.
Compressing a porous material will decrease the volume of the pore space, driving fluid out. Similarly, injecting fluid into a porous material can expand the pore space, distorting the solid skeleton. This poromechanical coupling has applications ranging from cell and tissue mechanics to geomechanics and hydrogeology. The classical theory of linear poroelasticity captures this coupling by combining Darcy's law with Terzaghi's effective stress and linear elasticity in a linearized kinematic framework. Linear poroelasticity is a good model for very small deformations, but it becomes increasingly inappropriate for moderate to large deformations, which are common in the context of phenomena such as swelling and damage, and for soft materials such as gels and tissues. The well-known theory of large-deformation poroelasticity combines Darcy's law with Terzaghi's effective stress and nonlinear elasticity in a rigorous kinematic framework. This theory has been used extensively in biomechanics to model large elastic deformations in soft tissues and in geomechanics to model large elastoplastic deformations in soils. Here, we first provide an overview and discussion of this theory with an emphasis on the physics of poromechanical coupling. We present the large-deformation theory in an Eulerian framework to minimize the mathematical complexity, and we show how this nonlinear theory simplifies to linear poroelasticity under the assumption of small strain. We then compare the predictions of linear poroelasticity with those of large-deformation poroelasticity in the context of two uniaxial model problems: fluid outflow driven by an applied mechanical load (the consolidation problem) and compression driven by a steady fluid throughflow. We explore the steady and dynamical errors associated with the linear model in both situations, as well as the impact of introducing a deformation-dependent permeability. We show that the error in linear poroelasticity is due primarily to kinematic
Tracking of object deformations in color and depth video: deformation models and applications
NASA Astrophysics Data System (ADS)
Jordt, Andreas; Reinhold, Stefan; Koch, Reinhard
The research on deformation tracking based on color image data has continuously gained a wide interest in the last 15 years. In addition, using depth sensors such as the Microsoft Kinect, allows to mitigate the ambiguity problems that arise when trying to solve the deformation tracking tasks on color images only, by adding depth information. However, the fusion of color and depth data is not straight forward, and the deformation tracking task is still ill-posed due to the lack of a general deformation model. The problem is usually circumvented by providing special deformation functions for the task at hand, e.g., skeleton-based for reconstructing people or triangle-based for tracking planar surfaces. In this article we summarize the Analysis by Synthesis (AbS) approach for deformation tracking in depth and color video and show some successful applications of specialized deformation functions. To overcome the issues with NURBS based deformation tracking we propose a new geodesic RBF-based deformation model, which can adapt to any surface topology and shape, while keeping the number of deformation parameters low. Example deformations for objects of different topologies are given, showing the versatility and efficiency of the proposed model.
Deformation mechanisms of antigorite serpentinite at subduction zone conditions determined from experimentally and naturally deformed rocks
NASA Astrophysics Data System (ADS)
Auzende, Anne-Line; Escartin, Javier; Walte, Nicolas P.; Guillot, Stéphane; Hirth, Greg; Frost, Daniel J.
We performed deformation-DIA experiments on antigorite serpentinite at pressures of 1-3.5 GPa and temperatures of between 400 and 650 °C, bracketing the stability of antigorite under subduction zone conditions. For each set of pressure-temperature (P-T) conditions, we conducted two runs at strain rates of 5 ×10-5 and 1 ×10-4 s-1. We complemented our study with a sample deformed in a Griggs-type apparatus at 1 GPa and 400 °C (Chernak and Hirth, 2010), and with natural samples from Cuba and the Alps deformed under blueschist/eclogitic conditions. Optical and transmission electron microscopies were used for microstructural characterization and determination of deformation mechanisms. Our observations on experimentally deformed antigorite prior to breakdown show that deformation is dominated by cataclastic flow with observable but minor contribution of plastic deformation (microkinking and (001) gliding mainly expressed by stacking disorder mainly). In contrast, in naturally deformed samples, plastic deformation structures are dominant (stacking disorder, kinking, pressure solution), with minor but also perceptible contribution of brittle deformation. When dehydration occurs in experiments, plasticity increases and is coupled to local embrittlement that we attribute to antigorite dehydration. In dehydrating samples collected in the Alps, embrittlement is also observed suggesting that dehydration may contribute to intermediate-depth seismicity. Our results thus show that semibrittle deformation operates within and above the stability field of antigorite. However, the plastic deformation recorded by naturally deformed samples was likely acquired at low strain rates. We also document that the corrugated structure of antigorite controls the strain accommodation mechanisms under subduction conditions, with preferred inter- and intra-grain cracking along (001) and gliding along both a and b. We also show that antigorite rheology in subduction zones is partly controlled
Time efficient aeroelastic simulations based on radial basis functions
NASA Astrophysics Data System (ADS)
Liu, Wen; Huang, ChengDe; Yang, Guowei
Aeroelasticity studies the interaction between aerodynamic forces and structural responses, and is one of the fundamental problems to be considered in the design of modern aircraft. The fluid-structure interpolation (FSI) and mesh deformation are two key issues in the CFD-CSD coupling approach (the partitioned approach), which is the mainstream numerical strategy in aeroelastic simulations. In this paper, a time efficient coupling scheme is developed based on the radial basis function interpolations. During the FSI process, the positive definite system of linear equations is constructed with the introduction of pseudo structural forces. The acting forces on the structural nodes can be calculated more efficiently via the solution of the linear system, avoiding the costly computations of the aerodynamic/structural coupling matrix. The multi-layer sequential mesh motion algorithm (MSM) is proposed to improve the efficiency of the volume mesh deformations, which is adequate for large-scale time dependent applications with frequent mesh updates. Two-dimensional mesh motion cases show that the MSM algorithm can reduce the computing cost significantly compared to the standard RBF-based method. The computations of the AGARD 445.6 wing flutter and the static deflections of the three-dimensional high-aspect-ratio aircraft demonstrate that the developed coupling scheme is applicable to both dynamic and static aeroelastic problems.
Weak associativity and deformation quantization
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.
Non-commutativity and non-associativity are quite natural in string theory. For open strings it appears due to the presence of non-vanishing background two-form in the world volume of Dirichlet brane, while in closed string theory the flux compactifications with non-vanishing three-form also lead to non-geometric backgrounds. In this paper, working in the framework of deformation quantization, we study the violation of associativity imposing the condition that the associator of three elements should vanish whenever each two of them are equal. The corresponding star products are called alternative and satisfy important for physical applications properties like the Moufang identities, alternative identities, Artin's theorem, etc. The condition of alternativity is invariant under the gauge transformations, just like it happens in the associative case. The price to pay is the restriction on the non-associative algebra which can be represented by the alternative star product, it should satisfy the Malcev identity. The example of nontrivial Malcev algebra is the algebra of imaginary octonions. For this case we construct an explicit expression of the non-associative and alternative star product. We also discuss the quantization of Malcev-Poisson algebras of general form, study its properties and provide the lower order expression for the alternative star product. To conclude we define the integration on the algebra of the alternative star products and show that the integrated associator vanishes.
Deformity in the "Boxing Boys".
Ferrence, Susan; Bendersky, Gordon
The late Bronze Age wall painting the Boxing Boys (c. 17th-16th century BCE) was excavated in the ancient town of Akrotiri on the Greek island of Thera. This article considers a medical interpretation for the spinal-pelvic anomaly in the anatomy of one of the boys. The artist has depicted a combination of structural anatomical adjustments diagnostic of spondylolisthesis, a forward slippage of one of the lumbar vertebrae. The accurate portrayal of the surface appearance of this condition suggests that the artist painted directly from a live subject. Thus, the Boxing Boys mural may be the earliest visual record of a sports-induced injury. Although the meaning of the wall paintings is unclear, the wild goats (agrimia) on the adjoining walls simulate swayback as a reflection of the boy's torso deformity and share other features with the boxers, adding to the unifying characteristics of the room. The abnormal morphology appears to be the earliest achievement of transforming disease into aesthetic charm on a monumental scale.
Mathematical textbook of deformable neuroanatomies.
Miller, M I; Christensen, G E; Amit, Y; Grenander, U
Mathematical techniques are presented for the transformation of digital anatomical textbooks from the ideal to the individual, allowing for the representation of the variabilities manifest in normal human anatomies. The ideal textbook is constructed on a fixed coordinate system to contain all of the information currently available about the physical properties of neuroanatomies. This information is obtained via sensor probes such as magnetic resonance, as well as computed axial and emission tomography, along with symbolic information such as white- and gray-matter tracts, nuclei, etc. Human variability associated with individuals is accommodated by defining probabilistic transformations on the textbook coordinate system, the transformations forming mathematical translation groups of high dimension. The ideal is applied to the individual patient by finding the transformation which is consistent with physical properties of deformable elastic solids and which brings the coordinate system of the textbook to that of the patient. Registration, segmentation, and fusion all result automatically because the textbook carries symbolic values as well as multisensor features.
Mathematical textbook of deformable neuroanatomies.
Miller, M I; Christensen, G E; Amit, Y; Grenander, U
Mathematical techniques are presented for the transformation of digital anatomical textbooks from the ideal to the individual, allowing for the representation of the variabilities manifest in normal human anatomies. The ideal textbook is constructed on a fixed coordinate system to contain all of the information currently available about the physical properties of neuroanatomies. This information is obtained via sensor probes such as magnetic resonance, as well as computed axial and emission tomography, along with symbolic information such as white- and gray-matter tracts, nuclei, etc. Human variability associated with individuals is accommodated by defining probabilistic transformations on the textbook coordinate system, the transformations forming mathematical translation groups of high dimension. The ideal is applied to the individual patient by finding the transformation which is consistent with physical properties of deformable elastic solids and which brings the coordinate system of the textbook to that of the patient. Registration, segmentation, and fusion all result automatically because the textbook carries symbolic values as well as multisensor features. Images Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 PMID:8265653
Crustal deformation: Earth vs Venus
NASA Technical Reports Server (NTRS)
Turcotte, D. L.
It is timely to consider the possible tectonic regimes on Venus both in terms of what is known about Venus and in terms of deformation mechanisms operative on the earth. Plate tectonic phenomena dominate tectonics on the earth. Horizontal displacements are associated with the creation of new crust at ridges and destruction of crust at trenches. The presence of plate tectonics on Venus is debated, but there is certainly no evidence for the trenches associated with subduction on the earth. An essential question is what kind of tectonics can be expected if there is no plate tectonics on Venus. Mars and the Moon are reference examples. Volcanic constructs appear to play a dominant role on Mars but their role on Venus is not clear. On single plate planets and satellites, tectonic structures are often associated with thermal stresses. Cooling of a planet leads to thermal contraction and surface compressive features. Delamination has been propsed for Venus by several authors. Delamination is associated with the subduction of the mantle lithosphere and possibly the lower crust but not the upper crust. The surface manifestations of delamination are unclear. There is some evidence that delamination is occurring beneath the Transverse Ranges in California. Delamination will certainly lead to lithospheric thinning and is likely to lead to uplift and crustal thinning.
Structural basis of spectrin elasticity
Shen, B.W.; Stevens, F.J.; Luthi, U.; Goldin, S.B.
A new model of human erythrocyte {alpha}-spectrin is proposed. The secondary structure of human erythrocyte {alpha}-spectrin and its folding into a condensed structure that can convert reversibly in situ, into an elongated configuration is predicted from its deduced protein sequence. Results from conformational and amphipathicity analyses suggest that {alpha}-spectrin consists mainly of short amphipathicity helices interconnected by flexible turns and/or coils. The distribution of charges and amphipathicity of the helices can facilitate their folding into stable domains of 4 and 3 helices surrounding a hydrophobic core. The association between adjacent four- and three-helix domains further organize them into recurring seven-helix motifs that might constitute the basic structural units of the extended {alpha}-spectrin. The elongated spectrin molecule packs, in a sinusoidal fashion, through interactions between neighboring motifs into a compact structure. We suggest that the reversible extension and contraction of this sigmoidally packed structure is the molecular basis of the mechanism by which spectrin contributes to the elasticity of the red cell membrane.
Structural basis for selectin mechanochemistry.
Springer, Timothy A
Selectins are adhesion molecules that resist large tensile forces applied by hydrodynamic forces to leukocytes binding to vessel walls. In crystals, the liganded (high-affinity) and unliganded (low-affinity) conformations differ in orientation between their tandem lectin and EGF domains. I examine how tensile force exerted on a selectin-ligand complex in vivo could favor the more extended, high-affinity conformation. Allostery is transmitted from the EGF-lectin domain interface to the ligand-binding interface on the lectin domain, 30 A away. Trp-1 of the lectin domain and the long axis of the EGF domain form an L-shaped prybar that is welded together by hydrogen bonds to the Trp-1 alpha-amino group. Pivoting of the prybar induced by force demolishes an interface between the Trp-1 side chain and the lectin domain at a switch1 region. These changes are transmitted by rigid body movement of the switch2 region to rearrangements in the switch3 region at the ligand binding site. Another switch region corresponds to a single residue in the EGF domain with large effects on ligand binding and rolling adhesion. Allostery in selectins, and the alignment of tensile force on a selectin-ligand complex with the transition pathway for conformational change, explain much of the structural basis for selectin mechanochemistry.
Advanced Fuel Cycle Cost Basis
D. E. Shropshire; K. A. Williams; W. B. Boore; J. D. Smith; B. W. Dixon; M. Dunzik-Gougar; R. D. Adams; D. Gombert; E. Schneider
This report, commissioned by the U.S. Department of Energy (DOE), provides a comprehensive set of cost data supporting a cost analysis for the relative economic comparison of options for use in the Advanced Fuel Cycle Initiative (AFCI) Program. The report describes the AFCI cost basis development process, reference information on AFCI cost modules, a procedure for estimating fuel cycle costs, economic evaluation guidelines, and a discussion on the integration of cost data into economic computer models. This report contains reference cost data for 25 cost modules—23 fuel cycle cost modules and 2 reactor modules. The cost modules were developed in the areas of natural uranium mining and milling, conversion, enrichment, depleted uranium disposition, fuel fabrication, interim spent fuel storage, reprocessing, waste conditioning, spent nuclear fuel (SNF) packaging, long-term monitored retrievable storage, near surface disposal of low-level waste (LLW), geologic repository and other disposal concepts, and transportation processes for nuclear fuel, LLW, SNF, transuranic, and high-level waste.
Advanced Fuel Cycle Cost Basis
D. E. Shropshire; K. A. Williams; W. B. Boore; J. D. Smith; B. W. Dixon; M. Dunzik-Gougar; R. D. Adams; D. Gombert
This report, commissioned by the U.S. Department of Energy (DOE), provides a comprehensive set of cost data supporting a cost analysis for the relative economic comparison of options for use in the Advanced Fuel Cycle Initiative (AFCI) Program. The report describes the AFCI cost basis development process, reference information on AFCI cost modules, a procedure for estimating fuel cycle costs, economic evaluation guidelines, and a discussion on the integration of cost data into economic computer models. This report contains reference cost data for 26 cost modules—24 fuel cycle cost modules and 2 reactor modules. The cost modules were developed in the areas of natural uranium mining and milling, conversion, enrichment, depleted uranium disposition, fuel fabrication, interim spent fuel storage, reprocessing, waste conditioning, spent nuclear fuel (SNF) packaging, long-term monitored retrievable storage, near surface disposal of low-level waste (LLW), geologic repository and other disposal concepts, and transportation processes for nuclear fuel, LLW, SNF, and high-level waste.