Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
P K Bera; J Datta
2006-12-01
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this spectral inverse method.
Schunck, N; McDonnell, J; Satula, W; Sheikh, J A; Staszczak, A; Stoitsov, M; Toivanen, P
2011-01-01
We describe the new version (v2.49s) 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...
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
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
An application of the 3-dimensional q-deformed harmonic oscillator to the nuclear shell model
Raychev, P P; Lo-Iudice, N; Terziev, P A
1998-01-01
An analysis of the construction of a q-deformed version of the 3-dimensional harmonic oscillator, which is based on the application of q-deformed algebras, is presented. The results together with their applicability to the shell model are compared with the predictions of the modified harmonic oscillator.
Braid group representations from a deformation of the harmonic oscillator algebra
Tarlini, Marco
2016-01-01
We describe a new technique to obtain representations of the braid group B_n from the R-matrix of a quantum deformed algebra of the one dimensional harmonic oscillator. We consider the action of the R-matrix not on the tensor product of representations of the algebra, that in the harmonic oscillator case are infinite dimensional, but on the subspace of the tensor product corresponding to the lowest weight vectors.
The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters
Bonatsos, Dennis; Raychev, P P; Roussev, R P; Terziev, P A; Bonatsos, Dennis
1999-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of alkali metal clusters.
An application of the three-dimensional q-deformed harmonic oscillator to the shell model
Energy Technology Data Exchange (ETDEWEB)
Raychev, P.P. [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Monte S Angelo, via Cintia, I-80125 Napoli (Italy); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, BG-1784 Sofia (Bulgaria); Roussev, R.P.; Terziev, P.A. [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, BG-1784 Sofia (Bulgaria); Lo Iudice, N. [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Monte S Angelo, via Cintia, I-80125 Napoli (Italy)
1998-10-01
A procedure for the construction of a q-deformed version of the Hamiltonian of the three-dimensional harmonic oscillator (HO), based on the application of q-deformed algebras, is presented. The spectrum of this Hamiltonian is not degenerated in the quantum number of the q-deformed angular momentum. The results together with their applicability to the shell model are compared with the predictions of the modified HO. (author)
Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2003-01-01
The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).
Deformed Relativistic Hartree Theory in Coordinate Space and in Harmonic Oscillator Basis
Institute of Scientific and Technical Information of China (English)
ZHOU Shan-Gui; MENG Jie; Shuhei YAMAJI; YANG Si-Chun
2000-01-01
The deformed relativistic Hartree theory (DRH) is solved both in coordinate space (DRH-c) and in harmonic oscillator basis (DRH-o). Results obtained from these two methods are compared in details. The DRH-c and DRH-o calculations give similar total binding energies, deformation, level structures and radii for nitrogen iso topes, while their descriptions on the density distributions for drip-line nuclei are very different. The large spatiai istributions of nucleon densities, which is crucial to understand a weakly bound system, can only be obtained by DRH-c calculations. This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.
Bonatsos, Dennis; Lenis, D; Raychev, P P; Roussev, R P; Terziev, P A
2000-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry ...
The q-DEFORMED SCHRÖDINGER Equation of the Harmonic Oscillator on the Quantum Euclidean Space
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.
Covariant harmonic oscillators and coupled harmonic oscillators
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
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 Harmonic Oscillator Group
Lopez, Raquel M; Vega-Guzman, Jose M
2011-01-01
We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. The invariance group of generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schroedinger group of the free particle.
Relativistic Harmonic Oscillators and Hadronic Structures in the Quantum-Mechanics Curriculum
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A relativistic harmonic-oscillator formalism which is mathematically simple as the nonrelativistic harmonic oscillator is given. In view of its effectiveness in describing Lorentz-deformed hadrons, the inclusion of this formalism in a first-year graduate course will make the results of high-energy experiments more understandable. (BB)
Quantizing the damped harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Latimer, D C [Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235 (United States)
2005-03-04
We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that the unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.
Anomalous Dissipative Quantum Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
CHEN Dian-Yong; BAI Zhan-Wu; DONG Yu-Bing
2008-01-01
We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators' spectral density, the coordinate and momentum correlation functions decay as r-4and r-6 respectively at zero temperature, where T is the correlation time. The low-temperature behavior of the mean energy does not violate the third law of thermodynamics, but differs largely from the Ohmic spectrum case.
Making space for harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /Fermilab
2004-11-01
If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.
Introduction to classical and quantum harmonic oscillators
Bloch, Sylvan C
2013-01-01
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con
Harmonic Oscillators and Elementary Particles
Sobouti, Y
2016-01-01
Two dynamical systems with same symmetry should have features in common, and as far as their shared symmetry is concerned, one may represent the other. The three light quark constituents of the hadrons, a) have an approximate flavor SU(3) symmetry, b) have an exact color SU(3) symmetry, and c) as spin 1/2 particles, have a Lorentz SO(3,1) symmetry. So does a 3D harmonic oscillator. a) Its Hamiltonian has the SU(3) symmetry, breakable if the 3 fundamental modes of oscillation are not identical. b) The 3 directions of oscillation have the permutation symmetry. This enables one to create three copies of unbreakable SU(3) symmetry for each mode of the oscillation, and mimic the color of the elementary particles. And c) The Lagrangian of the 3D oscillator has the SO(3,1) symmetry. This can be employed to accommodate the spin of the particles. In this paper we draw up a one-to-one correspondence between the eigen modes of the Poisson bracket operator of the 3D oscillator and the flavor multiplets of the particles, ...
Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.
2013-06-01
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
The harmonic oscillator and nuclear physics
Rowe, D. J.
1993-01-01
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.
Quantum dynamics of the damped harmonic oscillator
Philbin, T G
2012-01-01
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
The Berry Phase for Simple Harmonic Oscillators
Suslov, Sergei K
2011-01-01
We evaluate the Berry phase for a "missing" family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables. It is obtained by the action of the maximal kinematical invariance group on the standard solutions. An explicit simple formula for the phase is found by integration with the help of a computer algebra system.
Sobolev Spaces Associated to the Harmonic Oscillator
Indian Academy of Sciences (India)
B Bongioanni; J L Torrea
2006-08-01
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator $H= - + |x|^2$. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.
Pisot q-coherent states quantization of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)
2013-03-15
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0deformed 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.
Harmonic oscillator model for the helium atom
Carlsen, Martin
2015-01-01
A harmonic oscillator model in four dimensions is presented for the helium atom to estimate the distance to the inner and outer electron from the nucleus, the angle between electrons and the energy levels. The method is algebraic and is not based on the choice of correct trial wave function. Three harmonic oscillators and thus three quantum numbers are sufficient to describe the two-electron system. We derive a simple formula for the energy in the general case and in the special case of the Wannier Ridge. For a set of quantum numbers the distance to the electrons and the angle between the electrons are uniquely determined as the intersection between three surfaces. We show that the excited states converge either towards ionization thresholds or towards extreme parallel or antiparallel states and provide an estimate of the ground state energy.
Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
Cariñena, José F
2016-01-01
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 non-physical 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.
Hyperchaotic circuit with damped harmonic oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
2001-01-01
A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...... capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
N D Hari Dass; Pradeep Ganesh
2002-08-01
We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use of this perfect information cloning it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We deﬁne the notion of a measurement ﬁdelity and calculate it for our case as well as for the Gaussian cloners.
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
DEFF Research Database (Denmark)
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting...... U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
Institute of Scientific and Technical Information of China (English)
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
Effective harmonic oscillator description of anharmonic molecular vibrations
Indian Academy of Sciences (India)
Tapta Kanchan Roy; M Durga Prasad
2009-09-01
The validity of an effective harmonic oscillator approximation for anharmonic molecular vibrations is tested and compared with vibrational self consistent field and vibrational configurational interaction results. The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.
Quantum control of harmonic oscillator networks
Genoni, Marco G; Kim, M S; Burgarth, Daniel
2011-01-01
Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance spin systems, precise criterions to establish controllability, such as the so called rank criterion, are well known. However most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems -- encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nano-mechanical oscillators -- governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend t...
The noncommutative harmonic oscillator in more than one dimensions
Hatzinikitas, A; Hatzinikitas, Agapitos; Smyrnakis, Ioannis
2002-01-01
The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the $\\star$-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding two-dimensional harmonic oscillator are solved. The angular momentum operator is derived and its $\\star$-genvalue problem is shown to be equivalent to the usual eigenvalue problem. The $\\star$-genvalues for the angular momentum are found to depend on the energy difference of the oscillations in each dimension. Furthermore two examples of assymetric noncommutative harmonic oscillator are analysed. The first is the noncommutative two-dimensional Landau problem and the second is the three-dimensional harmonic oscillator with symmetrically noncommuting coordinates and momenta.
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
Bound states of two-dimensional relativistic harmonic oscillators
Institute of Scientific and Technical Information of China (English)
Qiang Wen-Chao
2004-01-01
We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.
A harmonic oscillator having “volleyball damping”
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2006-05-01
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.
Violation of smooth observable macroscopic realism in a harmonic oscillator.
Leshem, Amir; Gat, Omri
2009-08-14
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.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
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.
Mohammed-Azizi, B.; Medjadi, D. E.
2014-11-01
, 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
Maximal Regularity of the Discrete Harmonic Oscillator Equation
Directory of Open Access Journals (Sweden)
Airton Castro
2009-01-01
Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.
Wigner Functions for harmonic oscillator in noncommutative phase space
Wang, Jianhua; Li, Kang; Dulat, Sayipjamal
2009-01-01
We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schr\\"{o}dinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the harmonic oscillator on NC space and NC phase space respectively.
A Look at Damped Harmonic Oscillators through the Phase Plane
Daneshbod, Yousef; Latulippe, Joe
2011-01-01
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…
On a Hidden Symmetry of Quantum Harmonic Oscillators
Lopez, Raquel M; Vega-Guzman, Jose M
2011-01-01
We present a six parameter family of the square integrable wave functions for the linear harmonic oscillator, which cannot be obtained by the standard separation of variables. They are found by the action of corresponding maximal kinematical invariance group on the standard solutions. Some possible applications are briefly discussed.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...
Exact complex integrals in two dimensions for shifted harmonic oscillators
Indian Academy of Sciences (India)
Jasvinder Singh Virdi; S C Mishra
2012-07-01
We use rationalization method to study two-dimensional complex dynamical systems (shifted harmonic oscillator in complex plane) on the extended comples phase space (ECPS). The role and scope of the derived invatiants in the context of various physical problems are high-lighted.
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
Nita, Gelu M.
2010-01-01
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.)
The harmonic oscillator, dimensional analysis and inflationary solutions
San Costa, S
2002-01-01
In this work, focused on the production of exact inflationary solutions using dimensional analysis, it is shown how to explain inflation from a pragmatic and basic point of view, in a step-by-step process, starting from the one-dimensional harmonic oscillator.
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
Pendrill, Ann-Marie; Eager, David
2015-01-01
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…
Simulating Harmonic Oscillator and Electrical Circuits: A Didactical Proposal
Albano, Giovannina; D'Apice, Ciro; Tomasiello, Stefania
2002-01-01
A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…
Chou, C H; Yu, T; Chou, Chung-Hsien; Yu, Ting
2007-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment made up of many harmonic oscillators at arbitrary temperature for 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 known [Hu, Paz and Zhang, Phys. Rev. D \\textbf{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 evolution operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We ...
Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data.
Song, Qiang; Yu, Wenwu; Cao, Jinde; Liu, Fang
2016-07-01
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
Ataullah, Ali; Tippett, Mark
2007-08-01
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
Prado Reynoso, M. Á.; López Vázquez, P. C.; Gorin, T.
2017-02-01
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.
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Jeong-Ryeol Choi
2003-07-01
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator satisfying Leouville–von Neumann equation to calculate various expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola–Kanai oscillator.
A type of perturbation of the harmonic oscillator
López, Jesús A Álvarez
2011-01-01
Consider perturbations of the harmonic oscillator $H$ of the form $P=H-f_1\\frac{d}{dx}+f_2$ for functions $f_1$ and $f_2$. If $f_2$ can be given as certain expression of $f_1$ and a parameter $\\sigma>-1$, then many well known properties of $H$ are generalized to $P$: self-adjointness in the appropriate Hilbert space, description of the spectrum, recurrence formula for the eigenfunctions, eigenfunction estimates and embedding results.
Anisotropic Harmonic Oscillator in a Static Electromagnetic Field
Institute of Scientific and Technical Information of China (English)
LIN Qiong-Gui
2002-01-01
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneousstatic electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrodingerequation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. Insome of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherentand squeezed states and their time evolution axe discussed in detail.
Harmonic oscillator Floquet states in the Bargmann-Segal space
Energy Technology Data Exchange (ETDEWEB)
Palma, A. [Instituto Nacional de Astrofisica, Optica y Electronica (INAOE), Puebla (Mexico)]. E-mail: palma@sirio.ifuap.buap.mx; Leon, V. [Instituto de Fisica, BUAP, Puebla (Mexico); Lefebvre, R. [Laboratoire de Photophysique Moleculaire du CNRS, Universite Paris-Sud, Orsay (France); UFR de Physique Fondamentale et Appliquee, Universite Pierre et Marie Curie, Paris (France)
2002-01-18
The Floquet quasi-energies and eigenfunctions for the harmonic oscillator interacting with a monochromatic electric field are obtained by using the so-called Bargmann-Segal space. The Schroedinger second-order differential equation in configuration space is transformed into a linear first-order equation in such a space, which is easily solved by means of an auxiliary system (called the Lagrange system) of ordinary differential equations. This method compares favourably with others previously used. (author)
Coherent and squeezed states for the 3D harmonic oscillator
Mazouz, Amel; Bentaiba, Mustapha; Mahieddine, Ali
2017-01-01
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.
Unitary approach to the quantum forced harmonic oscillator
2014-01-01
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations are applied successively to Schr\\"odinger's equation reducing it to its simplest form. Therefore, instead of solving the original Schr\\"odinger's partial differential equation in time and space the problem is replaced by a system of ordinary differential eq...
An analogue of the Berry phase for simple harmonic oscillators
Suslov, S. K.
2013-03-01
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.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber
2009-04-01
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.
Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
Kim, Y S; Noz, Marilyn E.
2004-01-01
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. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, 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 $SL(2,c)$...
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Tang, J.
1994-02-01
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.
Anisotropic Harmonic Oscillator in s Static Electromagnetic Field
Institute of Scientific and Technical Information of China (English)
LINQiong－Gui
2002-01-01
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied.Several configurations of the electromagnetic field are considered.The Schoedinger equation is solved analytically in most of the cases.The energy levels and wave functions are obtained explicitly.In some of the cases,the ground state obtained is not a minimum wave packet,though it is of the Gaussian type.Coherent and squeezed states and their time evolution are discussed in detail.
Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator
Directory of Open Access Journals (Sweden)
Mohammad Heydari
2014-01-01
Full Text Available A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method.
Effective field theory in the harmonic-oscillator basis
Binder, S; Hagen, G; Papenbrock, T; Wendt, K A
2015-01-01
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. We derive useful analytical expressions for an exact and efficient calculation of matrix elements. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn exhibit a fast convergence of ground-state energies and radii in feasible model spaces.
Elementary derivation of the quantum propagator for the harmonic oscillator
Shao, Jiushu
2016-10-01
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.
Low Noise Second Harmonic Oscillator Using Mutually Synchronized Gunn Diodes
Kawasaki, Kengo; Tanaka, Takayuki; Aikawa, Masayoshi
This paper represents a low noise second harmonic oscillator using mutually synchronized Gunn diodes. A multi-layer MIC technology is adopted to reduce the circuit size of the oscillator. The oscillator consists of Gunn diodes, slot line resonators and strip lines. By embedding Gunn diodes in the slot line resonators, a harmonic RF signal can be generated very easily. The strip lines are used for the power combining output circuit. The shape of slot line resonator is square in order to achieve the low phase noise and the suppression of undesired harmonics. The second harmonic oscillator is designed and fabricated in K band. The output power is +8.89dBm at the design frequency of 18.75GHz (2f0) with the phase noise of -116.2dBc/Hz at the offset frequency of 1MHz. Excellent suppression of the undesired fundamental frequency signal (f0) of -33dBc is achieved. Also, the circuit size is reduced by three-tenths relative to that of the previously proposed circuit.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Chou, Chia-Chun
2016-10-01
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.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
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
Lee, Keeyung
2009-01-01
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
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
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.
Institute of Scientific and Technical Information of China (English)
CHEN CHANG-YUAN
2000-01-01
In this paper, the general formulas and the recurrence formulas for radial matrix elements of N-dimensional isotropic harmonic oscillator are obtained. The relevant results of 2- dimensional and 3- dimensiona] isotropic harmonic oscillators reported in the reference papers are contained in a more general equations derived in this paper as special cases.
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
Amitava Choudhuri; Subrata Ghosh; B Talukdar
2008-04-01
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, A.; Hagen, G.; Papenbrock, T.; Wendt, K. A.
2016-04-01
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. Many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.
Excitation with quantum light. I. Exciting a harmonic oscillator
Carreño, J. C. López; Laussy, F. P.
2016-12-01
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.
Chiral potential renormalized in harmonic-oscillator space
Yang, C -J
2016-01-01
We renormalize the chiral effective field theory (EFT) potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultra-violet 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 (NN) 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 $T_{lab}=100$ MeV with number of HO basis $n_{max}$ 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. Our work serves as the input to perform ab-initio calculations.
A method of solving simple harmonic oscillator Schroedinger equation
Maury, Juan Carlos F.
1995-01-01
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.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
DIÓGENES CAMPOS
2017-03-01
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.
Ecological optimization of an irreversible harmonic oscillators Carnot heat engine
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
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.
Ecolosical optimization of an irreversible harmonic oscillators Carnot heat engine
Institute of Scientific and Technical Information of China (English)
LIU XiaoWei; CHEN LinGen; WU Feng; SUN FengRui
2009-01-01
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.
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
Singh, Manu Pratap; Rajput, B. S.
2016-10-01
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.
Generalized Harmonic Oscillator and the Schr(o)dinger Equation with Position-Dependent Mass
Institute of Scientific and Technical Information of China (English)
JU Guo-Xing; CAI Chang-Ying; REN Zhong-Zhou
2009-01-01
We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties for the system with PDM are also discussed. We give the corresponding effective potentials for several mass functions, the systems with such potentials are isospectral to the usual harmonic oscillator.
Entangled Harmonic Oscillators and Space-time Entanglement
Baskal, Sibel; Noz, Marilyn E
2016-01-01
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of O(3,2) de Sitter group containing two O(3,1) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of...
On quantum harmonic oscillator being subjected to absolute potential state
Nityayogananda, Swami
2017-01-01
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.
On quantum harmonic oscillator being subjected to absolute potential state
Indian Academy of Sciences (India)
SWAMI NITYAYOGANANDA
2017-01-01
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 remainsdormant. 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 greaterwill 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.
Entanglement dynamics for a conditionally kicked harmonic oscillator
Arrais, Eric G.; Sales, J. S.; de Almeida, N. G.
2016-08-01
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.
The calculating formula for radial matrix elements of a relativistic harmonic oscillator
Institute of Scientific and Technical Information of China (English)
强稳朝
2003-01-01
A universal practical formula is given for calculating an integral which includes two confluent hypergeometric functions, power and exponential functions; then by means of this formula, the expressions of the radial matrix elements for a relativistic harmonic oscillator are given.
Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity
Institute of Scientific and Technical Information of China (English)
HUANG Bo-Wen; GU Zhi-Yu; QIAN Shang-Wu
2003-01-01
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity isobtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
On the limiting behavior of a harmonic oscillator with random external disturbance
Directory of Open Access Journals (Sweden)
G. L. Kulinich
1995-01-01
Full Text Available This paper deals with the limiting behavior of a harmonic oscillator under the external random disturbance that is a process of the white noise type. Influence of noises is investigated in resonance and non-resonance cases.
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Torres del Castillo, G.F. [Departamento de Fisica Matematica, Instituto de Ciencias, Universidad Autonoma de Puebla, 72570 Puebla (Mexico); Tepper G, T. [Escuela de Ciencias, Departamento de Fisica y Matematicas, Universidad de Las Americas-Puebla, Santa Catarina Martir, 72820 Cholula, Puebla (Mexico)
2002-07-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Transformation between harmonic-oscillator wave functions in different coordinate bases
Energy Technology Data Exchange (ETDEWEB)
Davies, K.T.R.; Krieger, S.J.
1981-10-01
Coefficients are derived for transformations between harmonic oscillator wave functions in different coordinate representations. Such coefficients have been found especially useful in performing static Hartree-Fock calculations for nuclei of widely varying shapes.
Harmonic oscillator in Snyder space: The classical case and the quantum case
Indian Academy of Sciences (India)
Carlos Leiva
2010-02-01
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual harmonic oscillator is obtained through an effective mass and an effective frequency introduced in the model. This modified parameters give us a modified energy spectrum also.
A Fulling-Kuchment theorem for the 1D harmonic oscillator
Guillemin, Victor
2011-01-01
We prove that there exists a pair of "non-isospectral" 1D semiclassical Schr\\"odinger operators whose spectra agree modulo h^\\infty. In particular, all their semiclassical trace invariants are the same. Our proof is based on an idea of Fulling-Kuchment and Hadamard's variational formula applied to suitable perturbations of the harmonic oscillator. Keywords: Inverse spectral problems, semiclassical Schr\\"odinger operators, trace invariants, Hadamard's variational formula, harmonic oscillator, Penrose mushroom, Sturm-Liouville theory.
Time dependent quantum harmonic oscillator subject to a sudden change of mass: continuous solution
Energy Technology Data Exchange (ETDEWEB)
Moya C, H. [INAOE, Coordinacion de Optica, AP 51 y 216, 72000 Puebla (Mexico); Fernandez G, M. [Depto. de Fisica, CBI, Universidad Autonoma Metropolitana - Iztapalapa, 09340, Mexico, D.F. AP 55-534 (Mexico)
2007-07-01
We show that a harmonic oscillator subject to a sudden change of mass produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a sub period function parameter. This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity. This formalism requires an ad hoc transformation of the original differential equation and is also applicable for rapid, although not necessarily instantaneous, mass variations. (Author)
Directory of Open Access Journals (Sweden)
Yilun Shang
2012-07-01
Full Text Available In this paper, we investigate the leader-follower synchronization ofcoupled second-order linear harmonic oscillators with the presence ofrandom noises and time delays. The interaction topology is modeledby a weighted directed graph and the weights are perturbed by whitenoise. On the basis of stability theory of stochastic differential delayequations, algebraic graph theory and matrix theory, we show that thecoupled harmonic oscillators can be synchronized almost surely withrandom perturbation and time delays. Numerical examples are presentedto illustrate our theoretical results.
Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium
Jafari, Marjan; Kheirandish, Fardin
2017-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Martinez, D [Universidad Autonoma de la Ciudad de Mexico, Plantel Cuautepec, Av. La Corona 320, Col. Loma la Palma, Delegacion Gustavo A. Madero, 07160, Mexico DF (Mexico); Flores-Urbina, J C; Mota, R D [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, Delegacion Gustavo A. Madero, 07340 Mexico DF (Mexico); Granados, V D [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)], E-mail: dmartinezs77@yahoo.com.mx
2010-04-02
We apply the Schroedinger factorization to construct the ladder operators for the hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the su(1, 1) Lie algebra.
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
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.
Institute of Scientific and Technical Information of China (English)
刘宇峰; 曾谨言
1997-01-01
The factorization of the radial Schrodinger equation of n-dimensional (n≥2) hydrogen atoms and isotropic harmonic oscillators was investigated and four kinds of raising and lowering operators were derived.The relation between n -dimensional (n≥2) and one-dimensional hydrogen atoms and harmonic oscillators was discussed.
Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes
Gauthier, N.
2004-01-01
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…
Bonatsos, Dennis; Kolokotronis, P; Lenis, D; Bonatsos, Dennis
1994-01-01
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems.
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
2010-01-01
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...
Coherent presentation of density operator of the harmonic oscillator in thermostat
Energy Technology Data Exchange (ETDEWEB)
Avakyan, R.M. [Department of Physics, Yerevan State University, 0025 Yerevan (Armenia); Hayrapetyan, A.G. [Institute of Applied Problems of Physics, National Academy of Sciences of Republic of Armenia, 0014 Yerevan (Armenia)], E-mail: armen@iapp.sci.am; Khachatryan, B.V.; Petrosyan, R.G. [Department of Physics, Yerevan State University, 0025 Yerevan (Armenia)
2007-12-10
Based on basis of the coherent states the density matrix of harmonic oscillator in thermostat is obtained. This method is mathematically refined and physically transparent for the interpretation of quantum phenomena in classical language. Such an approach gives an opportunity to easily find the density matrix in the multi-dimensional case.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M.
2004-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Convergence for Fourier Series Solutions of the Forced Harmonic Oscillator II
Fay, Temple H.
2002-01-01
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…
Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp(4, R) Lie Algebra
Institute of Scientific and Technical Information of China (English)
PAN Feng; DAI LianRong
2001-01-01
Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).``
Density Matrix and Squeezed Vacuum State for General Coupling Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
SONG Tong-Qiang
2003-01-01
By taking a unitary transformation approach, we study two harmonic oscillators with both kinetic coupling and coordinate coupling terms, and derive the density matrix of the system. The results show that the ground state of the system is a rotated two single-mode squeezed state.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M
2001-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, Miguel
2001-07-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Exact solutions of N-dimensional harmonic oscillator via Laplace transformation
Institute of Scientific and Technical Information of China (English)
Chen Gang
2005-01-01
The N-dimensional Schrodinger equation for the harmonic oscillator is reduced to a first-order differential equation in terms of the Laplace transformation and the exact bound state solutions are derived. It is shown that this method of solving Schrodinger equation may serve as a substitute for the standard functional, analytical approach also in lower dimensions.
Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation
Institute of Scientific and Technical Information of China (English)
WANG Fei; QIAN Shang-Wu; FU Li-Ping; WANG Jing-Shan; GUO Ke-Tao
2008-01-01
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A genera/ equation for obtaining gauge-invariant transition probability amplitudes is derived.
Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space
Das, Saurya; Walton, Mark A
2016-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Mota, R.D. [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, Mexico DF (Mexico)]. E-mail: mota@gina.esfm.ipn.mx; ravelo@esfm.ipn.mx; Granados, V.D.; Queijeiro, A.; Garcia, J. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Mexico DF (Mexico)
2002-03-29
For the quantum two-dimensional isotropic harmonic oscillator we show that the Infeld-Hull radial operators, as well as those of the supersymmetric approach for the radial equation, are contained in the constants of motion of the problem. (author)
su(2) Lie algebra approach for the Feynman propagator of the one-dimensional harmonic oscillator
Martínez, D.; Avendaño, C. G.
2014-04-01
We evaluate the Feynman propagator for the harmonic oscillator in one dimension. Considering the ladder operators for the Hamiltonian of this system, we construct a set of operators which satisfy the su(2) Lie algebra to obtain Mehler’s formula.
The study of entanglement and teleportation of the harmonic oscillator bipartite coherent states
Directory of Open Access Journals (Sweden)
A Rabeie and
2015-01-01
Full Text Available In this paper, we reproduce the harmonic oscillator bipartite coherent states with imperfect cloning of coherent states. We show that if these entangled coherent states are embedded in a vacuum environment, their entanglement is degraded but not totally lost . Also, the optimal fidelity of these states is worked out for investigating their teleportation
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
2014-11-01
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
López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.
2012-08-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... to the extent that it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes the effects...
Saha, Anirban
2015-01-01
We investigate the quantum mechanical transitions, induced by the combined effect of Gravitational wave (GW) and noncommutative (NC) structure of space, among the states of a 2-dimensional harmonic oscillator. The phonon modes excited by the passing GW within the resonant bar-detector are formally identical to forced harmonic oscillator and they represent a length variation of roughly the same order of magnitude as the characteristic length-scale of spatial noncommutativity estimated from the phenomenological upper bound of the NC parameter. This motivates our present work. We employ a number of different GW wave-forms that are typically expected from possible astronomical sources. We find that the transition probablities are quite sensitive to the nature of polarization of the GW. We further elaborate on the particular type of sources of GW radiation which can induce transitions that can be used as effective probe of the spatial noncommutative structure.
Directory of Open Access Journals (Sweden)
Sameer M. Ikhdair
2013-01-01
Full Text Available The Klein-Gordon (KG equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0 and AB flux field (ξ=0 cases. Effect of external fields on the nonrelativistic energy eigenvalues and wave function solutions is also precisely presented. Some special cases like harmonic oscillator and Coulombic fields are also studied.
Energy Technology Data Exchange (ETDEWEB)
Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)
2011-09-19
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2011-02-11
The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Midya, Bikashkali; Roychoudhury, Rajkumar
2011-01-01
The generalized Swanson Hamiltonian $H_{GS} = w (\\tilde{a}\\tilde{a}^\\dag+ 1/2) + \\alpha \\tilde{a}^2 + \\beta \\tilde{a}^{\\dag^2}$ with $\\tilde{a} = A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as $[\\tilde{a},\\tilde{a}^\\dag]=$ constant. However, the main objective of this paper is to show that though the commutator of $\\tilde{a}$ and $\\tilde{a}^\\dag$ is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. Reason for this anomaly is discussed in the frame work of position dependent mass models by choosing $A(x)$ as the inverse square root of the mass function.
Directory of Open Access Journals (Sweden)
Wayne Cheng-Wei Huang
2013-01-01
Full Text Available Stochastic electrodynamics (SED predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.
Ehlers, E. F.
1974-01-01
A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.
Equilibrium and stationary nonequilibrium states in a chain of colliding harmonic oscillators
Sano
2000-02-01
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.
Deymier, P. A.; Runge, K.; Vasseur, J. O.
2016-12-01
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.
Dynamics of a harmonic oscillator in a finite-dimensional Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Kuang Leman (CCAST (World Lab.), Beijing, BJ (China) Dept. of Physics and Inst. of Physics, Hunan Normal Univ. (China)); Wang Fabo (Dept. of Physics, Hunan Normal Univ. (China)); Zhou Yanguo (Dept. of Physics, Hunan Normal Univ. (China))
1993-11-29
Some dynamical properties of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are studied. The time evolution of the position and momentum operators and the second-order quadrature squeezing are investigated in detail. It is shown that the coherent states of the FDHSHO are not the minimum uncertainty states of the position and momentum operators of the FDHSHO. It is found that the second-order squeezing of the quadrature operators vanishes and reappears periodically in the time evolution. (orig.)
Chih-Chun Chang; Guang-Yin Chen; Lee Lin
2016-01-01
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 a...
(3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
LUO Xiang-Qian; XU Hao; YANG Jie-Chao; WANG Yu-Li; CHANG Di; LIN Yin; Helmut Kroger
2001-01-01
In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1+1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.``
Directory of Open Access Journals (Sweden)
P. A. Deymier
2016-12-01
Full Text Available 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.
Solution to the Master Equation of a Free Damped Harmonic Oscillator with Linear Driving
Institute of Scientific and Technical Information of China (English)
杨洁; 逯怀新; 赵博; 赵梅生; 张永德
2003-01-01
We use the Lie algebra representation theory for superoperators to solve the master equation for a harmonic oscillator with a linear driving term in a squeezed thermal reservoir. By using the quantum displacement transformation and squeeze transformation, we show that the master equation has an su(1, 1) Lie algebra structure,with which we obtain the explicit solution to the master equation. A simple but typical example is given to illustrate our method.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
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.
Das, A; Das, A; Wotzasek, C
1995-01-01
We study a supersymmetric 2-dimensional harmonic oscillator which carries a representation of the general graded Lie algebra GL(2\\vert1) formulate it on the superspace, and discuss its physical spectrum.
Institute of Scientific and Technical Information of China (English)
WEI Gao-Feng; LONG Chao-Yun; LONG Zheng-Wen; QIN Shui-Jie
2008-01-01
In this paper,the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space;the corresponding exact energy is obtained,and the analytic eigenfunction is presented in terms of the confluent hypergeometric function.It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.
A least squares finite element scheme for transonic flow around harmonically oscillating airfoils
Cox, C. L.; Fix, G. J.; Gunzburger, M. D.
1983-01-01
The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.
Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator's Wave Functions
Institute of Scientific and Technical Information of China (English)
LU Hai-Liang; FAN Hong-Yi
2007-01-01
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions.The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S(r)Hm,n(μa1+, μa2+)|00〉, which is the minimum uncertainty state for sum squeezing, in 〈η| representation is calculated.
Kurt, Arzu; Eryigit, Resul
2015-12-01
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.
Rosu, H. C.; Khmelnytskaya, K. V.
2011-09-01
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned.
Rosu, H C
2010-01-01
Previous research made us consider a simple but curious problem related to the kind of oscillators that are produced in the usual supersymmetric scheme when one introduces a constant shift of the Riccati solution R(t)=-omega _0 tan(omega _0t) of the classical harmonic oscillator. The corresponding mathematical scheme is presented in detail showing that at least some of these oscillators could be of physical nature. We give the solutions of the resulting second-order differential equations obtaining the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry
Guo, Feng; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Li, Heng
2016-10-01
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.
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-07-01
We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-09-02
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.
Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
Chen, Xi
2010-01-01
There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing 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.
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-11-01
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.
Energy Technology Data Exchange (ETDEWEB)
Mota, R D [Departamento de Matematicas, Centro de Investigacion y de Estudios Avenzados del IPN, 07000, Mexico DF (Mexico); Granados, V D [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Queijeiro, A [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Garcia, J [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Guzman, L [Unidad Profesional Interdisciplinaria en Ingenieria y Tecnologias Avanzadas, IPN Av. Instituto Politecnico Nacional No 2580, Col. La Laguna Ticoman, Delegacion Gustavo A Madero, CP 07340 Mexico DF (Mexico)
2003-05-02
We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method.
Pupasov-Maksimov, Andrey M.
2015-12-01
It is shown that fundamental solutions Kσ(x , y ; t) = of the non-stationary Schrödinger equation (Green functions, or propagators) for the rational extensions of the Harmonic oscillator Hσ =Hosc + ΔVσ are expressed in terms of elementary functions only. An algorithm to calculate explicitly Kσ for an arbitrary increasing sequence of positive integers σ is given, and compact expressions for K { 1 , 2 } and K { 2 , 3 } are presented. A generalization of Mehler's formula to the case of exceptional Hermite polynomials is given.
Wang, Zhiguo; Liang, Zhenguo
2017-04-01
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.
Use of videos for students to see the effect of changing gravity on harmonic oscillators
Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber
2010-03-01
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.
Haxton, Wick
2007-01-01
Semi-leptonic electroweak interactions in nuclei - such as \\beta decay, \\mu capture, charged- and neutral-current neutrino reactions, and electron scattering - are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |\\vec{p}|/M, where \\vec{p} and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q^2, where q is the magnitude of the three-momentum transfer. While results for such matrix elements a...
On the local virial theorems for linear and isotropic harmonic oscillator potentials in d dimensions
Energy Technology Data Exchange (ETDEWEB)
Bencheikh, K [Departement de Physique, Laboratoire de physique quantique et systemes dynamiques, Universite de Setif, Setif 19000 (Algeria); Nieto, L M, E-mail: bencheikh.kml@gmail.co [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain)
2010-09-17
For the system of noninteracting fermions in a one-body potential V(r-vector), the local virial theorems (LVT) are relations, at a given point r-vector in space, between this potential, kinetic energy and particle densities. It was recently shown (Brack et al 2010 J. Phys. A: Math. Theor. 43 255204) that for d-dimensional linear and also for isotropic harmonic oscillator potentials these LVTs are exactly satisfied. We present alternative and simple proofs of these theorems, by consideration of the canonical or Bloch density matrix and its relation to the kinetic energy density. The explicit analytical forms of the Bloch density matrix are used for the above-mentioned potentials to achieve the proofs. For the case of linear potential, we obtain a more general result for the so-called semilocal virial theorem, and for the harmonic oscillator potential case we derive a new relationship between the diagonal part of the canonical bloch density and the kinetic energy density.
Reduction of Sub-Harmonic Oscillations in Flyback Converter for High Power Factor
Directory of Open Access Journals (Sweden)
Mr.M.SubbaRao,
2011-03-01
Full Text Available For High power factor (HPFoperation of flyback converter in continuous conduction mode(CCM, a variety of current mode control techniques, such as peak current control, Average current control andcharge control techniques has been analyzed. But these are suffer from stability problem due to presence of sub-harmonic oscillations and noise immunity. This can be overcome by using slope compensationtechnique, but it increases complexity .So the proposed technique in this paper i.e., a Single-Reset Integrator based line current shaping controller is a simple and accurate line current shaping controllerwith reduced sub-harmonic oscillations. In this paper presents the comparison between charge control technique with proposed control i.e., A Single-Reset Integrator based line current shaping controller for a 200 W,140V A.C input and 48V D.C output single phase flyback converter for HPF.MATLAB/Simulink software is used for implementation and simulation results shows the performance of proposed controller.
Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
Li, Haifeng; Wang, Shikuan
2011-01-01
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 comes out. 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...
Indian Academy of Sciences (India)
Rajarshi Chakrabarti
2009-04-01
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.
Norrelykke, Simon F
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) Effects of finite sampling-rate and -time, described exactly here, are similar for other stochastic dynamical systems-e.g. motile micro-organisms and their time-lapse recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes effects of finite sampling rate and sampling time for these models as well. Finally, we give a brief discussion of nondimensio...
Institute of Scientific and Technical Information of China (English)
Sameer M.Ikhdair; Majid Hamzavi
2012-01-01
We study the effects of the perpendicular magnetic and Aharonov Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein-Gordon (KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator (PHO).We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter,magnetic field strength,AB flux field,and magnetic quantum number by means of the Nikiforov-Uvarov (NU) method.The non-relativistic limit,PHO,and harmonic oscillator solutions in the existence and absence of external fields are also obtained.
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ
Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.
2005-11-01
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.
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
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…
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
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.
Energy Technology Data Exchange (ETDEWEB)
Kurt, Arzu; Eryigit, Resul, E-mail: resul@ibu.edu.tr
2015-12-18
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. - Highlights: • Exact analytical expressions for up to the fourth-order master equation are obtained. • High and low temperature limits of anomalous diffusion coefficients are elucidated. • Convergence range of the oscillator and the bath parameters discussed.
Bose-Einstein condensation in a two-component Bose gas with harmonic oscillator interaction
Abulseoud, A. A.; Abbas, A. H.; Galal, A. A.; El-Sherbini, Th M.
2016-07-01
In this article a system containing two species of identical bosons interacting via a harmonic oscillator potential is considered. It is assumed that the number of bosons of each species is the same and that bosons belonging to the same species repel each other while those belonging to different species attract. The Hamiltonian is diagonalized and the energy spectrum of the system is written down. The behaviour of the system in the thermodynamic limit is studied within the framework of the grand canonical ensemble, and thermodynamic parameters, such as the internal energy, entropy and specific heat capacity are calculated. It is shown that the system exhibits a single species Bose-Einstein condensation when the coupling strengths are equal and a dual species condensation when they are different.
Directory of Open Access Journals (Sweden)
V. Mohammadi
2015-01-01
Full Text Available We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, the SO(3 group generators of the Schrödinger-like equation with the Kepler-Coulomb potential are represented. In addition, by Levi-Civita transformation, the Schrödinger-like equation with harmonic oscillator which is dual to the Kepler-Coulomb potential and the SU(2 group generators of associated system are studied. Also, we construct the quadratic algebra of the hyperboloid superintegrable system. Then, we obtain the corresponding Casimir operators and the structure functions and the relativistic energy spectra of the corresponding quasi-Hamiltonians by using the quadratic algebra approach.
The sojourn time of the inverted harmonic oscillator on the noncommutative plane
Energy Technology Data Exchange (ETDEWEB)
Guo Guangjie; Ren Zhongzhou; Ju Guoxing [Department of Physics, Nanjing University, Nanjing 210093 (China); Long Chaoyun, E-mail: woggj@126.com [Department of Physics, Guizhou University, Guiyang 550025 (China)
2011-10-21
The sojourn time of the Gaussian wavepacket that is stationed at the center of the inverted harmonic oscillator is investigated on the noncommutative plane in detail. In ordinary commutative space quantum mechanics, the sojourn time of the Gaussian wavepacket is always a monotonically decreasing function of the curvature parameter {omega} of the potential. However, in this paper, we find that the spatial noncommutativity makes the sojourn time a concave function of {omega} with a minimum at an inflection point {omega}{sub 0}. Furthermore, if {omega} is larger than a certain critical value the sojourn time will become infinity. Thus, the ordinary intuitive physical picture about the relation between the sojourn time and the shape of the inverted oscillator potential is changed when the spatial noncommutativity is considered. (paper)
Infrared and ultraviolet cutoffs in variational calculations with a harmonic oscillator basis
Coon, Sidney A
2013-01-01
I abstract from a recent publication [1] the motivations for, analysis in and conclusions of a study of the ultraviolet and infrared momentum regulators induced by the necessary truncation of the model spaces formed by a variational trial wave function. This trial function is built systematically from a complete set of many-body basis states based upon three-dimensional harmonic oscillator (HO) functions. Each model space is defined by a truncation of the expansion characterized by a counting number (N) and by the intrinsic scale ($\\hbar\\omega$) of the HO basis. Extending both the uv cutoff to infinity and the ir cutoff to zero is prescribed for a converged calculation. In [1] we established practical procedures which utilize these regulators to obtain the extrapolated result from sequences of calculations with model spaces. Finally, I update this subject by mentioning recent work on our extrapolation prescriptions which have appeared since the submission of [1]. The numerical example chosen for this contribu...
Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback
Directory of Open Access Journals (Sweden)
A.F. EL-Bassiouny
2006-01-01
Full Text Available Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.
A Novel SIW-Based Planar W-Band GaAs Gunn Harmonic Oscillator
Liu, Yong; Tang, Xiao-Hong; Cao, Zhou
2010-10-01
Based on the substrate integrated waveguide (SIW) technology, a novel W-band low phase noise GaAs Gunn planar harmonic oscillator is developed in this paper. The technique of harmonic extraction from Gunn diodes and SIW resonant cavity structures are discussed in detail. Due to the high quality factor and planar structure of the SIW cavity resonator, the oscillator is characterized by some advantages such as low phase noise, small size, low cost and planar integration. The measured phase noise is -108.56 dBc/Hz at 1 MHz offset and the output power is more than 9 dBm at 94.78 GHz. A 300 MHz of linear tuning range with power fluctuation less than 1.5 dB is observed when the Gunn diode is biased from 4 to 5.3 V.
Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System
Directory of Open Access Journals (Sweden)
Lock Yue Chew
2014-04-01
Full Text Available In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state.
Manipulating Fock states of a harmonic oscillator while preserving its linearity
Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.
2016-12-01
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 Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator
Govaerts, Jan; Mattelaer, Olivier
2009-01-01
The canonical operator quantisation formulation corresponding to the Klauder-Daubechies construction of the phase space path integral is considered. This formulation is explicitly applied and solved in the case of the harmonic oscillator, thereby illustrating in a manner complementary to Klauder and Daubechies' original work some of the promising features offered by their construction of a quantum dynamics. The Klauder-Daubechies functional integral involves a regularisation parameter eventually taken to vanish, which defines a new physical time scale. When extrapolated to the field theory context, besides providing a new regularisation of short distance divergences, keeping a finite value for that time scale offers some tantalising prospects when it comes to strong gravitational quantum systems.
A dynamical systems approach to Bohmian trajectories in a 2D harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Borondo, F [Departamento de Quimica, and Instituto Mixto de Ciencias Matematicas CSIC-UAM-UC3M-UCM, Universidad Autonoma de Madrid, Cantoblanco-28049 Madrid (Spain); Luque, A; Villanueva, J [Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, 08028 Barcelona (Spain); Wisniacki, D A [Departamento de Fisica ' J. J. Giambiagi' , FCEN, UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires (Argentina)], E-mail: f.borondo@uam.es, E-mail: alejandro.luque@upc.edu, E-mail: jordi.villanueva@upc.edu, E-mail: wisniacki@df.uba.ar
2009-12-11
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocity field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohm's quantum trajectories can be based. An application to the two-dimensional isotropic harmonic oscillator is presented as an illustration.
Directory of Open Access Journals (Sweden)
Xiaowei Liu, Lingen Chen, Feng Wu, Fengrui Sun
2015-01-01
Full Text Available The optimal performance of an irreversible quantum Carnot refrigerator with working medium consisting of many non-interacting harmonic oscillators is investigated in this paper. The quantum refrigerator cycle is composed of two isothermal processes and two irreversible adiabatic processes, and the irreversibilities of heat resistance, internal friction and bypass heat leakage are considered. By using the quantum master equation, semi-group approach and finite time thermodynamics (FTT, this paper derives the cooling load and coefficient of performance (COP of the quantum refrigeration cycle and provides detailed numerical examples. At high temperature limit, the cooling load versus COP characteristic curves are plotted, and effects of internal friction and bypass heat leakage on the optimal performance of the quantum refrigerator are discussed. Three special cases, i.e., endoreversible, frictionless and without bypass heat leakage, are discussed in brief.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
Lin Bi Hong; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here ...
Directory of Open Access Journals (Sweden)
Gilles Regniers
2009-11-01
Full Text Available In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case. In this paper, we take a more general approach and look at the system as a Wigner quantum system. Hereby, one does not assume the canonical commutation relations, but instead one just requires the compatibility between the Hamilton and Heisenberg equations. Solutions of this problem are related to the Lie superalgebras gl(1|n and osp(1|2n. We determine the spectrum of the considered Hamiltonian in specific representations of these Lie superalgebras and discuss the results in detail. We also make the connection with the well-known canonical case.
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
2016-09-01
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.
Time operator for the quantum harmonic oscillator resolution of an apparent paradox
Granik, A; Granik, Alex
2000-01-01
An apparent paradox is resolved that concerns the existence of time operators which have been derived for the quantum harmonic oscillator. There is an apparent paradox because, although a time operator is canonically conjugate to the Hamiltonian, it has been asserted that no operator exists that is canonically conjugate to the Hamiltonian. In order to resolve the apparent paradox, we work in a representation where the phase operator is diagonal. The boundary condition on wave functions is such that they be periodic in the phase variable, which is related to the (continuous) eigenvalue of the time operator. Matrix elements of the commutator of the time operator with the Hamiltonian involve the phase variable itself in addition to periodic functions of the phase variable. The Hamiltonian is not hermitian when operating in space that includes the phase variable itself. The apparent paradox is resolved when this non-hermeticity is taken into account correctly in the evaluation of matrix elements of the commutatio...
The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
Schliemann, John
2013-01-01
It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only neighboring states of its standard basis, and (ii) its matrix elements show a unique maximum as a function of internal angular momentum quantum numbers. These quantum numbers, considered as a continuous variable, are the coordinate of the oscillator describing its quadratic potential, while the corresponding derivative defines a momentum operator. We also analyze the scaling properties of the oscillator parameters as a function of the size of the tetrahedron, and the role of different angular momentum coupling schemes.
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
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.
Evolution of a quantum harmonic oscillator coupled to a minimal thermal environment
Vidiella-Barranco, A.
2016-10-01
In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled A), prepared in a coherent state. The environment itself consists of a second oscillator (labelled B), initially in a thermal state. Two types of interaction Hamiltonians are considered, and the time-evolution of the reduced density operator of oscillator A is compared to the one obtained from the usual master equation approach, i.e., assuming that oscillator A is coupled to a large reservoir. An analysis of the linear entropy evolution of oscillator A shows that simplified models may be able to describe important features related to the phenomenon of decoherence, such as the rapid growth of the linear entropy, as well as its dependence on the effective temperature of the environment.
Ita, B. I.; Obong, H. P.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-11-01
The solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for S-waves have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials.
Institute of Scientific and Technical Information of China (English)
侯邦品; 王顺金; 余万伦
2003-01-01
By using the algebraic structure in the operator dual space in the master equation for the driven dissipative harmonic oscillator, we have rewritten the master equation as a Schrodinger-like equation. Then we have used three gauge transformations and obtained an exact solution to the master equation in the particle number representation.
MAVRI, J; BERENDSEN, HJC
1994-01-01
A density-matrix evolution method [Berendsen and Mavri, J. Phys. Chem. 97, 13464 (1993)] coupled to a classical molecular dynamics simulation was applied to study a quantum harmonic oscillator immersed in a bath of Lennard-Jones particles. Eigenfunctions of the three, lowest levels of the unperturbe
Andrews, David L.; Romero, Luciana C. Davila
2009-01-01
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…
Linear Harmonic Oscillator and Uniform Circular Motion%线性谐振子与匀速圆周运动
Institute of Scientific and Technical Information of China (English)
岳小萍; 秦鑫
2012-01-01
This article discusses the relationship between uniform circular motion and harmonic vibration of particle by classical mechanics method. The expressions of displacement, velocity and acceleration of linear harmonic oscillator are given, and phase differences among the three are explained by causality and Newton’s second law of motion. This article obtains linear harmonic oscillator force constant k = Gm m / r in-3 1 2 gravitational field, and discusses its physical significance, corrects the mistake of energy of harmonic oscillator is invariably positive for a long time. Electric linear harmonic oscillator concept is introduced. Method of discussing electric linear harmonic oscilators of elliptic orbit and valence electron in different orbital are provided. The method of converting linear harmonic oscillator of real space to quantum mechanics is introduced.% 用经典力学的方法讨论了质点匀速圆周运动与谐振动的关系问题，给出了线性谐振子位移、速度、加速度表达式，用因果律和牛顿第二运动定律，说明了三者之间的位相差关系；得到了万有引力场中二质点系统线性谐振子力常量k = Gm m / r 的结果，讨论了其物理意义，纠正了长期以来认为谐振子能量总是-312大于零的错误认识。引入了线性电谐振子概念；给出了讨论椭圆轨道电线性谐振子、不同轨道上价电子线性电谐振子的方法；介绍了实空间电线性谐振子转化为量子力学线性谐振子的方法
Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator
Indian Academy of Sciences (India)
PETER A ROSE; ANDREW C McCLUNG; TYLER E KEATING; ADAM T C STEEGE; ERIC S EGGE; ARJENDU K PATTANAYAK
2016-08-01
We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates $|n\\ rangle$, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state $n*$ with maximal quantum-classical distance; the value $n*$ decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
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.
Bogdan, V. M.; Bond, V. B.
1980-01-01
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.
Teh, Mei-Hui; LeBohec, Stephan
2016-01-01
This article is the first in a series of two presenting the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. In this first paper, we present the definition of a complex "scale-covariant time-differential operator" and show that mechanics of non-differentiable paths is implemented in the same way as classical mechanics but with the replacement of the time derivative and velocity with the time-differential operator and associated complex velocity. With this, the generalized form of Newton's fundamental relation of dynamics is shown to take the form of a Langevin equation in the case of stationary motion characterized by a null average classical velocity. The numerical integration of the Langevin equation in the case of a harmonic oscillator reveals the same statistics as the stationary solutions of the Schrodinger equation for the same problem. This motivates the second paper which makes the relation to quantum mechanics explicit by discussing the axioms o...
Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.
2017-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Zhu Jiuyun (Department of Physics, Hunan Normal University, Hunan 410006 (China)); Kuang Leman (Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin 300071 (China) Department of Physics and Institute of Physics, Hunan Normal University, Hunan 410081 (China))
1994-10-03
The even and odd coherent states (CSs) of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are constructed and some properties of these states are studied. Their quadrature squeezing and amplitude-squared squeezing are investigated in detail. It is shown that, while the squeezing behaviour of the even and odd CSs of the FDHSHO approaches that of the even and odd CSs of the usual harmonic oscillator as the dimension of the Hilbert space tends to infinity, this behaviour is nontrivally different if the dimension of the Hilbert space is finite. In the latter case, it is found that the even and odd CSs exhibit both amplitude-squared squeezing and quadrature squeezing. ((orig.))
Energy Technology Data Exchange (ETDEWEB)
Guasti, M Fernandez [Depto de Fisica, CBI, Universidad A Metropolitana - Iztapalapa, 09340 Mexico, DF, Apdo Postal 55-534 (Mexico); Moya-Cessa, H [INAOE, Coordinacion de Optica, Apdo Postal 51 y 216, 72000 Puebla, Pue. (Mexico)
2003-02-28
An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schroedinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.
Le Yaouanc, A; Morénas, V; Oliver, L; Pène, O; Raynal, J C
2000-01-01
The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $\\delta m/m_b^2$.
Energy Technology Data Exchange (ETDEWEB)
Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)
2004-02-20
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
A new look at the quantum mechanics of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
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.
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
Energy Technology Data Exchange (ETDEWEB)
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Mendez, D.I. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Marini, S. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-08-03
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
A model of the two-dimensional quantum harmonic oscillator in an AdS{sub 3} background
Energy Technology Data Exchange (ETDEWEB)
Frick, R. [Universitaet zu Koeln, Institut fuer Theoretische Physik, Cologne (Germany)
2016-10-15
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a three-dimensional anti-de Sitter background. We use a generalized Schroedinger picture in which the analogs of the Schroedinger operators of the particle are independent of both the time and the space coordinates in different representations. The spacetime independent operators of the particle induce the Lie algebra of Killing vector fields of the AdS{sub 3} spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations. (orig.)
Bohá\\{v}cik, J; August\\'\\{i}n, P
2013-01-01
We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency.
Muralidhar, K.
2014-03-01
Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass and bivector spin has been derived in the form . Where, is the angular velocity bivector of complex rotations, is the velocity of light. The unit vector acts as an operator on the idempotents and to give the eigen values The constant represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed.
Miller, Julian F
2011-01-01
Cartesian Genetic Programming (CGP) is a highly effective and increasingly popular form of genetic programming. It represents programs in the form of directed graphs, and a particular characteristic is that it has a highly redundant genotype - phenotype mapping, in that genes can be noncoding. It has spawned a number of new forms, each improving on the efficiency, among them modular, or embedded, CGP, and self-modifying CGP. It has been applied to many problems in both computer science and applied sciences. This book contains chapters written by the leading figures in the development and appli
Institute of Scientific and Technical Information of China (English)
ZHAI Zhi-Yuan; YANG Tao; PAN Xiao-Yin
2012-01-01
The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated. Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.%The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated.Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.
Directory of Open Access Journals (Sweden)
Sameer M. Ikhdair
2014-10-01
Full Text Available The two-dimensional solution of the spinless Klein–Gordon (KG equation for scalar–vector harmonic oscillator potentials with and without the presence of constant perpendicular magnetic and Aharonov–Bohm (AB flux fields is studied within the asymptotic function analysis and Nikiforov–Uvarov (NU method. The exact energy eigenvalues and normalized wave functions are analytically obtained in terms of potential parameters, magnetic field strength, AB flux field and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0 and AB flux field (ξ = 0 case. Effects of external fields on the non-relativistic energy eigenvalues and wave functions solutions are also precisely presented.
Directory of Open Access Journals (Sweden)
Katarzyna Kolczyńska
2010-07-01
Full Text Available The HOMA (Harmonic Oscillator Model of Aromaticity index, reformulated in 1993, has been very often applied to describe π-electron delocalization for mono- and polycyclic π-electron systems. However, different measures of π-electron delocalization were employed for the CC, CX, and XY bonds, and this index seems to be inappropriate for compounds containing heteroatoms. In order to describe properly various resonance effects (σ-π hyperconjugation, n-π conjugation, π-π conjugation, and aromaticity possible for heteroatomic π-electron systems, some modifications, based on the original HOMA idea, were proposed and tested for simple DFT structures containing C, N, and O atoms. An abbreviation HOMED was used for the modified index.
Energy Technology Data Exchange (ETDEWEB)
Thantu, Napoleon; McMorrow, D.; Melinger, J. S.; Kleiman, V.; Lotshaw, W. T.
2001-07-01
The apparently-multicomponent subpicosecond intermolecular dynamics of carbon disulfide liquid are addressed in a unified manner in terms of an inhomogeneously broadened quantum mechanical harmonic oscillator model for a single vibrational coordinate. For an inhomogeneously broadened (Gaussian) distribution of oscillators, the model predicts naturally the bimodal character of the subpicosecond intermolecular dynamics of carbon disulfide liquid, and also the spectral evolution effects (spectral narrowing and saturation) that are observed for solutions of carbon disulfide in weakly interacting alkane solvents. The unique dynamical signature of these low-frequency vibrational coordinates is determined largely by the physical constraints on the coordinates (near equality of oscillator frequency, dephasing frequency, and inhomogeneous bandwidth), such that constructive and destructive interference effects play a dominant role in shaping the experimental observable.
Directory of Open Access Journals (Sweden)
M. K. Bahar
2013-01-01
Full Text Available Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.
Haxton, Wick; Lunardini, Cecilia
2008-09-01
Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Mandal, Swapan
2017-03-01
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.
Liu, Yongfang; Zhao, Yu; Chen, Guanrong
2016-11-01
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.
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Directory of Open Access Journals (Sweden)
Marcin Salamaga
2013-09-01
Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.
Institute of Scientific and Technical Information of China (English)
Liu Li; Zhang Liang-Ying; Cao Li
2009-01-01
The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ_3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Orustein-Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3)Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.
Graham Hoover, William; Clinton Sprott, Julien; Griswold Hoover, Carol
2016-10-01
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.
对称性方法在谐振子模型教学中的应用%Applications of Symmetry Method in Teaching of Harmonic Oscillator Model
Institute of Scientific and Technical Information of China (English)
夏丽莉
2016-01-01
利用对称性方法探索非线性谐振子的物理特性。给出一种简洁实用的探究系统守恒律的现代数学方法。有利于学生更深入地了解机械振动模型的规律，丰富了教材内容。%The physical properties of the harmonic oscillator are obtained by the symmetry method. The modern mathematical methods of exploring the conserved quantities are proposed. This will help the students to understand the laws of the harmonic oscillator model, and enrich the teaching materials.
q-Deformed Boson Oscillators and Zero Point Energy
Swamy, P. Narayana
1999-01-01
Just as for the ordinary quantum harmonic oscillators, we expect the zero-point energy to play a crucial role in the correct high temperature behavior. We accordingly reformulate the theory of the statistical distribution function for the q-deformed boson oscillators and develop an approximate theory incorporating the zero-point energy. We are then able to demonstrate that for small deformations, the theory reproduces the correct limits both for very high temperatures and for very low tempera...
Nonlinear harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Calogero, F [Dipartimento di Fisica, Universita di Roma ' La Sapienza' (Italy); Inozemtsev, V I [Joint Institute for Nuclear Research, Dubna (Russian Federation)
2002-12-06
The existence is noted of assemblies of an arbitrary number of complex oscillators, or equivalently, of an arbitrary even number of real oscillators, characterized by Newtonian equations of motion ('acceleration equal force') with one-body velocity-dependent linear forces and many-body velocity-independent cubic forces, all the nonsingular solutions of which are isochronous (completely periodic with the same period). As for the singular solutions, as usual they emerge, in the context of the initial-value problem, from a closed domain in phase space having lower dimensionality.
Sobhani, Hadi; Hassanabadi, Hassan
2016-08-01
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.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Neipp, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Belendez, T [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-02-15
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.
Wang, Chen-Wen; Yang, Ling; Zhu, Chaoyuan; Yu, Jian-Guo; Lin, Sheng-Hsien
2014-08-01
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.
Cartesian product of hypergraphs: properties and algorithms
Directory of Open Access Journals (Sweden)
Alain Bretto
2009-09-01
Full Text Available Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspects of Cartesian products of hypergraphs. We also extend a classical prime factorization algorithm initially designed for graphs to connected conformal hypergraphs using 2-sections of hypergraphs.
Structural Dynamics Model of a Cartesian Robot
1985-10-01
34 D FILE COPY AD-A198 053 *.CC Technical Report 1009 Structural Dynamics Model of a Cartesian Robot "DTIC SELEC T E 0 Alfonso Garcia Reynoso MIT...COVERED Structural Dynamics Model of a Cartesian Robot technical report G. PERFORMING ORG. REPORT NUM9ER 7. AUTHO0R(@) S. CONTRACT On GRANT NUMSER...8217 %S S Structural Dynamics Model of a Cartesian Robot by Alfonso Garcia Reynoso BSME Instituto Tecnol6gico de Veracruz (1967) MSME Instituto Tecnol6gico
q-deformed Lie algebras and fractional calculus
Herrmann, Richard
2007-01-01
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived. It is shown, that the resulting energy spectrum is an appropriate tool e.g. to describe the ground state spectra of even-even nuclei. In addition, the equivalence of rotational and vibrational spectra for fractional q-deformed Lie algebras is shown and the $B_\\alpha(E2)$ values for the fractional q-deformed symmetric rotor are calculated.
Relativistic Hartree-Fock-Bogoliubov model for deformed nuclei
Ebran, J -P; Arteaga, D Pena; Vretenar, D
2010-01-01
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is introduced. The model is based on an effective Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel, and the pairing part of the Gogny force is used in the pairing channel. The RHFBz quasiparticle equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Carbon, Neon and Magnesium isotopes. The effect of the explicitly including the pion field is investigated for binding energies, deformation parameters, and charge radii.
Edge-Transitive Lexicographic and Cartesian Products
Directory of Open Access Journals (Sweden)
Imrich Wilfried
2016-11-01
Full Text Available In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦ H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ∘ H is non-trivial and complete, then G ∘ H is edge-transitive if and only if H is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao [11]. For the Cartesian product it is shown that every connected Cartesian product of at least two non-trivial factors is edge-transitive if and only if it is the Cartesian power of a connected, edge- and vertex-transitive graph.
Influences in cartesian moral philosophy: general concepts
Solano Villareal, Diana
2015-01-01
In this first article, we explore the influences on the Cartesian moral philosophy which mainly refer to antiquity. Aristotle, Epicurus and the Stoics are the most in-depth sources. Moreover, the general concepts we consider most important to further develop the central thesis of this work (the role of moral philosophy Cartesian forms of domination towards the human being in modernity), are reviewed in this section. The concepts of virtue, habit, will, generosity, bliss, reason, wisdom, philo...
Energy Technology Data Exchange (ETDEWEB)
Ebran, J-P [CEA/DAM/DIF, F-91297 Arpajon (France); Khan, E; Arteaga, D Pena [Institut de Physique Nucleaire, University Paris-Sud, IN2P3-CNRS, F-91406 Orsay Cedex (France); Vretenar, D, E-mail: jean-paul.ebran@cea.fr [Physics Department, Faculty of Science, University of Zagreb, 10000 Zagreb (Croatia)
2011-09-16
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is presented. The model involves a phenomenological Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel and the central part of the Gogny force in the particle-particle channel. The RHFBz equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Neon isotopes.
Caligiuri, Luigi Maxmilian
2015-01-01
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.
Cartesian Grid Method for Gas Kinetic Scheme
Chen, Songze; Li, Zhihui
2015-01-01
A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four different categories, the fluid point, the solid point, the drop point, and the interpolation point. The boundaries are represented by a set of direction-oriented boundary points. A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points. Different boundary conditions, including isothermal boundary, adiabatic boundary, and Euler slip boundary, are presented by different interpolation strategies. We also propose a simplified gas kinetic scheme as the flux solver for both subsonic and supersonic flow computations. The methodology of constructing a simplified kinetic flux function can be extended to other flow systems. A few numerical examples are used to validate the Cartesian grid method and the simplified flux func...
Energy Technology Data Exchange (ETDEWEB)
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)
2015-11-15
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
Distinguishing Cartesian Products of Countable Graphs
Directory of Open Access Journals (Sweden)
Estaji Ehsan
2017-02-01
Full Text Available The distinguishing number D(G of a graph G is the minimum number of colors needed to color the vertices of G such that the coloring is preserved only by the trivial automorphism. In this paper we improve results about the distinguishing number of Cartesian products of finite and infinite graphs by removing restrictions to prime or relatively prime factors.
Static Aeroelastic Analysis with an Inviscid Cartesian Method
Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.
2014-01-01
An embedded-boundary Cartesian-mesh flow solver is coupled with a three degree-offreedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves the complete system of aero-structural equations using a modular, loosely-coupled strategy which allows the lower-fidelity structural model to deform the highfidelity CFD model. The approach uses an open-source, 3-D discrete-geometry engine to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. This extended abstract includes a brief description of the architecture, along with some preliminary validation of underlying assumptions and early results on a generic 3D transport model. The final paper will present more concrete cases and validation of the approach. Preliminary results demonstrate convergence of the complete aero-structural system and investigate the accuracy of the approximations used in the formulation of the structural model.
Masood, Syed; Faizal, Mir; Zaz, Zaid; Ali, Ahmed Farag; Raza, Jamil; Shah, Mushtaq B.
2016-12-01
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.
Directory of Open Access Journals (Sweden)
Syed Masood
2016-12-01
Full Text Available 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.
Masood, Syed; Zaz, Zaid; Ali, Ahmed Farag; Raza, Jamil; Shah, Mushtaq B
2016-01-01
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 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.
Conversion of contours to cartesian grids
Energy Technology Data Exchange (ETDEWEB)
Mann, J.; Broe, B. Riget
2006-07-15
A robust and efficient method of calculating a cartesian grid of heights or roughnesses from contour line maps is developed. The purpose of the grids is to serve as input for atmospheric flow solvers such as WAsP Engineering or EllipSys3D. The method builds on Delaunay triangulation constrained to include all contour segments in the triangulation. It is furthermore refined to avoid spurious flat areas produced by the Delaunay triangulation. Robust ways to extrapolate beyond the convex hull of the map points are provided. (au)
Conversion of contours to cartesian grids
DEFF Research Database (Denmark)
Mann, Jakob; Broe, Brian Riget
A robust and efficient method of calculating a cartesian grid of heights or roughnesses from contour line maps is developed. The purpose of the grids is to serve as input for atmospheric flow solvers such as WAsP Engineering or EllipSys3D. The method builds on Delaunay triangulation constrained t...... to include all contour segments in the triangulation. It is furthermore refined to avoid spurious flat areas produced by the Delaunay triangulation. Robust ways to extrapolate beyond the convex hull of the map points are provided....
Cartesian impedance control of dexterous robot hand
Institute of Scientific and Technical Information of China (English)
JIANG Li; LIU Hong; CAI He-gao
2005-01-01
Presents a novel compliant motion control for a robot hand using the Cartesian impedance approach based on fingertip force measurements. The fingertip can accurately track desired motion in free space and appear as mechanical impedance in constrained space. In the position based impedance control strategy, any switching mode in contact transition phase is not needed. The impedance parameters can be adjusted in a certain range according to various tasks. In this paper, the analysis of the finger's kinematics and dynamics is given. Experimental results have shown the effectiveness of this control strategy.
What Is Un-Cartesian Linguistics?
Directory of Open Access Journals (Sweden)
Wolfram Hinzen
2014-10-01
Full Text Available Un-Cartesian linguistics is a research program with the aim of rethinking the nature of grammar as a domain of scientific inquiry, raising new questions about the constitutive role of grammar in the organization of our (rational minds and selves. It reformulates the ‘Cartesian’ foundations of the modern Universal Grammar project, shifting emphasis away from the study of a domain-specific ‘innate’ module separate from thought, to the study of a sapiens-specific mode of cognition conditioned by both grammatical and lexical organization, and thus a particular cognitive phenotype, which is uniquely also a linguistic one. The purpose of this position paper is to introduce and motivate this new concept in its various dimensions and in accessible terms, and to define the ‘Un-Cartesian Hypothesis’: that the grammaticalization of the hominin brain in the evolutionary transition to our species uniquely explains why our cognitive mode involves a capacity for thought in a propositional format.
Electrostatic PIC with adaptive Cartesian mesh
Kolobov, Vladimir I
2016-01-01
We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a corresponding increase of the numerical noise. The developed ES-PIC solver is validated for capacitively coupled plasma, its AMR capabilities are demonstrated for simulations of streamer development during high-pressure gas breakdown. It is shown that cell-based AMR provides a convenient particle management algorithm for exponential multiplications of electrons and ions in the ionization events.
Deformation of supersymmetric and conformal quantum mechanics through affine transformations
Spiridonov, Vyacheslav
1993-01-01
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.
The adaptive, cut-cell Cartesian approach (warts and all)
Powell, Kenneth G.
1995-01-01
Solution-adaptive methods based on cutting bodies out of Cartesian grids are gaining popularity now that the ways of circumventing the accuracy problems associated with small cut cells have been developed. Researchers are applying Cartesian-based schemes to a broad class of problems now, and, although there is still development work to be done, it is becoming clearer which problems are best suited to the approach (and which are not). The purpose of this paper is to give a candid assessment, based on applying Cartesian schemes to a variety of problems, of the strengths and weaknesses of the approach as it is currently implemented.
Cartesian Trajectory Tracking for Manipulators Using Optimal Control Theory
Directory of Open Access Journals (Sweden)
Olav Egeland
1987-07-01
Full Text Available A Cartesian trajectory tracking system for manipulators is developed using optimal control theory. By including the Cartesian position in the state vector, transformation of the trajectory from Cartesian space to manipulator joint space is avoided, and the Jacobian matrix need not be inverted. The tracking system may also be applied to kinematically redundant manipulators. For this type of manipulator, singularities are avoided by choosing a suitable performance index in the optimal control problem. Simulation using a simple kinematically redundant manipulator shows that a small tracking error can be achieved with low motor torques.
An adaptive phase alignment algorithm for cartesian feedback loops
Gimeno-Martin, A.; Pardo-Martin, J.; Ortega-Gonzalez, F.
2010-01-01
An adaptive algorithm to correct phase misalignments in Cartesian feedback linearization loops for power amplifiers has been presented. It yields an error smaller than 0.035 rad between forward and feedback loop signals once convergence is reached. Because this algorithm enables a feedback system to process forward and feedback samples belonging to almost the same algorithm iteration, it is suitable to improve the performance not only of power amplifiers but also any other digital feedback system for communications systems and circuits such as all digital phase locked loops. Synchronizing forward and feedback paths of Cartesian feedback loops takes a small period of time after the system starts up. The phase alignment algorithm needs to converge before the feedback Cartesian loop can start its ideal behavior. However, once the steady state is reached, both paths can be considered synchronized, and the Cartesian feedback loop will only depend on the loop parameters (open-loop gain, loop bandwidth, etc.). It means that the linearization process will also depend only on these parameters since the misalignment effect disappears. Therefore, this algorithm relieves the power amplifier linearizer circuit design of any task required for solving phase misalignment effects inherent to Cartesian feedback systems. Furthermore, when a feedback Cartesian loop has to be designed, the designer can consider that forward and feedback paths are synchronized, since the phase alignment algorithm will do this task. This will reduce the simulation complexity. Then, all efforts are applied to determining the suitable loop parameters that will make the linearization process more efficient.
Common aspects of q-deformed Lie algebras and fractional calculus
Herrmann, Richard
2010-01-01
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. A new class of fractional q-deformed Lie algebras is proposed, which for the first time allows a smooth transition between different Lie algebras. For the fractional harmonic oscillator, the corresponding fractional q-number is derived. It is shown, that the resulting energy spectrum is an appropriate tool to describe e.g. the ground state spectra of even-even nuclei. In addition, the equivalence of rotational and vibrational spectra for fractional q-deformed Lie algebras is shown and the $B_\\alpha(E2)$ values for the fractional q-deformed symmetric rotor are calculated. A first interpretation of half integer representations of the fractional rotation group is given in terms of a description of $K=1/2^-$ band spectra of odd-even nuclei.
A Cartesian grid-based unified gas kinetic scheme
Chen, Songze; Xu, Kun
2014-12-01
A Cartesian grid-based unified gas kinetic scheme is developed. In this approach, any oriented boundary in a Cartesian grid is represented by many directional boundary points. The numerical flux is evaluated on each boundary point. Then, a boundary flux interpolation method (BFIM) is constructed to distribute the boundary effect to the flow evolution on regular Cartesian grid points. The BFIM provides a general strategy to implement any kind of boundary condition on Cartesian grid. The newly developed technique is implemented in the unified gas kinetic scheme, where the scheme is reformulated into a finite difference format. Several typical test cases are simulated with different geometries. For example, the thermophoresis phenomenon for a plate with infinitesimal thickness immersed in a rarefied flow environment is calculated under different orientations on the same Cartesian grid. These computational results validate the BFIM in the unified scheme for the capturing of different thermal boundary conditions. The BFIM can be extended to the moving boundary problems as well.
Time-dependent q-deformed bi-coherent states for generalized uncertainty relations
Gouba, Laure
2015-07-01
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
DEFF Research Database (Denmark)
V. Marchukov, O.; G. Volosniev, A.; V. Fedorov, D.;
2013-01-01
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 implies that the few- and many-body physics of spin-orbit coupled systems can be manipulated by variation of these parameters....
Spectral gaps of spin-orbit coupled particles in deformed traps
Marchukov, O. V.; Volosniev, A. G.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.
2013-07-01
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.
Cartesian grid method for gas kinetic scheme on irregular geometries
Chen, Songze; Xu, Kun; Li, Zhihui
2016-12-01
A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the boundaries are represented by a set of direction-oriented boundary points, and the computational grid points are classified into four different categories, the fluid point, the solid point, the drop point, and the interpolation point. A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points. Different boundary conditions, including isothermal boundary, adiabatic boundary, and Euler slip boundary, are presented by different interpolation strategies. We adopt a simplified gas kinetic scheme as the flux solver for both subsonic and supersonic flow computations. The methodology of constructing a simplified kinetic flux function can be extended to other flow systems. A few numerical examples are used to validate the Cartesian grid method and the simplified flux solver. The reconstruction scheme for recovering the boundary conditions of compressible viscous and heat conducting flow with a Cartesian mesh can provide a smooth distribution of physical quantities at solid boundary, and present an accurate solution for the flow study with complex geometry.
GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES
Institute of Scientific and Technical Information of China (English)
Li Qingguo; Wu Xiuhua
2009-01-01
In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuons. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly sernicontinuons lattice category is a Cartesian closed category.
A Lot of Good Physics in the Cartesian Diver
De Luca, Roberto; Ganci, Salvatore
2011-01-01
The Cartesian diver experiment certainly occupies a place of honour in old physics textbooks as a vivid demonstration of Archimedes' buoyancy. The original experiment, as described in old textbooks, shows Archimedes buoyancy qualitatively: when the increased weight of the diver is not counterbalanced by Archimedes' buoyancy, the diver sinks. When…
Institute of Scientific and Technical Information of China (English)
江洵
2005-01-01
构造了有限维希尔伯特空间变形非简谐振子偶广义相干态,讨论了该量子态的压缩效应和反聚束效应,结果表明该量子态存在压缩效应和反聚束效应.并给出量子效应出现的条件.
Institute of Scientific and Technical Information of China (English)
王德华; 李红艳; 马晓光; 王美山; 杨传路
2007-01-01
Using the periodic orbit theory, we computed the quantum level density of a particle in the two-dimensional harmonic oscillator potential with and without the magnetic flux line for different cases. Especially discuss the influence of the magnetic flux line on the quantum level density. The results show when the frequency ratio of the two-dimensional harmonic potential is a rational number, the quantum level density is discrete. Each peak in the level density corresponds to one energy. However, when the frequency ratio is an irrational number, the level density is oscillating, when the magnetic flux is added, the amplitude of the oscillation decreased. This can be considered as a consequence of Aharonov-Bohm effect.%利用周期轨道理论,我们计算了在不同情况下,一个粒子在二维谐振子势中存在和不存在磁通量时的量子能级密度.重点讨论了磁通量对量子能级密度的影响.计算结果表明:当二维谐振子势的频率比值是有理数时,量子能级是分立的,能级密度中的每一条峰正好对应一个量子能级.然而,当频率比是无理数时,能级密度发生振荡,当加上磁通量后,振荡减小.这可以看作是Aharonov-Bohm效应的结果.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
The Approach to Steady State Using Homogeneous and Cartesian Coordinates
Directory of Open Access Journals (Sweden)
D. F. Gochberg
2013-01-01
Full Text Available Repeating an arbitrary sequence of RF pulses and magnetic field gradients will eventually lead to a steady-state condition in any magnetic resonance system. While numerical methods can quantify this trajectory, analytic analysis provides significantly more insight and a means for faster calculation. Recently, an analytic analysis using homogeneous coordinates was published. The current work further develops this line of thought and compares the relative merits of using a homogeneous or a Cartesian coordinate system.
Irreducible Cartesian tensors of highest weight, for arbitrary order
Mane, S. R.
2016-03-01
A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.
Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.
Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H
2013-05-01
In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction.
Institute of Scientific and Technical Information of China (English)
杨双波; 韦栋
2012-01-01
This paper studies the classical dynamics and quasienergy spectral statistics for a periodically kicked Harmonic oscillator system,under the nonresonance condition.It is found that as we increase the kicking strength Κ ,and the phase space structure starts from tori for integrable system to completely chaotic for nonintegrable system,the nearest neighbor spacing distribution for the quasienergy spectral keeps the Poissonian distribution,and this is similar to that of the peri odically kicked free rotor.The result of spectral rigidities shows that except the case of Κ=30,the rigidities for Κ= 0.13,1.6,2.0,2.6,bunched,increase linearly with L for L 0.1.The number variance∑2 ,skewness γ1,,excess γ2 are not sensitive to the change of Κ.%研究一个周期受击简谐振子系统在非谐振情况下的经典动力学与准能谱统计.研究发现,随着打击强度κ的增加,经典相空间结构从可积(环)到完全混沌时,准能谱按最近邻能级间距分布仍保持Poisson分布不变,这与周期受击转子系统的结果相同.谱刚度的计算表明,除了κ=30的情况外,κ=0.13、1.6、2.0、2.6等的谱刚度在L＜0.1的范围内随L线性变化,呈束状；在L＞0.1以后发散开来,呈非线性变化,且κ=0.13的谱刚度趋于饱和.数方差∑2及高阶矩γ1,γ2随κ的变化不敏感.
Chabab, M; Lahbas, A; Oulne, M
2016-01-01
In this paper, we present a theoretical study of a conjonction of $\\gamma$-rigid and $\\gamma$-stable collective motions in critical point symmetries of the phase transitions from spherical to deformed shapes of nuclei using exactly separable version of the Bohr Hamiltonian with deformation-dependent mass term. The deformation-dependent mass is applied simultaneously to $\\gamma$-rigid and $\\gamma$-stable parts of this famous collective Hamiltonian. Moreover, the $\\beta$ part of the problem is described by means of Davidson potential, while the $\\gamma$-angular part corresponding to axially symmetric shapes is treated by a Harmonic Osillator 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 tran...
ADAPTIVE LAYERED CARTESIAN CUT CELL METHOD FOR THE UNSTRUCTURED HEXAHEDRAL GRIDS GENERATION
Institute of Scientific and Technical Information of China (English)
WU Peining; TAN Jianrong; LIU Zhenyu
2007-01-01
Adaptive layered Cartesian cut cell method is presented to solve the difficulty of the unstructured hexahedral anisotropic Cartesian grids generation from the complex CAD model. Vertex merging algorithm based on relaxed AVL tree is investigated to construct topological structure for stereo lithography (STL) files, and a topology-based self-adaptive layered slicing algorithm with special features control strategy is brought forward. With the help of convex hull, a new points-in-polygon method is employed to improve the Cartesian cut cell method. By integrating the self-adaptive layered slicing algorithm and the improved Cartesian cut cell method, the adaptive layered Cartesian cut cell method gains the volume data of the complex CAD model in STL file and generates the unstructured hexahedral anisotropic Cartesian grids.
A Cartesian embedded boundary method for hyperbolic conservation laws
Energy Technology Data Exchange (ETDEWEB)
Sjogreen, B; Petersson, N A
2006-12-04
The authors develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. They show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, they discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.
Efficient Cartesian-grid-based modeling of rotationally symmetric bodies
DEFF Research Database (Denmark)
Shyroki, Dzmitry
2007-01-01
Axially symmetric waveguides, resonators, and scatterers of arbitrary cross section and anisotropy in the cross section can be modeled rigorously with use of 2-D Cartesian-grid based codes by means of mere redefinition of material permittivity and permeability profiles. The method is illustrated...... by the frequencydomain simulations of resonant modes in a circular-cylinder cavity with perfectly conducting walls, a shielded uniaxial anisotropic dielectric cylinder, and an open dielectric sphere for which, after proper implementation of the perfectly matched layer boundary conditions, the radiation quality factor...
Remarks on the stability of Cartesian PMLs in corners
Bécache, Eliane
2011-01-01
This work is a contribution to the understanding of the question of stability of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete levels. First, stability results are presented for the Cartesian PMLs associated to a general first-order hyperbolic system. Then, in the context of the pressure-velocity formulation of the acoustic wave propagation, an unsplit PML formulation is discretized with spectral mixed finite elements in space and finite differences in time. It is shown, through the stability analysis of two different schemes, how a bad choice of the time discretization can deteriorate the CFL stability condition. Some numerical results are finally presented to illustrate these stability results.
[Cartesian misunderstanding as a cause of therapeutic failure].
Isler, H
1986-01-01
Headache patients disassociate themselves from their own automatic responses, relying on the traditional separation of body and mind. On the other hand, patients who obtain voluntary control of automatic functions by biofeedback training modify not only vegetative but also voluntary behaviour patterns, losing "neurotic" traits. The basic misconception of the separation of body and mind, Cartesian dualism, is now ingrained in our culture. In the 17th century Descartes asserted that concepts applied to the soul must be entirely different from those used for the body in order to improve comprehension of the immortality of the soul. This dualism also led to "enlightenment" and to many later social and philosophical developments. But his basic neurophysiology was obsolete when he wrote it down. Other models from mainstream natural philosophy were better compatible with observation and experiments. Gassendi assumed a "body soul" consisting of energy as the functional principle of the nervous system, and Willis accommodated a series of anticipations of 19th century discoveries within this model. No comparable progress resulted from Descartes' own medieval model. Cartesian dualism has become untenable in view of recent neuropsychology but it still obstructs our management of functional patients. Instead of reinforcing the delusion of separation of psyche and soma, we ought to encourage patients to understand that their malfunctioning organs are on-line with their emotions, and with their mind.
Chaotic motion in axially symmetric potentials with oblate quadrupole deformation
Energy Technology Data Exchange (ETDEWEB)
Letelier, Patricio S. [Departamento de Matematica Aplicada, IMECC, Universidade Estadual de Campinas, 13083-859, Campinas, SP (Brazil); Ramos-Caro, Javier, E-mail: javier@ime.unicamp.br [Departamento de Matematica Aplicada, IMECC, Universidade Estadual de Campinas, 13083-859, Campinas, SP (Brazil); Lopez-Suspes, Framsol, E-mail: framsol@gmail.com [Facultad de Telecomunicaciones, Universidad Santo Tomas and Escuela de Fisica, Universidad Industrial de Santander, Bucaramanga (Colombia)
2011-10-03
By computing the Poincare's surfaces of section and Lyapunov exponents, we study the effect of introducing an oblate quadrupole in the dynamics associated with two generic spherical potentials of physical interest: the central monopole and the isotropic harmonic oscillator. In the former case we find saddle points in the effective potential, in contrast to the statements presented by Gueron and Letelier in [E. Gueron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. The results we show in the second case have application in nuclear or atomic physics. In particular, we find values of oblate deformation leading to a disappearance of shell structure in the single-particle spectrum. -- Highlights: → We find chaotic motion around a monopole with oblate quadrupole deformation. → This corrects the statements introduced in [E. Gueron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. → We present an alternative model for the potential due to an oblate deformed nuclei. → This leads to stochastic regions in the phase space of classical orbits. → It suggests that the shell structure of single-particle spectrum tends to disappear.
Optimal online robot trajectory generation in Cartesian space
Bazaz, Shafat A.; Tondu, Bertrand
1997-12-01
We propose the use of cubic quadratic cubic squared (CQCS) spline for the trajectory generation in Cartesian space. Use of CQCS spline gives simple analytical solution to minimum time trajectory generation with velocity and acceleration constraints. The expressions for wandering time and wandering acceleration are also calculated. A straight line path with constant maximum allowed speed in minimum time can be generated with this method. This property leads to interpolate two position points by constant speed straight line motion with smooth transition. The advantage of this method is that the trajectory thus obtained is traversed in minimum time while passing through the given intermediate points. The simplicity of this method makes its on-line computation possible.
Neural Network Schemes in Cartesian Space Control of Robot Manipulators
Directory of Open Access Journals (Sweden)
Yiannis S. BOUTALIS
2001-12-01
Full Text Available In this paper we are studying the Cartesian space robot manipulator control problem by using Neural Networks (NN. Although NN compensation for model uncertainties has been traditionally carried out by modifying the joint torque/force of the robot, it is also possible to achieve the same objective by using the NN to modify other quantities of the controller. We present and evaluate four different NN controller designs to achieve disturbance rejection for an uncertain system. The design perspectives are dependent on the compensated position by NN. There are four quantities that can be compensated: torque , force F, control input U and the input trajectory Xd. By defining a unified training signal all NN control schemes have the same goal of minimizing the same objective functions. We compare the four schemes in respect to their control performance and the efficiency of the NN designs, which is demonstrated via simulations.
Computing global offensive alliances in Cartesian product graphs
Yero, Ismael G
2012-01-01
A global offensive alliance in a graph $G$ is a set $S$ of vertices with the property that every vertex not belonging to $S$ has at least one more neighbor in $S$ than it has outside of $S$. The global offensive alliance number of $G$, $\\gamma_o(G)$, is the minimum cardinality of a global offensive alliance in $G$. A set $S$ of vertices of a graph $G$ is a dominating set for $G$ if every vertex not belonging to $S$ has at least one neighbor in $S$. The domination number of $G$, $\\gamma(G)$, is the minimum cardinality of a dominating set of $G$. In this work we obtain closed formulas for the global offensive alliance number of several families of Cartesian product graphs, we also prove that $\\gamma_o(G\\square H)\\ge \\frac{\\gamma(G)\\gamma_o(H)}{2}$ for any graphs $G$ and $H$ and we show that if $G$ has an efficient dominating set, then $\\gamma_o(G\\square H)\\ge \\gamma(G)\\gamma_o(H).$ Moreover, we present a Vizing-like conjecture for the global offensive alliance number and we prove it for several families of grap...
Roman domination in Cartesian product graphs and strong product graphs
Yero, Ismael G
2011-01-01
A set $S$ of vertices of a graph $G$ is a dominating set for $G$ if every vertex outside of $S$ is adjacent to at least one vertex belonging to $S$. The minimum cardinality of a dominating set for $G$ is called the domination number of $G$. A map $f : V \\rightarrow \\{0, 1, 2\\}$ is a Roman dominating function on a graph $G$ if for every vertex $v$ with $f(v) = 0$, there exists a vertex $u$, adjacent to $v$, such that $f(u) = 2$. The weight of a Roman dominating function is given by $f(V) =\\sum_{u\\in V}f(u)$. The minimum weight of a Roman dominating function on $G$ is called the Roman domination number of $G$. In this article we study the Roman domination number of Cartesian product graphs and strong product graphs. More precisely, we study the relationships between the Roman domination number of product graphs and the (Roman) domination number of the factors.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-06-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.
Tolerating Correlated Failures for Generalized Cartesian Distributions via Bipartite Matching
Energy Technology Data Exchange (ETDEWEB)
Ali, Nawab; Krishnamoorthy, Sriram; Halappanavar, Mahantesh; Daily, Jeffrey A.
2011-05-05
Faults are expected to play an increasingly important role in how algorithms and applications are designed to run on future extreme-scale systems. A key ingredient of any approach to fault tolerance is effective support for fault tolerant data storage. A typical application execution consists of phases in which certain data structures are modified while others are read-only. Often, read-only data structures constitute a large fraction of total memory consumed. Fault tolerance for read-only data can be ensured through the use of checksums or parities, without resorting to expensive in-memory duplication or checkpointing to secondary storage. In this paper, we present a graph-matching approach to compute and store parity data for read-only matrices that are compatible with fault tolerant linear algebra (FTLA). Typical approaches only support blocked data distributions with each process holding one block with the parity located on additional processes. The matrices are assumed to be blocked by a cartesian grid with each block assigned to a process. We consider a generalized distribution in which each process can be assigned arbitrary blocks. We also account for the fact that multiple processes might be part of the same failure unit, say an SMP node. The flexibility enabled by our novel application of graph matching extends fault tolerance support to data distributions beyond those supported by prior work. We evaluate the matching implementations and cost to compute the parity and recover lost data, demonstrating the low overhead incurred by our approach.
A System for Acoustic Field Measurement Employing Cartesian Robot
Directory of Open Access Journals (Sweden)
Szczodrak Maciej
2016-09-01
Full Text Available A system setup for measurements of acoustic field, together with the results of 3D visualisations of acoustic energy flow are presented in the paper. Spatial sampling of the field is performed by a Cartesian robot. Automatization of the measurement process is achieved with the use of a specialized control system. The method is based on measuring the sound pressure (scalar and particle velocity(vector quantities. The aim of the system is to collect data with a high precision and repeatability. The system is employed for measurements of acoustic energy flow in the proximity of an artificial head in an anechoic chamber. In the measurement setup an algorithm for generation of the probe movement path is included. The algorithm finds the optimum path of the robot movement, taking into account a given 3D object shape present in the measurement space. The results are presented for two cases, first without any obstacle and the other - with an artificial head in the sound field.
Precision characteristics of two-position radar station in Cartesian coordinate system
Directory of Open Access Journals (Sweden)
D. I. Docenko
2008-05-01
Full Text Available Two-position radar station is examined. Analytic expressions for dispersion and intercorrelation of measurement errors in Cartesian coordinate system are obtained. For exampl eerror estimation and analysis were performed.
On the research of flow around obstacle using the viscous Cartesian grid technique
Directory of Open Access Journals (Sweden)
Liu Yan-Hua
2012-01-01
Full Text Available A new 2-D viscous Cartesian grid is proposed in current research. It is a combination of the existent body-fitted grid and Cartesian grid technology. On the interface of the two different type of grid, a fined triangular mesh is used to connect the two grids. Tests with flow around the cylinder and aerofoil NACA0012 show that the proposed scheme is easy for implement with high accuracy.
Early Cartesianism and the Journal des Sçavans, 1665–1671
Directory of Open Access Journals (Sweden)
Mihnea Dobre
2012-03-01
Full Text Available The appearance of scientific journals in the second half of the seventeenth century not only presented new opportunities for the dissemination of knowledge, but also offers the historian a privileged view of the shared knowledge within the scientific community. The Journal des Sçavans, founded in 1665, proclaimed its ambition to disseminate news about books and people concerning the République des lettres. Given the reportedly high interest in and opposition to the rise of Cartesianism among contemporary philosophers, this paper explores the discussion of Cartesianism within the pages of the Journal. It is shown that debates on Cartesianism formed only a small portion of the articles in the Journal. Although the majority of commentaries referred to the metaphysical foundations of Cartesian philosophy, a considerable number of instances were found referring to empirical tests of the theory. Finally, as the Journal does not mention the condemnations or censorship of Cartesianism, we cannot speak of a general feeling of hostility against Cartesian philosophers among the editors or intended audience of the Journal.
Civicioglu, Pinar
2012-09-01
In order to solve numerous practical navigational, geodetic and astro-geodetic problems, it is necessary to transform geocentric cartesian coordinates into geodetic coordinates or vice versa. It is very easy to solve the problem of transforming geodetic coordinates into geocentric cartesian coordinates. On the other hand, it is rather difficult to solve the problem of transforming geocentric cartesian coordinates into geodetic coordinates as it is very hard to define a mathematical relationship between the geodetic latitude (φ) and the geocentric cartesian coordinates (X, Y, Z). In this paper, a new algorithm, the Differential Search Algorithm (DS), is presented to solve the problem of transforming the geocentric cartesian coordinates into geodetic coordinates and its performance is compared with the performances of the classical methods (i.e., Borkowski, 1989; Bowring, 1976; Fukushima, 2006; Heikkinen, 1982; Jones, 2002; Zhang, 2005; Borkowski, 1987; Shu, 2010 and Lin, 1995) and Computational-Intelligence algorithms (i.e., ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES). The statistical tests realized for the comparison of performances indicate that the problem-solving success of DS algorithm in transforming the geocentric cartesian coordinates into geodetic coordinates is higher than those of all classical methods and Computational-Intelligence algorithms used in this paper.
Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”
Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, S. Amiri
2016-12-01
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.
A deformable generic 3D model of haptoral anchor of Monogenean.
Directory of Open Access Journals (Sweden)
Bee Guan Teo
Full Text Available In this paper, a digital 3D model which allows for visualisation in three dimensions and interactive manipulation is explored as a tool to help us understand the structural morphology and elucidate the functions of morphological structures of fragile microorganisms which defy live studies. We developed a deformable generic 3D model of haptoral anchor of dactylogyridean monogeneans that can subsequently be deformed into different desired anchor shapes by using direct manipulation deformation technique. We used point primitives to construct the rectangular building blocks to develop our deformable 3D model. Point primitives are manually marked on a 2D illustration of an anchor on a Cartesian graph paper and a set of Cartesian coordinates for each point primitive is manually extracted from the graph paper. A Python script is then written in Blender to construct 3D rectangular building blocks based on the Cartesian coordinates. The rectangular building blocks are stacked on top or by the side of each other following their respective Cartesian coordinates of point primitive. More point primitives are added at the sites in the 3D model where more structural variations are likely to occur, in order to generate complex anchor structures. We used Catmull-Clark subdivision surface modifier to smoothen the surface and edge of the generic 3D model to obtain a smoother and more natural 3D shape and antialiasing option to reduce the jagged edges of the 3D model. This deformable generic 3D model can be deformed into different desired 3D anchor shapes through direct manipulation deformation technique by aligning the vertices (pilot points of the newly developed deformable generic 3D model onto the 2D illustrations of the desired shapes and moving the vertices until the desire 3D shapes are formed. In this generic 3D model all the vertices present are deployed for displacement during deformation.
Multiscale geometric modeling of macromolecules I: Cartesian representation.
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo Wei
2014-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Advances in non-Cartesian parallel magnetic resonance imaging using the GRAPPA operator
Energy Technology Data Exchange (ETDEWEB)
Seiberlich, Nicole
2008-07-21
This thesis has presented several new non-Cartesian parallel imaging methods which simplify both gridding and the reconstruction of images from undersampled data. A novel approach which uses the concepts of parallel imaging to grid data sampled along a non-Cartesian trajectory called GRAPPA Operator Gridding (GROG) is described. GROG shifts any acquired k-space data point to its nearest Cartesian location, thereby converting non-Cartesian to Cartesian data. The only requirements for GROG are a multi-channel acquisition and a calibration dataset for the determination of the GROG weights. Then an extension of GRAPPA Operator Gridding, namely Self-Calibrating GRAPPA Operator Gridding (SC-GROG) is discussed. SC-GROG is a method by which non-Cartesian data can be gridded using spatial information from a multi-channel coil array without the need for an additional calibration dataset, as required in standard GROG. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. Thereafter a simple, novel method for performing modified Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG to arrive at a non-aliased image is introduced. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. Finally a novel method of using GROG to mimic the bunched phase encoding acquisition (BPE) scheme is discussed. In MRI, it is generally assumed that an artifact-free image can be reconstructed only from sampled points which fulfill the Nyquist criterion. However, the BPE reconstruction is based on the Generalized Sampling Theorem of Papoulis, which states that a continuous signal can be reconstructed from sampled points as long as the points are on average sampled at the Nyquist frequency. A novel
Institute of Scientific and Technical Information of China (English)
朱思峰; 刘芳; 柴争义; 戚玉涛; 吴建设
2012-01-01
In heterogeneous wireless network environment, wireless local area network （WLAN） are usually deployed within the coverage of a cellular network to provide users with the convenience of seamless roaming among heterogeneous wireless access networks. Vertical handoffs between the WLAN and the cellular network could occur frequently, with regard to vertical handoff performance, there is a critical need for developing algorithms for connection management and optimal resource allocation for seamless mobility. In this paper, we develop a mathematical model for vertical handoff decision problem, propose an artificial simple harmonic oscillator immune algorithm-based vertical handoff decision scheme, and perform the simulation experiments to validate proposed solution. Experimental result shows that the proposed solution, compared with literature solutions, can not only balance the overall load among all networks but also increase the collective battery lifetime of mobile terminals, and has the advantage of good application value.%本文设计了垂直切换判决方案问题的数学模型,给出了一种基于简谐振子免疫优化算法的垂直切换判决方案.并与文献方案进行了对比实验实验结果表明,本文方案能够有效地平衡网络负载、增加终端电池的生存时间,具有较好的应用价值.
Directory of Open Access Journals (Sweden)
O. A. Domínguez-Ramírez
2006-01-01
Full Text Available Perception and interaction with virtual surfaces, through kinaesthetic sensation and visual stimuli, is the basic issue of a haptic interface. When the virtual or real object is in a remote location, and guidance is required to perceive kinaesthetic feedback, a haptic guidance scheme is required. In this document, with purpose of haptic-guided exploration, a new scheme for simultaneous control of force and cartesian position is proposed without using inverse kinematics, and without using the dynamic model of PHANToM, though a strict stability analysis includes the dynamic model of PHANToM. We rely on our previously proposed results to propose a new haptic cartesian controller to reduce the burden of computing cartesian forces in PHANToM. Furthermore, a time base generator for finite-time tracking is also proposed to achieve very fast tracking and high precision, which translated into high fidelity kinaesthetic feedback.
A Hybrid Advection Scheme for Conserving Angular Momentum on a Refined Cartesian Mesh
Byerly, Zachary D; Tohline, Joel E; Marcello, Dominic C
2014-01-01
We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as a straightforward implementation of mesh refinement. Our test focuses on measuring the real and imaginary parts of the eigenfrequency of unstable axisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios, and quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima (1986) and from nonlinear hydrodynamic simulations performed on a cylindrical coordinate mesh by Woodward et al. (1994). When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the...
Lyapunov-based Low-thrust Optimal Orbit Transfer: An approach in Cartesian coordinates
Zhang, Hantian; Cao, Qingjie
2014-01-01
This paper presents a simple approach to low-thrust optimal-fuel and optimal-time transfer problems between two elliptic orbits using the Cartesian coordinates system. In this case, an orbit is described by its specific angular momentum and Laplace vectors with a free injection point. Trajectory optimization with the pseudospectral method and nonlinear programming are supported by the initial guess generated from the Chang-Chichka-Marsden Lyapunov-based transfer controller. This approach successfully solves several low-thrust optimal problems. Numerical results show that the Lyapunov-based initial guess overcomes the difficulty in optimization caused by the strong oscillation of variables in the Cartesian coordinates system. Furthermore, a comparison of the results shows that obtaining the optimal transfer solution through the polynomial approximation by utilizing Cartesian coordinates is easier than using orbital elements, which normally produce strongly nonlinear equations of motion. In this paper, the Eart...
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.
Yan, Su; Arslanbekov, Robert R; Kolobov, Vladimir I; Jin, Jian-Ming
2016-01-01
A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian meshes (ACM) is developed for a full-wave analysis of electromagnetic fields in dispersive media. Hierarchical Cartesian grids offer simplicity close to that of structured grids and the flexibility of unstructured grids while being highly suited for adaptive mesh refinement (AMR). The developed DGTD-ACM achieves a desired accuracy by refining non-conformal meshes near material interfaces to reduce stair-casing errors without sacrificing the high efficiency afforded with uniform Cartesian meshes. Moreover, DGTD-ACM can dynamically refine the mesh to resolve the local variation of the fields during propagation of electromagnetic pulses. A local time-stepping scheme is adopted to alleviate the constraint on the time-step size due to the stability condition of the explicit time integration. Simulations of electromagnetic wave diffraction over conducting and dielectric cylinders and spheres demonstrate that the proposed meth...
Piecewise oblique boundary treatment for the elastic-plastic wave equation on a cartesian grid
Giese, Guido
2009-11-01
Numerical schemes for hyperbolic conservation laws in 2-D on a Cartesian grid usually have the advantage of being easy to implement and showing good computational performances, without allowing the simulation of “real-world” problems on arbitrarily shaped domains. In this paper a numerical treatment of boundary conditions for the elastic-plastic wave equation is developed, which allows the simulation of problems on an arbitrarily shaped physical domain surrounded by a piece-wise smooth boundary curve, but using a PDE solver on a rectangular Cartesian grid with the afore-mentioned advantages.
Moment-of-fluid analytic reconstruction on 2D Cartesian grids
Lemoine, Antoine; Glockner, Stéphane; Breil, Jérôme
2017-01-01
Moment-of-Fluid (MoF) is a piecewise linear interface reconstruction method that tracks fluid through its volume fraction and centroid, which are deduced from the zeroth and first moments. We present a method that replaces the original minimization stage by an analytic reconstruction algorithm on bi-dimensional Cartesian grids. This algorithm provides accurate results for a lower computational cost than the original minimization algorithm. When more than two fluids are involved, this algorithm can be used coupled with the minimization algorithm. Although this paper deals with Cartesian grids, everything remains valid for any meshes that are made of rectangular cells.
Euler solution using adaptive Cartesian grid with a gridless boundary treatment
Institute of Scientific and Technical Information of China (English)
Liang Xiang; Guowei Yang
2009-01-01
A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid.First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indicate the developed method is reasonable for complex flows.
Directory of Open Access Journals (Sweden)
V. Ashok
2014-01-01
Full Text Available A hybrid solution methodology has been developed to solve chemically reacting laminar hypersonic flow in chemical Non-equilibrium and thermal equilibrium, by a Cartesian mesh based hybrid solution methodology, which uses an unstructured prism layer solution near the wall and a Cartesian mesh solution away from the wall. The unstructured prism layer for near wall solution is obtained from the normal projection of wall panels of the Cartesian mesh and are stitched with the outer Cartesian mesh. The solver, developed based on this approach when compared with other chemically reacting CFD codes and limited experimental results show good comparison. This procedure has a good potential to handle near-wall resolution for chemically reacting flows with a Cartesian mesh for complex geometries as well.
[Odontology and the beginning of cartesianism (1673--1650) (Rene Descartes)].
Gysel, C
1979-01-01
In the seventeenth century the universities of the Netherlands underwent the influence of Descartes in all the faculties. In medicine three periods can be distinguished: in the first, pathology and therapy are still galenic; the second, by the application of the cartesian method, triumphs in physiology; and the third, corrected by the views of Newton is integrated in a moderate biomechanism.
New advance on non-hydrostatic shallow granular flow model in a global Cartesian coordinate system
Yuan, L; Zhai, J; Wu, S F; Patra, A K; Pitman, E B
2016-01-01
Mathematical modeling of granular avalanche flows over a general topography needs appropriate forms of shallow granular flow models. Current shallow granular flow models suited to arbitrary topography can be grossly divided into two types, those formulated in bed-fitted curvilinear coordinates (e.g., Ref.~\\cite{{Puda2003}}), and those formulated in global Cartesian coordinates (e.g., Refs.~\\cite{{Bouchut2004},{Denlinger2004},{Castro2014}}). In the recent years, several improvements have been made in global Cartesian formulations for shallow granular flows. In this paper, we first perform a review of the Cartesian model of Denlinger and Iverson \\cite{Denlinger2004} and the Cartesian Boussinesq-type granular flow theory of Castr-Ogaz \\emph{et al.} \\cite{Castro2014}. Both formulations account for the effect of nonzero vertical acceleration on depth-averaged momentum fluxes and stress states. We then further calculate the vertical normal stress of Castr-Ogaz \\emph{et al.}~\\cite{Castro2014} and the basal normal st...
Embodying Learning: Post-Cartesian Pedagogy and the Academic Study of Religion
Lelwica, Michelle Mary
2009-01-01
This paper explores the concept and practice of "embodied pedagogy" as an alternative to the Cartesian approach to knowledge that is tacitly embedded in traditional modes of teaching and learning about religion. My analysis highlights a class I co-teach that combines the study of Aikido (a Japanese martial art) with seminar-style discussions of…
Rapid Non-Cartesian Parallel Imaging Reconstruction on Commodity Graphics Hardware
DEFF Research Database (Denmark)
Sørensen, Thomas Sangild; Atkinson, David; Boubertakh, Redha;
2008-01-01
time per frame is now below the acquisition time providing non-Cartesian reconstruction with only minimal delay between acquisition and subsequent display of images. This is demonstrated by four-fold and eight-fold undersampled real-time radial imaging reconstructed in 25 ms to 55 ms per frame....
Adjacent Vertex Distinguishing Incidence Coloring of the Cartesian Product of Some Graphs
Institute of Scientific and Technical Information of China (English)
Qian WANG; Shuang Liang TIAN
2011-01-01
An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors. We obtain the adjacent vertex distinguishing incidence chromatic number of the Cartesian product of a path and a path, a path and a wheel, a path and a fan, and a path and a star.
Quantum integrable systems in three-dimensional magnetic fields: the Cartesian case
Zhalij, Alexander
2015-06-01
In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems obtained are new and not related to the separation of variables in the corresponding Schrödinger equation.
Quantum integrable systems in three-dimensional magnetic fields: the Cartesian case
Zhalij, Alexander
2008-01-01
In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems obtained are new and not related to the separation of variables in the corresponding Schr\\"odinger equation.
Aleixo, A. N. F.; Balantekin, A. B.
2015-12-01
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.
DEFF Research Database (Denmark)
Hansen, N.; Huang, X.; Hughes, D.A.
2004-01-01
Microstructural characterization and modeling has shown that a variety of metals deformed by different thermomechanical processes follows a general path of grain subdivision, by dislocation boundaries and high angle boundaries. This subdivision has been observed to very small structural scales of...
... to follow the surgeon’s instructions for postsurgical care. Prevention To help prevent a recurrence of Haglund’s deformity: wear appropriate shoes; avoid shoes with a rigid heel back use arch supports or orthotic devices perform stretching exercises to prevent the Achilles tendon from tightening ...
Mean square optimal NUFFT approximation for efficient non-Cartesian MRI reconstruction
Yang, Zhili; Jacob, Mathews
2014-05-01
The fast evaluation of the discrete Fourier transform of an image at non-uniform sampling locations is key to efficient iterative non-Cartesian MRI reconstruction algorithms. Current non-uniform fast Fourier transform (NUFFT) approximations rely on the interpolation of oversampled uniform Fourier samples. The main challenge is high memory demand due to oversampling, especially when multidimensional datasets are involved. The main focus of this work is to design an NUFFT algorithm with minimal memory demands. Specifically, we introduce an analytical expression for the expected mean square error in the NUFFT approximation based on our earlier work. We then introduce an iterative algorithm to design the interpolator and scale factors. Experimental comparisons show that the proposed optimized NUFFT scheme provides considerably lower approximation errors than the previous designs [1] that rely on worst case error metrics. The improved approximations are also seen to considerably reduce the errors and artifacts in non-Cartesian MRI reconstruction.
Aligning Spinoza with Descartes: An informed Cartesian account of the truth bias.
Street, Chris N H; Kingstone, Alan
2016-08-11
There is a bias towards believing information is true rather than false. The Spinozan account claims there is an early, automatic bias towards believing. Only afterwards can people engage in an effortful re-evaluation and disbelieve the information. Supporting this account, there is a greater bias towards believing information is true when under cognitive load. However, developing on the Adaptive Lie Detector (ALIED) theory, the informed Cartesian can equally explain this data. The account claims the bias under load is not evidence of automatic belief; rather, people are undecided, but if forced to guess they can rely on context information to make an informed judgement. The account predicts, and we found, that if people can explicitly indicate their uncertainty, there should be no bias towards believing because they are no longer required to guess. Thus, we conclude that belief formation can be better explained by an informed Cartesian account - an attempt to make an informed judgment under uncertainty.
CUDA accelerated uniform re-sampling for non-Cartesian MR reconstruction.
Feng, Chaolu; Zhao, Dazhe
2015-01-01
A grid-driven gridding (GDG) method is proposed to uniformly re-sample non-Cartesian raw data acquired in PROPELLER, in which a trajectory window for each Cartesian grid is first computed. The intensity of the reconstructed image at this grid is the weighted average of raw data in this window. Taking consider of the single instruction multiple data (SIMD) property of the proposed GDG, a CUDA accelerated method is then proposed to improve the performance of the proposed GDG. Two groups of raw data sampled by PROPELLER in two resolutions are reconstructed by the proposed method. To balance computation resources of the GPU and obtain the best performance improvement, four thread-block strategies are adopted. Experimental results demonstrate that although the proposed GDG is more time consuming than traditional DDG, the CUDA accelerated GDG is almost 10 times faster than traditional DDG.
On the Use of Parmetric-CAD Systems and Cartesian Methods for Aerodynamic Design
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
2004-01-01
Automated, high-fidelity tools for aerodynamic design face critical issues in attempting to optimize real-life geometry arid in permitting radical design changes. Success in these areas promises not only significantly shorter design- cycle times, but also superior and unconventional designs. To address these issues, we investigate the use of a parmetric-CAD system in conjunction with an embedded-boundary Cartesian method. Our goal is to combine the modeling capabilities of feature-based CAD with the robustness and flexibility of component-based Cartesian volume-mesh generation for complex geometry problems. We present the development of an automated optimization frame-work with a focus on the deployment of such a CAD-based design approach in a heterogeneous parallel computing environment.
Energy Technology Data Exchange (ETDEWEB)
OTAHAL,THOMAS J.; GALLIS,MICHAIL A.; BARTEL,TIMOTHY J.
2000-06-27
This paper presents an investigation of a technique for using two-dimensional bodies composed of simple polygons with a body decoupled uniform Cmtesian grid in the Direct Simulation Monte Carlo method (DSMC). The method employs an automated grid pre-processing scheme beginning form a CAD geometry definition file, and is based on polygon triangulation using a trapezoid algorithm. A particle-body intersection time comparison is presented between the Icarus DSMC code using a body-fitted structured grid and using a structured body-decoupled Cartesian grid with both linear and logarithmic search techniques. A comparison of neutral flow over a cylinder is presented using the structured body fitted grid and the Cartesian body de-coupled grid.
Multipole analysis for electromagnetism and linearized gravity with irreducible Cartesian tensors
Energy Technology Data Exchange (ETDEWEB)
Damour, T.; Iyer, B.R. (Institut des Hautes Etudes Scientifiques 91440 Bures sur Yvette, France Departement d' Astrophysique Relativiste et de Cosmologie, Centre National de la Recherche Scientifique-Observatoire de Paris, 92195 Meudon CEDEX, France (FR))
1991-05-15
The relativistic time-dependent multipole expansion for electromagnetism and linearized gravity in the region outside a spatially compact source has been obtained directly using the formalism of irreducible Cartesian (i.e., symmetric trace-free) tensors. In the electromagnetic case, our results confirm the validity of the results obtained earlier by Campbell, Macek, and Morgan using the Debye potential formalism. However, in the more complicated linearized gravity case, the greater algebraic transparence of the Cartesian multipole approach has allowed us to obtain, for the first time, fully correct closed-form expressions for the time-dependent mass and spin multipole moments (the results of Campbell {ital et} {ital al}. for the mass moments turning out to be incorrect). The first two terms in the slow-motion expansion of the gravitational moments are explicitly calculated and shown to be equivalent to earlier results by Thorne and by Blanchet and Damour.
Generic multiset programming with discrimination-based joins and symbolic Cartesian products
DEFF Research Database (Denmark)
Henglein, Fritz; Larsen, Ken Friis
2010-01-01
: symbolic (term) repre- sentations of multisets, specifically for Cartesian products, for facilitating dynamic symbolic computation, which intersperses algebraic simplification steps with conventional data pro- cessing; and discrimination-based joins, a generic technique for computing equijoins based......This paper presents GMP, a library for generic, SQL-style programming with multisets. It generalizes the querying core of SQL in a number of ways: Multisets may contain elements of arbitrary first-order data types, including references (pointers), recur- sive data types and nested multisets...... in selections; and it allows user-defined aggregation functions. Most significantly, it avoids many cases of asymptotically inefficient nested iteration through Cartesian products that occur in a straightforward stream-based implementation of multisets. It accomplishes this by employing two novel techniques...
Development and application of a 3D Cartesian grid Euler method
Melton, John E.; Aftosmis, Michael J.; Berger, Marsha J.; Wong, Michael D.
1995-01-01
This report describes recent progress in the development and application of 3D Cartesian grid generation and Euler flow solution techniques. Improvements to flow field grid generation algorithms, geometry representations, and geometry refinement criteria are presented, including details of a procedure for correctly identifying and resolving extremely thin surface features. An initial implementation of automatic flow field refinement is also presented. Results for several 3D multi-component configurations are provided and discussed.
Cartesian Stiffness Matrix Mapping of a Translational Parallel Mechanism with Elastic Joints
Directory of Open Access Journals (Sweden)
Maurizio Ruggiu
2012-11-01
Full Text Available This paper is devoted to calculating the Cartesian stiffness matrix of a translational parallel manipulator with elastic joints. The calculation takes into account the contribution of the Jacobian variation because of the change of manipulator configuration due to the elasticity and it covers the entire theoretical workspace of the manipulator. Three kineto‐static adimensional indices are proposed to measure the response of the manipulator in terms of stiffness.
A Twist (with Pike) for the Simple Harmonic Oscillator
Filewood, G
2003-01-01
Extension of the formalism of Q.M. to resolve mathematical anomalies in the structure of anti-unitary operators; implications for vacuum structure and spin-statistics arising from an analysis applied to the S.H.O. Outline of the derived properties of the S.M. Higgs boson.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...
On harmonic oscillators and their Kemmer relativistic forms
Debergh, Nathalie; Beckers, Jules
1993-01-01
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.
Cooling a harmonic oscillator by optomechanical modification of its bath
Xu, Xunnong; Purdy, Thomas; Taylor, Jacob M.
2016-01-01
Optomechanical systems show tremendous promise for high sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser 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 effect...
Kim, Seungil
2010-01-01
In this paper, we study the spectrum of the operator which results when the Perfectly Matched Layer (PML) is applied in Cartesian geometry to the Laplacian on an unbounded domain. This is often thought of as a complex change of variables or "complex stretching." The reason that such an operator is of interest is that it can be used to provide a very effective domain truncation approach for approximating acoustic scattering problems posed on unbounded domains. Stretching associated with polar or spherical geometry lead to constant coefficient operators outside of a bounded transition layer and so even though they are on unbounded domains, they (and their numerical approximations) can be analyzed by more standard compact perturbation arguments. In contrast, operators associated with Cartesian stretching are non-constant in unbounded regions and hence cannot be analyzed via a compact perturbation approach. Alternatively, to show that the scattering problem PML operator associated with Cartesian geometry is stable for real nonzero wave numbers, we show that the essential spectrum of the higher order part only intersects the real axis at the origin. This enables us to conclude stability of the PML scattering problem from a uniqueness result given in a subsequent publication. © 2009 Elsevier Inc. All rights reserved.
Spatial pattern of Amazonian timber species using cartesian and spatial coordinates method
Directory of Open Access Journals (Sweden)
Tiago Monteiro Condé
2016-06-01
Full Text Available Geographic information system (GIS applied to forest analysis permit the recognition and analysis of spatial patterns of species in two and three dimensional. The aim of this study to demonstrate the efficiency of cartesian and spatial coordinates method (MCCE, method of correcting UTM coordinates of trees location in accordance with the location of field or Cartesian (X ,Y, combined with natural neighbor index (ANND in recognition and analysis of spatial distribution patterns of four commercial timber species in forest management in Caracaraí, Roraima State, Brazil. Simulations were performed on 9 ha, divided into 100 plots of 100 m2 each. Collected data were DBH > 10 cm, commercial and total heights, cartesian coordinates (X,Y and spatial coordinates (UTM. Random spatial patterns were observed in Eschweilera bracteosa and Manilkara huberi. The dispersed and rare spatial patterns were observed in Dinizia excelsa and Cedrelinga cateniformis. MCCE proved to be an efficient method in the recognition and analysis of spatial patterns of native species from Amazon rain forest, as forest planning becomes easier by 2D and 3D simulations.
Continuous Genetic Algorithms for Collision-Free Cartesian Path Planning of Robot Manipulators
Directory of Open Access Journals (Sweden)
Za'er S. Abo-Hammour
2011-12-01
Full Text Available A novel continuous genetic algorithm (CGA along with distance algorithm for solving collisions‐free path planning problem for robot manipulators is presented in this paper. Given the desired Cartesian path to be followed by the manipulator, the robot configuration as described by the D‐H parameters, and the available stationary obstacles in the workspace of the manipulator, the proposed approach will autonomously select a collision free path for the manipulator that minimizes the deviation between the generated and the desired Cartesian path, satisfy the joints limits of the manipulator, and maximize the minimum distance between the manipulator links and the obstacles. One of the main features of the algorithm is that it avoids the manipulator kinematic singularities due to the inclusion of forward kinematics model in the calculations instead of the inverse kinematics. The new robot path planning approach has been applied to two different robot configurations; 2R and PUMA 560, as non‐ redundant manipulators. Simulation results show that the proposed CGA will always select the safest path avoiding obstacles within the manipulator workspace regardless of whether there is a unique feasible solution, in terms of joint limits, or there are multiple feasible solutions. In addition to that, the generated path in Cartesian space will be of very minimal deviation from the desired one.
Ion induced deformation of soft tissue.
Myers, T G; Aldis, G K; Naili, S
1995-01-01
In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Lai et al. (1990, Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myers et al. (1984, ASME J. biomech. Engng, 106, 151-158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to account for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility of approximate analytic solutions in certain cases.
The Classical Thermodynamics of Deformable Materials
McLellan, A. G.
2011-02-01
Part I. The Mathematical Foundations of Finite Strain Theory: 1. Introduction; 2. Mathematical description of homogeneous deformations; 3. Infinitesimal deformation; 4. Transformations describing deformations of a material medium; 5. Forces; 6. Boundary conditions and work; 7. Another unique factorisation of D; 8. Virtual work; 9. Transformation of cartesian tensors; Part II. Non-Hydrostatic Thermodynamics: 10. The thermodynamic basis; 11. Thermodynamic relations; 12. Thermodynamic functions, equations of state; 13. Thermodynamic quantities, definitions, and geometrical situation; 14. Thermal expansion coefficients; 15. Specific heats; 16. Elastic stiffness and compliances; 17. Tensorial forms for the elastic stiffness and compliance matrices; 18. The effects of symmetry on the thermodynamic properties of crystals; 19. Equilibrium and stability conditions for thermodynamic systems; 20. Equilibrium conditions for diffusion in phases under non-hydrostatic stresses; 21. The equilibrium of a stressed solid in contact with a solution of the solid; 22. The thermodynamic stability of a phase; 23. Discussion of the elastic stability conditions; 24. Phase transitions and instability; 25. An example of a phase transition involving a simple shear; 26. Limiting the values of thermodynamic quantities at an instability; 27. The a-β quartz transition; 28. The thermodynamic theory of the growth of Dauphiné twinning in quartz under stress; 29. The tetragonal/cubic ferroelectric transition of barium titanate; References; Index.
Institute of Scientific and Technical Information of China (English)
卢道明
2003-01-01
构造了有限维希尔伯特空间q变形非简谐振子广义相干态,研究了它的振幅平方压缩效应. 结果表明,该量子态存在振幅平方压缩效应,并且给出了压缩条件与参数s,r,q之间的关系.
Institute of Scientific and Technical Information of China (English)
朱从旭
1999-01-01
从一般形式上构造了有限维希尔伯特(Hilbert)空间q-畸变谐振子的偶相干态, 并讨论了其量子统计特性. 发现有限维希尔伯特空间的偶q-相干态与通常无限维空间的偶q-相干态或偶相干态有明显不同的压缩和反聚束特性. 前者的偶q-相干态不仅出现正交压缩, 而且出现反聚束效应.
Fara, Patricia
2008-12-01
Few original portraits exist of René Descartes, yet his theories of vision were central to Enlightenment thought. French philosophers combined his emphasis on sight with the English approach of insisting that ideas are not innate, but must be built up from experience. In particular, Denis Diderot criticised Descartes's views by describing how Nicholas Saunderson--a blind physics professor at Cambridge--relied on touch. Diderot also made Saunderson the mouthpiece for some heretical arguments against the existence of God.
Lin, Dejun
2015-09-01
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green's function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4-16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
Analysis of a Cartesian PML approximation to acoustic scattering problems in and
Bramble, James H.
2013-08-01
We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift ("stretching") and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior. © 2013 Elsevier B.V. All rights reserved.
System Wide Joint Position Sensor Fault Tolerance in Robot Systems Using Cartesian Accelerometers
Aldridge, Hal A.; Juang, Jer-Nan
1997-01-01
Joint position sensors are necessary for most robot control systems. A single position sensor failure in a normal robot system can greatly degrade performance. This paper presents a method to obtain position information from Cartesian accelerometers without integration. Depending on the number and location of the accelerometers. the proposed system can tolerate the loss of multiple position sensors. A solution technique suitable for real-time implementation is presented. Simulations were conducted using 5 triaxial accelerometers to recover from the loss of up to 4 joint position sensors on a 7 degree of freedom robot moving in general three dimensional space. The simulations show good estimation performance using non-ideal accelerometer measurements.
KNOT POINT PLANNING FOR CARTESIAN TRAJECTORY GENERATION BASED ON INHERITANCE BISECTION ALGORITHM
Institute of Scientific and Technical Information of China (English)
Yan Bo; Yan Guozheng
2005-01-01
The computation algorithm of knot point planning for Cartesian trajectory generation of manipulator is investigated. A novel inheritance bisection algorithm (IBA) based on conventional bisection algorithm (BA) is proposed. IBA has two steps. The first step is the 1st knot point planning under lower set position accuracy; the second step is the 2nd knot point planning that inherits the results of the 1st planning under higher set position accuracy. The simulation results reveal that the number of inverse kinematical calculation (IKC) caused by IBA is decreased compared with BA. IBA is more efficient to plan knot points.
Elking, Dennis M
2016-08-15
New equations for torque and atomic force are derived for use in flexible molecule force fields with atomic multipoles. The expressions are based on Cartesian tensors with arbitrary multipole rank. The standard method for rotating Cartesian tensor multipoles and calculating torque is to first represent the tensor with n indexes and 3(n) redundant components. In this work, new expressions for directly rotating the unique (n + 1)(n + 2)/2 Cartesian tensor multipole components Θpqr are given by introducing Cartesian tensor rotation matrix elements X(R). A polynomial expression and a recursion relation for X(R) are derived. For comparison, the analogous rotation matrix for spherical tensor multipoles are the Wigner functions D(R). The expressions for X(R) are used to derive simple equations for torque and atomic force. The torque and atomic force equations are applied to the geometry optimization of small molecule crystal unit cells. In addition, a discussion of computational efficiency as a function of increasing multipole rank is given for Cartesian tensors. © 2016 Wiley Periodicals, Inc.
Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries
Aftosmis, M. J.; Berger, M. J.; Kwak, Dochan (Technical Monitor)
2002-01-01
This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.
The Numerical Simulation of Ship Waves Using Cartesian Grid Methods with Adaptive Mesh Refinement
Dommermuth, Douglas G; Beck, Robert F; O'Shea, Thomas T; Wyatt, Donald C; Olson, Kevin; MacNeice, Peter
2014-01-01
Cartesian-grid methods with Adaptive Mesh Refinement (AMR) are ideally suited for simulating the breaking of waves, the formation of spray, and the entrainment of air around ships. As a result of the cartesian-grid formulation, minimal input is required to describe the ships geometry. A surface panelization of the ship hull is used as input to automatically generate a three-dimensional model. No three-dimensional gridding is required. The AMR portion of the numerical algorithm automatically clusters grid points near the ship in regions where wave breaking, spray formation, and air entrainment occur. Away from the ship, where the flow is less turbulent, the mesh is coarser. The numerical computations are implemented using parallel algorithms. Together, the ease of input and usage, the ability to resolve complex free-surface phenomena, and the speed of the numerical algorithms provide a robust capability for simulating the free-surface disturbances near a ship. Here, numerical predictions, with and without AMR,...
Darwin's evolution theory, brain oscillations, and complex brain function in a new "Cartesian view".
Başar, Erol; Güntekin, Bahar
2009-01-01
Comparatively analyses of electrophysiological correlates across species during evolution, alpha activity during brain maturation, and alpha activity in complex cognitive processes are presented to illustrate a new multidimensional "Cartesian System" brain function. The main features are: (1) The growth of the alpha activity during evolution, increase of alpha during cognitive processes, and decrease of the alpha entropy during evolution provide an indicator for evolution of brain cognitive performance. (2) Human children younger than 3 years are unable to produce higher cognitive processes and do not show alpha activity till the age of 3 years. The mature brain can perform higher cognitive processes and demonstrates regular alpha activity. (3) Alpha activity also is significantly associated with highly complex cognitive processes, such as the recognition of facial expressions. The neural activity reflected by these brain oscillations can be considered as constituent "building blocks" for a great number of functions. An overarching statement on the alpha function is presented by extended analyzes with multiple dimensions that constitute a "Cartesian Hyperspace" as the basis for oscillatory function. Theoretical implications are considered.
Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft
Directory of Open Access Journals (Sweden)
Yuma Fukushima
2015-01-01
Full Text Available The linearized Euler equations (LEEs solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.
Finley, Dennis B.
1995-01-01
This report documents results from the Euler Technology Assessment program. The objective was to evaluate the efficacy of Euler computational fluid dynamics (CFD) codes for use in preliminary aircraft design. Both the accuracy of the predictions and the rapidity of calculations were to be assessed. This portion of the study was conducted by Lockheed Fort Worth Company, using a recently developed in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages for this study, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaptation of the volume grid during the solution convergence to resolve high-gradient flow regions. This proved beneficial in resolving the large vortical structures in the flow for several configurations examined in the present study. The SPLITFLOW code predictions of the configuration forces and moments are shown to be adequate for preliminary design analysis, including predictions of sideslip effects and the effects of geometry variations at low and high angles of attack. The time required to generate the results from initial surface definition is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.
Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.
Chen, Lin; Huang, Jianpan; Zhang, Ting; Li, Jing; Cai, Congbo; Cai, Shuhui
2016-11-01
Spatiotemporally encoded (SPEN) single-shot MRI is an emerging ultrafast technique, which is capable of spatially selective acquisition and reduced field-of-view imaging. Compared to uniform sampling, variable density sampling has great potential in reducing aliasing artifacts and improving sampling efficiency. In this study, variable density spiral trajectory and non-Cartesian super-resolved (SR) reconstruction method are developed for SPEN MRI. The gradient waveforms design of spiral trajectory is mathematically described as an optimization problem subjected to the limitations of hardware. Non-Cartesian SR reconstruction with specific gridding method is developed to retrieve a resolution enhanced image from raw SPEN data. The robustness and efficiency of the proposed methods are demonstrated by numerical simulation and various experiments. The results indicate that variable density SPEN MRI can provide better spatial resolution and fewer aliasing artifacts compared to Cartesian counterpart. The proposed methods will facilitate the development of variable density SPEN MRI.
Chen, Lin; Huang, Jianpan; Zhang, Ting; Li, Jing; Cai, Congbo; Cai, Shuhui
2016-11-01
Spatiotemporally encoded (SPEN) single-shot MRI is an emerging ultrafast technique, which is capable of spatially selective acquisition and reduced field-of-view imaging. Compared to uniform sampling, variable density sampling has great potential in reducing aliasing artifacts and improving sampling efficiency. In this study, variable density spiral trajectory and non-Cartesian super-resolved (SR) reconstruction method are developed for SPEN MRI. The gradient waveforms design of spiral trajectory is mathematically described as an optimization problem subjected to the limitations of hardware. Non-Cartesian SR reconstruction with specific gridding method is developed to retrieve a resolution enhanced image from raw SPEN data. The robustness and efficiency of the proposed methods are demonstrated by numerical simulation and various experiments. The results indicate that variable density SPEN MRI can provide better spatial resolution and fewer aliasing artifacts compared to Cartesian counterpart. The proposed methods will facilitate the development of variable density SPEN MRI.
Sifounakis, Adamandios; Lee, Sangseung; You, Donghyun
2016-12-01
A second-order-accurate finite-volume method is developed for the solution of incompressible Navier-Stokes equations on locally refined nested Cartesian grids. Numerical accuracy and stability on locally refined nested Cartesian grids are achieved using a finite-volume discretization of the incompressible Navier-Stokes equations based on higher-order conservation principles - i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithms. Hanging nodes at the interface are virtually slanted to improve the pressure-velocity projection, while the other parts of the grid maintain an orthogonal Cartesian grid topology. The present method is straight-forward to implement and shows superior conservation of mass, momentum, and kinetic energy compared to the conventional methods employing interpolation at the interface between coarse and fine grids.
Parametric Deformation of Discrete Geometry for Aerodynamic Shape Design
Anderson, George R.; Aftosmis, Michael J.; Nemec, Marian
2012-01-01
We present a versatile discrete geometry manipulation platform for aerospace vehicle shape optimization. The platform is based on the geometry kernel of an open-source modeling tool called Blender and offers access to four parametric deformation techniques: lattice, cage-based, skeletal, and direct manipulation. Custom deformation methods are implemented as plugins, and the kernel is controlled through a scripting interface. Surface sensitivities are provided to support gradient-based optimization. The platform architecture allows the use of geometry pipelines, where multiple modelers are used in sequence, enabling manipulation difficult or impossible to achieve with a constructive modeler or deformer alone. We implement an intuitive custom deformation method in which a set of surface points serve as the design variables and user-specified constraints are intrinsically satisfied. We test our geometry platform on several design examples using an aerodynamic design framework based on Cartesian grids. We examine inverse airfoil design and shape matching and perform lift-constrained drag minimization on an airfoil with thickness constraints. A transport wing-fuselage integration problem demonstrates the approach in 3D. In a final example, our platform is pipelined with a constructive modeler to parabolically sweep a wingtip while applying a 1-G loading deformation across the wingspan. This work is an important first step towards the larger goal of leveraging the investment of the graphics industry to improve the state-of-the-art in aerospace geometry tools.
Lin, Dejun
2015-01-01
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis
2016-11-01
A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates
Energy Technology Data Exchange (ETDEWEB)
Lin, Dejun, E-mail: dejun.lin@gmail.com [Department of Biochemistry and Biophysics, University of Rochester Medical Center, Rochester, New York 14642 (United States)
2015-09-21
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
Indian Academy of Sciences (India)
A K De
2014-10-01
A discrete forcing based Cartesian grid method is presented. The nonstaggered arrangement of velocity and pressure is considered. The pressure gradient in localized discrete form is added separately with the velocity making them explicitly coupled. The governing equation is time-integrated implicitly with both linearized and non-linear forms are investigated. Both linear and bi-linear reconstruction techniques are tested for extrapolation of velocity near a complex boundary. The present method is tested for vortical flow in an inclined cavity, flow past circular and inclined square cylinder. Both homogeneous and non-homogeneous Dirichlet forcing problems are tested. The parallelized version of the method is applied to 2D-to-3D transitional flow behind a single and multiple circular cylinders. The present numerical results compare well with the previously documented results.
Best of Both Worlds: Uniform sampling in Cartesian and Cayley Molecular Assembly Configuration Space
Ozkan, Aysegul
2014-01-01
EASAL (efficient atlasing and sampling of assembly landscapes) is a recently reported geometric method for representing, visualizing, sampling and computing integrals over the potential energy landscape tailored for small molecular assemblies. EASAL's efficiency arises from the fact that small assembly landscapes permit the use of so-called Cayley parameters (inter-atomic distances) for geometric representation and sampling of the assembly configuration space regions; this results in their isolation, convexification, customized sampling and systematic traversal using a comprehensive topological roadmap, ensuring reasonable coverage of crucial but narrow regions of low effective dimension. However, this alone is inadequate for accurate computation of configurational entropy and other integrals, required for estimation of both free energy and kinetics - where it is essential to obtain uniform sampling in appropriate cartesian or moduli space parameterization. Standard adjustment of Cayley sampling via the Jacob...
A Cartesian quasi-classical model to nonequilibrium quantum transport: the Anderson impurity model.
Li, Bin; Levy, Tal J; Swenson, David W H; Rabani, Eran; Miller, William H
2013-03-14
We apply the recently proposed quasi-classical approach for a second quantized many-electron Hamiltonian in Cartesian coordinates [B. Li and W. H. Miller, J. Chem. Phys. 137, 154107 (2012)] to correlated nonequilibrium quantum transport. The approach provides accurate results for the resonant level model for a wide range of temperatures, bias, and gate voltages, correcting the flaws of our recently proposed mapping using action-angle variables. When electron-electron interactions are included, a Gaussian function scheme is required to map the two-electron integrals, leading to quantitative results for the Anderson impurity model. In particular, we show that the current mapping is capable of capturing quantitatively the Coulomb blockade effect and the temperature dependence of the current below and above the blockade.
Construction of freeforms in illumination systems via generalized Cartesian oval representation
Michaelis, D.; Schreiber, P.; Li, Chen; Bräuer, A.
2011-10-01
Freeforms in illumination systems are directly constructed by adapting some ideas of Oliker and co-workers [1]. The freeform is created by a set of primitive surface elements which are generalized Cartesian ovals including the optical response of the residual system. Hamiltonian theory of ray optics can be used to determine the family of primitives which is in particular a simple task if the freeform is the exit surface of the illumination system. For simple optical systems an analytical description of the primitives is possible. Contrarily, for more complex optics a conventional raytracer is additionally utilized to determine the required system's information, like the optical path lengths or mixed characteristics. To this end a discrete set of rays is traced through the residual systems and the required relations are interpolated to obtain a quasi-analytic representation of the primitives. The potential of this approach is demonstrated by some examples, e.g. freeform optics including collimating or deflection elements.
A new DFT method for atoms and molecules in Cartesian grid
Roy, Amlan K
2013-01-01
Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a rigorous, tractable manner keeping the computational cost at a manageable level. With recent advances in methodological development, algorithmic progress as well as computer technology, larger physical, chemical and biological systems are amenable to quantum mechanical calculations than ever before. Here we report the development of a new method for accurate reliable description of atoms, molecules within the Hohenberg-Kohn-Sham density functional theory (DFT). In a Cartesian grid, atom-centered localized basis set, electron density, molecular orbitals, two-body potentials are directly built on the grid. We employ a Fourier convolution method for classical Coulomb potentials by making an Ewald-type decomposition technique in terms of short- and long-range interactions. One-body ma...
Density functional calculation of many-electron systems in cartesian coordinate grid
Roy, Amlan K
2011-01-01
A recently developed density functional method, within Hohenberg-Kohn-Sham framework, is used for faithful description of atoms, molecules in Cartesian coordinate grid, by using an LCAO-MO ansatz. Classical Coulomb potential is obtained by means of a Fourier convolution technique. All two-body potentials (including exchange-correlation (XC)) are constructed directly on real grid, while their corresponding matrix elements are computed from numerical integration. Detailed systematic investigation is made for a representative set of atoms/molecules through a number of properties like total energies, component energies, ionization energies, orbital energies, etc. Two nonlocal XC functionals (FT97 and PBE) are considered for pseudopotential calculation of 35 species while preliminary all-electron results are reported for 6 atoms using the LDA XC density functional. Comparison with literature results, wherever possible, exhibits near-complete agreement. This offers a simple efficient route towards accurate reliable...
Energy Technology Data Exchange (ETDEWEB)
Courau, T.; Moustafa, S.; Plagne, L.; Poncot, A. [EDF R and D, 1, Av du General de Gaulle, F92141 Clamart cedex (France)
2013-07-01
As part of its activity, EDF R and D is developing a new nuclear core simulation code named COCAGNE. This code relies on DIABOLO, a Simplified PN (SPN) method to compute the neutron flux inside the core for eigenvalue calculations. In order to assess the accuracy of SPN calculations, we have developed DOMINO, a new 3D Cartesian SN solver. The parallel implementation of DOMINO is very efficient and allows to complete an eigenvalue calculation involving around 300 x 10{sup 9} degrees of freedom within a few hours on a single shared-memory supercomputing node. This computation corresponds to a 26-group S{sub 8} 3D PWR core model used to assess the SPN accuracy. At the pin level, the maximal error for the SP{sub 5} DIABOLO fission production rate is lower than 0.2% compared to the S{sub 8} DOMINO reference for this 3D PWR core model. (authors)
Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
Nemec, Marian; Aftosmis, Michael J.
2006-01-01
A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design
Deformations of crystal frameworks
Borcea, Ciprian S
2011-01-01
We apply our deformation theory of periodic bar-and-joint frameworks to tetrahedral crystal structures. The deformation space is investigated in detail for frameworks modelled on quartz, cristobalite and tridymite.
Peano—A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids
Weinzierl, Tobias
2011-01-01
Almost all approaches to solving partial differential equations (PDEs) are based upon a spatial discretization of the computational domain-a grid. This paper presents an algorithm to generate, store, and traverse a hierarchy of d-dimensional Cartesian grids represented by a (k = 3)- spacetree, a generalization of the well-known octree concept, and it also shows the correctness of the approach. These grids may change their adaptive structure throughout the traversal. The algorithm uses 2d + 4 stacks as data structures for both cells and vertices, and the storage requirements for the pure grid reduce to one bit per vertex for both the complete grid connectivity structure and the multilevel grid relations. Since the traversal algorithm uses only stacks, the algorithm\\'s cache hit rate is continually higher than 99.9 percent, and the runtime per vertex remains almost constant; i.e., it does not depend on the overall number of vertices or the adaptivity pattern. We use the algorithmic approach as the fundamental concept for a mesh management for d-dimensional PDEs and for a matrix-free PDE solver represented by a compact discrete 3 d-point operator. In the latter case, one can implement a Jacobi smoother, a Krylov solver, or a geometric multigrid scheme within the presented traversal scheme which inherits the low memory requirements and the good memory access characteristics directly. © 2011 Society for Industrial and Applied Mathematics.
Folio, Les; Fischer, Tatjana; Shogan, Paul J; Frew, Michael; Bunger, Rolf; Provenzale, James M
2011-11-01
Our purpose was to demonstrate the consistency of radiologists' three-dimensional measurements of simulated blast fragment locations in vitro in an effort to objectively localize retained fragments and wound paths. We designed a phantom consisting of 10 nail heads (simulating blast fragments) glued to wooden pegs that were randomly situated at distances from a reference point within a plastic tub. The x, y, and z coordinates of simulated fragments were recorded in Cartesian 3-space relative to the reference point. Computed tomography images of the phantom were acquired. Differences in x, y, and z positions as determined by three observers were summed for each fragment. Agreement between recordings of coordinates across readers was assessed using the intraclass correlation coefficient. Summed differences in coordinate positions as determined by readers ranged between 0.00 and 1.204 cm (mean: 0.732 cm). Across readers, the intraclass correlation coefficient for each dimension was >0.99. We found excellent agreement among readers with minimal discrepancy of measured locations of simulated fragments. Our results provide a foundation for trajectory analysis necessary to lead to automated organ damage reporting for immediate assessment in the emergency department and for forensic investigation and long-term epidemiological analysis.
Cartesian Kerr-Schild variation on the Newman-Janis ansatz
Nawarajan, Deloshan
2016-01-01
The Newman-Janis ansatz is a procedure (an "ansatz" or "trick") for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 year old "trick" continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman-Janis procedure can be upgraded to the status of an "algorithm", or if it is perhaps merely an inspired "ansatz", or possibly just a random "trick" of no deep physical significance. (That the Newman-Janis procedure very quickly led to the discovery of the Kerr-Newman spacetime is a point very much in its favour.) In the current article we will not answer these deeper questions, we shall instead present a much simpler alternative variation on the theme of the Newman-Janis ansatz that might be easier to work with. We shall present a 2-step version of the Newman-Janis trick that works directly with the Kerr-Schild "Cartesian" metric presentation of the Kerr spacetime. That is, we show how the original 4-step Newman--Janis procedure can, (usin...
A novel 3D Cartesian random sampling strategy for Compressive Sensing Magnetic Resonance Imaging.
Valvano, Giuseppe; Martini, Nicola; Santarelli, Maria Filomena; Chiappino, Dante; Landini, Luigi
2015-01-01
In this work we propose a novel acquisition strategy for accelerated 3D Compressive Sensing Magnetic Resonance Imaging (CS-MRI). This strategy is based on a 3D cartesian sampling with random switching of the frequency encoding direction with other K-space directions. Two 3D sampling strategies are presented. In the first strategy, the frequency encoding direction is randomly switched with one of the two phase encoding directions. In the second strategy, the frequency encoding direction is randomly chosen between all the directions of the K-Space. These strategies can lower the coherence of the acquisition, in order to produce reduced aliasing artifacts and to achieve a better image quality after Compressive Sensing (CS) reconstruction. Furthermore, the proposed strategies can reduce the typical smoothing of CS due to the limited sampling of high frequency locations. We demonstrated by means of simulations that the proposed acquisition strategies outperformed the standard Compressive Sensing acquisition. This results in a better quality of the reconstructed images and in a greater achievable acceleration.
ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach
Directory of Open Access Journals (Sweden)
M. Jähn
2015-02-01
Full Text Available In this work, the fully compressible, three-dimensional, nonhydrostatic atmospheric model called All Scale Atmospheric Model (ASAM is presented. A cut cell approach is used to include obstacles and orography into the Cartesian grid. Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied. Necessary shifting and interpolation techniques are outlined. The method can be generalized to any other orthogonal grids, e.g., a lat–long grid. A linear implicit Rosenbrock time integration scheme ensures numerical stability in the presence of fast sound waves and around small cells. Analyses of five two-dimensional benchmark test cases from the literature are carried out to show that the described method produces meaningful results with respect to conservation properties and model accuracy. The test cases are partly modified in a way that the flow field or scalars interact with cut cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid-scale model, a two-moment bulk microphysics scheme, and precipitation and surface fluxes using a sophisticated multi-layer soil model are implemented and described. Results of an idealized three-dimensional simulation are shown, where the flow field around an idealized mountain with subsequent gravity wave generation, latent heat release, orographic clouds and precipitation are modeled.
López-Muñoz, Francisco; Rubio, Gabriel; Molina, Juan D; Alamo, Cecilio
2011-04-25
The relationship between the "passions" (emotions or feelings) and psychopathology has been a constant throughout the history of medicine. In this context, melancholy was considered a perversion of the soul (corruption of the passions). One of the most influential authors on this subject was René Descartes, who discussed it in his work The Treatise on the Passions of the Soul (1649). Descartes believed that "passions" were sensitive movements that the soul experienced due to its union with the body (res extensa). According to this theory, the soul was located in the pineal gland, where it was actively involved in overseeing the functions of the "human machine" and kept its dysfunctions under control, by circulating animal spirits. Descartes described sadness as one of "the six primitive passions of the soul", which leads to melancholy if not remedied. Cartesian theories had a great deal of influence on the way that mental pathologies were considered throughout the entire 17th century (Spinoza, Willis, Pitcairn) and during much of the 18th century (Le Cat, Tissot). From the 19th century onwards, emotional symptomatology finally began to be used in diagnostic criteria for mood disorders.
Practical conversion from torsion space to Cartesian space for in silico protein synthesis.
Parsons, Jerod; Holmes, J Bradley; Rojas, J Maurice; Tsai, Jerry; Strauss, Charlie E M
2005-07-30
Many applications require a method for translating a large list of bond angles and bond lengths to precise atomic Cartesian coordinates. This simple but computationally consuming task occurs ubiquitously in modeling proteins, DNA, and other polymers as well as in many other fields such as robotics. To find an optimal method, algorithms can be compared by a number of operations, speed, intrinsic numerical stability, and parallelization. We discuss five established methods for growing a protein backbone by serial chain extension from bond angles and bond lengths. We introduce the Natural Extension Reference Frame (NeRF) method developed for Rosetta's chain extension subroutine, as well as an improved implementation. In comparison to traditional two-step rotations, vector algebra, or Quaternion product algorithms, the NeRF algorithm is superior for this application: it requires 47% fewer floating point operations, demonstrates the best intrinsic numerical stability, and offers prospects for parallel processor acceleration. The NeRF formalism factors the mathematical operations of chain extension into two independent terms with orthogonal subsets of the dependent variables; the apparent irreducibility of these factors hint that the minimal operation set may have been identified. Benchmarks are made on Intel Pentium and Motorola PowerPC CPUs.
Features of CPB: a Poisson-Boltzmann solver that uses an adaptive Cartesian grid.
Fenley, Marcia O; Harris, Robert C; Mackoy, Travis; Boschitsch, Alexander H
2015-02-05
The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (ϕrf ) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ at the molecular surface. All surfaces, which include solvent excluded, Gaussians, and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ϕ and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other Poisson-Boltzmann equation solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software.
ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach
Jähn, M.; Knoth, O.; König, M.; Vogelsberg, U.
2015-02-01
In this work, the fully compressible, three-dimensional, nonhydrostatic atmospheric model called All Scale Atmospheric Model (ASAM) is presented. A cut cell approach is used to include obstacles and orography into the Cartesian grid. Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied. Necessary shifting and interpolation techniques are outlined. The method can be generalized to any other orthogonal grids, e.g., a lat-long grid. A linear implicit Rosenbrock time integration scheme ensures numerical stability in the presence of fast sound waves and around small cells. Analyses of five two-dimensional benchmark test cases from the literature are carried out to show that the described method produces meaningful results with respect to conservation properties and model accuracy. The test cases are partly modified in a way that the flow field or scalars interact with cut cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid-scale model, a two-moment bulk microphysics scheme, and precipitation and surface fluxes using a sophisticated multi-layer soil model are implemented and described. Results of an idealized three-dimensional simulation are shown, where the flow field around an idealized mountain with subsequent gravity wave generation, latent heat release, orographic clouds and precipitation are modeled.
Path Planning of Free-Floating Robot in Cartesian Space Using Direct Kinematics
Directory of Open Access Journals (Sweden)
Wenfu Xu
2008-11-01
Full Text Available Dynamic singularities make it difficult to plan the Cartesian path of freefloating robot. In order to avoid its effect, the direct kinematic equations are used for path planning in the paper. Here, the joint position, rate and acceleration are bounded. Firstly, the joint trajectories are parameterized by polynomial or sinusoidal functions. And the two parametric functions are compared in details. It is the first contribution of the paper that polynomial functions can be used when the joint angles are limited(In the similar work of other researchers, only sinusoidla functions could be used. Secondly, the joint functions are normalized and the system of equations about the parameters is established by integrating the differential kinematics equations. Normalization is another contribution of the paper. After normalization, the boundary of the parameters is determined beforehand, and the general criterion to assign the initial guess of the unknown parameters is supplied. The criterion is independent on the planning conditions such as the total time tf. Finally, the parametes are solved by the iterative Newtonian method. Modification of tf may not result in the recalculation of the parameters. Simulation results verify the path planning method.
A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity
Thornburg, J
2004-01-01
In 3+1 numerical simulations of dynamic black hole spacetimes, it's useful to be able to find the apparent horizon(s) (AH) in each slice of a time evolution. A number of AH finders are available, but they often take many minutes to run, so they're too slow to be practically usable at each time step. Here I present a new AH finder,_AHFinderDirect_, which is very fast and accurate, typically taking only a few seconds to find an AH to $sim 10^{-5} m$ accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlk"orper (star-shaped region) with respect to some local origin, and so parameterize the AH shape by $r = h(angle)$ for some single-valued function $h: S^2 to Re^+$. The AH equation then becomes a nonlinear elliptic PDE in $h$ on $S^2$, whose coefficients are algebraic functions of $g_{ij}$, $K_{ij}$, and the Cartesian-coordinate spatial derivatives of $g_{ij}$. I discretize $S^2$ using 6 angular patches (one each in the neighborhood of the $pm x$, $pm y$, and $pm z$ axes) to avoid c...
Extending a CAD-Based Cartesian Mesh Generator for the Lattice Boltzmann Method
Energy Technology Data Exchange (ETDEWEB)
Cantrell, J Nathan [ORNL; Inclan, Eric J [ORNL; Joshi, Abhijit S [ORNL; Popov, Emilian L [ORNL; Jain, Prashant K [ORNL
2012-01-01
This paper describes the development of a custom preprocessor for the PaRAllel Thermal Hydraulics simulations using Advanced Mesoscopic methods (PRATHAM) code based on an open-source mesh generator, CartGen [1]. PRATHAM is a three-dimensional (3D) lattice Boltzmann method (LBM) based parallel flow simulation software currently under development at the Oak Ridge National Laboratory. The LBM algorithm in PRATHAM requires a uniform, coordinate system-aligned, non-body-fitted structured mesh for its computational domain. CartGen [1], which is a GNU-licensed open source code, already comes with some of the above needed functionalities. However, it needs to be further extended to fully support the LBM specific preprocessing requirements. Therefore, CartGen is being modified to (i) be compiler independent while converting a neutral-format STL (Stereolithography) CAD geometry to a uniform structured Cartesian mesh, (ii) provide a mechanism for PRATHAM to import the mesh and identify the fluid/solid domains, and (iii) provide a mechanism to visually identify and tag the domain boundaries on which to apply different boundary conditions.
Directory of Open Access Journals (Sweden)
Goran Lešaja
2011-02-01
Full Text Available We present an interior point method for Cartesian P*(k-Linear Complementarity Problems over Symmetric Cones (SCLCPs. The Cartesian P*(k-SCLCPs have been recently introduced as the generalization of the more commonly known and more widely used monotone SCLCPs. The IPM is based on the barrier functions that are defined by a large class of univariate functions called eligible kernel function which have recently been successfully used to design new IPMs for various optimization problems. Eligible barrier (kernel functions are used in calculating the Nesterov-Todd search directions and the default step-size which leads to a very good complexity results for the method. For some specific eligilbe kernel functions we match the best known iteration bound for the long-step methods while for the short-step methods the best iteration bound is matched for all cases.
Başar, Erol; Güntekin, Bahar
2007-04-01
The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications of Newtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causality principle became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept of cloudy wave packets. The approach to the brain-body-mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis of the brain-body-mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiple causalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulences in the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g. chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physical processes in the body. The brain shows deterministic chaos with a correlation dimension of approx. D(2)=6, the smooth muscles approx. D(2)=3. According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze the processes in the brain-body-mind system. If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this "New Cartesian System" is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite this chain of reasoning we can still provide predictions on brain-body-mind incorporations. We tentatively assume that the processes or mechanisms of the brain-body-mind system can be analyzed and predicted similar to the
Issack, Bilkiss B; Roy, Pierre-Nicholas
2005-08-22
An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.
An interior-point method for the Cartesian P*(k-linear complementarity problem over symmetric cones
Directory of Open Access Journals (Sweden)
B Kheirfam
2014-06-01
Full Text Available A novel primal-dual path-following interior-point algorithm for the Cartesian P*(k-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-update approach is the best-available bound.
Liu, Yangfan; Bolton, J Stuart
2016-08-01
The (Cartesian) multipole series, i.e., the series comprising monopole, dipoles, quadrupoles, etc., can be used, as an alternative to the spherical or cylindrical wave series, in representing sound fields in a wide range of problems, such as source radiation, sound scattering, etc. The proofs of the completeness of the spherical and cylindrical wave series in these problems are classical results, and it is also generally agreed that the Cartesian multipole series spans the same space as the spherical waves: a rigorous mathematical proof of that statement has, however, not been presented. In the present work, such a proof of the completeness of the Cartesian multipole series, both in two and three dimensions, is given, and the linear dependence relations among different orders of multipoles are discussed, which then allows one to easily extract a basis from the multipole series. In particular, it is concluded that the multipoles comprising the two highest orders in the series form a basis of the whole series, since the multipoles of all the lower source orders can be expressed as a linear combination of that basis.
Deformable Nanolaminate Optics
Energy Technology Data Exchange (ETDEWEB)
Olivier, S S; Papavasiliou, A P; Barbee, T W; Miles, R R; Walton, C C; Cohn, M B; Chang, K
2006-05-12
We are developing a new class of deformable optic based on electrostatic actuation of nanolaminate foils. These foils are engineered at the atomic level to provide optimal opto-mechanical properties, including surface quality, strength and stiffness, for a wide range of deformable optics. We are combining these foils, developed at Lawrence Livermore National Laboratory (LLNL), with commercial metal processing techniques to produce prototype deformable optics with aperture sizes up to 10 cm and actuator spacing from 1 mm to 1 cm and with a range of surface deformation designed to be as much as 10 microns. The existing capability for producing nanolaminate foils at LLNL, coupled with the commercial metal processing techniques being used, enable the potential production of these deformable optics with aperture sizes of over 1 m, and much larger deformable optics could potentially be produced by tiling multiple deformable segments. In addition, based on the fabrication processes being used, deformable nanolaminate optics could potentially be produced with areal densities of less than 1 kg per square m for applications in which lightweight deformable optics are desirable, and deformable nanolaminate optics could potentially be fabricated with intrinsically curved surfaces, including aspheric shapes. We will describe the basic principles of these devices, and we will present details of the design, fabrication and characterization of the prototype deformable nanolaminate optics that have been developed to date. We will also discuss the possibilities for future work on scaling these devices to larger sizes and developing both devices with lower areal densities and devices with curved surfaces.
Sato, Norikazu; Takeuchi, Shintaro; Kajishima, Takeo; Inagaki, Masahide; Horinouchi, Nariaki
2016-09-01
A new discretization scheme on Cartesian grids, namely, a "consistent direct discretization scheme", is proposed for solving incompressible flows with convective and conjugate heat transfer around a solid object. The Navier-Stokes and the pressure Poisson equations are discretized directly even in the immediate vicinity of a solid boundary with the aid of the consistency between the face-velocity and the pressure gradient. From verifications in fundamental flow problems, the present method is found to significantly improve the accuracy of the velocity and the wall shear stress. It is also confirmed that the numerical results are less sensitive to the Courant number owing to the consistency between the velocity and pressure fields. The concept of the consistent direct discretization scheme is also explored for the thermal field; the energy equations for the fluid and solid phases are discretized directly while satisfying the thermal relations that should be valid at their interface. It takes different forms depending on the thermal boundary conditions: Dirichlet (isothermal) and Neumann (adiabatic/iso-heat-flux) boundary conditions for convective heat transfer and a fluid-solid thermal interaction for conjugate heat transfer. The validity of these discretizations is assessed by comparing the simulated results with analytical solutions for the respective thermal boundary conditions, and it is confirmed that the present schemes also show high accuracy for the thermal field. A significant improvement for the conjugate heat transfer problems is that the second-order spatial accuracy and numerical stability are maintained even under severe conditions of near-practical physical properties for the fluid and solid phases.
Martini, M; Hilaire, S; Goriely, S; Lechaftois, F
2016-01-01
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 $E1$ $\\gamma$-ray strength function obtained in the framework of the axially-symmetric deformed QRPA 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 cut-off energy introduced in the 2-quasiparticle (2-$qp$) excitation space is analyzed. The calculations performed with two different Gogny interactions, namely D1S and D1M, are compared. A systematic energy shift of the $E1$ 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...
Indian Academy of Sciences (India)
Ramaswamy Jaganathan; Sudeshna Sinha
2005-03-01
Motivated by studies on -deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the concept of -deformed nonlinear maps is introduced. As a specific example, a -deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family of -logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors – a phenomenon rare in one-dimensional maps.
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Fluctuations as stochastic deformation
Kazinski, P. O.
2008-04-01
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
Diffeomorphic Statistical Deformation Models
DEFF Research Database (Denmark)
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al....... The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear...
Experimental force modeling for deformation machining stretching mode for aluminum alloys
Indian Academy of Sciences (India)
ARSHPREET SINGH; ANUPAM AGRAWAL
2017-02-01
Deformation machining is a hybrid process that combines two manufacturing processes—thin structure machining and single-point incremental forming. This process enables the creation of complex structures and geometries, which would be rather difficult or sometimes impossible to manufacture. A comprehensive experimental study of forces induced in deformation machining stretching mode has been performedin the present work. A table-type force dynamometer has been used to record the deforming forces in three Cartesian directions. The influence of five process parameters—floor thickness, tool diameter, wall angle,incremental step size, and floor size on the deforming forces—is investigated. Individual as well as combined empirical models of the parameters with regard to the forces have been formed. The results of this study indicatethat the average resultant force primarily depends on the floor thickness to be deformed and the incremental depth in the tool path. This could be due to the variation in local stiffness of the sheet with change in floor thickness. The effect of tool diameter, deforming wall angle, and floor size is not significant.
Intracrystalline deformation of calcite
de Bresser, Hans
1991-01-01
It is well established from observations on natural calcite tectonites that intracrystalline plastic mechanisms are important during the deformation of calcite rocks in nature. In this thesis, new data are presented on fundamental aspects of deformation behaviour of calcite under conditions where 'd
The Spherical Deformation Model
DEFF Research Database (Denmark)
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...
On Cartesian Prosucts ofα-Topological Spaces%α拓扑空间的乘积性
Institute of Scientific and Technical Information of China (English)
龚亚英
2014-01-01
In this paper,the author has investigatedα-closure,α-interior andα-boundary ofα-topological space (X,Tα).The author obtains Tαα=Tαand Cartesian products ofα-topological spaces.%研究了由拓扑空间(X,T)诱导出的α拓扑空间(X,Tα)中的α闭包、α内部、α边界,证明了Tα=Tα,得到了α拓扑空间的乘积性,研究了αT2空间的一些性质。
Institute of Scientific and Technical Information of China (English)
GONG Yan-Jun; WU Zhen-Sen; WU Jia-Ji
2009-01-01
We present an analytical model of Doppler spectra in backscattering from arbitrary rough convex bodies of revolution rotating around their axes in the global Cartesian coordinate system. This analytical model is applied to analyse Doppler spectra in backscatter from two cones and two cylinders, as well as two ellipsoids of revolution. We numerically analyse the influences of attitude and geometry size of objects on Doppler spectra. The analytical model can give contribution of the surface roughness, attitude and geometry size of convex bodies of revolution to Doppler spectra and may contribute to laser Doppler velocimetry as well as ladar applications.
Deformations of Superconformal Theories
Cordova, Clay; Intriligator, Kenneth
2016-01-01
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \\geq 3$ 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 deformat...
Deformation mechanisms in experimentally deformed Boom Clay
Desbois, Guillaume; Schuck, Bernhard; Urai, Janos
2016-04-01
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
Verma, Siddhartha; Novati, Guido; Koumoutsakos, Petros
2016-01-01
The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self-propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers, and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body-fitted grids are used. Alternatively, such simulations may employ penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow- induced forces on the surface of both rigid and deforming bodies, in simulations using re-...
Finley, Dennis B.; Karman, Steve L., Jr.
1996-01-01
The objective of the second phase of the Euler Technology Assessment program was to evaluate the ability of Euler computational fluid dynamics codes to predict compressible flow effects over a generic fighter wind tunnel model. This portion of the study was conducted by Lockheed Martin Tactical Aircraft Systems, using an in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaption of the volume grid during the solution to resolve high-gradient regions. The SPLITFLOW code predictions of configuration forces and moments are shown to be adequate for preliminary design, including predictions of sideslip effects and the effects of geometry variations at low and high angles-of-attack. The transonic pressure prediction capabilities of SPLITFLOW are shown to be improved over subsonic comparisons. The time required to generate the results from initial surface data is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.
Li, Bin; Miller, William H
2012-10-21
A new classical model for the general second-quantized many-electron Hamiltonian in Cartesian coordinates and momenta is presented; this makes semiclassical (SC) calculations using an initial value representation (IVR) more useful than the classical Hamiltonian in action-angle variables given earlier by Miller and White [J. Chem. Phys. 84, 5059-5066 (1986)]. If only 1-electron terms are included in this Hamiltonian, the classical equations of motion for the Cartesian variables are linear, and the SC-IVR gives exact results for the propagator (and thus for transition probabilities, the energy spectrum, etc.), as confirmed by analytic proof and numerical calculations. Though this new Hamiltonian is not exact when 2-electron interactions are included, we observe good results for the SC-IVR transition probabilities for times that are not too long. Test calculations, for example, show that the SC-IVR is accurate for times long enough to obtain good result for the eigenvalue spectrum (i.e., the energy levels of the electronic system).
Evans, D
1975-08-01
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.
r-MDR CODES AND Pr-MDS CODES ON CARTESIAN PRODUCT CODES%卡氏积码的r-MDR码与P-MDS码
Institute of Scientific and Technical Information of China (English)
唐刚
2012-01-01
In this paper, the r-th generalized Hamming weight with respect to rank and the r-th generalized singleton bound are studied. According to that the subcodes of Cartesian codes are Cartesian codes, we can prove that Cartesian product code of r-MDR(Pr-MDR) code is r-MDR(Pr-MDR) code. Meanwhile the part inverse proposition for the results are given.%本文研究了卡氏积码的r-广义Hamming重量计算公式和广义Singleton界,利用r-卡氏积码的子码仍为卡氏积码,证明了r-MDR码或P-MDR码的卡氏积码仍为r-MDR码或P-MDR码.同时也给出了这一个结果的部分逆命题.
Extremely deformable structures
2015-01-01
Recently, a new research stimulus has derived from the observation that soft structures, such as biological systems, but also rubber and gel, may work in a post critical regime, where elastic elements are subject to extreme deformations, though still exhibiting excellent mechanical performances. This is the realm of ‘extreme mechanics’, to which this book is addressed. The possibility of exploiting highly deformable structures opens new and unexpected technological possibilities. In particular, the challenge is the design of deformable and bi-stable mechanisms which can reach superior mechanical performances and can have a strong impact on several high-tech applications, including stretchable electronics, nanotube serpentines, deployable structures for aerospace engineering, cable deployment in the ocean, but also sensors and flexible actuators and vibration absorbers. Readers are introduced to a variety of interrelated topics involving the mechanics of extremely deformable structures, with emphasis on ...
Deformation in nanocrystalline metals
Helena Van Swygenhoven; Julia R. Weertman
2006-01-01
It is now possible to synthesize polycrystalline metals made up of grains that average less than 100 nm in size. Such nanocrystalline metals contain a significant volume fraction of interfacial regions separated by nearly perfect crystals. The small sizes involved limit the conventional operation of dislocation sources and thus a fundamental question arises: how do these materials deform plastically? We review the current views on deformation mechanisms in nanocrystalline, face-centered cubic...
Deformation quantization of principal bundles
Aschieri, Paolo
2016-01-01
We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles, and more in general to the deformation of Hopf-Galois extensions. First we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next we twist deform a subgroup of the group of authomorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations we obtain noncommutative principal bundles with noncommutative fiber and base space as well.
Hamilton, Scott; Hamilton, Trevor J
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes's "radical" or "mind-body" dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes's famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student's understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student's understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur.
Blanc, Emilie; Chiavassa, Guillaume; Lombard, Bruno
2014-10-01
A time-domain numerical modeling of transversely isotropic Biot poroelastic waves is proposed in two dimensions. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency. In the time-domain, these coefficients introduce shifted fractional derivatives of order 1/2, involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations, resulting in the Biot-DA (diffusive approximation) model. The properties of both the Biot-JKD and the Biot-DA models are analyzed: hyperbolicity, decrease of energy, dispersion. To determine the coefficients of the diffusive approximation, two approaches are analyzed: Gaussian quadratures and optimization methods in the frequency range of interest. The nonlinear optimization is shown to be the better way of determination. A splitting strategy is then applied to approximate numerically the Biot-DA equations. The propagative part is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. An immersed interface method is implemented to take into account heterogeneous media on a Cartesian grid and to discretize the jump conditions at interfaces. Numerical experiments are presented. Comparisons with analytical solutions show the efficiency and the accuracy of the approach, and some numerical experiments are performed to investigate wave phenomena in complex media, such as multiple scattering across a set of random scatterers.
Cerezo, Javier; Zúñiga, José; Requena, Alberto; Ávila Ferrer, Francisco J; Santoro, Fabrizio
2013-11-12
When large structural displacements take place between the ground state (GS) and excited state (ES) minima of polyatomic molecules, the choice of a proper set of coordinates can be crucial for a reliable simulation of the vibrationally resolved absorption spectrum. In this work, we study two carotenoids that undergo structural displacements from GS to ES minima of different magnitude, from small displacements for violaxanthin to rather large ones for β-carotene isomers. Their finite-temperature (77 and 300 K) spectra are simulated at the harmonic level, including Duschinsky effect, by time-dependent (TD) and time-independent (TI) approaches, using (TD)DFT computed potential energy surfaces (PES). We adopted two approaches to construct the harmonic PES, the Adiabatic (AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate frames: Cartesian and valence internal coordinates. Our results show that when large displacements take place, Cartesian coordinates dramatically fail to describe curvilinear displacements and to account for the Duschinsky matrix, preventing a realistic simulation of the spectra within the AH model, where the GS and ES PESs are quadratically expanded around their own equilibrium geometry. In contrast, internal coordinates largely amend such deficiencies and deliver reasonable spectral widths. As expected, both coordinate frames give similar results when small displacements occur. The good agreement between VH and experimental line shapes indicates that VH model, in which GS and ES normal modes are both evaluated at the GS equilibrium geometry, is a good alternative to deal with systems exhibiting large displacements. The use of this model can be, however, problematic when imaginary frequencies arise. The extent of the nonorthogonality of the Dushinsky matrix in internal coordinates and its correlation with the magnitude of the displacement of the GS and ES geometries is analyzed in detail.
Hamilton, Scott; Hamilton, Trevor J.
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes’s “radical” or “mind-body” dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes’s famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student’s understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student’s understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur. PMID:26321981
Deformable Simplicial Complexes
DEFF Research Database (Denmark)
Misztal, Marek Krzysztof
In this dissertation we present a novel method for deformable interface tracking in 2D and 3D|deformable simplicial complexes (DSC). Deformable interfaces are used in several applications, such as fluid simulation, image analysis, reconstruction or structural optimization. In the DSC method......, the interface (curve in 2D; surface in 3D) is represented explicitly as a piecewise linear curve or surface. However, the domain is also subject to discretization: triangulation in 2D; tetrahedralization in 3D. This way, the interface can be alternatively represented as a set of edges/triangles separating...... demonstrate those strengths in several applications. In particular, a novel, DSC-based fluid dynamics solver has been developed during the PhD project. A special feature of this solver is that due to the fact that DSC maintains an explicit interface representation, surface tension is more easily dealt with...
Kanada-Enyo, Y
2004-01-01
Systematic analysis of the deformations of proton and neutron densities in even-even C isotopes was done based on the method of antisymmetrized molecular dynamics. The $E2$ transition strength was discussed in relation to the deformation. We analyze the $B(E2;2^+_1\\to 0^+_1)$ in $^{16}$C, which has been recently measured to be abnormally small. The results suggest the difference of the deformations between proton and neutron densities in the neutron-rich C isotopes. It was found that stable proton structure in C isotopes plays an important role in the enhancement the neutron skin structure as well as in the systematics of $B(E2)$ in the neutron-rich C.
Directory of Open Access Journals (Sweden)
Fabiano Stumpf Lutz
2014-12-01
Full Text Available Objective: To present the deformities and evaluate the results of their treatment. Methods: Retrospective study of patients with deformity following surgical access to the spinal canal. Fifteen patients who met the inclusion criteria were included. Patients without complete data in medical records were excluded. Results: Fourteen patients underwent surgical treatment and one patient received conservative treatment with vest type TLSO. The average angle of kyphosis correction was 87° preoperatively to 38° postoperatively, while the associated scoliosis correction was 69° preoperatively to 23° postoperatively. Conclusions: The prevention of deformity should be emphasized to avoid laminectomy alone, while laminoplasty should be the procedure of choice for canal access in surgeries where there is no need for resection of the posterior elements.
Autogenous Deformation of Concrete
DEFF Research Database (Denmark)
Autogenous deformation of concrete can be defined as the free deformation of sealed concrete at a constant temperature. A number of observed problems with early age cracking of high-performance concretes can be attributed to this phenomenon. During the last 10 years , this has led to an increased...... focus on autogenous deformation both within concrete practice and concrete research. Since 1996 the interest has been significant enough to hold international, yearly conferences entirely devoted to this subject. The papers in this publication were presented at two consecutive half-day sessions...... at the American Concrete Institute’s Fall Convention in Phoenix, Arizona, October 29, 2002. All papers have been reviewed according to ACI rules. This publication, as well as the sessions, was sponsored by ACI committee 236, Material Science of Concrete. The 12 presentations from 8 different countries indicate...
Deformation in nanocrystalline metals
Directory of Open Access Journals (Sweden)
Helena Van Swygenhoven
2006-05-01
Full Text Available It is now possible to synthesize polycrystalline metals made up of grains that average less than 100 nm in size. Such nanocrystalline metals contain a significant volume fraction of interfacial regions separated by nearly perfect crystals. The small sizes involved limit the conventional operation of dislocation sources and thus a fundamental question arises: how do these materials deform plastically? We review the current views on deformation mechanisms in nanocrystalline, face-centered cubic metals based on insights gained by atomistic computer simulations. These insights are discussed with reference to recent striking experimental observations that can be compared with predictions made by the simulations.
Energy Technology Data Exchange (ETDEWEB)
Bavaro, A. (Soliveri SpA, Caravaggio (Italy))
1990-02-01
Types and causes of heat treatement derived isotropic and anisotropic dilatancies in ferrous materials are reviewed. The concepts are developed in such a way as to allow extension to all materials exhibiting martensitic tempering behaviour. This paper intends to illustrate the basic processes of dimensional variations undergone by the materials under heat treatments. The parametric analysis includes an analysis of the interactions amongst the parameters themselves. The relative importance of each parameter is assessed in order to determine methods to attenuate deformation action. Simplified examples are offered to provide technicians explanations as to why specific deformations occur and indications on improved materials working techniques.
Marginally Deformed Starobinsky Gravity
DEFF Research Database (Denmark)
Codello, A.; Joergensen, J.; Sannino, Francesco
2015-01-01
We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\\alpha)}$, with $R$ the Ricci scalar and $\\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes....
Bhalla, Amneet Pal Singh; Bale, Rahul; Griffith, Boyce E.; Patankar, Neelesh A.
2013-10-01
Many problems of interest in biological fluid mechanics involve interactions between fluids and solids that require the coupled solution of momentum equations for both the fluid and the solid. In this work, we develop a mathematical framework and an adaptive numerical method for such fluid-structure interaction (FSI) problems in which the structure may be rigid, deforming, or elastic. We employ an immersed boundary (IB) formulation of the problem that permits us to avoid body conforming discretizations and to use fast Cartesian grid solvers. Rigidity and deformational kinematic constraints are imposed using a formulation based on distributed Lagrange multipliers, and a conventional IB method is used to describe the elasticity of the immersed body. We use Cartesian grid adaptive mesh refinement (AMR) to discretize the equations of motion and thereby obtain a solution methodology that efficiently captures thin boundary layers at fluid-solid interfaces as well as flow structures shed from such interfaces. This adaptive methodology is validated for several benchmark problems in two and three spatial dimensions. In addition, we use this scheme to simulate free swimming, including the maneuvering of a two-dimensional model eel and a three-dimensional model of the weakly electric black ghost knifefish.
Deformed Algebras and Generalizations of Independence on Deformed Exponential Families
Directory of Open Access Journals (Sweden)
Hiroshi Matsuzoe
2015-08-01
Full Text Available A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems. Though the deformed exponential families are defined by deformed exponential functions, these functions do not satisfy the law of exponents in general. The deformed algebras have been introduced based on the deformed exponential functions. In this paper, after summarizing such deformed algebraic structures, it is clarified how deformed algebras work on deformed exponential families. In fact, deformed algebras cause generalization of expectations. The three kinds of expectations for random variables are introduced in this paper, and it is discussed why these generalized expectations are natural from the viewpoint of information geometry. In addition, deformed algebras cause generalization of independences. Whereas it is difficult to check the well-definedness of deformed independence in general, the κ-independence is always well-defined on κ-exponential families. This is one of advantages of κ-exponential families in complex systems. Consequently, we can well generalize the maximum likelihood method for the κ-exponential family from the viewpoint of information geometry.
Deformation of chlorite in naturally deformed low-grade rocks
Bons, A.J.
1988-01-01
The intracrystalline deformation of chlorite in naturally deformed low-grade rocks was investigated with transmission electron microscopy (TEM). As in other phyllosilicates, the deformation of chlorite is dominated by the (001) slip plane. Slip along this plane is very easy through the generation an
Nonperturbative effects in deformation quantization
Periwal, V
2000-01-01
The Cattaneo-Felder path integral form of the perturbative Kontsevich deformation quantization formula is used to explicitly demonstrate the existence of nonperturbative corrections to na\\"\\i ve deformation quantization.
Postural deformities in Parkinson's disease
Doherty, K.M.; Warrenburg, B.P.C. van de; Peralta, M.C.; Silveira-Moriyama, L.; Azulay, J.P.; Gershanik, O.S.; Bloem, B.R.
2011-01-01
Postural deformities are frequent and disabling complications of Parkinson's disease (PD) and atypical parkinsonism. These deformities include camptocormia, antecollis, Pisa syndrome, and scoliosis. Recognition of specific postural syndromes might have differential diagnostic value in patients prese
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
2005-10-01
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
2009-01-01
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.
Deformation twinning in monazite
Energy Technology Data Exchange (ETDEWEB)
Hay, R.S.; Marshall, D.B
2003-10-20
Polycrystalline monazite (LaPO{sub 4}) was deformed at room temperature by a spherical indenter. Deformation twins were identified by TEM in 70 grains. Five twin planes were found: (100) was by far the most common; (001) and (120) were less common; (122-bar)was rare, and kinks in (120) twins were identified as irrational '(483)' twin planes. The twinning modes on these planes were inferred from the expression of twinning shear at free surfaces, predictions of classical deformation twinning theory, and various considerations of twin morphology and crystal structure. Atomic shuffle calculations that allow formation of either a glide plane or a mirror plane at the twin interface were used to analyze twin modes. The inferred twin modes all have small atomic shuffles. For (001) twins, the smallest shuffles were obtained with a glide plane at the interface, with displacement vector R=((1)/(2))[010]. The results do not uniquely define a twin mode on (100), leaving open the possibility of more than one mode operating on this plane. Factors that may determine the operative deformation twinning modes are discussed. Crystal structure considerations suggest that the relative abundance of twinning modes may correlate with low shear modulus on the twin plane in the direction of twinning shear, and with a possible low-energy interface structure consisting of a layer of xenotime of one half-unit-cell thickness that could form at (100) and (001) twins. The three most common twins have low strains to low {sigma} coincidence site lattices (CSLs)
Localization of plastic deformation
Energy Technology Data Exchange (ETDEWEB)
Rice, J R
1976-04-01
The localization of plastic deformation into a shear band is discussed as an instability of plastic flow and a precursor to rupture. Experimental observations are reviewed, a general theoretical framework is presented, and specific calculations of critical conditions are carried out for a variety of material models. The interplay between features of inelastic constitutive description, especially deviations from normality and vertex-like yielding, and the onset of localization is emphasized.
Strauss, Karl F.; Sheldon, Douglas J.
2011-01-01
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
Hassouna, M Sabry; Farag, A A
2007-09-01
A wide range of computer vision applications require an accurate solution of a particular Hamilton- Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of the point, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.
Trost, Nico; Jiménez, Javier; Imke, Uwe; Sanchez, Victor
2014-06-01
TWOPORFLOW is a thermo-hydraulic code based on a porous media approach to simulate single- and two-phase flow including boiling. It is under development at the Institute for Neutron Physics and Reactor Technology (INR) at KIT. The code features a 3D transient solution of the mass, momentum and energy conservation equations for two inter-penetrating fluids with a semi-implicit continuous Eulerian type solver. The application domain of TWOPORFLOW includes the flow in standard porous media and in structured porous media such as micro-channels and cores of nuclear power plants. In the latter case, the fluid domain is coupled to a fuel rod model, describing the heat flow inside the solid structure. In this work, detailed profiling tools have been utilized to determine the optimization potential of TWOPORFLOW. As a result, bottle-necks were identified and reduced in the most feasible way, leading for instance to an optimization of the water-steam property computation. Furthermore, an OpenMP implementation addressing the routines in charge of inter-phase momentum-, energy- and mass-coupling delivered good performance together with a high scalability on shared memory architectures. In contrast to that, the approach for distributed memory systems was to solve sub-problems resulting by the decomposition of the initial Cartesian geometry. Thread communication for the sub-problem boundary updates was accomplished by the Message Passing Interface (MPI) standard.
Low-dimensional model of turbulent Rayleigh-Benard convection in a Cartesian cell with square domain
Bailon-Cuba, Jorge
2011-01-01
A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The empirical eigenfunctions are obtained from a joint Proper Orthogonal Decomposition (POD) of the velocity and temperature fields using the Snapshot Method on the basis of a direct numerical simulation (DNS). The resulting LDM is a quadratic inhomogeneous system of coupled ordinary differential equations which we use to describe the long-time temporal evolution of the large-scale mode amplitudes for a Rayleigh number of 1e5 and a Prandtl number of 0.7. The truncation to a finite number of degrees of freedom, that does not exceed a number of 310 for the present, requires the additional implementation of an eddy viscosity-diffusivity to capture the missing dissipation of the small-scale modes. The magnitude of this additional dissipation mechanism is determined by requiring statis...
Wu, Xiongwu; Pickard, Frank C.; Brooks, Bernard R.
2016-10-01
Isotropic periodic sum (IPS) is a method to calculate long-range interactions based on the homogeneity of simulation systems. By using the isotropic periodic images of a local region to represent remote structures, long-range interactions become a function of the local conformation. This function is called the IPS potential; it folds long-ranged interactions into a short-ranged potential and can be calculated as efficiently as a cutoff method. It has been demonstrated that the IPS method produces consistent simulation results, including free energies, as the particle mesh Ewald (PME) method. By introducing the multipole homogeneous background approximation, this work derives multipole IPS potentials, abbreviated as IPSMm, with m being the maximum order of multipole interactions. To efficiently calculate the multipole interactions in Cartesian space, we propose a vector relation that calculates a multipole tensor as a dot product of a radial potential vector and a directional vector. Using model systems with charges, dipoles, and/or quadrupoles, with and without polarizability, we demonstrate that multipole interactions of order m can be described accurately with the multipole IPS potential of order 2 or m - 1, whichever is higher. Through simulations with the multipole IPS potentials, we examined energetic, structural, and dynamic properties of the model systems and demonstrated that the multipole IPS potentials produce very similar results as PME with a local region radius (cutoff distance) as small as 6 Å.
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Azmy, Yousry Y., E-mail: snschune@ncsu.edu, E-mail: yyazmy@ncsu.edu [Department of Nuclear Engineering, North Carolina State University, Raleigh, NC (United States); Fournier, Damien; Le Tellier, Romain, E-mail: damien.fournier@cea.fr, E-mail: romain.le-tellier@cea.fr [CEA, DEN, DER/SPRC/LEPh, Cadarache, Saint Paul-lez-Durance (France)
2011-07-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen's benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semi analytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation. (author)
Energy Technology Data Exchange (ETDEWEB)
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
Coco, Armando; Russo, Giovanni
2013-05-01
In this paper we present a numerical method for solving elliptic equations in an arbitrary domain (described by a level-set function) with general boundary conditions (Dirichlet, Neumann, Robin, etc.) on Cartesian grids, using finite difference discretization and non-eliminated ghost values. A system of Ni+Ng equations in Ni+Ng unknowns is obtained by finite difference discretization on the Ni internal grid points, and second order interpolation to define the conditions for the Ng ghost values. The resulting large sparse linear system is then solved by a multigrid technique. The novelty of the papers can be summarized as follows: general strategy to discretize the boundary condition to second order both in the solution and its gradient; a relaxation of inner equations and boundary conditions by a fictitious time method, inspired by the stability conditions related to the associated time dependent problem (with a convergence proof for the first order scheme); an effective geometric multigrid, which maintains the structure of the discrete system at all grid levels. It is shown that by increasing the relaxation step of the equations associated to the boundary conditions, a convergence factor close to the optimal one is obtained. Several numerical tests, including variable coefficients, anisotropic elliptic equations, and domains with kinks, show the robustness, efficiency and accuracy of the approach.
Lyra, W; Klahr, H; Piskunov, N
2007-01-01
We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to show that Cartesian codes are comparable to cylindrical and spherical ones in handling the magnetohydrodynamics of the disk simulations, as the disk-in-a-box models presented here develop and sustain MHD turbulence. We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure. The turbulent stresses depend on the thermal pressure obeying a power law of 0.24+/-0.03, compatible with the value of 0.25 found in shearing box calculations. The ratio of stresses decreased with increasing temperature. We also study the dynamics of boulders in the hydromagnetic turbulence. The vertical turbulent diffusion of the embedded boulders is comparable to the...
Sawada, Ryohto; Ishikawa, Kenichi L
2016-01-01
We report a three-dimensional numerical implementation of multiconfiguration time-dependent Hartree-Fock (MCTDHF) based on a multi-resolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully compute high-harmonic generation (HHG) of H2 and H2O. The present implementation will open a way to the first-principle theoretical study of intense-field and attosecond-pulse induced ultrafast phenomena in general molecules.
Kalinić, Hrvoje; Mihanović, Hrvoje; Cosoli, Simone; Vilibić, Ivica
2015-11-01
In this paper, the Self-Organizing Map (SOM) method was applied to the surface currents data obtained between February and November 2008 by a network of high-frequency (HF) radars in the northern Adriatic. The sensitivity of the derived SOM solutions was tested in respect to the change of coordinate system of the data introduced to the SOM. In one experiment the original radial data measurements were used, and in the other experiment the Cartesian (total) current vectors derived from original radar data were analyzed. Although the computation of SOM solutions was not a demanding task, comparing both neural lattices yielded the nondeterministic polynomial time (NP) problem for which is difficult to propose a solution that will be globally optimal. Thus, we suggested utilizing the greedy algorithm with underlying assumption of 1-to-1 mapping between lattices. The results suggested that such solution could be local, but not global optimum and that the latter assumption could lower the obtained correlations between the patterns. However, without the assumption of 1-to-1 mapping between lattices, correlation between the derived SOM patterns was quite high, indicating that SOM mapping introduced to the radial current vectors and subsequent transformation into Cartesian coordinate system does not significantly affect obtained patterns in comparison to the SOM mapping done on the derived Cartesian current vectors. The documented similarity corroborates the use of total current vectors in various oceanographic studies, as being representative derivative of original radial measurements.
Quantizing Earth surface deformations
Directory of Open Access Journals (Sweden)
C. O. Bowin
2015-03-01
Full Text Available The global analysis of Bowin (2010 used the global 14 absolute Euler pole set (62 Myr history from Gripp and Gordon (1990 and demonstrated that plate tectonics conserves angular momentum. We herein extend that analysis using the more detailed Bird (2003 52 present-day Euler pole set (relative to a fixed Pacific plate for the Earth's surface, after conversion to absolute Euler poles. Additionally, new analytical results now provide new details on upper mantle mass anomalies in the outer 200 km of the Earth, as well as an initial quantizing of surface deformations.
Space Deformations, Surface Deformations and the Opportunities In-Between
Institute of Scientific and Technical Information of China (English)
Daniel Cohen-Or
2009-01-01
In recent years we have witnessed a large interest in surface deformation techniques. This has been a reaction that can be attributed to the ability to develop techniques which are detail-preserving. Space deformation techniques, on the other hand, received less attention, but nevertheless they have many advantages over surface-based techniques. This paper explores the potential of these two approaches to deformation and discusses the opportunities that the fusion of the two may lead to.
A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Bagchi, B. [Calcutta Univ. (India). Dept. of Applied Mathematics; Roy, P.K. [Department of Physics, Haldia Government College, Haldia 721 657, West Bengal (India)
1995-05-08
In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.)).
Castro-Palacio, Juan Carlos; Gimenez, Marcos H; Monsoriu, Juan A
2012-01-01
The mobile acceleration sensor has been used to in Physics experiments on free and damped oscillations. Results for the period, frequency, spring constant and damping constant match very well to measurements obtained by other methods. The Accelerometer Monitor application for Android has been used to get the outputs of the sensor. Perspectives for the Physics laboratory have also been discussed.
Propagator for the general time-dependent harmonic oscillator with application to an ion trap
Energy Technology Data Exchange (ETDEWEB)
Harari, Gal; Ben-Aryeh, Yacob; Mann, Ady [Department of Physics, Technion-Israel Institute of Technology, IL-32000 Haifa (Israel)
2011-12-15
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.
Forced harmonic oscillations of the Euler-Bernoulli beam with resistance forces
Directory of Open Access Journals (Sweden)
Yuriy S. Krutiy
2015-12-01
Full Text Available The important issue in the oscillation theory is the study of resistance impact on oscillatory processes. Unlike the calculations of free oscillations, that reside in determination of natural frequencies and waveshapes and unlike the calculations of forced oscillations far away from resonance, that are performing without reference to friction, the oscillations researches in vicinity of resonance need accounting of friction forces. Special attention is paid to forced transverse fluctuations in beams as an important technical problem for engineering and building. Aim: The aim of the work is constructing of analytical solution of the problem of forced transverse vibrations of a straight rod with constant cross-section, which is under the influence of the harmonic load taking into account external and internal resistances. Materials and Methods: The internal resistance is taken into account using the corrected hypothesis of Kelvin-Voigt which reflects the empirically proven fact about the frequency-independent internal friction in the material. The external friction is also considered as frequency-independent. Results: An analytical solution is built for the differential equation of forced transverse oscillations of a straight rod with constant cross-section which is under the influence of the harmonic load taking into account external and internal resistances. As a result, analytically derived formulae are presented which describe the forced dynamic oscillations and the dynamic internal forces due to the harmonic load applied to the rod thus reducing the problem with any possible fixed ends to the search of unknown integration constants represented in a form of initial parameters.
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
2009-01-01
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.
On Noether's theorem for the invariant of the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru [Department of Physical Engineering, Mie University, Mie 514-8507 (Japan)
2009-11-15
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.
Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Brouard, S; Sokolovski, D
2010-01-01
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.
Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator
Gallagher, I; Nier, F
2008-01-01
Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\\epsilon = -\\partial_x^2 + x^2 + i\\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued function and $\\epsilon > 0$ a small parameter. We define $\\Sigma(\\epsilon)$ as the infimum of the real part of the spectrum of $H_\\epsilon$, and $\\Psi(\\epsilon)^{-1}$ as the supremum of the norm of the resolvent of $H_\\epsilon$ along the imaginary axis. Under appropriate conditions on $f$, we show that both quantities $\\Sigma(\\epsilon)$, $\\Psi(\\epsilon)$ go to infinity as $\\epsilon \\to 0$, and we give precise estimates of the growth rate of $\\Psi(\\epsilon)$. We also provide an example where $\\Sigma(\\epsilon)$ is much larger than $\\Psi(\\epsilon)$ if $\\epsilon$ is small. Our main results are established using variational "hypocoercive" methods, localization techniques and semiclassical subelliptic estimates.
Directory of Open Access Journals (Sweden)
Suchuan Zhong
2016-01-01
Full Text Available The stochastic resonance (SR characteristics of a generalized Langevin linear system driven by a multiplicative noise and a periodically modulated noise are studied (the two noises are correlated. In this paper, we consider a generalized Langevin equation (GLE driven by an internal noise with long-memory and long-range dependence, such as fractional Gaussian noise (fGn and Mittag-Leffler noise (M-Ln. Such a model is appropriate to characterize the chemical and biological solutions as well as to some nanotechnological devices. An exact analytic expression of the output amplitude is obtained. Based on it, some characteristic features of stochastic resonance phenomenon are revealed. On the other hand, by the use of the exact expression, we obtain the phase diagram for the resonant behaviors of the output amplitude versus noise intensity under different values of system parameters. These useful results presented in this paper can give the theoretical basis for practical use and control of the SR phenomenon of this mathematical model in future works.
Demonstration of double EIT using coupled harmonic oscillators and RLC circuits
Harden, Joshua; Serna, Juan D
2010-01-01
Single and double electromagnetically induced transparency in a medium (EIT), consisting of four-level atoms in the inverted-Y configuration, are discussed by using mechanical and electrical analogies. A spring-mass system subject to damping and driven by an external force is used to represent mechanically the four-level atom. The equations of motion of this system are solved analytically, and the revealed single and double EIT studied numerically. On the other hand, three coupled RLC circuits are used, as the electrical analog, to explore and demonstrate experimentally single and double EIT. The simplicity of these two models makes this experiment appropriate for undergraduate students and easy to incorporate into a college physics laboratory.
Differential invariants of feedback transformations for quasi-harmonic oscillation equations
Gritsenko, Dmitry S.; Kiriukhin, Oleg M.
2017-03-01
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].
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W. P.
2009-01-01
For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl...
Modeling a nanocantilever based biosensor using a stochastically perturbed harmonic oscillator
Snyder, Patrick; Serna, Juan D
2013-01-01
A nanoscale biosensor most suitable for clinical purposes could be based on the use of nanocantilevers. These microscopic `diving boards' are coated with binding probes that have an affinity to a specific amino acid, enzyme or protein in the body. The binding probes on the silicon cantilever attract target particles, and as target biomolecules bind to the cantilever, it changes the vibrating frequency of the cantilever. The process of target binding is a random process and hence creates fluctuations in the frequency and damping mechanism of the cantilever. The effect of such fluctuations are given in our model calculations to provide a broader quantitative understanding of nanocantilever biosensors.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
Performance of a quantum heat engine cycle working with harmonic oscillator systems
Institute of Scientific and Technical Information of China (English)
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are dis-cussed in brief.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
Institute of Scientific and Technical Information of China (English)
WANG JianHui; HE JiZhou; MAO ZhiYuan
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are discussed in brief.
Formation and subdivision of deformation structures during plastic deformation
DEFF Research Database (Denmark)
Jakobsen, B.; Poulsen, H.F.; Lienert, U.;
2006-01-01
During plastic deformation of metals and alloys, dislocations arrange in ordered patterns. How and when these self-organization processes take place have remained elusive, because in situ observations have not been feasible. We present an x-ray diffraction method that provided data on the dynamics...... of individual, deeply embedded dislocation structures. During tensile deformation of pure copper, dislocation-free regions were identified. They showed an unexpected intermittent dynamics, for example, appearing and disappearing with proceeding deformation and even displaying transient splitting behavior....... Insight into these processes is relevant for an understanding of the strength and work-hardening of deformed materials....
Rotary deformity in degenerative spondylolisthesis
Energy Technology Data Exchange (ETDEWEB)
Kang, Sung Gwon; Kim, Jeong; Kho, Hyen Sim; Yun, Sung Su; Oh, Jae Hee; Byen, Ju Nam; Kim, Young Chul [Chosun University College of Medicine, Gwangju (Korea, Republic of)
1994-05-15
We studied to determine whether the degenerative spondylolisthesis has rotary deformity in addition to forward displacement. We have made analysis of difference of rotary deformity between the 31 study groups of symptomatic degenerative spondylolisthesis and 31 control groups without any symptom, statistically. We also reviewed CT findings in 15 study groups. The mean rotary deformity in study groups was 6.1 degree(the standard deviation is 5.20), and the mean rotary deformity in control groups was 2.52 degree(the standard deviation is 2.16)(p < 0.01). The rotary deformity can be accompanied with degenerative spondylolisthesis. We may consider the rotary deformity as a cause of symptomatic degenerative spondylolisthesis in case that any other cause is not detected.
Deformation analysis: The Fredericton approach
Vrečko, Anja; Ambrožič, Tomaž
2013-01-01
In this article, the Fredericton approach to deformation analysis is presented. It is possible to use several deformation models to determine the differences between the geodetic observations or between the coordinates of points in geodetic network in more epochs. The most appropriate deformation model has been chosen based on statistical testing and available information about dynamics at the area of interest. First, a theoretical background of the approach ...
Muralidharan, Balaji; Menon, Suresh
2016-09-01
A new adaptive finite volume conservative cut-cell method that is third-order accurate for simulation of compressible viscous flows is presented. A high-order reconstruction approach using cell centered piecewise polynomial approximation of flow quantities, developed in the past for body-fitted grids, is now extended to the Cartesian based cut-cell method. It is shown that the presence of cut-cells of very low volume results in numerical oscillations in the flow solution near the embedded boundaries when standard small cell treatment techniques are employed. A novel cell clustering approach for polynomial reconstruction in the vicinity of the small cells is proposed and is shown to achieve smooth representation of flow field quantities and their derivatives on immersed interfaces. It is further shown through numerical examples that the proposed clustering method achieves the design order of accuracy and is fairly insensitive to the cluster size. Results are presented for canonical flow past a single cylinder and a sphere at different flow Reynolds numbers to verify the accuracy of the scheme. Investigations are then performed for flow over two staggered cylinders and the results are compared with prior data for the same configuration. All the simulations are carried out with both quadratic and cubic reconstruction, and the results indicate a clear improvement with the cubic reconstruction. The new cut-cell approach with cell clustering is able to predict accurate results even at relatively low resolutions. The ability of the high-order cut-cell method in handling sharp geometrical corners and narrow gaps is also demonstrated using various examples. Finally, three-dimensional flow interactions between a pair of spheres in cross flow is investigated using the proposed cut-cell scheme. The results are shown to be in excellent agreement with past studies, which employed body-fitted grids for studying this complex case.
Sunvisson, Helena; Habermann, Barbara; Weiss, Sara; Benner, Patricia
2009-10-01
Using three paradigm cases of persons living with Parkinson's Disease (PD) the authors make a case for augmenting and enriching a Cartesian medical account of the pathophysiology of PD with an enriched understanding of the lived body experience of PD, the lived implications of PD for a particular person's concerns and coping with the illness. Linking and adding a thick description of the lived experience of PD can enrich caregiving imagination and attunement to the patient's possibilities, concerns and constraints. The work of Merleau-Ponty is used to articulate the middle terms of the lived experience of dwelling in a lifeworld. Examining lived experience of embodied intentionality, skilled bodily capacities as highlighted in Merleau-Ponty's non-mechanistic physiology opens new therapeutic, coping and caregiving possibilities. Matching temporal rhythms can decrease the stress of being assisted with activities of daily living. For example, caregivers and patients alike can be taught strategies for extending their lived bodily capacities by altering rhythms, by shifting hyperactivity to different parts of the body and other strategies that change the perceptual experience associated with walking in different environment. A medical account of the pathophysiology of PD is nessessary and useful, but not sufficient for designing caregiving in ways that enrich and extend the existential skills of dwelling of persons with PD. The dominance of mechanistic physiology makes caregivers assume that it is the 'real discourse' about the disease, causing researchers and caregivers alike to overlook the equally real lived experience of the patient which requires different descriptive discourses and different sources of understanding. Lack of dialogue between the two discourses is tragic for patients because caregivers need both in order to provide attuned, effective caregiving.
Deformation of the ABJM Theory
Faizal, Mir
2012-01-01
In this paper we analyse the ABJM theory on deformed spacetime. We show that this theory reduces to a deformed super-Yang-Mills theory when one of the scalar superfields is given a non-vanishing vacuum expectation value. Our analyse is done in N=1 superspace formulism.
Permanent deformation of asphalt mixes
Muraya, P.M.
2007-01-01
This dissertation describes the results of a research that was conducted on the permanent deformation of asphalt mixtures. Central to this research was the separate characterization of the contribution of the aggregate skeleton and the bituminous mortar towards resistance to permanent deformation. T
Metastable vacua and geometric deformations
Amariti, A; Girardello, L; Mariotti, A
2008-01-01
We study the geometric interpretation of metastable vacua for systems of D3 branes at non isolated toric deformable singularities. Using the L^{aba} examples, we investigate the relations between the field theoretic susy breaking and restoration and the complex deformations of the CY singularities.
Deformation of Man Made Objects
Ibrahim, Mohamed
2012-07-01
We introduce a framework for 3D object deformation with primary focus on man-made objects. Our framework enables a user to deform a model while preserving its defining characteristics. Moreover, our framework enables a user to set constraints on a model to keep its most significant features intact after the deformation process. Our framework supports a semi-automatic constraint setting environment, where some constraints could be automatically set by the framework while others are left for the user to specify. Our framework has several advantages over some state of the art deformation techniques in that it enables a user to add new features to the deformed model while keeping its general look similar to the input model. In addition, our framework enables the rotation and extrusion of different parts of a model.
Making Deformable Template Models Operational
DEFF Research Database (Denmark)
Fisker, Rune
2000-01-01
Deformable template models are a very popular and powerful tool within the field of image processing and computer vision. This thesis treats this type of models extensively with special focus on handling their common difficulties, i.e. model parameter selection, initialization and optimization...... published during the Ph.D. project. To put these articles into the general context of deformable template models and to pass on an overview of the deformable template model literature, the thesis starts with a compact survey of the deformable template model literature with special focus on representation....... A proper handling of the common difficulties is essential for making the models operational by a non-expert user, which is a requirement for intensifying and commercializing the use of deformable template models. The thesis is organized as a collection of the most important articles, which has been...
Kagan, Mikhail
2011-01-01
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely powerful problem-solving tool. While the former idea is typically discussed in the context of Newton's Laws, the latter starts with introducing conservation of energy even later. This work presents an elegant example of implementing both aforementioned ideas in the kinematical context, thus providing a "warm-up" introduction to the standard tools used later on in dynamics. Both the choice of the (non-orthogonal) reference frame and the conserved quantities are rather non-standard, yet at the same time quite intuitive to the problem at hand. Two such problems are discussed in detail with two alternative approaches. The first approach does not even require knowledge of calculus. In the appendix, I also present the brute-force solution involving a coupled system of differential equat...
Directory of Open Access Journals (Sweden)
Emílio Borges
2007-04-01
Full Text Available A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational analysis. Examples are given for diatomic and triatomic molecules.
Supersymmetric q-deformed quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
Involvement of valgus hindfoot deformity in hallux valgus deformity in rheumatoid arthritis.
Yamada, Shutaro; Hirao, Makoto; Tsuboi, Hideki; Akita, Shosuke; Matsushita, Masato; Ohshima, Shiro; Saeki, Yukihiko; Hashimoto, Jun
2014-09-01
The involvement of valgus hindfoot deformity in hallux valgus deformity was confirmed in a rheumatoid arthritis case with a destructive valgus hindfoot deformity. Correction of severe valgus, calcaneal lateral offset, and pronated foot deformity instantly normalized hallux valgus deformities postoperatively. Thus, careful hindfoot status evaluation is important when assessing forefoot deformity, including hallux valgus, in rheumatoid arthritis cases.
Perceptual transparency from image deformation.
Kawabe, Takahiro; Maruya, Kazushi; Nishida, Shin'ya
2015-08-18
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.
Inelastic deformation in crystalline rocks
Rahmani, H.; Borja, R. I.
2011-12-01
The elasto-plastic behavior of crystalline rocks, such as evaporites, igneous rocks, or metamorphic rocks, is highly dependent on the behavior of their individual crystals. Previous studies indicate that crystal plasticity can be one of the dominant micro mechanisms in the plastic deformation of crystal aggregates. Deformation bands and pore collapse are examples of plastic deformation in crystalline rocks. In these cases twinning within the grains illustrate plastic deformation of crystal lattice. Crystal plasticity is governed by the plastic deformation along potential slip systems of crystals. Linear dependency of the crystal slip systems causes singularity in the system of equations solving for the plastic slip of each slip system. As a result, taking the micro-structure properties into account, while studying the overall behavior of crystalline materials, is quite challenging. To model the plastic deformation of single crystals we use the so called `ultimate algorithm' by Borja and Wren (1993) implemented in a 3D finite element framework to solve boundary value problems. The major advantage of this model is that it avoids the singularity problem by solving for the plastic slip explicitly in sub steps over which the stress strain relationship is linear. Comparing the results of the examples to available models such as Von Mises we show the significance of considering the micro-structure of crystals in modeling the overall elasto-plastic deformation of crystal aggregates.
Deforming tachyon kinks and tachyon potentials
Afonso, V. I.; Bazeia, D.; Brito, F. A.
2006-01-01
In this paper we investigate deformation of tachyon potentials and tachyon kink solutions. We consider the deformation of a DBI type action with gauge and tachyon fields living on D1-brane and D3-brane world-volume. We deform tachyon potentials to get other consistent tachyon potentials by using properly a deformation function depending on the gauge field components. Resolutions of singular tachyon kinks via deformation and applications of deformed tachyon potentials to scalar cosmology scena...
ROCK DEFORMATION. Final Progress Report
Energy Technology Data Exchange (ETDEWEB)
None
2002-05-24
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.
Shape Deformations in Atomic Nuclei
Hamamoto, Ikuko
2011-01-01
The ground states of some nuclei are described by densities and mean fields that are spherical, while others are deformed. The existence of non-spherical shape in nuclei represents a spontaneous symmetry breaking.
Plastic Deformation of Metal Surfaces
DEFF Research Database (Denmark)
Hansen, Niels; Zhang, Xiaodan; Huang, Xiaoxu
2013-01-01
parameters by TEM and EBSD and apply strength-structural relationships established for the bulk metal deformed to high strains. This technique has been applied to steel deformed by high energy shot peening and a calculated stress gradient at or near the surface has been successfully validated by hardness......Plastic deformation of metal surfaces by sliding and abrasion between moving parts can be detrimental. However, when the plastic deformation is controlled for example by applying different peening techniques hard surfaces can be produced which can increase the fracture resistance and fatigue life...... of metal components. An optimization of processes and material parameters must be based on a quantification of stress and strain gradients at the surface and in near surface layer where the structural scale can reach few tens of nanometers. For such fine structures it is suggested to quantify structural...
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
Deformed Calabi-Yau Completions
Keller, Bernhard
2009-01-01
We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories. Important examples are: deformed preprojective algebras of connected non Dynkin quivers, Ginzburg dg algebras associated to quivers with potentials and dg categories associated to the category of coherent sheaves on the canonical bundle of a smooth variety. We show that deformed Calabi-Yau completions do have the Calabi-Yau property and that their construction is compatible with derived equivalences and with localizations. In particular, Ginzburg dg algebras have the Calabi-Yau property. We show that deformed 3-Calabi-Yau completions of algebras of global dimension at most 2 are quasi-isomorphic to Ginzburg dg algebras and apply this to the study of cluster-tilted algebras and to the construction of derived equivalences associated to mutations of quivers with potentials. In the appendix, Michel Van den Bergh uses non commutative differential geometry to give an alternative proof of the fac...
Properties of deformed Λ hypernuclei
Institute of Scientific and Technical Information of China (English)
ZHOU Xian-Rong
2009-01-01
The properties of Be and B isotopes and the corresponding Λ hypernuclei are studied by using a deformed Skyrme Hartree-Fock approach with realistic nucleonic Skyrme forces, pairing correlations, and a microscopically determined lambda-nucleon interaction based on Brueckner-Hartree-Fock calculations of hypernuclear matter. The results suggest that the core nuclei and the corresponding hypernuclei have similar deformations with the same sign.
Symmetries in Connection Preserving Deformations
Directory of Open Access Journals (Sweden)
Christopher M. Ormerod
2011-05-01
Full Text Available e wish to show that the root lattice of Bäcklund transformations of the q-analogue of the third and fourth Painlevé equations, which is of type (A_2+A_1^{(1}, may be expressed as a quotient of the lattice of connection preserving deformations. Furthermore, we will show various directions in the lattice of connection preserving deformations present equivalent evolution equations under suitable transformations. These transformations correspond to the Dynkin diagram automorphisms.
机器人手臂笛卡尔空间轨迹计算机仿真规划%Cartesian Space Trajectory of Robot Arm Computer Simulation Program
Institute of Scientific and Technical Information of China (English)
周源
2016-01-01
This paper mainly studies based on Cartesian robot arm joint space trajectory planning problems.By com-puter under the environment of MATLAB software for computer simulation test of the algorithm,continuously and smoothly making the planning of the trajectory path so as to ensure the stability of the robot movement,verify that the algorithm feasi-bi-lity in the process of the machine arm trajectory planning.The major disscussion was based on the Cartesian robot arm empty movement trajectory planning and path generation method.%研究了基于机器人手臂关节笛卡尔空间的轨迹规划问题。通过在MATLAB软件环境下对该算法的计算机仿真测试试验，使规划的轨迹路径连续而平滑，从而保证机器人运动的平稳性，验证该算法在机器手臂轨迹规划过程中的可行性。重点讨论基于机器人手臂笛卡儿空间运动的轨迹规划和轨迹生成方法。
Götze, Jan P; Karasulu, Bora; Thiel, Walter
2013-12-21
We address the effects of using Cartesian or internal coordinates in the adiabatic Franck-Condon (AFC) and vertical Franck-Condon (VFC) approaches to electronic spectra. The adopted VFC approach is a simplified variant of the original approach [A. Hazra, H. H. Chang, and M. Nooijen, J. Chem. Phys. 151, 2125 (2004)], as we omit any contribution from normal modes with imaginary frequency. For our test molecules ranging from ethylene to flavin compounds, VFC offers several advantages over AFC, especially by preserving the properties of the FC region and by avoiding complications arising from the crossing of excited-state potential surfaces or from the failure of the harmonic approximation. The spectral quality for our target molecules is insensitive to the chosen approach. We also explore the effects of Duschinsky rotation and relate the need for internal coordinates to the absence of symmetry elements. When using Duschinsky rotation and treating larger systems without planar symmetry, internal coordinates are found to outperform Cartesian coordinates in the AFC spectral calculations.
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
Kaercher, P. M.; Zepeda-Alarcon, E.; Prakapenka, V.; Kanitpanyacharoen, W.; Smith, J.; Sinogeikin, S. V.; Wenk, H. R.
2014-12-01
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.
Bilateral cleft lip nasal deformity
Directory of Open Access Journals (Sweden)
Singh Arun
2009-01-01
Full Text Available 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
Deformation of second and third quantization
Faizal, Mir
2015-03-01
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.
Deformation of Second and Third Quantization
Faizal, Mir
2015-01-01
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.
Mixing of discontinuously deforming media
Smith, L. D.; Rudman, M.; Lester, D. R.; Metcalfe, G.
2016-02-01
Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations—such as shear banding or wall slip—creates new mechanisms for mixing and transport beyond those predicted by classical dynamical systems theory. Here, we show how a novel mixing mechanism combining stretching with cutting and shuffling yields exponential mixing rates, quantified by a positive Lyapunov exponent, an impossibility for systems with cutting and shuffling alone or bounded systems with stretching alone, and demonstrate it in a fluid flow. While dynamical systems theory provides a framework for understanding mixing in smoothly deforming media, a theory of discontinuous mixing is yet to be fully developed. New methods are needed to systematize, explain, and extrapolate measurements on systems with discontinuous deformations. Here, we investigate "webs" of Lagrangian discontinuities and show that they provide a template for the overall transport dynamics. Considering slip deformations as the asymptotic limit of increasingly localised smooth shear, we also demonstrate exactly how some of the new structures introduced by discontinuous deformations are analogous to structures in smoothly deforming systems.
The Crossing Numbers of Cartesian Products of Paths with 6-Vertex Graphs%6-阶图与路的笛卡儿积交叉数
Institute of Scientific and Technical Information of China (English)
王晶; 黄元秋
2005-01-01
图的交叉数是指把图画在平面上边与边产生的交叉数目的最小值.图的交叉数只在好画法中得到,好画法是指满足边自身不交叉,相关联的边不交叉,任意两条交叉的边至多交叉一次的画法.图的交叉数已被证明是一个NP-完全问题,由于其难度,要知道图的确切交叉数是非常困难的.到目前为止,只知道少数图的交叉数,其中大部分是特殊图的笛卡儿积图的交叉数,比如路,圈以及星图与点数较"少"的图的笛卡儿积交叉数.在这些基础上,应用数学归纳法,把相关结果拓展到4个6-阶图与长为的路的笛卡儿积交叉数.%The crossing number of a graph is the minimum number of pairwise intersections of edges in a drawing of in the plane. It is well known that the crossing number of a graph is attained only in good drawings ofthe graph, which are those drawings where no edge crosses itself, no adjacent edges cross each other, and no two edges intersect more than once. Computing the crossing number of a given graph hasbeen proved to be NP-complete. It is very difficult to determine the exact crossing number of a given graph for its complicity. The crossing numbers of few families of graphs are known so far, most of which are Cartesian Products of special graphs, such as Cartesian Products of paths,cycles or stars with "small" vertex graphs. On these basis,this paper extends the results to the Cartesian Products of paths of length with four special 6-vertex graphs by using the induction method.
Finite Deformation of Magnetoelastic Film
Energy Technology Data Exchange (ETDEWEB)
Barham, Matthew Ian [Univ. of California, Berkeley, CA (United States)
2011-05-31
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.
Shock metamorphism of deformed quartz
Gratz, Andrew J.; Christie, John; Tyburczy, James; Ahrens, Thomas; Pongratz, Peter
1988-01-01
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.
On deformations of triangulated models
De Deken, Olivier
2012-01-01
This paper is the first part of a project aimed at understanding deformations of triangulated categories, and more precisely their dg and A infinity models, and applying the resulting theory to the models occurring in the Homological Mirror Symmetry setup. In this first paper, we focus on models of derived and related categories, based upon the classical construction of twisted objects over a dg or $A_{\\infty}$-algebra. For a Hochschild 2 cocycle on such a model, we describe a corresponding "curvature compensating" deformation which can be entirely understood within the framework of twisted objects. We unravel the construction in the specific cases of derived A infinity and abelian categories, homotopy categories, and categories of graded free qdg-modules. We identify a purity condition on our models which ensures that the structure of the model is preserved under deformation. This condition is typically fulfilled for homotopy categories, but not for unbounded derived categories.
Mixing of discontinuously deforming media
Smith, Lachlan D; Lester, Daniel R; Metcalfe, Guy
2016-01-01
Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations - such as shear banding or wall slip - creates new mechanisms for mixing and transport beyond those predicted by classical dynamical systems theory. Here we show how a novel mixing mechanism combining stretching with cutting and shuffling yields exponential mixing rates, quantified by a positive Lyapunov exponent, an impossibility for systems with cutting and shuffling alone or bounded systems with stretching alone, and demonstrate it in a fluid flow. While dynamical systems theory provides a framework for understanding mixing in smoothly deforming media, a theory of discontinuous mixing is yet to be fully developed. New methods are needed to systematize, explain and extrapolate measurements on systems with discontinuous deformations. Here we investigate 'webs' of Lagrangian discontinuities and show that they provide a template for the overall transport dynamics. Considering sl...
Computing layouts with deformable templates
Peng, Chihan
2014-07-27
In this paper, we tackle the problem of tiling a domain with a set of deformable templates. A valid solution to this problem completely covers the domain with templates such that the templates do not overlap. We generalize existing specialized solutions and formulate a general layout problem by modeling important constraints and admissible template deformations. Our main idea is to break the layout algorithm into two steps: a discrete step to lay out the approximate template positions and a continuous step to refine the template shapes. Our approach is suitable for a large class of applications, including floorplans, urban layouts, and arts and design. Copyright © ACM.
Cavity coalescence in superplastic deformation
Energy Technology Data Exchange (ETDEWEB)
Stowell, M.J.; Livesey, D.W.; Ridley, N.
1984-01-01
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.
Deforming baryons into confining strings
Hartnoll, S A; Hartnoll, Sean A.; Portugues, Ruben
2004-01-01
We find explicit probe D3-brane solutions in the infrared of the Maldacena-Nunez background. The solutions describe deformed baryon vertices: q external quarks are separated in spacetime from the remaining N-q. As the separation is taken to infinity we recover known solutions describing infinite confining strings in ${\\mathcal{N}}=1$ gauge theory. We present results for the mass of finite confining strings as a function of length. We also find probe D2-brane solutions in a confining type IIA geometry, the reduction of a G_2 holonomy M theory background. The interpretation of these solutions as deformed baryons/confining strings is not as straightforward.
Space-based monitoring of ground deformation
Nobakht Ersi, Fereydoun; Safari, Abdolreza; Gamse, Sonja
2016-07-01
Ground deformation monitoring is valuable to understanding of the behaviour of natural phenomena. Space-Based measurement systems such as Global Positioning System are useful tools for continuous monitoring of ground deformation. Ground deformation analysis based on space geodetic techniques have provided a new, more accurate, and reliable source of information for geodetic positioning which is used to detect deformations of the Ground surface. This type of studies using displacement fields derived from repeated measurments of space-based geodetic networks indicates how crucial role the space geodetic methods play in geodynamics. The main scope of this contribution is to monitor of ground deformation by obtained measurements from GPS sites. We present ground deformation analysis in three steps: a global congruency test on daily coordinates of permanent GPS stations to specify in which epochs deformations occur, the localization of the deformed GPS sites and the determination of deformations.
Directory of Open Access Journals (Sweden)
Jiran L.
2016-06-01
Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.
Highly deformable nanofilaments in flow
Pawłowska, S.
2016-10-01
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.
Bethe ansatz and Isomonodromic deformations
Talalaev, D
2008-01-01
We study symmetries of the Bethe equations for the Gaudin model appeared naturally in the framework of the geometric Langlands correspondence under the name of Hecke operators and under the name of Schlesinger transformations in the theory of isomonodromic deformations, and particularly in the theory of Painlev\\'e transcendents.
Dotsenko, V.; Shadrin, S.; Vallette, B.
2016-01-01
In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for preLie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this case, we provide a homotopical description of the associated
Deformable Models for Eye Tracking
DEFF Research Database (Denmark)
Vester-Christensen, Martin; Leimberg, Denis; Ersbøll, Bjarne Kjær;
2005-01-01
A deformable template method for eye tracking on full face images is presented. The strengths of the method are that it is fast and retains accuracy independently of the resolution. We compare the me\\$\\backslash\\$-thod with a state of the art active contour approach, showing that the heuristic...
Some Results of the Cartesian Composition of Fuzzy Finite State Machines%模糊有限状态机笛卡尔合成的一些结果
Institute of Scientific and Technical Information of China (English)
杨京开
2012-01-01
In this paper, some properties of the cartesian composition of fuzzy finite state machines are discussed utilizing algebraic techniques, the cartesian composition of fuzzy finite state machines satisfy commutative law and associative law in the sense of strong isomorphism are obtained, the similar properties between the cartesian composition of fuzzy finite state machines and the factors in subsystem (strong subsystem), free subset, basis and so on are discussed, a decomposition theorem for the cartesian composition of fuzzy finite state machines in terms of primary submachines is given, the admissible relation of the cartesian composition of fuzzy finite state machines under the projection mapping is the factors's admissible relations is proved.%讨论了模糊有限状态机的笛卡尔合成的一些性质,得到了模糊有限状态机的笛卡尔合成在强同构意义下满足交换律,结合律,讨论了模糊有限状态机的笛卡尔合成与其因子在子系统(强子系统),自由子集,基等方面的相似的结构性质,给出了模糊有限状态机的笛卡尔合成的准素子机分解,证明了模糊有限状态机的笛卡尔合成的容许关系的投影是其因子的容许关系.
Highly deformable bones: unusual deformation mechanisms of seahorse armor.
Porter, Michael M; Novitskaya, Ekaterina; Castro-Ceseña, Ana Bertha; Meyers, Marc A; McKittrick, Joanna
2013-06-01
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.
Prediction of deformity in spinal tuberculosis
Jutte, Paul; Wuite, Sander; The, Bertram; van Altena, Richard; Veldhuizen, Albert
2007-01-01
Tuberculosis of the spine may cause kyphosis, which may in turn cause late paraplegia, respiratory compromise, and unsightly deformity. Surgical correction therefore may be considered for large or progressive deformities. We retrospectively analyzed clinical and radiographic parameters to predict th
Airborne Repeat Pass Interferometry for Deformation Measurements
Groot, J.; Otten, M.; Halsema, E. van
2000-01-01
In ground engineering the need for deformation measurements is urgent. SAR interferometry can be used to measure small (sub-wavelength) deformations. An experiment to investigate this for dike deformations was set up, using the C-band SAR system PHARUS (PHased ARray Universal SAR). This paper descri
Variational approach and deformed derivatives
Weberszpil, J.; Helayël-Neto, J. A.
2016-05-01
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.
Variational Approach and Deformed Derivatives
Weberszpil, José
2015-01-01
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 Nether current, are worked out.
Molecular deformation mechanisms in polyethylene
Coutry, S
2001-01-01
adjacent labelled stems is significantly larger when the DPE guest is a copolymer molecule. Our comparative studies on various types of polyethylene lead to the conclusion that their deformation behaviour under drawing has the same basis, with additional effects imputed to the presence of tie-molecules and branches. Three major points were identified in this thesis. The changes produced by drawing imply (1) the crystallisation of some of the amorphous polymer and the subsequent orientation of the newly formed crystals, (2) the re-orientation of the crystalline ribbons and (3) the beginning of crystallite break-up. However, additional effects were observed for the high molecular weight linear sample and the copolymer sample and were attributed, respectively, to the presence of tie-molecules and of branches. It was concluded that both the tie-molecules and the branches are restricting the molecular movement during deformation, and that the branches may be acting as 'anchors'. This work is concerned with details...
Deformation of noncommutative quantum mechanics
Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan
2016-09-01
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 .
Deformation quantization and Nambu mechanics
Dito, G; Sternheimer, D; Takhtajan, L A; Dito, Giuseppe; Flato, Moshe; Sternheimer, Daniel; Takhtajan, Leon
1996-01-01
Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After considering some impossibilities and pushing some analogies with field quantization, a solution to the quantization problem is presented in what we call the Zariski quantization of fields (observables, functions, in this case polynomials). This quantization is based on the factorization over {\\Bbb R} of polynomials in several real variables. We quantize the algebra of fields generated by the polynomials by defining a deformation of this algebra which is Abelian, associative and distributive. This procedure is then adapted to derivatives (needed for the Nambu brackets), which ensures the validity of the Fundamental Identity of Nambu Mechanics also at the quantum level. Our construction is in fact more general than the particular case considered here: it can be utilized for quite general defining identities and for much more general star-products.
Constructal Hypothesis for Mechanical Deformation
Directory of Open Access Journals (Sweden)
Atanu Chatterjee
2012-08-01
Full Text Available Mild Steel specimen, when subjected to tensile forces shows considerable plastic deformation before fracture. A cross-section of the fractured specimen has the familiar cup – cone form and shows traces of a three – dimensional parabolic geometry. The morphing of the steel specimen from a volume to a point as a spontaneous, entropy producing or energy dispersing process is analysed using the Constructal law.
Spinal deformities in tall girls.
Skogland, L B; Steen, H; Trygstad, O
1985-04-01
In a prospective study, 62 girls who consulted the paediatric department because of tall stature were examined for spinal deformities. Thirteen cases of scoliosis measuring 10 degrees or more were found. Eighteen girls had a thoracic kyphosis of more than 40 degrees and 11 had additional vertebral abnormalities indicating Scheuermann's disease. The incidence of scoliosis and Scheuermann's disease was much higher in our material than normal.
Deformation Driven Alloying and Transformation
2015-03-03
Rolling, Acta Materiala (08 2014) Zhe Wang , John H Perepezko, David Larson, David Reinhard. Mixing Behaviors in Cu/Ni and Ni/V Multilayers Induced...by Cold Rolling, Journal of Alloys and Compounds (07 2014) Zhe Wang , John H. Perepezko. Deformation-Induced Nanoscale Mixing Reactions in Cu/Ni...FTE Equivalent: Total Number: Discipline Zhe Wang 0.50 0.50 1 Names of Post Doctorates Names of Faculty Supported Names of Under Graduate students
Deformations of extremal toric manifolds
Rollin, Yann
2012-01-01
Let $X$ be a compact toric extremal K\\"ahler manifold. Using the work of Sz\\'ekelyhidi, we provide a simple criterion on the fan describing $X$ to ensure the existence of complex deformations of $X$ that carry extremal metrics. As an example, we find new CSC metrics on 4-points blow-ups of $\\C\\P^1\\times\\C\\P^1$.
Quantification and validation of soft tissue deformation
DEFF Research Database (Denmark)
Mosbech, Thomas Hammershaimb; Ersbøll, Bjarne Kjær; Christensen, Lars Bager
2009-01-01
We present a model for soft tissue deformation derived empirically from 10 pig carcases. The carcasses are subjected to deformation from a known single source of pressure located at the skin surface, and the deformation is quantified by means of steel markers injected into the tissue. The steel...... markers are easy to distinguish from the surrounding soft tissue in 3D computed tomography images. By tracking corresponding markers using methods from point-based registration, we are able to accurately quantify the magnitude and propagation of the induced deformation. The deformation is parameterised...
Stochastic deformation of a thermodynamic symplectic structure
Kazinski, P. O.
2009-01-01
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation is analogous to the deformation of an algebra of observables such as deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered.
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Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2015-06-15
We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformed oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.