International Nuclear Information System (INIS)
We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by using a deformed Cartesian harmonic oscillator basis. The complete list of expressions required to calculate local densities, total energy, and self-consistent fields is presented, and an implementation of the self-consistent symmetries is discussed. Formulas to calculate matrix elements in the Cartesian harmonic oscillator basis are derived for the nuclear and Coulomb interactions. (authors)
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.
Deformed quantum harmonic oscillator with diffusion and dissipation
ISAR, A.; Scheid, W.
2007-01-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator i...
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...
International Nuclear Information System (INIS)
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.
q-Deformed Harmonic Oscillator in Phase Space
Aringazin, A K; Baskoutas, S; Brodimas, G; Jannussis, A; Vlachos, E
1993-01-01
Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation and annihilation operators, both the usual and $q$-deformed, is investigated. We found that the Bopp-Kubo formulation is just non-commuting coordinates representation of the symbol calculus. The Wigner operator for the $q$-deformed harmonic oscillator is shown to be proportional to the 3-axis spherical angular momentum operator of the algebra $su_{q}(2)$. The relation of the Fock space for the harmonic oscillator and double Hilbert space of the Gelfand-Naimark-Segal construction is established. The quantum extension of the classical ergodiicity condition is proposed.
Macroscopic detection of deformed QM by the harmonic oscillator
Maziashvili, Michael
2016-01-01
Based on the nonperturbative analysis, we show that the classical motion of harmonic oscillator derived from the deformed QM is manifestly in contradiction with observations. For this reason, we take an alternate way for estimating the effect and discuss its possible observational manifestations in macrophysics.
First, Second Quantization and Q-Deformed Harmonic Oscillator
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2015-06-01
Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed.
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
RLC circuit realization of a q-deformed harmonic oscillator with time dependent mass
International Nuclear Information System (INIS)
We consider an RLC circuit type realization of a q-deformed harmonic oscillator. The differential equations of motion characterizing this circuit are derived, and it is shown that the RLC circuit gets modified as a result of the q-deformation. The natural frequency, the capacitance and the external power source are all modified and become q-dependent. The energy aspects of the circuit are also studied and the effects of the deformation are shown. - Highlights: • Classically q-deformed harmonic oscillators are equivalent to driven oscillators. • RLC circuit realization of q-deformed harmonic oscillators is derived. • A mass dependent q-deformed harmonic oscillator is used for this realization. • The capacitance and natural frequency are modified because of the deformation. • Energy aspects of the circuit are studied and the effect of deformation is observed
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.
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 ...
Interbasis expansions for isotropic harmonic oscillator
International Nuclear Information System (INIS)
The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n. -- Highlights: ► Exact solutions of harmonic oscillator are reviewed in three coordinates. ► Interbasis expansions of the eigenfunctions is solved completely. ► This is occurred only for those degenerated states for given quantum number n.
Stoitsov, M. V.; Dobaczewski, J.; Nazarewicz, W.; Ring, P.
2005-04-01
We describe the program HFBTHO for axially deformed configurational Hartree-Fock-Bogolyubov calculations with Skyrme-forces and zero-range pairing interaction using Harmonic-Oscillator and/or Transformed Harmonic-Oscillator states. The particle-number symmetry is approximately restored using the Lipkin-Nogami prescription, followed by an exact particle number projection after the variation. The program can be used in a variety of applications, including systematic studies of wide ranges of nuclei, both spherical and axially deformed, extending all the way out to nucleon drip lines. Program summaryTitle of the program: HFBTHO (v1.66p) Catalogue number: ADUI Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI Licensing provisions: none Computers on which the program has been tested: Pentium-III, Pentium-IV, AMD-Athlon, IBM Power 3, IBM Power 4, Intel Xeon Operating systems: LINUX, Windows Programming language used: FORTRAN-95 Memory required to execute with typical data: 59 MB when using N=20 No. of bits in a word: 64 No. of processors used: 1 Has the code been vectorized?: No No. of bytes in distributed program, including test data, etc.: 195 285 No. of lines in distributed program: 12 058 Distribution format: tar.gz Nature of physical problem: The solution of self-consistent mean-field equations for weakly bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasiparticle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the Transformed Harmonic Oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines. Method of solution: The program uses the axially Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes
On detecting harmonic oscillations
Juditsky, Anatoli; Nemirovski, Arkadi
2013-01-01
In this paper, we focus on the following testing problem: assume that we are given observations of a real-valued signal along the grid $0,1,\\ldots,N-1$, corrupted by white Gaussian noise. We want to distinguish between two hypotheses: (a) the signal is a nuisance – a linear combination of $d_{n}$ harmonic oscillations of known frequencies, and (b) signal is the sum of a nuisance and a linear combination of a given number $d_{s}$ of harmonic oscillations with unknown frequencies, and such that...
Harmonic oscillator with complex frequency
International Nuclear Information System (INIS)
In the present paper it is studied the problem of the harmonic oscillator with complex frequency. A special case of this problem is the determination of the eigenvalues and eigenfunctions of the squeeze operator in quantum optics. The Hamilton operator of the complex harmonic oscillator is non-Hermitian and its study leads to the Lie-admissible theory. Because of the complex frequency the eigenvalues of the energy are complex numbers and the partition function of Boltzman and the free energy of Helmoltz are complex functions. Especially the imaginary part of the free energy describes the metastable states
Harmonic oscillator: an analysis via Fourier series
de Castro, A. S.
2013-01-01
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.
Stoitsov, M V; Kortelainen, M; Michel, N; Nam, H; Olsen, E; Sarich, J; Wild, S
2012-01-01
We describe the new version 2.00c of the code HFBTHO that solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (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.
Quantum Dynamics of a Harmonic Oscillator in a Defomed Bath in the Presence of Lamb Shift
Daeimohamad, M.; Mohammadi, M.
2012-10-01
In this paper, we investigate the dissipative quantum dynamics of a harmonic oscillator in the presence a deformed bath by considering the Lamb shift term. The deformed bath is modelled by a collection of deformed quantum harmonic oscillators as a generalization of Hopfield model. The Langevin equation for both the photon number and the fluctuation spectrum under the Weisskopf-Winger approximation are obtained and discussed.
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
Argand diagrams, harmonic oscillators, and record-playing tonearms
Piccard, Richard D.
1986-04-01
The complex analysis of the driven, damped, harmonic oscillator is reviewed for the specific case that the driving force is produced by ``wiggling the other end of the spring,'' a case which many find intuitively appealing. The solution is examined using the Cartesian and polar presentations in the complex plane. The record-playing tonearm is particularly suited as a ``practical example'' because it naturally leads to a question that is much easier to answer in terms of the Argand diagram: What will the cartridge output be?
Quantum wormholes and harmonic oscillators
Garay, Luis J.
1993-01-01
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.
Pisot q-coherent states quantization of the harmonic oscillator
International Nuclear Information System (INIS)
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0−1 is a quadratic unit Pisot number, since then the q-deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: ► Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. ► For q,0< q<1 these normalized states form an overcomplete set that resolves the unity with respect to an explicit measure. ►q-Deformed numbers are Fibonacci-like integer sequences (1/q a quadratic unit Pisot number). ► We examine the main physical characteristics of the corresponding quantum oscillator.
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, ...
Supersymmetric partners of the truncated harmonic oscillator
International Nuclear Information System (INIS)
First and second order supersymmetric transformations are applied to the truncated harmonic oscillator to generate new Hamiltonians with known spectra. We also study the effect of these transformations on the eigenfunctions of the initial Hamiltonian. Finally the link between first and the second order supersymmetric partners of the truncated harmonic oscillator which possess third-order differential ladder operators with the Painlevé IV equation is used to obtain several solutions of this non-linear second-order differential equation.
Entanglement entropies of coupled harmonic oscillators
Nakagawa, Koichi
2016-01-01
We investigate the quantum entanglement of systems of coupled harmonic oscillators on the basis of thermo-field dynamics (TFD). For coupled harmonic oscillators at equilibrium, the extended entanglement entropy is derived using the TFD method, and it is demonstrated to be controlled by temperature and coupling parameters. For non-equilibrium systems, in addition to temperature and coupling parameters, the time dependence of the extended entanglement entropy is calculated in accordance with th...
Instanton solutions on the polymer harmonic oscillator
Olivares, Joan A Austrich; Vergara, J David
2016-01-01
Instanton methods are applied to the polymer harmonic oscillator. The zeroth energy eigenvalue on the entire polymer Hilbert space is obtained. The result is consistent with the band structure of the standard regular quantum pendulum. The band structure of the energy spectrum emerges with discrete topology and disappears in the formal limit $\\mu \\rightarrow 0$, which gives rise to the standard quantum harmonic oscillator spectrum.
Harmonic Oscillators as Bridges between Theories
International Nuclear Information System (INIS)
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. It is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called SL(2, c). Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics
Harmonic Oscillators as Bridges between Theories
Kim, Y. S.; Noz, Marilyn E.
2005-03-01
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. It is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called SL(2, c). Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.
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.
Deepening the vector coherent state analysis: Revisiting the harmonic oscillator
Aremua, I; Hounkonnou, M N
2011-01-01
Vector coherent states (VCS) viewed as a generalization of ordinary coherent states for higher rank tensor Hilbert spaces are investigated. We consider a systematic way of generating classes of VCS which are solvable (i.e., in the present context, normalizable states satisfying a resolution of the identity) on the Hilbert space of 2D and 3D harmonic oscillators. Thanks to the type of construction, these VCS are classified according to specific criteria. Furthermore, in many cases, the found classes of VCS are continuously deformable one onto another, still remaining solvable.
Quantum phases for a generalized harmonic oscillator
Bracken, Paul
2008-03-01
An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.
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.
Factorization method for the truncated harmonic oscillator
Fernández C, D. J.; Morales-Salgado, V. S.
2015-04-01
Factorization procedures of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. Certain systems obtained in a straightforward way through said method possess differential ladder operators of both types, third and fourth order. Since systems with this kind of operators are linked with the Painlevé IV and V equations respectively, several solutions of these non-linear second-order differential equations will be simply found.
Casimir Friction Force for Moving Harmonic Oscillators
Høye, Johan S.; Brevik, Iver
2011-01-01
Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving non-relativistically with constant velocity. We use a statistical-mechanical description where time-dependent correlations are involved. This description is physical and direct, and, in spite of its simplicity, is able to elucidate the essentials of the problem. This treatment elaborates upon, and extends, ...
Harmonic Oscillator Potential to describe Internal Dissipation
Peters, R D
2003-01-01
Assuming that a constant potential energy function has meaning for a dissipated harmonic oscillator, then an important issue is the time dependence of the turning points. Turning point studies demonstrate that the common model of external (viscous) damping fails to properly describe those many systems where structural (internal friction) damping is the most important source of dissipation. For internal friction damping, the better model of potential energy is one in which the function is not stationary.
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 by...
On the Quantization of Damped Harmonic Oscillator
International Nuclear Information System (INIS)
We derive results for two constants of the motion of a one-dimensional damped harmonic oscillator with position-dependent frictional coefficient and use them to obtain two alternative Lagrangian representations, which are not connected by a gauge term. The Hamiltonians corresponding to these Lagrangians lead to canonically inequivalent phase-space descriptions. We could, however, make use of a perturbation theoretic approach to quantize the classical motion using both Hamiltonians and thus demonstrate that the corresponding quantum systems are entirely different. (author)
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.
Quasi coherent states for time dependent harmonic oscillators
International Nuclear Information System (INIS)
Full text: (author)In this study, first it is discussed the duality between the time dependent hydrogen atom problem and time dependent harmonic oscillators. Second, it is generalized the holomorphic coordinates for the time dependent harmonic oscillators and reduce the solution of the Schrodinger equation into Riccati equation. It is found the solution of Riccati equation for time dependent harmonic oscillators in some special cases and discuss the uncertainties
Unitary relations in time-dependent harmonic oscillators
Song, Dae-Yup
1998-01-01
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as well as operators. For a driven harmonic oscillator, it is also shown that, there are unitary transformations which give the driven system from the system of same mass and frequency without driving force. The transformation for a driven oscillator depends on...
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.
Introduction to Classical and Quantum Harmonic Oscillators
International Nuclear Information System (INIS)
As the title aptly states, this book deals with harmonic oscillators of various kinds, from classical mechanical and electrical oscillations up to quantum oscillations. It is written in a lively language, and occasional interspersed anecdotes make the reading of an otherwise mathematically oriented text quite a pleasure. Although the author claims to have written an 'elementary introduction', it is certainly necessary to have a good deal of previous knowledge in physics (mechanics, electrodynamics, quantum theory), electrical engineering and, of course, mathematics in order to follow the general line of his arguments. The book begins with a thorough treatment of classical oscillators (free, damped, forced) that is followed by an elaboration on Fourier analysis. Lagrange and Hamilton formalisms are then introduced before the problem of coupled oscillations is attacked. A chapter on statistical perspectives leads over to the final discussion of quantum oscillations. With the book comes a diskette containing a number of worksheets (Microsoft Excel) that can be used by the reader for instant visualization to get a better qualitative and quantitative understanding of the material. To the reviewer it seems difficult to pinpoint exactly the range of prospective readership of the book. It can certainly not be intended as a textbook for students, but rather as a reference book for teachers of physics or researchers, who want to look up one or other aspect of harmonic oscillations, for which purpose the diskette represents a very valuable tool. (book review)
Interbasis expansions for the isotropic 3D harmonic oscillator and bivariate Krawtchouk polynomials
International Nuclear Information System (INIS)
An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk polynomials occur as matrix elements of the unitary reducible representations of SO(3) on the energy eigenspaces of the three-dimensional isotropic harmonic oscillator and the explicit formula is obtained from the decomposition of these representations into their irreducible components. The decomposition entails expanding the Cartesian basis states in the spherical bases that span irreducible SO(3) representations. The overlap coefficients are obtained from the Clebsch–Gordan problem for the su(1,1) Lie algebra. (paper)
Quesne, C
2014-01-01
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian coordinates, whose form was previously guessed. In addition, the nature of the classical orthogonal polynomials entering the bound-state radial wavefunctions of the corresponding quantum model is identified.
Casimir Friction Force for Moving Harmonic Oscillators
Høye, Johan S
2011-01-01
Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving non-relativistically with constant velocity. We use a statistical-mechanical description where time-dependent correlations are involved. This description is physical and direct, and, in spite of its simplicity, is able to elucidate the essentials of the problem. This treatment elaborates upon, and extends, an earlier theory of ours back in 1992. The energy change Delta E turns out to be finite in general, corresponding to a finite friction force. In the limit of zero temperature the formalism yields, however, Delta E ->0, this being due to our assumption about constant velocity, meaning slowly varying coupling. For couplings varying more rapidly, there will also be a finite friction force at T=0. As second part of our work, we consider the friction problem using time-dependent perturbation theory. The dissipation, basically...
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 stretched harmonic oscillator. A test of semiclassical approximations
International Nuclear Information System (INIS)
We test the validity of semiclassical approximations (WKB, Miller and Good) in phase space in the one-dimensional case of independent particles confined by a stretched harmonic oscillator potential. This potential provides an illustrative example for many properties of atomic nuclei related to the saturation property of nuclear forces, while keeping the same mathematical simplicity as the usual harmonic oscillator
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.
Improving Density Functionals with Quantum Harmonic Oscillators
Tkatchenko, Alexandre
2013-03-01
Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).
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.
Arbitrary-order parasupersymmetric coherent states of quantum harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Fakhri, H. [Faculty of Physics, Tabriz University, Tabriz (Iran, Islamic Republic of) and Research Institute for Fundamental Sciences, Tabriz (Iran, Islamic Republic of)]. E-mail: Hfakhri@ark.tabrizu.ac.ir; Bahadori, M.E. [Faculty of Physics, Tabriz University, Tabriz (IR): Research Institute for Fundamental Sciences, Tabriz (Iran)]. E-mail: Msph0977@ark.tabrizu.ac.ir
2000-10-13
The eigenstates of arbitrary-order parasupersymmetric Hamiltonian p corresponding to a particle with spin p/2 in the presence of a harmonic oscillator potential and constant magnetic field directed along the z-axis are constructed in terms of eigenstates of a one-dimensional harmonic oscillator. Also, parasupersymmetric coherent states with degenerate multiplicity of an ad hoc bosonic annihilation operator of parasupersymmetric eigenstates of the Hamiltonian mentioned above are calculated. (author)
Arbitrary-order parasupersymmetric coherent states of quantum harmonic oscillator
International Nuclear Information System (INIS)
The eigenstates of arbitrary-order parasupersymmetric Hamiltonian p corresponding to a particle with spin p/2 in the presence of a harmonic oscillator potential and constant magnetic field directed along the z-axis are constructed in terms of eigenstates of a one-dimensional harmonic oscillator. Also, parasupersymmetric coherent states with degenerate multiplicity of an ad hoc bosonic annihilation operator of parasupersymmetric eigenstates of the Hamiltonian mentioned above are calculated. (author)
Damping the zero-point energy of a harmonic oscillator
Philbin, T. G; Horsley, S. A. R.
2013-01-01
The physics of quantum electromagnetism in an absorbing medium is that of a field of damped harmonic oscillators. Yet until recently the damped harmonic oscillator was not treated with the same kind of formalism used to describe quantum electrodynamics in a arbitrary medium. Here we use the techniques of macroscopic QED, based on the Huttner--Barnett reservoir, to describe the quantum mechanics of a damped oscillator. We calculate the thermal and zero-point energy of the oscillator for a rang...
On the truncation of the harmonic oscillator wavepacket
Energy Technology Data Exchange (ETDEWEB)
Rebollo-Neira, L; Jain, S [Aston University, Birmingham B4 7ET (United Kingdom)
2005-04-29
We present an interesting result regarding the implication of truncating the wavepacket of the harmonic oscillator. We show that disregarding the non-significant tails of a function which is the superposition of eigenfunctions of the harmonic oscillator has a remarkable consequence: namely, there exist infinitely many different superpositions giving rise to the same function on the interval. Uniqueness, in the case of a wavepacket, is restored by a postulate of quantum mechanics. (letter to the editor)
On the truncation of the harmonic oscillator wavepacket
Rebollo-Neira, L
2005-01-01
We present an interesting result regarding the implication of truncating the wavepacket of the harmonic oscillator. We show that disregarding the non-significant tails of a function which is the superposition of eigenfunctions of the harmonic oscillator has a remarkable consequence: namely, there exist infinitely many different superpositions giving rise to the same function on the interval. Uniqueness, in the case of a wavepacket, is restored by a postulate of quantum mechanics.
On the truncation of the harmonic oscillator wavepacket
International Nuclear Information System (INIS)
We present an interesting result regarding the implication of truncating the wavepacket of the harmonic oscillator. We show that disregarding the non-significant tails of a function which is the superposition of eigenfunctions of the harmonic oscillator has a remarkable consequence: namely, there exist infinitely many different superpositions giving rise to the same function on the interval. Uniqueness, in the case of a wavepacket, is restored by a postulate of quantum mechanics. (letter to the editor)
Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
Y. S. Kim; 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...
3-D harmonic oscillator using the Quon algebra
International Nuclear Information System (INIS)
Quons are particles that violate statistics by a small amount, which is controlled by a single parameter q. The range of variation of the parameter is between -1 and +1, and the limits of the interval correspond respectively to fermionic an bosonic statistics. The particular commutation relations obeyed by quons define an algebra (the so called Quon Algebra), which, for a single degree of freedom, gives results very similar to the ones obtained using Deformed (or Quantum) Algebras, once we keep the interval for q as above defined. For more than a single degree of freedom however, there are some important differences between both algebras. One consequence of those differences is that it is possible to define quonic operators that behave as irreducible SU(2) tensors. In other words, it is possible to assume that quons follow the usual angular momentum coupling rules. This last result opens up the possibility of applying the Quon Algebra to the study of many-body systems, with some important technical advantages over Deformed Algebras. However, those very same differences also introduce some complications when we try to build many-body quonic states, as the appearance of mixed symmetry states in the basis wave-function. In this work we investigate this point, as well as the connection with the possible observables for the theory. A simple application using a quonic version of a three-dimensional harmonic oscillator is also considered in some detail. A comparison between our quonic version and the deformed algebra result for the oscillator is made. (author)
The relativistic bound states for a new ring-shaped harmonic oscillator
International Nuclear Information System (INIS)
In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed
Calculation of four-particle harmonic-oscillator transformation brackets
Germanas, D.; Kalinauskas, R. K.; Mickevičius, S.
2010-02-01
A procedure for precise calculation of the three- and four-particle harmonic-oscillator (HO) transformation brackets is presented. The analytical expressions of the four-particle HO transformation brackets are given. The computer code for the calculations of HO transformation brackets proves to be quick, efficient and produces results with small numerical uncertainties. Program summaryProgram title: HOTB Catalogue identifier: AEFQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1247 No. of bytes in distributed program, including test data, etc.: 6659 Distribution format: tar.gz Programming language: FORTRAN 90 Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix RAM: 8 MB Classification: 17.17 Nature of problem: Calculation of the three-particle and four-particle harmonic-oscillator transformation brackets. Solution method: The method is based on compact expressions of the three-particle harmonics oscillator brackets, presented in [1] and expressions of the four-particle harmonics oscillator brackets, presented in this paper. Restrictions: The three- and four-particle harmonic-oscillator transformation brackets up to the e=28. Unusual features: Possibility of calculating the four-particle harmonic-oscillator transformation brackets. Running time: Less than one second for the single harmonic-oscillator transformation bracket. References:G.P. Kamuntavičius, R.K. Kalinauskas, B.R. Barret, S. Mickevičius, D. Germanas, Nuclear Physics A 695 (2001) 191.
Lie-algebraic structure of 2D harmonic oscillator with non-separable complex coupling
Ganguly, Asish
2011-01-01
Using SU(2)X SU(2) Lie-group structure we obtain the algebraization of 2D harmonic oscillator model with complex quadratic coupling. It is shown that the original time-independent Schr\\"odinger equation in Cartesian coordinates, when mapped to a curved manifold (in general) of arbitrary metric, is expressible as a quadratic combination of group generators modulo a gauge freedom. We propose an improvisation of the usual Lie-algebraic scheme for two critical values of the coupling parameter which makes the problem non-diagonalizable and non-separable. Recently reported results about this interesting non-Hermitian Hamiltonian are confirmed by solving the corresponding spectral problem in a purely algebraic procedure.
Coherent States of Harmonic Oscillator and Generalized Uncertainty Principle
Nozari, K; Nozari, Kourosh; Azizi, Tahereh
2005-01-01
In this paper dynamics and quantum mechanical coherent states of a simple harmonic oscillator are considered in the framework of Generalized Uncertainty Principle(GUP). Equations of motion for simple harmonic oscillator are derived and some of their new implications are discussed. Then coherent states of harmonic oscillator in the case of GUP are compared with relative situation in ordinary quantum mechanics. It is shown that in the framework of GUP there is no considerable difference in definition of coherent states relative to ordinary quantum mechanics. But, considering expectation values and variances of some operators, based on quantum gravitational arguments one concludes that although it is possible to have complete coherency and vanishing broadening in usual quantum mechanics, gravitational induced uncertainty destroys complete coherency in quantum gravity and it is not possible to have a monochromatic ray in principle.
Digitization of the harmonic oscillator in extended relativity
International Nuclear Information System (INIS)
Extended relativistic dynamics (ERD) admits only solutions that have speed bounded by the speed of light c and acceleration bounded by an assumed universal maximal acceleration am. Here we explore the harmonic oscillator under ERD. For oscillators with small natural frequency ω, we recover the classical solutions, while for large ω, the solutions differ significantly from the classical one. The solutions for large ω are a ‘digitization’ of the standard signals of the classical harmonic oscillator. The spectrum of these signals coincides with the energy spectrum of the quantum harmonic oscillator. While for small ω, the thermal radiation is a wave type, for large ω, it becomes pulses of radiation. This provides a possible explanation for the difference in the blackbody radiation for small and large ω and is another indication of the validity of ERD. (paper)
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
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.
Quaternion vector coherent states and supersymmetric harmonic oscillator
International Nuclear Information System (INIS)
By analogy with the standard canonical coherent states of the standard harmonic oscillator the quaternion vector coherent states are realized as the coherent states of the supersymmetric harmonic oscillator with a broken symmetry. In terms of the mentioned states one studies the nonclassical features of the oscillator such as the distribution of the phonon number and the signal-to-quantum noise ratio. One discusses the properties of compressibility and time stability of the coherent states. One plots the orthogonal polynomials associated with the quanternion vector coherent states
Band structure in the polymer quantization of the harmonic oscillator
International Nuclear Information System (INIS)
We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies that the point spectrum consists of bands similar to the ones appearing in the treatment of periodic potentials. This feature of the spectrum of the polymeric harmonic oscillator may be relevant for the discussion of the polymer quantization of the scalar field and may have interesting consequences for the statistical mechanics of these models. (paper)
The One-Dimensional Damped Forced Harmonic Oscillator Revisited
Flores-Hidalgo, G.; Barone, F. A.
2011-01-01
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.
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 nonlinearity...
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 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…
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.
Asymptotic Formula for Quantum Harmonic Oscillator Tunneling Probabilities
Jadczyk, Arkadiusz
2015-10-01
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.
Asymptotic formula for quantum harmonic oscillator tunneling probabilities
Jadczyk, Arkadiusz
2015-01-01
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.
Harmonic oscillator with time - dependent mass and frequency
International Nuclear Information System (INIS)
A general treatment of the quantal harmonic oscillator with time-dependent mass and frequency is presented. The treatment is based on the use of some time-dependent transformations in the method of invariants of Lewis and Riesenfeld. Exact coherent states for such a system are also constructed. (A.C.A.S.)
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…
Time-dependent harmonic oscillators and squeezed states
International Nuclear Information System (INIS)
Utilizing time-dependent operators whose associated states are squeezed states, it is shown that the general time-dependent harmonic-oscillator Hamiltonian belongs to the class of quadratic Hamiltonians that generate squeezed states. An illustrative example is also considered. (Author)
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.)
A new analytical approximation to the Duffing-harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Fesanghary, M. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States); Pirbodaghi, T. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of); Asghari, M. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: asghari@sharif.edu; Sojoudi, H. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States)
2009-10-15
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
Symmetry algebra of a generalized anisotropic harmonic oscillator
Castanos, O.; Lopez-Pena, R.
1993-01-01
It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.
Reduction of superintegrable systems: the anisotropic harmonic oscillator
Rodriguez, Miguel A.; Tempesta, Piergiulio; Winternitz, Pavel
2008-01-01
We introduce a new 2N--parametric family of maximally superintegrable systems in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a 2N--dimensional configuration space. These systems possess closed bounded orbits and integrals of motion which are polynomial in the momenta. They generalize known examples of superintegrable models in the Euclidean plane.
International Nuclear Information System (INIS)
A stationary Green function is calculated for the Schroedinger Hamiltonian of the multidimensional isotropic harmonic oscillator and for physical systems, which may, somehow, have their Hamiltonian reduced to one in the form of a harmonic oscillator, for any dimension
Time-dependent coupled harmonic oscillators: classical and quantum solutions
International Nuclear Information System (INIS)
In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0. (author)
Harmonic Oscillator States with Non-Integer Orbital Angular Momentum
Land, Martin
2009-01-01
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as represents of their respective symmetry groups: O(2), O(3), and O(2,1). Solving the Schrodinger equation by separating variables in polar coordinates, we obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and one observable component of orbital angular momentum, with eigenvalue $m+s$, for integer $m$ and real constant param...
Casimir Friction Force and Energy Dissipation for Moving Harmonic Oscillators
Høye, Johan S.; Brevik, Iver
2010-01-01
The Casimir friction problem for a pair of dielectric particles in relative motion is analyzed, utilizing a microscopic model in which we start from statistical mechanics for harmonically oscillating particles at finite temperature moving nonrelativistically with constant velocity. The use of statistical mechanics in this context has in our opinion some definite advantages, in comparison with the more conventional quantum electrodynamic description of media that involves the use of a refracti...
Deepening the vector coherent state analysis: Revisiting the harmonic oscillator
Aremua, I.; Geloun, J Ben; Hounkonnou, M. N.
2011-01-01
Vector coherent states (VCS) viewed as a generalization of ordinary coherent states for higher rank tensor Hilbert spaces are investigated. We consider a systematic way of generating classes of VCS which are solvable (i.e., in the present context, normalizable states satisfying a resolution of the identity) on the Hilbert space of 2D and 3D harmonic oscillators. Thanks to the type of construction, these VCS are classified according to specific criteria. Furthermore, in many cases, the found c...
Rabi oscillation between states of a coupled harmonic oscillator
International Nuclear Information System (INIS)
Rabi oscillation between bound states of a single potential is well known. However the corresponding formula between the states of two different potentials has not been obtained yet. In this work, we derive Rabi formula between the states of a coupled harmonic oscillator which may be used as a simple model for the electron transfer. The expression is similar to typical Rabi formula for a single potential. This result may be used to describe transitions between coupled diabatic potential curves
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.
Trajectory of the harmonic oscillator in the Schreodinger wave
Nishiyama, Yoshio
2001-01-01
A trajectory of a harmonic oscillator obeying the Schreodinger wave equation is exactly derived and illustrated. The trajectory resembles well the classical orbit between the turning points, and also runs through the tunneling region. The dynamics of the `particle' motion and the wave function associated with the motion are proposed. The period of a round trip on the trajectory is exactly equal to that obtained in classical mechanics.
Trajectory of the harmonic oscillator in the Schrodinger wave
Nishiyama, Yoshio
1999-01-01
A trajectory of a harmonic oscillator obeying the Schrodinger equation is exactly derived and illustrated. The trajectory resembles well the classical orbit between the turning points, and also runs through the tunneling region. The dynamics of the 'particle' motion and the wave function associated with the motion are proposed. The period of a round trip on the trajectory is exactly equal to that obtained in classical mechanics.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
International Nuclear Information System (INIS)
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments
Specific heat of the harmonic oscillator within generalized equilibrium statistics
International Nuclear Information System (INIS)
Within the generalized equilibrium statistics recently introduced by Tsallis, we calculate the thermal dependence of the specific heat corresponding to a harmonic-oscillator-likes spectrum, namely, εn = ω(n-α), (where ω >O,n = 0,1,2,...). The influences of q and α are exhibited. Physically inaccessible and/or thermally frozen gaps are obtained in the low temperature region, and, for q > 1, oscillations are observed in the high temperature region. The specific heat of the two-level system is also shown. (author)
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.
Optimal control of a harmonic oscillator: Economic interpretations
Janová, Jitka; Hampel, David
2013-10-01
Optimal control is a popular technique for modelling and solving the dynamic decision problems in economics. A standard interpretation of the criteria function and Lagrange multipliers in the profit maximization problem is well known. On a particular example, we aim to a deeper understanding of the possible economic interpretations of further mathematical and solution features of the optimal control problem: we focus on the solution of the optimal control problem for harmonic oscillator serving as a model for Phillips business cycle. We discuss the economic interpretations of arising mathematical objects with respect to well known reasoning for these in other problems.
Measuring irreversible dynamics of a quantum harmonic oscillator
Morigi, Giovanna; Solano, Enrique; Englert, Berthold-Georg; Walther, Herbert
2002-01-01
We show that the unitary evolution of a harmonic oscillator coupled to a two-level system can be undone by a suitable manipulation of the two-level system—more specifically, by a quasi-instantaneous phase change. This enables us to isolate the dissipative evolution to which the oscillator may be exposed in addition. With this method we study the decoherence time of a photon mode in cavity QED, and that of the quantized harmonic motion of trapped ions. We comment on the relation to spin echoes...
High spin rotations of nuclei with the harmonic oscillator potential
International Nuclear Information System (INIS)
Calculations of the nuclear properties at high angular momentum have been performed recently. They are based on the liquid drop model of a nucleus and/or on the assumption of the single particle shell structure of the nucleonic motion. The calculations are usually complicated and involve long computer codes. In this article we shall discuss general trends in fast rotating nuclei in the approximation of the harmonic oscillator potential. We shall see that using the Bohr Mottelson simplified version of the rigorous solution of Valatin one can perform a rather simple analysis of the rotational bands, structure of the yrast line, moments of inertia etc. in the rotating nucleus. While the precision fit to experimental data in actual nuclei is not the purpose of this paper, one can still hope to reach some general understanding within the model of the simple relations resulting in nuclei at high spin. (author)
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.
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.
Analytical Solution of Smoluchowski Equation in Harmonic Oscillator Potential
Institute of Scientific and Technical Information of China (English)
SUN Xiao-Jun; LU Xiao-Xia; YAN Yu-Liang; DUAN Jun-Feng; ZHANG Jing-Shang
2005-01-01
Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. This analytical solution is able to describe the probability distribution and the diffusive current with the variable x and t. The results indicate that the probability distribution and the diffusive current are relevant to the initial distribution shape, initial position, and the nuclear temperature T; the time to reach the quasi-stationary state is proportional to friction coefficient β, but is independent of the initial distribution status and the nuclear temperature T. The prerequisites of negative diffusive current are justified. This method provides an approach to describe the diffusion process for fissile process in complicated potentials analytically.
Basic Canonical Brackets Without Canonical Conjugate Momenta: Supersymmetric Harmonic Oscillator
Shukla, A; Malik, R P
2014-01-01
We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) supersymmetric (SUSY) harmonic oscillator without taking the help of the mathematical definition of the canonical conjugate momenta with respect to the bosonic and fermionic variables of this toy model for the Hodge theory (where the continuous and discrete symmetries of the theory provide the physical realizations of the de Rham cohomological operators of differential geometry). In our present endeavor, it is the full set of continuous symmetries and their corresponding generators that lead to the derivation of basic (anti)commutators amongst the creation and annihilation operators that appear in the normal mode expansions of the dynamical variables of our theory.
Multiquark Cluster Form Factors In the Relativistic Harmonic Oscillator Model
Wu, Qing; Xiang, Qian-fei; Ma, Wei-xin
2014-01-01
A QCD multiquark cluster system is studied in the relativistic harmonic oscillator potential model (RHOPM), and the electromagnetic form factors of the pion, proton and deuteron in the RHOPM are predicted. The calculated theoretical results are then compared with existing experimental data, finding very good agreement between the theoretical predictions and experimental data for these three target particles. We claim that this model can be applied to study QCD hadronic properties, particularly neutron properties, and to find six-quark cluster and/or nine-quark cluster probabilities in light nuclei such as helium $^{3}He$ and tritium $^{3}H$. This is a problem of particular importance and interest in quark nuclear physics.
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.
Quantized Excitation Spectrum of the Classical Harmonic Oscillator in Zero-Point Radiation
Huang, Wayne Cheng-Wei
2012-01-01
We report that upon excitation by a single pulse, the classical harmonic oscillator immersed in classical electromagnetic zero-point radiation, as described by random electrodynamics, exhibits a quantized excitation spectrum in agreement to that of the quantum harmonic oscillator. This numerical result is interesting in view of the generally accepted idea that classical theories do not support quantized energy spectra.
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.
Deformations and Nonlinear Systems
Man'ko, V. I.; Marmo, G.; F. Zaccaria
1997-01-01
The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities related to other types of deformations. The nonlinear noncanonical transforms used in the deformation procedure are shown to preserve in some cases the linear dynamical equations, for instance, for the harmonic oscillators. The nonlinear coherent states and ...
International Nuclear Information System (INIS)
In this paper, we study the Dirac equation with spin and pseudospin symmetry by the quadratic algebra approach for the 4-dimensional harmonic oscillator. By realization of the quadratic algebras in the deformed oscillator algebra, we obtain the relativistic energy spectrum. Also, by regarding the generalized Kustaanheimo–Stiefel transformation, we obtain the relativistic energy spectrum for the charge-dyon system with the U(1) monopole. (author)
Aghaei, S.; Chenaghlou, A.
2015-01-01
In this paper, we study the Dirac equation with spin and pseudospin symmetry by the quadratic algebra approach for the 4-dimensional harmonic oscillator. By realization of the quadratic algebras in the deformed oscillator algebra, we obtain the relativistic energy spectrum. Also, by regarding the generalized Kustaanheimo-Stiefel transformation, we obtain the relativistic energy spectrum for the charge-dyon system with the U(1) monopole.
International Nuclear Information System (INIS)
We consider a Generalized Uncertainty Principle (GUP) framework which predicts a maximal uncertainty in momentum and minimal uncertainties both in position and momentum. We apply supersymmetric quantum mechanics method and the shape invariance condition to obtain the exact harmonic oscillator eigenvalues in this GUP context. We find the supersymmetric partner Hamiltonians and show that the harmonic oscillator belongs to a hierarchy of Hamiltonians with a shift in momentum representation and different masses and frequencies. We also study the effect of a uniform electric field on the harmonic oscillator energy spectrum in this setup
Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation
International Nuclear Information System (INIS)
A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity-intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator
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.
Even and Odd Coherent States for Time-Dependent Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
WEI Lian-Fu; YANG Qing-Yi; WANG Shun-Jin
2002-01-01
The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.
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...
Harmonic Oscillator Trap and the Phase-Shift Approximation
Köhler, H S
2016-01-01
The energy-spectrum of two point-like particles interacting in a 3-D isotropic Harmonic Oscillator (H.O.) trap is related to the free scattering phase-shifts $\\delta$ of the particles by a formula first published by Busch et al. It is here used to find an expression for the \\it shift \\rm of the energy levels, caused by the interaction, rather than the perturbed spectrum itself. In the limit of high energy (large quantum number $n$ of the H.O.) this shift is shown to be given by $-2\\frac{\\delta}{\\pi}$, also valid in the limit of infinite as well as zero scattering length at all H.O. energies. Numerical investigation shows that the shifts differ from the exact result of Busch et al, by less than $<\\frac{1}{2}\\%$ except for $n=0$ when it can be as large as $\\approx 2.5\\%$. This approximation for the energy-shift is well known from another exactly solvable model, namely that of two particles interacting in a spherical infinite square-well trap (or box) of radius $R$ in the limit $R\\rightarrow \\infty$, and/or i...
De Souza, M M
2003-01-01
Discrete interaction models for the classical harmonic oscillator are used for introducing new mathematical generalizations in the usual continuous formalism. The inverted harmonic potential and generalized discrete hyperbolic and trigonometric functions are defined.
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.
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.
Forced Time-Dependent Harmonic Oscillators in Non-Commutative Space
Institute of Scientific and Technical Information of China (English)
LIANG Mai-Lin
2011-01-01
For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant.Coherent states are obtained as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.
Time dependent quaritum harmonic oscillator subject to a sudden change of mass: continuous solution
Moya-Cessa, H.; M. Fernández Guasti
2007-01-01
We show that a harmonic oscillator subject to a sudden change of mas s produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a subperiod 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 isalso applicable for rapid, a...
Exact Solutions of the Equations with Scalar and Vector Harmonic Oscillator
International Nuclear Information System (INIS)
In this study, the energy spectra and eigenfunctions of the electrons at the spherical quantum dots in Kane type semiconductors have been analytically found in the case of the scalar type harmonic oscillator potential being equal to the vector type harmonic oscillator potential by using Kane model with three bands. In the result of calculation, it has been understood that the analytical expression obtained for energy spectra of electrons is not parabolic
U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator
International Nuclear Information System (INIS)
We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case
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.
Shang, Yilun
2009-01-01
In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white noise. On the basis of stability theory of stochastic differential delay equations, algebraic graph theory and matrix theory, we show that the coupled harmonic oscillators can be synchronized almost surely with perturbation and time delays. Numerical examples are presented to illustrate our theoretical results.
Yilun Shang
2009-01-01
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...
Wayne Cheng-Wei Huang; Herman Batelaan
2013-01-01
In the past decades, Random Electrodynamics (also called Stochastic Electrodynamics) has been used to study the classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation. Random Electrodynamics (RED) predicts an identical probability distribution for the harmonic oscillator compared to the quantum mechanical prediction for the ground state. Moreover, the Heisenberg minimum uncertainty relation is also recovered with RED. To understand the dynamics that gives...
Quantum dynamics of deformed open systems
International Nuclear Information System (INIS)
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model using perturbation theory . The coefficient of the master equation depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation. (author)
Falaye, B. J.; Dong, Shi-Hai; Oyewumi, K. J.; Ilaiwi, K. F.; Ikhdair, S. M.
2015-10-01
We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [x̂,p̂] = iℏ(1 + ηp2). In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the SU(1, 1) ˜SO(2, 1) algebra is satisfied by the operators ℒ±̂ and ℒẑ.
On the effects of a screw dislocation and a linear potential on the harmonic oscillator
Bueno, M. J.; Furtado, C.; Bakke, K.
2016-09-01
Quantum effects on the harmonic oscillator due to the presence of a linear scalar potential and a screw dislocation are investigated. By searching for bound states solutions, it is shown that an Aharonov-Bohm-type effect for bound states and a restriction of the values of the angular frequency of the harmonic oscillator can be obtained, where the allowed values are determined by the topology of the screw dislocation and the quantum numbers associated with the radial modes and the angular momentum. As particular cases, the angular frequency and the energy levels associated with the ground state and the first excited state of the system are obtained.
SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÃ–DINGER
Directory of Open Access Journals (Sweden)
T B Prayitno
2012-02-01
Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master SchrÃ¶dinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution canâ€™t be normalized. Â Keywords : harmonic oscillator, nonlinear SchrÃ¶dinger.
Numerical solution of the Schroedinger equation for a quantum harmonic oscillator
International Nuclear Information System (INIS)
A numerical method, which is used extensively to obtain graphical solutions of first and second-order differential equations and which has been applied to the Schroedinger equation and used to plot the ground state wavefunction for the hydrogen atom by students, is here utilised to obtain the wavefunctions of the quantum harmonic oscillator. This approach provides a more sophisticated view of harmonic oscillator wavefunctions than does the normal teaching method and in particular illustrates that physically well behaved solutions of the time-dependent Schroedinger equation occur only for discrete values of the total energy, providing students with a worthwhile extension of work on hydrogen. (U.K.)
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.
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)
International Nuclear Information System (INIS)
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.
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
International Nuclear Information System (INIS)
Fourth-order moments in momentum p and coordinate q of an open one-dimensional harmonic oscillator are studied in two different representations (Weyl-Wigner-Moyal and Heisenberg). It is shown that both representations lead to the same explicit expressions of the fourth-order moments in terms of first (centroids) and second order moments (variances). (Author)
International Nuclear Information System (INIS)
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)
Misbelief and misunderstandings on the non--Markovian dynamics of a damped harmonic oscillator
Maniscalco, S; Piilo, J; Messina, A
2003-01-01
We use the exact solution for the damped harmonic oscillator to discuss some relevant aspects of its open dynamics often mislead or misunderstood. We compare two different approximations both referred to as Rotating Wave Approximation. Using a specific example, we clarify some issues related to non--Markovian dynamics, non--Lindblad type dynamics, and positivity of the density matrix.
Hadron and Quark Form Factors in the Relativistic Harmonic Oscillator Model
Burov, V. V.; De Pace, A.; Dorkin, S. M.; P. Saracco(INFN, Sezione di Genova)
1993-01-01
Nucleon, pion and quark form factors are studied within the relativistic harmonic oscillator model including the quark spin. It is shown that the nucleon charge, magnetic and axial form factors and the pion charge form factor can be explained with one oscillator parameter if one accounts for the scaling rule and the size of the constituent quarks.
On the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential
Czech Academy of Sciences Publication Activity Database
Novák, Radek
2015-01-01
Roč. 54, č. 11 (2015), s. 4142-4153. ISSN 0020-7748 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : pseudospectrum * harmonic oscillator * imaginary qubic potential * PT-symmetry * semiclassical method Subject RIV: BE - Theoretical Physics Impact factor: 1.184, year: 2014
The general harmonic-oscillator brackets: compact expression, symmetries, sums and Fortran code
International Nuclear Information System (INIS)
We present a very simple expression and a Fortran code for the fast and precise calculation of three-dimensional harmonic-oscillator transformation brackets. The complete system of symmetries for the brackets along with analytical expressions for sums containing products of two and three brackets is given
International Nuclear Information System (INIS)
For any planar motion a constant of the motion called generalized Laplace-Runge-Lenz vector is defined with the matrix representation. Taking the tensor product of the generalized vector with itself, the conserved symmetric tensor corresponding to the Hamiltonian of a two-dimensional isotropic harmonic oscillator is simply constructed
Root System of Singular Perturbations of the Harmonic Oscillator Type Operators
Czech Academy of Sciences Publication Activity Database
Mityagin, B.; Siegl, Petr
2016-01-01
Roč. 106, č. 2 (2016), s. 147-167. ISSN 0377-9017 Institutional support: RVO:61389005 Keywords : non-self-adjoint operators * harmonic oscillator * Riesz basis * quadratic forms * singular petentials Subject RIV: BE - Theoretical Physics Impact factor: 1.939, year: 2014
Constant of Motion for One-Diemnsional Non Autonomous Linear Systems and Harmonic Oscillator
Lopez, Gustavo
1999-01-01
For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic oscillator with an additional time depending force.
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…
Quantum chaos in an ion trap: the delta-kicked harmonic oscillator
Gardiner, S. A.; Cirac, J. I.; Zoller, P.
1997-01-01
We propose an experimental configuration, within an ion trap, by which a quantum mechanical delta-kicked harmonic oscillator could be realized, and investigated. We show how to directly measure the sensitivity of the ion motion to small variations in the external parameters.
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
Harmonic-oscillator pattern arising from an algebraic approach to chiral symmetry
Buccella, F; Savoy, C A
1972-01-01
The Weinberg equation for the (mass)/sup 2/ operator (Q/sub 5//sup +/, (Q/sub 5//sup +/, m/sup 2/))=0, between meson states, is saturated in a perturbative approach. The generator Z of the mixing operators is completely established as Z=(W*M)/sub z/, where W is the W-spin operator and M is the co-ordinate of the three-dimensional harmonic oscillator. In a perturbative expansion of the (mass)/sup 2/ operator, the lowest term consists of two parts, the harmonic-oscillator energy and a spin-orbit coupling of the form (-1)/sup L+1/(L.S+/sup 1///sub 2 /). The resulting (mass)/sup 2/ consists of families of equispaced linearly rising trajectories. (11 refs).
Coherent dynamics of a flux qubit coupled to a harmonic oscillator.
Chiorescu, I; Bertet, P; Semba, K; Nakamura, Y; Harmans, C J P M; Mooij, J E
2004-09-01
In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits (qubits). Single-qubit operations, direct coupling between two qubits and the realization of a quantum gate have been reported. However, complex manipulation of entangled states-such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments and cavity quantum electrodynamics-has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system. PMID:15356624
On the Bandgap quantum coupler and the harmonic oscillator interacting with a reservoir
Quijas, P C G
2007-01-01
In order to be able to study dissipation, the interaction between a single system and their environment was introduced in quantum mechanics. Master and quantum Langeving equations was derived and, also, decoherence was studied using this approach. One of the most used model in this field of research is a single harmonic oscillator interacting with an infinite number of harmonic oscillators. In this work we analytically solve, with the evolution operator method, the Schrodinger equation for this model in the case of resonance. Also we address a different aspect of the quantum computing with linear optics. That is, we propose the linear bandgap quantum coupler, in the cases N=2 and N=3, to generate a new phase operator $U_{dp}^{\\pi} $ working on the two and three qubits basis like an alternative realization of a quantum phase gate.
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.
The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator
Govaerts, Jan; Bwayi, Calvin Matondo; 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...
The complex quantum harmonic oscillator: A model for the fractional quantum Hall effect
Arbab, A I
2012-01-01
The recently introduced model of a complex (two dimensional) quantum harmonic oscillator is found to account for the observed Fractional quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained. The two sequences are found to express a quantity and its complex conjugated partner. The oscillator is found to have two degenerates states, $\\psi_n$, with angular momenta $\\pm n\\,\\hbar$., where $h = 2\\pi \\hbar $ is the Planck's constant.
Truncated harmonic oscillator and Painlevé IV and V equations
Fernández C, David J.; Morales-Salgado, V. S.
2015-06-01
Quantum systems described by second and third order polynomial Heisenberg algebras are obtained applying supersymmetric quantum mechanics to the harmonic oscillator with an infinite potential barrier. These systems are linked with the Painlevé IV and V equations, respectively, thus several solutions of these non-linear second-order differential equations will be found, along with a chain of Bäcklund transformations connecting such solutions.
A non-orthogonal harmonic-oscillator basis for three-body problems
International Nuclear Information System (INIS)
A set of harmonic-oscillator states suitable for the representation of the wave function of the bound states of a system of three identical particles, is presented. As an illustration of the possibilities of the states defined in this paper, they are applied in a variational determination of the lowest symmetric S state of 12C, in the model of three structureless α particles interacting through the Coulomb force plus a phenomenological two-body force. (author)
Corrections to the Born-Oppenheimer approximation for a harmonic oscillator
International Nuclear Information System (INIS)
We derive simple expressions for the energy corrections to the Born-Oppenheimer approximation valid for a harmonic oscillator. We apply these corrections to the electronic and rotational ground state of H2+ and show that the diabatic energy corrections are linearly dependent on the vibrational quantum numbers as seen in recent variational calculations [D. A. Kohl and E. J. Shipsey, J. Chem. Phys. 84, 2707 (1986)
N = 2 Supersymmetric Harmonic Oscillator: Basic Brackets Without Canonical Conjugate Momenta
Srinivas, N.; Shukla, A.; Malik, R. P.
2014-01-01
We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) N = 2 supersymmetric (SUSY) harmonic oscillator (HO) without taking the help of the mathematical definition of canonical conjugate momenta with respect to the bosonic and fermionic variables of this toy model for the Hodge theory (where the continuous and discrete symmetries of the theory p...
Xiaowei Liu, Lingen Chen, Feng Wu, Fengrui Sun
2015-01-01
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 p...
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.
Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum Aspects
Ghosh, Subir; Majhi, Bibhas Ranjan
2007-01-01
We study complexified Harmonic Oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga \\cite{sm} who initiated the study of these Crypto-gauge invariant models that can be related to $PT$-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints, (in contrast to \\cite{sm} where one deals with a single constraint), with a much richer constraint structure. Some common as well as distinct featur...
Bogdanov, Alexander V.; Gevorkyan, Ashot S.
1997-01-01
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the extended space. This wave functional obeys some stochastic differential equation (SDE). Based on the nonlinear Langevin type SDE of second order, introduced in the functional space R{W(t)}, the variables in original equation are separated. The general measure in...
Velocity quantization approach of the one-dimensional dissipative harmonic oscillator
Lopez, Gustavo; Lopez, Pablo
2005-01-01
Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian.
Born-Jordan and Weyl quantizations of the 2D anisotropic harmonic oscillator
Rastelli, Giovanni
2016-01-01
We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the algebra of the constants of motion after the different quantization procedures. In the examples considered, we have that the Weyl formula always preserves the original superintegrable structure of the system, while the Born-Jordan formula, when producing d...
Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
Gurappa, N.; Panigrahi, Prasanta K.
1997-01-01
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This equivalence provides a straightforward method to find the complete set of eigenfunctions, the exact constants of motion and a linear $W_{1+\\infty}$ algebra associated with this model. It is also demonstrated that a large class of models with long-range interaction...
Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator
Doll, Roland; Ingold, Gert-Ludwig
2006-01-01
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic oscillator with incommensurate frequencies and the isotropic oscillator to the case with commensurate frequencies for which the Lissajous curves appear as classical periodic orbits. Because of the three different scenarios depending on the ratio of its frequencies, ...
The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature
Cariñena, José F; Santander, Mariano
2007-01-01
The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these `curved' harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK) type approach, with two free parameters $\\ki, \\kii$ which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere ${\\bf S}^2$, hyperbolic plane ${\\bf H}^2$, AntiDeSitter sphere ${\\bf AdS}^{\\unomasuno}$ and DeSitter sphere ${\\bf dS}^{\\unomasuno}$) appear in this family, with the Euclidean and Minkowski spaces as flat limits. We solve the equations of motion for the `curved' harmonic oscillator and obtain explicit expressions for the orb...
Quantization in terms of symplectic groups: The harmonic oscillator as a generic example
International Nuclear Information System (INIS)
The conventional quantization of the harmonic oscillator in terms of operators Q and P can be implemented with the help of irreducible unitary representations of the Heisenberg-Weyl group which acts transitively and effectively on the simply connected classical phase space Sq,p ≅ R2. In the description of the harmonic oscillator in terms of angle and action variables φ and I the associated phase space Sφ,I corresponds to the multiply connected punctured plane R2 - {0}, on which the 3-dimensional symplectic group Sp(2, R) acts transitively, leaving the origin invariant. As this group contains the compact subgroup U(1) it has infinitely many covering groups. In the here relevant irreducible unitary representations (positive discrete series) the self-adjoint generator Ko of U(l) represents the classical action variable I. It has the possible spectra n + k, n = 0,1,...; k > 0, where k depends on the covering group. This implies different possible spectra for the action variable Hamiltonian hωK0 of the harmonic oscillator. On the other hand, expressing the operators Q and P (non-linearly) in terms of the three generators K0 etc. of Sp(2, R) leads to the usual framework. Possible physical (experimental) implications and generalizations to higher dimensions are discussed briefly.
Protective measurement of the wave function of a single squeezed harmonic-oscillator state
Alter, Orly; Yamamoto, Yoshihisa
1996-05-01
A scheme for the "protective measurement" [Phys. Rev. A 47, 4616 (1993)] of the wave function of a squeezed harmonic-oscillator state is described. This protective measurement is shown to be equivalent to a measurement of an ensemble of states. The protective measurement, therefore, allows for a definition of the quantum wave function on a single system. Yet, this equivalency also suggests that both measurement schemes account for the epistemological meaning of the wave function only. The protective measurement requires a full a priori knowledge of the measured state. The intermediate cases, in which only partial a priori information is given, are also discussed.
International Nuclear Information System (INIS)
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
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./.
Coherent states for nonlinear harmonic oscillator and some of its properties
Energy Technology Data Exchange (ETDEWEB)
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk [School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Pavsic, Matej
1998-01-01
The harmonic oscillator in pseudo euclidean space is studied. A straightforward procedure reveals that although such a system may have negative energy, it is stable. In the quantized theory the vacuum state has to be suitably defined and then the zero-point energy corresponding to a positive-signature component is canceled by the one corresponding to a negative-signature component. This principle is then applied to a system of scalar fields. The metric in the space of fields is assumed to hav...
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.
Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators
Directory of Open Access Journals (Sweden)
Müller H.
2009-04-01
Full Text Available Logarithmic scaling invariance is a wide distributed natural phenomenon and was proved in the distributions of physical properties of various processes — in high en- ergy physics, chemistry, seismicity, biology, geology and technology. Based on the Gantmacher-Krein continued fraction method the present paper introduces fractal scal- ing models of resonant oscillations in chain systems of harmonic oscillators. These models generate logarithmic scaling spectra. The introduced models are not based on any statements about the nature of the link or interaction between the elements of the oscillating system. Therefore the model statements are quite generally, what opens a wide field of possible applications.
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.
International Nuclear Information System (INIS)
A Schroedinger eigenvalue problem is solved for the 2D quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, (i) an application of the Kelly error estimator, and (ii) a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver. (general)
Radiative decays of vector mesons in the relativistic harmonic oscillator model
Energy Technology Data Exchange (ETDEWEB)
Govorkov, A.B.; Drenska, S.B.
1977-10-01
Radiative M1 transitions both of ordinary vector mesons ..omega.., rho/sup 0/, K/sup 0/*, and also of the new J/psi meson into pseudoscalar mesons ..pi../sup 0/, eta, eta', and K/sup 0/ are discussed in terms of the relativistic model of a four-dimensional harmonic oscillator. The parameters of the oscillator were determined from the experimental data on the decay widths of vector mesons into a lepton pair. For the J/psi meson the relativistic effects lead to an appreciable additional suppression of radiative transitions.
Spectroscopy of mesons in the QCD-inspired potential model with harmonic oscillator approximation
International Nuclear Information System (INIS)
The spectrum of pseudoscalar, scalar, vector and axial-vector mesons are investigated in the frame of QCD-inspired potential model with harmonic oscillator approximation. Numerical solutions of the Bethe-Salpeter (BS) equation with the using of continuous analogy of Newton's method (CANM) have been obtained. It was shown that solutions of BS equation in harmonic approximation at quantity level describes observed spectrum of mesons and their radial- and orbital-excited states. The contrary 'progonka' (driving) method for numerical solution of the BS equation was briefly described. (author). 9 refs.; 4 tabs
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
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./
Hoover, Wm. G.; Hoover, Carol G.
2012-02-01
We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved analytically. The three-dimensional and four-dimensional problems studied here are simultaneously chaotic, time-reversible, and dissipative. Our treatment is intended to be pedagogical, for use in an updated version of our book on Time Reversibility, Computer Simulation, and Chaos. Comments are very welcome.
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.
Regular phase operator and SU(1,1) coherent states of the harmonic oscillator
Varro, Sandor
2014-01-01
A new solution is proposed to the long-standing problem of describing the quantum phase of a harmonic oscillator. In terms of an'exponential phase operator', defined by a new 'polar decomposition' of the quantized amplitude of the oscillator, a regular phase operator is constructed in the Hilbert-Fock space as a strongly convergent power series. It is shown that the eigenstates of the new 'exponential operators are SU(1,1) coherent states in the Holstein-Primakoff realization. In terms of the...
Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum Aspects
Ghosh, Subir
2007-01-01
We study complexified Harmonic Oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga \\cite{sm} who initiated the study of these Crypto-gauge invariant models that can be related to $PT$-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints, (in contrast to \\cite{sm} where one deals with a single constraint), with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator.
Generalized Hopf Fibration and Geometric SO(3) Reduction of the 4DOF Harmonic Oscillator
van der Meer, J. C.; Crespo, F.; Ferrer, S.
2016-04-01
It is shown that the generalized Hopf map ℍ × ℍ → ℍ × ℝ × ℝ quaternion formulation can be interpreted as an SO(3) orbit map for a symplectic SO(3) action. As a consequence the generalized Hopf fibration S7 → S4 appears in the SO(3) geometric symplectic reduction of the 4DOF isotropic harmonic oscillator. Furthermore it is shown how the Hopf fibration and associated twistor fibration play a role in the geometry of the Kepler problem and the rigid body problem.
Chang, L. N.; D. MINIC; Okamura, N; Takeuchi, T.
2001-01-01
We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations [(x) over cap (i),(p) over cap (j)]=i (h) over bar[(1+beta(p) over cap (2))delta(ij)+beta(')(p) over cap (i)(p) over cap (j)]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relations which appear in perturbative string theory. Our solutions illustrate how certain featu...
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
Quintela, T S; Nogueira, J A
2015-01-01
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 still periodic with the new period depending on the minimal length. This result is very important since it can be used to probe the Planck-scale physics. We show applications of our results in spectroscopy and gravity.
International Nuclear Information System (INIS)
We present a general, asymptotical solution for the discretized harmonic oscillator. The corresponding Schroedinger equation is canonically conjugate to the Mathieu differential equation, the Schroedinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretized harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalized Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalized in order to accommodate several variables
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...
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.
International Nuclear Information System (INIS)
Radiative decay widths are calculated for the radiative decay processes observed experimentally in the charmonium system. The model uses a Bethe-Salpeter equation with a static kernel and harmonic oscillator potentials to model the c-anti c system. Each decay width is calculated for 21 different choices of the c-quark mass. The potential used was a linear combination of a vector coupled and a scalar coupled harmonic oscillator potential. The quark mass and the scalar to vector coupling ratio were determined by trying to fit simultaneously the psi'(3685) - psi(3095) mass difference, the psi(3095) → e+ + e-decay width and the 3P/sub J/ mass splittings. A single choice of the quark mass and scalar to vector coupling ratio could not simultaneously fit all these constraints. The best fit to these constraints occurred when the quark mass was 5.5 and the scalar to vector coupling ratio parameter was -0.16. The decay width calculations are shown graphically for values of the quark mass from 0.00 to 16 GeV. The decay widths were calculated two different ways: (1) using the matrix elements of the quark momentum; (2) using the matrix elements of the quark position. Most of the published calculations use method (2). The widths computed by methods (1) and (2) are quite different for all masses and all transitions implying that the usual method (2) give incorrect results, and the fits with experimental data are fortuitous
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...
Revised calculation of four-particle harmonic-oscillator transformation brackets matrix
Mickevičius, S.; Germanas, D.; Kalinauskas, R. K.
2013-02-01
In this article we present a new, considerably enhanced and more rapid method for calculation of the matrix of four-particle harmonic-oscillator transformation brackets (4HOB). The new method is an improved version of 4HOB matrix calculations which facilitates the matrix calculation by finding the eigenvectors of the 4HOB matrix explicitly. Using this idea the new Fortran code for fast and 4HOB matrix calculation is presented. The calculation time decreases more than a few hundred times for large matrices. As many problems of nuclear and hadron physics structure are modeled on the harmonic oscillator (HO) basis our presented method can be useful for large-scale nuclear structure and many-particle identical fermion systems calculations. Program summaryTitle of program: HOTB_M Catalogue identifier: AEFQ_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 2149 No. of bytes in distributed program, including test data, etc.: 17576 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any computer with Fortran 90 compiler. Operating system: Windows, Linux, FreeBSD, True64 Unix. RAM: Up to a few Gigabytes (see Tables 1 and 2 included in the distribution package) Classification: 17.16, 17.17. Catalogue identifier of previous version: AEFQ_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1377 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the matrix of the 4HOB in a more effective way, which allows us to calculate the matrix of the brackets up to a few hundred times more rapidly than in a previous version. Solution method: The method is based on compact expressions of 4HOB, presented in [1] and its simplifications presented in this paper. Reasons for new version
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
2008-12-01
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved. PMID:19123623
International Nuclear Information System (INIS)
The type III Hermite Xm exceptional orthogonal polynomial family is generalized to a double-indexed one Xm1,m2 (with m1 even and m2 odd such that m2 > m1) and the corresponding rational extensions of the harmonic oscillator are constructed by using second-order supersymmetric quantum mechanics. The new polynomials are proved to be expressible in terms of mixed products of Hermite and pseudo-Hermite ones, while some of the associated potentials are linked with rational solutions of the Painlevé IV equation. A novel set of ladder operators for the extended oscillators is also built and shown to satisfy a polynomial Heisenberg algebra of order m2 − m1 + 1, which may alternatively be interpreted in terms of a special type of (m2 − m1 + 2)th-order shape invariance property. (paper)
Directory of Open Access Journals (Sweden)
Piyarut Moonsri
2014-01-01
Full Text Available We apply a Feynmans technique for calculation of a canonical density matrix of a single particle under harmonic oscillator asymmetric potential and solving the Bloch equation of the statistical mechanics system. The density matrix (P^u and kinetic energy per unit length (τ^L can be directly evaluated from the solving solutions. From the evaluation, it was found that both of the density matrix and kinetic energy per unit length depended on the parameter of the value of asymmetric potential (λ, the value of axes-shift potential (g, and temperature (T. Comparison of the Helmholtz free energy was derived by the Feynmans technique and the path-integral method. The results illustrated are slightly different.
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...
Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, Wm.; Tobias, B. J.; Yan, Z.
2015-11-01
In quiescent H-mode (QH) regime, the edge harmonic oscillations (EHO) play an important role in avoiding the transient ELM power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n peeling mode properties of the ideal MHD code ELITE. The numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the toroidal rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that the low-n EHO can be destabilized in principle with rotation in both directions. These modeling results are consistent with experimental observations of the EHO and support the proposed theory of the EHO as a rotational shear driven kink/peeling mode.
Inhomogeneity of the phase space of the damped harmonic oscillator under Levy noise
Cao, Zhan; Luo, Hong-Gang; 10.1103/PhysRevE.85.042101
2012-01-01
The damped harmonic oscillator under symmetric L\\'{e}vy white noise shows inhomogeneous phase space, which is in contrast to the homogeneous one of the same oscillator under the Gaussian white noise, as shown in a recent paper [I. M. Sokolov, W. Ebeling, and B. Dybiec, Phys. Rev. E \\textbf{83}, 041118 (2011)]. The inhomogeneity of the phase space shows certain correlation between the coordinate and the velocity of the damped oscillator under symmetric L\\'{e}vy white noise. In the present work we further explore the physical origin of these distinguished features and find that it is due to the combination of the damped effect and heavy tail of the noise. We demonstrate directly this in the reduced coordinate $\\tilde{x}$ versus velocity $\\tilde{v}$ plots and identify the physics of the anti-association of the coordinate and velocity.
Study of Bose-Einstein condensation in a harmonic oscillator potential
International Nuclear Information System (INIS)
Bose-Einstein condensation is an accumulation of population in the ground state of a system of bosons as the temperature of the system is reduced below a critical temperature. This condensation is entirely a consequence of the quantum statistics of the Bose-Einstein distribution. We consider this statistics for our calculation. The ground state occupation numbers of a fixed number of bosons in an isotropic threedimensional harmonic oscillator potential above and below the critical temperature are found numerically by a method that was done previously [1]. This potential more closely approximates the conditions of the experiments performed to date on alkali atoms. Energy, heat capacity and chemical potential are found numerically. Finally all the results are compared with analytical calculations
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 ...
Occupation probability of harmonic-oscillator quanta for microscopic cluster-model wave functions
Suzuki, Y; Ogawa, Y; Varga, K
1996-01-01
We present a new and simple method of calculating the occupation probability of the number of total harmonic-oscillator quanta for a microscopic cluster-model wave function. Examples of applications are given to the recent calculations including \\alpha+n+n-model for ^6He, \\alpha+t+n+n-model for ^9Li, and \\alpha+\\alpha+n-model for ^9Be as well as the classical calculations of \\alpha+p+n-model for ^6Li and \\alpha+\\alpha+\\alpha-model for ^{12}C. The analysis is found to be useful for quantifying the amount of excitations across the major shell as well as the degree of clustering. The origin of the antistretching effect is discussed.
International Nuclear Information System (INIS)
A new method for continuum discretization in continuum-discretized coupled-channels calculations is proposed. The method is based on an analytic local-scale transformation of the harmonic-oscillator wave functions proposed for other purposes in a recent work [Karatagladis et al., Phys. Rev. C 71, 064601 (2005)]. The new approach is compared with the standard method of continuum discretization in terms of energy bins for the reactions d+58Ni at 80 MeV, 6Li+40Ca at 156 MeV, and 6He+208Pb at 22 MeV and 240 MeV/nucleon. In all cases very good agreement between both approaches is found.
Harmonic oscillator representation in the theory of scattering and nuclear reactions
Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.
1995-01-01
The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.
Crypto-harmonic oscillator in higher dimensions: classical and quantum aspects
International Nuclear Information System (INIS)
We study complexified harmonic oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) who initiated the study of these Crypto-gauge invariant models that can be related to PT-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints (in contrast to Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) where one deals with a single constraint) with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator
Electroproduction of φ-meson from proton within relativistic harmonic oscillator model
International Nuclear Information System (INIS)
We analyze electroproduction of φ-meson from a proton within a uud-s anti s cluster model as a probe of the strangeness content of the proton. Our consideration is based on the relativistic harmonic oscillator quark model which takes into account the Lorentz-contraction effect of the hadron wave functions. We show that the knockout mechanisms are comparable to the vector meson-dominance model of diffractive production if only (1-2)% strange quark admixture is assumed. The uud- and s anti s-knockout cross sections have a qualitatively different dependence on the four-momentum transfer squared to the proton and may be distinguished experimentally. 19 refs., 5 figs
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 transfo...... transforms of the constants of the motion. We derive conditions for which this is actually the case. The Wigner functions of the energy eigenstates of a two-dimensional isotropic harmonic oscillator serve as an important illustration.......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...
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-laps...
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.
Zhao, Liyun; Zhou, Jin; Wu, Quanjun
2016-01-01
This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.
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...
MAVRI, J; LENSINK, M; BERENDSEN, HJC
1994-01-01
A density matrix evolution (DME) method (Berendsen, H. J. C., and Mavri, J., 1993, J. phys. Chem., 97, 13464) to simulate the dynamics of quantum systems embedded in a classical environment is applied to study the inelastic collisions of a classical particle with a five level quantum harmonic oscill
Henein, Simon; Vardi, Ilan; Rubbert, Lennart
2015-01-01
The mechanical isotropic harmonic oscillator comprises at least a two degrees of freedom linkage supporting an orbiting mass with respect to a fixed base with springs having isotropic and linear restoring force properties wherein the mass has a tilting motion. The oscillator may be used in a timekeeper, such a watch.
Lopez, G
2000-01-01
The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results show that there are qualitative and quantitative differences for both approaches, suggesting that the quantization of this constant of motion may be verified experimentally.
Quantization and instability of the damped harmonic oscillator subject to a time-dependent force
International Nuclear Information System (INIS)
We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity (-γx) and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: L=mxy-U(x+1/2 y)+U(x-1/2 y)+(γ)/2 (xy-yx)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x±y/2)=1/2 k(x±y/2)2 specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian H. The Heisenberg equations of motion utilizing the quantized Hamiltonian H surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force. - Highlights: → A method of quantizing dissipative systems is presented. → In order to obtain the method, we apply Bateman's dual system approach. → A formula for a transition amplitude is derived. → We use the formula to study the instability of the dissipative systems.
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
International Nuclear Information System (INIS)
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 boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of the solution of the harmonic oscillator problem.
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.
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-02-01
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high-frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency modulation of the different oscillators. We illustrate how the topologically protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally, we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.
Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
Demarie, Tommaso F.; Linjordet, Trond; Menicucci, Nicolas C.; Brennen, Gavin K.
2014-08-01
The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology.
𝒩 = 2 supersymmetric harmonic oscillator: Basic brackets without canonical conjugate momenta
Srinivas, N.; Shukla, A.; Malik, R. P.
2015-09-01
We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) 𝒩 = 2 supersymmetric (SUSY) harmonic oscillator (HO) without taking the help of the mathematical definition of canonical conjugate momenta with respect to the bosonic and fermionic variables of this toy model for the Hodge theory (where the continuous and discrete symmetries of the theory provide the physical realizations of the de Rham cohomological operators of differential geometry). In our present endeavor, it is the full set of continuous symmetries and their corresponding generators that lead to the derivation of basic (anti)commutators amongst the creation and annihilation operators that appear in the normal mode expansions of the dynamical fermionic and bosonic variables of our present 𝒩 = 2 SUSY theory of a HO. These basic brackets are in complete agreement with such kind of brackets that are derived from the standard canonical method of quantization scheme.
Electroweak scattering of the nucleon in the covariant harmonic oscillator model
International Nuclear Information System (INIS)
The covariant harmonic oscillator model is shown to provide a theoretical framework capable of combining the principles of special relativity and those of quantum mechanics, and which can also be used to describe observed hadronic phenomenon. The results of this current for elastic form factors for nucleons are reviewed. It is then used to calculate matrix elements involved in the electroproduction of resonances. These results are compared to similar previous results, in which different types of wave functions are used and to data, and resonably good agreement is found. Compton scattering of the proton is also studied. Functionally, the calculated cross section agrees well with experimental results. However, the magnitude of the calculated curve is smaller than the data. Given the success of the calculated electromagnetic form factors, it is natural to ask if the weak interaction can be treated in a similar manner. The minimal coupling of the Weinberg-Salam model is used to obtain the weak current of the nucleon in a way similar to that of the electromagnetic case. From this, the weak form factors for the quasi-elastic process nun → μ-p are found and compared to the standard dipole fits. The cross section is calculated and compared with recent data. Both these comparisons are shown to be favorable. Finally, the weak currents are used to calculate matrix elements of the weak production of the Δ(1232) resonance. The cross section for this reaction is found to agree with experimental results
Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
International Nuclear Information System (INIS)
The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology. (paper)
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
International Nuclear Information System (INIS)
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 are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily
International Nuclear Information System (INIS)
A particle produced in a hard collision can lose energy through bremsstrahlung. It has long been of interest to calculate the effect on bremsstrahlung if the particle is produced inside a finite-size QCD medium such as a quark-gluon plasma. For the case of very high-energy particles traveling through the background of a weakly coupled quark-gluon plasma, it is known how to reduce this problem to an equivalent problem in nonrelativistic two-dimensional quantum mechanics. Analytic solutions, however, have always resorted to further approximations. One is a harmonic oscillator approximation to the corresponding quantum mechanics problem, which is appropriate for sufficiently thick media. Another is to formally treat the particle as having only a single significant scattering from the plasma (known as the N=1 term of the opacity expansion), which is appropriate for sufficiently thin media. In a broad range of intermediate cases, these two very different approximations give surprisingly similar but slightly differing results if one works to leading logarithmic order in the particle energy, and there has been confusion about the range of validity of each approximation. In this paper, I sort out in detail the parametric range of validity of these two approximations at leading logarithmic order. For simplicity, I study the problem for small αs and large logarithms but αslog<<1.
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. PMID:27575089
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...
耦合谐振子的魏格纳函数%Wigner Function for Coupled Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
吾拉依木江·司提瓦力地; 沙依甫加马力·达吾来提
2011-01-01
In this article,first we have calculated the Wigner function for coupled harmonic oscillator by solving the time-independent star-eigenvalue equation on usual space.Then by using the Bopp's shift method we evaluated the Wigner function for coupled harmonic oscillator on non-commutative space(NCS) and on non-commutative phase space(NCPS).%本文首先通过求解星本征方程得到了在二维对易空间中耦合谐振子的魏格纳函数,然后利用Bopp平移进一步讨论了在非对易空间和非对易相空间中耦合谐振子的魏格纳函数.
Vladimirov, Igor G.; Petersen, Ian R.
2016-01-01
This paper is concerned with quantum harmonic oscillators consisting of a quantum plant and a directly coupled coherent quantum observer. We employ discounted quadratic performance criteria in the form of exponentially weighted time averages of second-order moments of the system variables. A coherent quantum filtering (CQF) problem is formulated as the minimization of the discounted mean square of an estimation error, with which the dynamic variables of the observer approximate those of the p...
International Nuclear Information System (INIS)
The solutions of the Schrödinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov—Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained. (general)
International Nuclear Information System (INIS)
We present a space-time transformation which changes a quadratic action into a free-particle action.This transformation is used to derive the propagator beyond caustics for a quadratic Lagrangian from the propagator for a free particle. The propagator is in turn derived by the Feynman path integral method. Also, the wavefunction for the damped harmonic oscillator is obtained using an inverse quadratic potential
Sameer M. Ikhdair; Falaye, Babatunde J.
2014-01-01
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 ...
International Nuclear Information System (INIS)
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 δm/mb2. (authors)
Wang, W.-M.
2008-01-01
We prove that the 1- d quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their 1983 paper [EV] in the general quasi-periodic setting. The motivation of the present paper also comes from construction of quasi-periodic solutions for the corresponding nonlinear equation.
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.
Quantum theory of motion of a time-dependent harmonic oscillator in the pilot-wave theory
Ji, J Y; Ji, Jeong-Young; Soh, Kwang-Sup
1998-01-01
The de Broglie-Bohm quantum trajectories are found in analytically closed forms for the eigenstates and the coherent state of the Lewis-Riesenfeld (LR) invariant of a time-dependent harmonic oscillator. It is also shown that an eigenstate (a coherent state) of an invariant can be interpreted as squeezed states obtained by squeezing an eigenstate (a coherent state) of another invariant. This provides ways for a whole description of squeezed states.
Um, C I; Yeon, K H
2000-01-01
We present a space-time transformation which changes a quadratic action into a free-particle action.This transformation is used to derive the propagator beyond caustics for a quadratic Lagrangian from the propagator for a free particle. The propagator is in turn derived by the Feynman path integral method. Also, the wavefunction for the damped harmonic oscillator is obtained using an inverse quadratic potential.
International Nuclear Information System (INIS)
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
M. K. Bahar; Yasuk, ; F.
2013-01-01
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.
International Nuclear Information System (INIS)
The harmonic oscillator approach to the bound states of few-body systems is developed and the lower-energy states are introduced as basis vectors and mixed with a part of harmonic oscillator vectors to calculate the binding energy. The lower energy levels of 3-α system and Λ9Be are presented and compared with experiments or other calculations. The results are satisfactory
A new look at the quantum mechanics of the harmonic oscillator
International Nuclear Information System (INIS)
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 φ element of R mod 2π and I>0. However, the transformation q√(2I)cos φ, p=-√(2I)sin φ is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {(q,p)} has the topological structure of the plane R2, whereas the phase space {(φ,I)} corresponds globally to the punctured plane R2-(0,0) or to a simple cone S1 x R+ 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 R2 consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {q,p,1}, whereas the corresponding canonical group of the phase space {(φ,I)} is the group SO↑(1,2)=Sp(2,R)/Z2, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {h0=I,h1=Icosφ,h2=-Isinφ} which provides also the basic ''observables'' on {(φ, I)}. In the quantum mechanics of the (φ,I)-model of the HO the three hj correspond to self-adjoint generators Kj, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO↑(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 Ek,n=0=ℎωk of the (φ,I)-Hamiltonian H(anti K)=ℎωK0. 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 the usual approach in terms of the operators Q and P which are now expressed as functions of the Kj, but keep their usual properties. The richer structure of the Kj quantum model of the HO is ''erased'' when passing to the simpler Q,P model. This more refined approach to the
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
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.
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
International Nuclear Information System (INIS)
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.
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.
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
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
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
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.
A model of the two-dimensional quantum harmonic oscillator in an $AdS_3$ background
Frick, Rudolf
2016-01-01
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\\"odinger picture in which the analogs of the Schr\\"odinger 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 $AdS_3$ spacetime. In this picture, we have a metamorphosis of the Heisenberg's uncertainty relations.
Directory of Open Access Journals (Sweden)
Sadolah Nasiri
2008-02-01
Full Text Available In a previous work the concept of quantum potential is generalized into extended phase space (EPS for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mechanics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this representation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to Q-function.
International Nuclear Information System (INIS)
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and γ5 chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states
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.
International Nuclear Information System (INIS)
Full text: Edge localized modes (ELMs) can generate unacceptable heat loads to plasma facing components in a reactor scale tokamak or spherical torus, and therefore ELM control is a critical issue in ITER. ELM control using non-axisymmetric (3D) fields is a promising concept, but the 3D coil requirements are demanding in cost and engineering. An alternative means may be to use internally driven 3D field oscillations such as edge harmonic oscillations (EHOs), but the relevant operational window is possibly more limited than the external 3D field applications. The disadvantages of each approach can be mitigated if the external and the internal drive of 3D fields can be constructively combined. This paper presents two important topics for this vision: Experimental observations of edge harmonic oscillations in NSTX (not necessarily the same as EHOs in DIII-D), and theoretical study of its audio-frequency drive using the high harmonic fast wave (HHFW) antenna as 3D field coils. Edge harmonic oscillations were observed particularly well in NSTX ELM-free operation with low n = 1 core modes, with various diagnostics confirming n = 4 - 6 coherent oscillations in 2 - 8 kHz frequency range. These oscillations, which share some characteristics with the n = 1 dominated modes observed in small-ELM regimes in NSTX, seem to have a favored operational window in rotational shear, similarly to EHOs in DIII-D QH modes. However, in NSTX, they are not observed to provide particle or impurity control, possibly due to their weak amplitudes, of a few mm displacements, as measured by reflectometry. The external drive of these modes has been proposed in NSTX, by utilizing audio-frequency currents in the HHFW antenna straps. Analysis shows that the HHFW straps can be optimized to maximize n = 4 - 6 while minimizing n = 1 - 3. Also, IPEC calculations show that the optimized configuration with only 1 kAt current can produce twice larger displacements than the observed internal modes, ∼ 6 mm
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.
Teichmann, Karen; Wenderoth, Martin; Prüser, Henning; Pierz, Klaus; Schumacher, Hans W; Ulbrich, Rainer G
2013-08-14
InAs quantum dots embedded in an AlAs matrix inside a double barrier resonant tunneling diode are investigated by cross-sectional scanning tunneling spectroscopy. The wave functions of the bound quantum dot states are spatially and energetically resolved. These bound states are known to be responsible for resonant tunneling phenomena in such quantum dot diodes. The wave functions reveal a textbook-like one-dimensional harmonic oscillator behavior showing up to five equidistant energy levels of 80 meV spacing. The derived effective oscillator mass of m* = 0.24m0 is 1 order of magnitude higher than the effective electron mass of bulk InAs that we attribute to the influence of the surrounding AlAs matrix. This underlines the importance of the matrix material for tailored QD devices with well-defined properties. PMID:23777509
Quesne, C
2016-01-01
The classical and quantum solutions of a nonlinear model describing harmonic oscillators on the sphere and the hyperbolic plane, derived in polar coordinates in a recent paper [Phys.\\ Lett.\\ A 379 (2015) 1589], are extended by the inclusion of an isotonic term.
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.
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.
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.
International Nuclear Information System (INIS)
The Fisher-Shannon information and a statistical measure of complexity are calculated in position and momentum spaces for the wavefunctions of the quantum isotropic harmonic oscillator. We show that these quantities are independent of the strength of the harmonic potential. Moreover, for each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the classical (circular) orbits in the Bohr-like quantum image, just those with the highest orbital angular momentum
International Nuclear Information System (INIS)
Arguments are presented to show that the new resonance parameters obtained by Alston-Garnjost et al. in a recent analysis of the K-barN system from 365 to 1320 MeV/c provide a prima facie case for the even-wave harmonic-oscillator theory of baryonic states in the framework of SU(6)/sub W/ x O(3). A new quantum classification of the Λ states belonging to the (70,1-) is also proposed
Generalized deformed oscillator for vortices in superfluid films
Bonatsos, Dennis; Daskaloyannis, C.
1997-01-01
The algebra of observables of a system of two identical vortices in a superfluid thin film is described as a generalized deformed oscillator with a structure function containing a linear (harmonic oscillator) term and a quadratic term. In contrast to the deformed oscillators occuring in other physical systems (correlated fermion pairs in a single-$j$ nuclear shell, Morse oscillator), this oscillator is not amenable to perturbative treatment and cannot be approximated by quons. From the mathem...
Deformation Quantization of a Class of Open Systems
Becher, Florian; Waldmann, Stefan
2009-01-01
We give an approach to open quantum systems based on well-known results of formal deformation quantization. It is shown that a certain class of classical open systems can be systematically quantized (in the sense of formal deformation quantization) into a quantum open system preserving the complete positivity of the open time evolution. The usual example of linearly coupled harmonic oscillators shows that some convergent models are included.
Sibel Başkal; Young S. Kim; Noz, Marilyn E.
2014-01-01
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp(2)$. It is shown that this oscillator system contains the essential features of Wigner's little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle ...
Probing deformed quantum commutators
Rossi, Matteo A. C.; Giani, Tommaso; Paris, Matteo G. A.
2016-07-01
Several quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose their physical meaning. In quantum mechanics, the insurgence of such a minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on position measurements has a lower bound. The value of the minimal length is not predicted by theories and must be estimated experimentally. In this paper, we address the quantum bound to the estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra induced by the deformed commutation relations.
Maireche Abdelmadjid
2015-01-01
In present search, we have studied the effect of the both non commutativity of three dimensional space and phase on the Schrödinger equation with companied Harmonic oscillator potential and it’s inverse, know by isotopic Harmonic oscillator plus inverse quadratic (h.p.i.) potential, we shown that the Hermitian NC Hamiltonian formed anisotropic operator and described many physics phenomena’s, we have also derived the exact degenerated spectrum for studied potential in the first order of two in...
Directory of Open Access Journals (Sweden)
Maireche Abdelmadjid
2015-12-01
Full Text Available In present search, we have studied the effect of the both non commutativity of three dimensional space and phase on the Schrödinger equation with companied Harmonic oscillator potential and it’s inverse, know by isotopic Harmonic oscillator plus inverse quadratic (h.p.i. potential, we shown that the Hermitian NC Hamiltonian formed anisotropic operator and described many physics phenomena’s, we have also derived the exact degenerated spectrum for studied potential in the first order of two infinitesimal parameters Θ and associated for noncommutative space and phase, respectively.
Abreu, Everton M C; Mendes, Albert C R; Oliveira, Wilson
2013-01-01
In this work we have investigated some properties of classical phase-space with symplectic structures consistent, at the classical level, with two noncommutative (NC) algebras: the Doplicher-Fredenhagen-Roberts algebraic relations and the NC approach which uses an extended Hilbert space with rotational symmetry. This extended Hilbert space includes the operators $\\theta^{ij}$ and their conjugate momentum $\\pi_{ij}$ operators. In this scenario, the equations of motion for all extended phase-space coordinates with their corresponding solutions were determined and a rotational invariant NC Newton's second law was written. As an application, we treated a NC harmonic oscillator constructed in this extended Hilbert space. We have showed precisely that its solution is still periodic if and only if the ratio between the frequencies of oscillation is a rational number. We investigated, analytically and numerically, the solutions of this NC oscillator in a two-dimensional phase-space. The result led us to conclude that...
Energy Technology Data Exchange (ETDEWEB)
Ilakovac, A.; Tadic-acute-accent, D.D.; Coutinho, F.A.B.; Krmpotic-acute-accent, F.
1986-04-15
We study the introduction of the internal dynamical variables for consituent quarks. These variables are related to the center-of-mass of a nucleon. The problem is connected with the description of spinorial properties of the quarks. The spinors must be artificially introduced in a harmonic oscillator (HO) model. Experimental values of the magnetic moment and the axial-vector coupling constant of a nucleon can be easily reproduced. The theoretical results are not sensitive to the theoretical details; they follow from the general properties of the quark structure of baryons. The connections with the relativistic HO models are also discussed. The case of a very small confinement radius is explored in the Appendix.
International Nuclear Information System (INIS)
We study the introduction of the internal dynamical variables for consituent quarks. These variables are related to the center-of-mass of a nucleon. The problem is connected with the description of spinorial properties of the quarks. The spinors must be artificially introduced in a harmonic oscillator (HO) model. Experimental values of the magnetic moment and the axial-vector coupling constant of a nucleon can be easily reproduced. The theoretical results are not sensitive to the theoretical details; they follow from the general properties of the quark structure of baryons. The connections with the relativistic HO models are also discussed. The case of a very small confinement radius is explored in the Appendix
Cartesian approach for constrained mechanical systems
Ramírez, Rafael
2010-01-01
In the history of mechanics, there have been two points of view for studying mechanical systems: Newtonian and Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential equations in the N dimensional configuration space . In this paper we develop the Cartesian approach for mechanical systems with constraints which are linear with respect to velocity.
Institute of Scientific and Technical Information of China (English)
GENG Li-Sheng; MENG Jie; Toki Hiroshi
2007-01-01
A reflection asymmetric relativistic mean field (RAS-RMF) approach is developed by expanding the equations of motion for both the nucleons and the mesons on the eigenfunctions of the two-centre harmonic-oscillator potential.The efficiency and reliability of the RAS-RMF approach are demonstrated in its application to the well-known octupole deformed nucleus 226Ra and the available data, including the binding energy and the deformation parameters, are well reproduced.
New version of $q$-deformed supersymmetric quantum mechanics
Gavrilik, A M; Lukash, A V
2013-01-01
A new version of the q-deformed supersymmetric quantum mechanics (q-SQM), which is inspired by the Tamm--Dankoff-type (TD-type) deformation of quantum harmonic oscillator, is constructed. The obtained algebra of q-SQM is similar to that in Spiridonov's approach. However, within our version of q-SQM, the ground state found explicitly in the special case of superpotential yiealding q-superoscillator turns out to be non-Gaussian and takes the form of special (TD-type) q-deformed Gaussian.
Turing instabilities on Cartesian product networks
Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline
2015-08-01
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory.
Directory of Open Access Journals (Sweden)
Sibel Başkal
2014-06-01
Full Text Available The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2. It is shown that this oscillator system contains the essential features of Wigner’s little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle invariant. It is shown that the damping modes of the oscillator correspond to the little groups for massive and imaginary-mass particles respectively. When the system makes the transition from the oscillation to damping mode, it corresponds to the little group for massless particles. Rotations around the momentum leave the four-momentum invariant. This degree of freedom extends the Sp(2 symmetry to that of SL(2, c corresponding to the Lorentz group applicable to the four-dimensional Minkowski space. The Poincaré sphere contains the SL(2, c symmetry. In addition, it has a non-Lorentzian parameter allowing us to reduce the mass continuously to zero. It is thus possible to construct the little group for massless particles from that of the massive particle by reducing its mass to zero. Spin-1/2 particles and spin-1 particles are discussed in detail.
Baskal, Sibel; Noz, Marilyn E
2014-01-01
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp(2)$. It is shown that this oscillator system contains the essential features of Wigner's little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle invariant. It is shown that the damping modes of the oscillator correspond to the little groups for massive and imaginary-mass particles respectively. When the system makes the transition from the oscillation to damping mode, it corresponds to the little group for massless particles. Rotations around the momentum leave the four-momentum invariant. This degree of freedom extends the $Sp(2)$ symmetry to that of $SL(2,c)$ corresponding to the Lorentz group applicable to the four-dimensional Minkowski space. The Poincar\\'e sp...
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 to...
Comparison between the Morse eigenfunctions and deformed oscillator wavefunctions
International Nuclear Information System (INIS)
In this work we introduce deformed creation and annihilation operators which differ from the usual harmonic oscillator operators a, a† by a number operator function A circumflex = a circumflex f(n circumflex ), A circumflex † = f(n circumflex )a circumflex †. We construct the deformed coordinate and momentum in terms of the deformed operators and maintain only up to first order terms in the deformed operators. By application of the deformed annihilation operator upon the vacuum state we get the ground state wavefunction in the configuration space and the wavefunctions for excited states are obtained by repeated application of the deformed creation operator. Finally, we compare the wavefunctions obtained with the deformed operators with the corresponding Morse eigenfunctions
Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers
Zanchi, Marta G.; Pauly, John M.; Scott, Greig C
2010-01-01
A modified Cartesian feedback method called “frequency-offset Cartesian feedback” and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems.
Relation of deformed nonlinear algebras with linear ones
International Nuclear Information System (INIS)
The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator. (paper)
Petrenko, Taras; Neese, Frank
2012-12-21
In this work, an improved method for the efficient automatic simulation of optical band shapes and resonance Raman (rR) intensities within the "independent mode displaced harmonic oscillator" is described. Despite the relative simplicity of this model, it is able to account for the intensity distribution in absorption (ABS), fluorescence, and rR spectra corresponding to strongly dipole allowed electronic transitions with high accuracy. In order to include temperature-induced effects, we propose a simple extension of the time dependent wavepacket formalism developed by Heller which enables one to derive analytical expressions for the intensities of hot bands in ABS and rR spectra from the dependence of the wavepacket evolution on its initial coordinate. We have also greatly optimized the computational procedures for numerical integration of complicated oscillating integrals. This is important for efficient simulations of higher-order rR spectra and excitation profiles, as well as for the fitting of experimental spectra of large molecules. In particular, the multimode damping mechanism is taken into account for efficient reduction of the upper time limit in the numerical integration. Excited state energy gradient as well as excited state geometry optimization calculations are employed in order to determine excited state dimensionless normal coordinate displacements. The gradient techniques are highly cost-effective provided that analytical excited state derivatives with respect to nuclear displacements are available. Through comparison with experimental spectra of some representative molecules, we illustrate that the gradient techniques can even outperform the geometry optimization method if the harmonic approximation becomes inadequate. PMID:23267471
Irreducible Cartesian tensor expansions of scalar fields
International Nuclear Information System (INIS)
It is shown how a scalar function V(parallel R + Σ/sub i equals 1/sup n/ a/sub i/parallel) of a sum of n + 1 vectors can be expanded as a multiple Cartesian tensor series in the vectors a/ sub i/. This expansion is a rearrangement of the multiple Taylor series expansion of such a function. In order to prove the fundamental theorem, generalized Cartesian Legendre polynomials are defined. The theorem is applied to the eigenfunctions of the Laplace operator and to inverse powers. The expansion of the latter type of function leads to forms involving generalized hypergeometric functions in several variables. As a special case, the Cartesian form of the multipole expansion of the electrostatic potential between two linear molecules is derived. A number of sum rules for hypergeometric functions and addition formulas for (standard and modified) spherical Bessel functions are proved by using a reduction property of the generalized Legendre polynomials. The case of the expansion of a tensorial function is also briefly discussed
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-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized 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 coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.
Quality-based generation of weather radar Cartesian products
K. Ośródka; J. Szturc
2015-01-01
Weather radar data volumes are commonly processed to obtain various 2-D Cartesian products based on the transfer from polar to Cartesian representations through a certain interpolation method. In this research an algorithm of the spatial interpolation of polar reflectivity data employing quality index data is applied to find the Cartesian reflectivity as plan position indicator products. On this basis, quality-based versions of standard algorithms for the generation of the foll...
Double Wave Description of the Motion of Harmonic Oscillator with Time-dependent Mass%质量含时谐振子运动的双波描述
Institute of Scientific and Technical Information of China (English)
吴奇学
2001-01-01
Double wave function is used to decribe the motion of the harmonic oscillator with time-dependent mass. The time evolution equations of related physical quantities are obtained. The classical limit of double wave description could have exactly the same results as those of the classical mechanics.%应用双波理论描述质量含时谐振子的量子运动,得到了振子各相关物理量的时间演化方程以及双波描述的经典极限与纯经典力学结果一致的结论.
Emergent Soft Monopole Modes in Weakly-Bound Deformed Nuclei
Pei, J C; Zhang, Y N; Xu, F R
2014-01-01
Based on the Hartree-Fock-Bogoliubov solutions in large deformed coordinate spaces, the finite amplitude method for quasiparticle random phase approximation (FAM-QRPA) has been implemented, providing a suitable approach to probe collective excitations of weakly-bound nuclei embedded in the continuum. The monopole excitation modes in Magnesium isotopes up to the neutron drip line have been studied with the FAM-QRPA framework on both the coordinate-space and harmonic oscillator basis methods. Enhanced soft monopole strengths and collectivity as a result of weak-binding effects have been unambiguously demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Wang, Chen-Wen; Zhu, Chaoyuan, E-mail: cyzhu@mail.nctu.edu.tw; Lin, Sheng-Hsien [Institute of Molecular Science, Department of Applied Chemistry and Center for Interdisciplinary Molecular Science, National Chiao-Tung University, Hsinchu 30050, Taiwan (China); Yang, Ling [Institute of Molecular Science, Department of Applied Chemistry and Center for Interdisciplinary Molecular Science, National Chiao-Tung University, Hsinchu 30050, Taiwan (China); Institute of Theoretical and Simulation Chemistry, Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Harbin 150080 (China); Yu, Jian-Guo [Department of Chemistry, Beijing Normal University, Beijing 100875 (China)
2014-08-28
Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang–Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X {sup 1}A{sub g} ↔ A{sup 1}B{sub 1u} absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v{sub 10} is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases.
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.
Electrostatic PIC with adaptive Cartesian mesh
Kolobov, Vladimir; Arslanbekov, Robert
2016-05-01
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.
Density- and wavefunction-normalized Cartesian spherical harmonics for l≤ 20
International Nuclear Information System (INIS)
The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l≤7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily for I≤4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l≤ 7. In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle & Coppens method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l≤20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics
Cartesian anisotropic mesh adaptation for compressible flow
International Nuclear Information System (INIS)
Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This paper discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for compressible flow. This technique, developed for laminar flow by Ham, Lien and Strong, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this paper the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. The convection scheme used is the Advective Upstream Splitting Method (Plus), and the refinement/ coarsening criteria are based on work done by Ham et al. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant. (author)
Bilateral Teleoperation in Cartesian Space with Time-Varying Delay
Directory of Open Access Journals (Sweden)
Zhang Chen
2012-10-01
Full Text Available The bilateral control of a teleoperator in Cartesian space with time‐varying delay is studied in this paper. Compared with the traditional joint‐space teleoperation mode, bilateral control in Cartesian space has advantages when dealing with the kinematically dissimilar (KDS teleoperation systems. A Cartesian space‐based PD‐like bilateral controller with dissipation factors is designed. Considering the fact that attitude errors derived by rotation matrix cannot be directly used for PD control, a quaternion‐based approach is adopted to calculate the attitude errors in Cartesian space. In order to overcome the instability brought about by communication delay, local damping components are employed at both ends of the teleoperator system. The variation of time delay may generate extra energy and influence the stability of the system, thus dissipation factors are introduced into the controller. The stability of the proposed bilateral controller is proved and the simulations show the effectiveness of the approach.
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.
Hegel's Solution to Cartesian Dualism of Mind and Body
Farzad Haji Mirzaie
2015-01-01
In this paper, I am going to review the Hegelian solution to solve Cartesian doctrine of the mind body dualism. Such a dichotomy refers to the fact that in the recognition we are dealing with two completely different and separate domains, i.e., the internal world (ideas, beliefs, concepts, and mentalities), and the external world (the domain of objects) that which refers to the first domain. Hegel believes that Cartesian dualism arises from a categorical mistake. He says that subjectivism is ...
A simple Cartesian scheme for compressible multimaterials
Gorsse, Yannick; Milcent, Thomas; TELIB, Haysam
2014-01-01
We present a simple numerical method to simulate the interaction of two non-miscible compressible materials separated by an interface. The media considered may have significantly different physical properties and constitutive laws, describing for example fluids or hyperelastic solids. The model is fully Eulerian and the scheme is the same for all materials. We show stiff numerical illustrations in case of gas--gas, gas--water, gas--elastic solid interactions in the large deformation regime.
Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers.
Zanchi, Marta G; Pauly, John M; Scott, Greig C
2010-05-01
A modified Cartesian feedback method called "frequency-offset Cartesian feedback" and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems.In this method, the reference input and feedback signals are down-converted and compared at a low intermediate frequency (IF) instead of at DC. The polyphase difference amplifiers create a complex control bandwidth centered at this low IF, which is typically offset from DC by 200-1500 kHz. Consequently, the loop gain peak does not overlap DC where voltage offsets, drift, and local oscillator leakage create errors. Moreover, quadrature mismatch errors are significantly attenuated in the control bandwidth. Since the polyphase amplifiers selectively amplify the complex signals characterized by a +90° phase relationship representing positive frequency signals, the control system operates somewhat like single sideband (SSB) modulation. However, the approach still allows the same modulation bandwidth control as classic Cartesian feedback.In this paper, the behavior of the polyphase difference amplifier is described through both the results of simulations, based on a theoretical analysis of their architecture, and experiments. We then describe our first printed circuit board prototype of a frequency-offset Cartesian feedback transmitter and its performance in open and closed loop configuration. This approach should be especially useful in magnetic resonance imaging transmit array systems. PMID:20814450
Estimation of Cartesian Space Robot Trajectories Using Unit Quaternion Space
Directory of Open Access Journals (Sweden)
Aleš Ude
2014-08-01
Full Text Available The ability to estimate Cartesian space trajectories that include orientation is of great importance for many practical applications. While it is becoming easier to acquire trajectory data by computer vision methods, data measured by general-purpose vision or depth sensors are often rather noisy. Appropriate smoothing methods are thus needed in order to reconstruct smooth Cartesian space trajectories given noisy measurements. In this paper, we propose an optimality criterion for the problem of the smooth estimation of Cartesian space trajectories that include the end-effector orientation.Based on this criterion, we develop an optimization method for trajectory estimation which takes into account the special properties of the orientation space, which we represent by unit quaternions.The efficiency of the developed approach is discussed and experimental results are presented.
An infinite family of superintegrable deformations of the Coulomb potential
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah [Centre de recherches mathematiques, CP 6128 succ. Centre-Ville, Montreal, QC H3C 3J7 (Canada); Winternitz, Pavel, E-mail: post@CRM.UMontreal.C, E-mail: wintern@CRM.UMontreal.C [Centre de recherches mathematiques and Departement de mathematiques et de statistique, CP 6128 succ. Centre-Ville, Montreal, QC H3C 3J7 (Canada)
2010-06-04
We introduce a new family of Hamiltonians with a deformed Kepler-Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the classical trajectories and quantum wavefunctions. We show that this system is related, via coupling constant metamorphosis, to a family of superintegrable deformations of the harmonic oscillator given by Tremblay, Turbiner and Winternitz. In doing so, we prove that all Hamiltonians with an oscillator term are related by coupling constant metamorphosis to systems with a Kepler-Coulomb term, both on Euclidean space. We also look at the effect of the transformation on the integrals of the motion, the classical trajectories and the wavefunctions, and give the transformed integrals explicitly for the classical system. (fast track communication)
An infinite family of superintegrable deformations of the Coulomb potential
Post, S
2010-01-01
We introduce a new family of Hamiltonians with a deformed Kepler- Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the classical trajectories and quantum wave functions. We show that this system is related, via coupling constant metamorphosis, to a family of superintegrable deformations of the harmonic oscillator given by Tremblay, Turbiner and Winternitz. In doing so, we prove that all Hamiltonians with an oscillator term are related by coupling constant metamorphosis to systems with a Kepler-Coulomb term, both on Euclidean space. We also look at the effect of the transformation on the integrals of the motion, the classical trajectories and the wave functions and give the transformed integrals explicitly for the classical system.
An infinite family of superintegrable deformations of the Coulomb potential
International Nuclear Information System (INIS)
We introduce a new family of Hamiltonians with a deformed Kepler-Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the classical trajectories and quantum wavefunctions. We show that this system is related, via coupling constant metamorphosis, to a family of superintegrable deformations of the harmonic oscillator given by Tremblay, Turbiner and Winternitz. In doing so, we prove that all Hamiltonians with an oscillator term are related by coupling constant metamorphosis to systems with a Kepler-Coulomb term, both on Euclidean space. We also look at the effect of the transformation on the integrals of the motion, the classical trajectories and the wavefunctions, and give the transformed integrals explicitly for the classical system. (fast track communication)
Oblate deformation of light neutron-rich even-even nuclei
Hamamoto, Ikuko
2014-01-01
Light neutron-rich even-even nuclei, of which the ground state is oblately deformed, are looked for, examining the Nilsson diagram based on the realistic Woods-Saxon potentials. One-particle energies of the Nilsson diagram are calculated by solving the coupled differential equations obtained from the Schr\\"{o}dinger equation in coordinate space with the proper asymptotic behavior for $r \\rightarrow \\infty$ for both one-particle bound and resonant levels. The eigenphase formalism is used in the calculation of one-particle resonant energies. Large energy gaps on the oblate side of the Nilsson diagrams are found to be related to the magic numbers for the oblate deformation of the harmonic-oscillator potential where the frequency ratios ($\\omega_{\\perp} : \\omega_{z}$) are simple rational numbers. In contrast, for the prolate deformation the magic numbers obtained from simple rational ratios of ($\\omega_{\\perp} : \\omega_{z}$) of the harmonic-oscillator potential are hardly related to the particle numbers, at which...
具有有界干扰的耦合谐振子网络的一致性%The Consistency of Coupled Harmonic Oscillator Network with Bounded Disturbance
Institute of Scientific and Technical Information of China (English)
范龙云; 朱善华; 徐承杰; 文平; 文伟
2015-01-01
为了研究具有有界外部干扰的耦合谐振子网络的一致性，先利用变结构控制方法提出具有有界外部干扰的耦合谐振子网络的一致性协议；再运用Lyapunov稳定性理论、代数图论和矩阵理论，得到谐振子网络实现一致的充分条件；最后利用数值模拟验证提出协议的有效性。%For investigating the consistency of coupled harmonic oscillator network with bounded external disturbances,firstly proposed the consensus protocol by using the variable structure control method; Secondly based on Lyapunov stability theory, algebraic graph theory and matrix theory, obtained sufficient conditions for realizing the network consistency. Finally, used numerical simulation to verify the validity of the proposed protocol.
Mixed connectivity of Cartesian graph products and bundles
Erves, Rija
2010-01-01
Mixed connectivity is a generalization of vertex and edge connectivity. A graph is $(p,0)$-connected, $p>0$, if the graph remains connected after removal of any $p-1$ vertices. A graph is $(p,q)$-connected, $p\\geq 0$, $q>0$, if it remains connected after removal of any $p$ vertices and any $q-1$ edges. Cartesian graph bundles are graphs that generalize both covering graphs and Cartesian graph products. It is shown that if graph $F$ is $(p_{F},q_{F})$-connected and graph $B$ is $(p_{B},q_{B})$-connected, then Cartesian graph bundle $G$ with fibre $F$ over the base graph $B$ is $(p_{F}+p_{B},q_{F}+q_{B})$-connected. Furthermore, if $q_{F},q_{B}>0$, then $G$ is also $(p_{F}+p_{B}+1,q_{F}+q_{B}-1)$-connected. Finally, let graphs $G_i, i=1,...,n,$ be $(p_i,q_i)$-connected and let $k$ be the number of graphs with $q_i>0$. The Cartesian graph product $G=G_1\\Box G_2\\Box ... \\Box G_n$ is $(\\sum p_i,\\sum q_i)$-connected, and, for $ k\\geq 1$, it is also $(\\sum p_i+k-1,\\sum q_i-k+1)$-connected.
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 Cartesian Diver, Surface Tension and the Cheerios Effect
Chen, Chi-Tung; Lee, Wen-Tang; Kao, Sung-Kai
2014-01-01
A Cartesian diver can be used to measure the surface tension of a liquid to a certain extent. The surface tension measurement is related to the two critical pressures at which the diver is about to sink and about to emerge. After sinking because of increasing pressure, the diver is repulsed to the centre of the vessel. After the pressure is…
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…
Cartesian to geodetic coordinates conversion on a triaxial ellipsoid
Ligas, Marcin
2012-04-01
A new method of transforming Cartesian to geodetic (or planetographic) coordinates on a triaxial ellipsoid is presented. The method is based on simple reasoning coming from essentials of vector calculus. The reasoning results in solving a nonlinear system of equations for coordinates of the point being the projection of a point located outside or inside a triaxial ellipsoid along the normal to the ellipsoid. The presented method has been compared to a vector method of Feltens (J Geod 83:129-137, 2009) who claims that no other methods are available in the literature. Generally, our method turns out to be more accurate, faster and applicable to celestial bodies characterized by different geometric parameters. The presented method also fits to the classical problem of converting Cartesian to geodetic coordinates on the ellipsoid of revolution.
Cartesian grid methods for the compressible Navier-Stokes equations
Skøien, Are Arstad
2012-01-01
A Cartesian grid method has been developed for solving the 2D Euler and Navier-Stokes equations for viscous and inviscid compressible flow, respectively. Both steady and unsteady flows have been considered. Using a simplified ghost point treatment, we consider the closest grid points as mirror points of the ghost points. Wall boundary conditions are imposed at the ghost points of the immersed boundary. The accuracy of the method has been investigated for various test cases. We show computed e...
Cognitive Semantics: An Extension of the Cartesian Legacy
Karmakar, Samir
2006-01-01
The basic intention of this article is to show how the cognitive semantics inherits its ancestry from the Cartesian foundation. The emergence of the cognitive semantics is envisaged here as an integral part of the knowledge evolution, in terms of shifts, which ultimately determines the future direction of our epistemological quest. Basically two questions have been emphasized here: (a) how (and what amount of) common sense metaphysics can be incorporated within the existing system of knowledg...
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
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.
ONMCGP: Orthogonal Neighbourhood Mutation Cartesian Genetic Programming for Evolvable Hardware
International Nuclear Information System (INIS)
Evolvable Hardware is facing the problems of scalability and stalling effect. This paper proposed a novel Orthogonal Neighbourhood Mutation (ONM) operator in Cartesian genetic programming (CGP), to reduce the stalling effect in CGP and improve the efficiency of the algorithms.The method incorporates with Differential Evolution strategy. Demonstrated by experiments on benchmark, the proposed Orthogonal Neighbourhood Search can jump out of Local optima, reduce the stalling effect in CGP and the algorithm convergence faster
Hegel's Solution to Cartesian Dualism of Mind and Body
Directory of Open Access Journals (Sweden)
Farzad
2015-10-01
Full Text Available In this paper, I am going to review the Hegelian solution to solve Cartesian doctrine of the mind body dualism. Such a dichotomy refers to the fact that in the recognition we are dealing with two completely different and separate domains, i.e., the internal world (ideas, beliefs, concepts, and mentalities, and the external world (the domain of objects that which refers to the first domain. Hegel believes that Cartesian dualism arises from a categorical mistake. He says that subjectivism is the starting point that fundamentally is wrong. Hegel argues that a genuine philosophy could overcome the dichotomy. According to Hegel, it is only by the idea of "absolute" and “identity in differences” that could be possible to go out of this dualism. The role of philosophy, for him, is theorizing "about the real world”. Hegel says that these contradictions are within the "structure of consciousness." By adopting the right approach in explaining Cartesian doctrine of the mind body dualism from a phenomenological perspective, it can be possible to show the mind’s Odyssey within reality.
Topology preserving advection of implicit interfaces on Cartesian grids
Qin, Zhipeng; Delaney, Keegan; Riaz, Amir; Balaras, Elias
2015-06-01
Accurate representation of implicit interface topology is important for the numerical computation of two phase flow on Cartesian grids. A new method is proposed for the construction of signed distance function by geometrically projecting interface topology onto the Cartesian grid using a multi-level projection framework. The method involves a stepwise improvement in the approximation to the signed distance function based on pointwise, piecewise and locally smooth reconstructions of the interface. We show that this approach provides accurate representation of the projected interface and its topology on the Cartesian grid, including the distance from the interface and the interface normal and curvature. The projected interface can be in the form of either a connected set of marker particles that evolve with Lagrangian advection, or a discrete set of points associated with an implicit interface that evolves with the advection of a scalar function. The signed distance function obtained with geometric projection is independent of the details of the scaler field, in contrast to the conventional approach where advection and reinitialization cannot be decoupled. As a result, errors introduced by reinitialization do not amplify advection errors, which leads to substantial improvement in both volume conservation and topology representation.
Development of a Cartesian grid based CFD solver (CARBS)
International Nuclear Information System (INIS)
Formulation for 3D transient incompressible CFD solver is developed. The solution of variable property, laminar/turbulent, steady/unsteady, single/multi specie, incompressible with heat transfer in complex geometry will be obtained. The formulation can handle a flow system in which any number of arbitrarily shaped solid and fluid regions are present. The solver is based on the use of Cartesian grids. A method is proposed to handle complex shaped objects and boundaries on Cartesian grids. Implementation of multi-material, different types of boundary conditions, thermo physical properties is also considered. The proposed method is validated by solving two test cases. 1st test case is that of lid driven flow in inclined cavity. 2nd test case is the flow over cylinder. The 1st test case involved steady internal flow subjected to WALL boundaries. The 2nd test case involved unsteady external flow subjected to INLET, OUTLET and FREE-SLIP boundary types. In both the test cases, non-orthogonal geometry was involved. It was found that, under such a wide conditions, the Cartesian grid based code was found to give results which were matching well with benchmark data. Convergence characteristics are excellent. In all cases, the mass residue was converged to 1E-8. Based on this, development of 3D general purpose code based on the proposed approach can be taken up. (author)
The Constraints and Spectra of a Deformed Quantum Mechanics
Ching, Chee-Leong; Singh, Kuldip
2012-01-01
We examine a deformed quantum mechanics in which the commutator between coordinates and momenta is a function of momenta. The Jacobi identity constraint on a two-parameter class of such modified commutation relations (MCR's) shows that they encode an intrinsic maximum momentum; a sub-class of which also imply a minimum position uncertainty. Maximum momentum causes the bound state spectrum of the one-dimensional harmonic oscillator to terminate at finite energy, whereby classical characteristics are observed for the studied cases. We then use a semi-classical analysis to discuss general concave potentials in one dimension and isotropic power-law potentials in higher dimensions. Among other conclusions, we find that in a subset of the studied MCR's, the leading order energy shifts of bound states are of opposite sign compared to those obtained using string-theory motivated MCR's, and thus these two cases are more easily distinguishable in potential experiments.
Miao, Sha; Hendrickson, Kelli; Liu, Yuming; Subramani, Hariprasad
2015-11-01
This work presents a novel and efficient Cartesian-grid based simulation capability for the study of an incompressible, turbulent gas layer over a liquid flow with disparate Reynolds numbers in two phases. This capability couples a turbulent gas-flow solver and a liquid-layer based on a second-order accurate Boundary Data Immersion Method (BDIM) at the deformable interface. The turbulent gas flow solver solves the incompressible Navier-Stokes equations via direct numerical simulation or through turbulence closure (unsteady Reynolds-Averaged Navier-Stokes Models) for Reynolds numbers O(106). In this application, a laminar liquid layer solution is obtained from depth-integrated Navier-Stokes equations utilizing shallow water wave assumptions. The immersed boundary method (BDIM) enforces the coupling at the deformable interface, the boundary conditions to turbulence closure equations and defines the domain geometry on the Cartesian grid. Validations are made for the turbulent gas channel flow over high-viscosity liquid. This simulation capability can be applied to problems in the oil and industrial sector such as channel and pipe flows with heavy oils as well as wind wave generation in shallow waters. Sponsored by the Chevron Energy Technology Company.
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
DEFF Research Database (Denmark)
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
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...
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.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
Moustafa, Salli; Dutka Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-01-01
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, DOM...
Cartesian Dualism and Conceptual Change of the Soul
İlyas Altuner
2013-01-01
Cartesian philosophy inserts into philosophy the conception of consciousness which is a source for modern psychology, by leaving traditional understanding on the soul. Whereas Descartes reduces the soul to an organism which animates only or animal spirits, he connects thought to faculty of mind or rational soul that which he exalts as a gift of God. Thus, human being is named a mental thing in that he thinks, and a machine in that he acts. The exaltation of thought means that the only thing w...
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.
The Wigner-Eckart Theorem for Reducible Symmetric Cartesian Tensor Operators
Bouzas, Antonio O.
2015-01-01
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that constitute simultaneously a basis of the spaces of cartesian and spherical irreducible tensors. As a consequence, we extend the Wigner--Eckart theorem to cartesian irreducible tensor operators of any rank, and to totally symmetric reducible ones. We also discuss t...
Shell Corrections for Finite-Depth Deformed Potentials Green's Function Oscillator Expansion Method
Vertse, T; Nazarewicz, W
2000-01-01
Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are affected by the spurious contribution from the unphysical particle gas. In the new method, the shell correction approaches the exact limit provided that the dimension of the single-particle (harmonic oscillator) basis is sufficiently large. For spherical potentials, the present method is faster than the exact one in which the contribution from the particle continuum states is explicitly calculated. For deformed potentials, the Green's function method offers a practical and reliable way of calculating shell corrections for weakly bound nuclei.
Orbital 1+ strengths from self-consistent deformed mean field calculations
International Nuclear Information System (INIS)
We present results for summed orbital 1+ strengths in Sm and Nd isotopes obtained from deformed Hartree-Fock+BCS calculations, using a microscopic formulation of the scissors mode (the PHFB model) that excludes spurious contributions. It is found that the calculated 1+ strengths for the two chains of isotopes are proportional to δ2 and that the summed strengths up to 4 MeV are in fair agreement with experimental data. It is also found that when pairing is neglected the total scissors mode strength is proportional to δ rather than to δ2. Analytical expressions are given for the explicit dependence on the deformation parameter with and without pairing, valid for the anisotropic harmonic oscillator model
[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. PMID:2420000
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...
Adjoint Formulation for an Embedded-Boundary Cartesian Method
Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.
2004-01-01
Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code
Freitas, Andreia C.; Wylezinska, Marzena; BIRCH, MALCOLM J.; Petersen, Steffen E; Miquel, Marc E
2016-01-01
Dynamic imaging of the vocal tract using real-time MRI has been an active and growing area of research, having demonstrated great potential to become routinely performed in the clinical evaluation of speech and swallowing disorders. Although many technical advances have been made in regards to acquisition and reconstruction methodologies, there is still no consensus in best practice protocols. This study aims to compare Cartesian and non-Cartesian real-time MRI sequences, regarding image qual...
The Numerical Simulation of Ship Waves using Cartesian Grid Methods
Sussman, Mark
2014-01-01
Two different cartesian-grid methods are used to simulate the flow around the DDG 5415. The first technique uses a "coupled level-set and volume-of-fluid" (CLS) technique to model the free-surface interface. The no-flux boundary condition on the hull is imposed using a finite-volume technique. The second technique uses a level-set technique (LS) to model the free-surface interface. A body-force technique is used to impose the hull boundary condition. The predictions of both numerical techniques are compared to whisker-probe measurements of the DDG 5415. The level-set technique is also used to investigate the breakup of a two-dimensional spray sheet.
A variant of Marstrand's theorem for projections of cartesian products
Velázquez, Jorge Erick López
2011-01-01
We prove the following variant of Marstrand's theorem about projections of cartesian products of sets: Consider the space $\\Lambda_m=\\set{(t,O), t\\in\\R, O\\in SO(m)}$ with the natural measure and set $\\Lambda=\\Lambda_{m_1}\\times\\ppp\\times\\Lambda_{m_n}$. For every $\\la=(t_1,O_1,\\ppp,t_n,O_n)\\in\\Lambda$ and every $x=(x^1,\\ppp,x^n)\\in\\R^{m_1}\\times\\ppp\\times\\R^{m_n}$ we define $\\pi_\\la(x)=\\pi(t_1O_1x^1,\\ppp,t_nO_nx^n)$. Suppose that $\\pi$ is surjective and set $$\\mathfrak{m}:=\\min\\set{\\sum_{i\\in I}\\dim_H(K_i) + \\dim\\pi(\\bigoplus_{i\\in I^c}\\R^{m_i}), I\\subset\\set{1,\\ppp,n}, I\
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.
Multi-fault Tolerance for Cartesian Data Distributions
Energy Technology Data Exchange (ETDEWEB)
Ali, Nawab; Krishnamoorthy, Sriram; Halappanavar, Mahantesh; Daily, Jeffrey A.
2013-06-01
Faults are expected to play an increasingly important role in how algorithms and applications are designed to run on future extreme-scale sys- tems. Algorithm-based fault tolerance (ABFT) is a promising approach that involves modications to the algorithm to recover from faults with lower over- heads than replicated storage and a signicant reduction in lost work compared to checkpoint-restart techniques. Fault-tolerant linear algebra (FTLA) algo- rithms employ additional processors that store parities along the dimensions of a matrix to tolerate multiple, simultaneous faults. Existing approaches as- sume regular data distributions (blocked or block-cyclic) with the failures of each data block being independent. To match the characteristics of failures on parallel computers, we extend these approaches to mapping parity blocks in several important ways. First, we handle parity computation for generalized Cartesian data distributions with each processor holding arbitrary subsets of blocks in a Cartesian-distributed array. Second, techniques to handle corre- lated failures, i.e., multiple processors that can be expected to fail together, are presented. Third, we handle the colocation of parity blocks with the data blocks and do not require them to be on additional processors. Several al- ternative approaches, based on graph matching, are presented that attempt to balance the memory overhead on processors while guaranteeing the same fault tolerance properties as existing approaches that assume independent fail- ures on regular blocked data distributions. The evaluation of these algorithms demonstrates that the additional desirable properties are provided by the pro- posed approach with minimal overhead.
Chaotic motion in axially symmetric potentials with oblate quadrupole deformation
International Nuclear Information System (INIS)
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.
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.
Ring, P; Lalazissis, G A
1997-01-01
A Fortran program for the calculation of the ground state properties of axially deformed even-even nuclei in the relativistic framework is presented. In this relativistic mean field (RMF) approach a set of coupled differential equations namely the Dirac equation with potential terms for the nucleons and the Glein-Gordon type equations with sources for the meson and the electromagnetic fields are to be solved self-consistently. The well tested basis expansion method is used for this purpose. Accordingly a set of harmonic oscillator basis generated by an axially deformed potential are used in the expansion. The solution gives the nucleon spinors, the fields and level occupancies, which are used in the calculation of the ground state properties.
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.
A note on the partition dimension of Cartesian product graphs
Yero, Ismael G
2010-01-01
Let $G=(V,E)$ be a connected graph. The distance between two vertices $u,v\\in V$, denoted by $d(u, v)$, is the length of a shortest $u-v$ path in $G$. The distance between a vertex $v\\in V$ and a subset $P\\subset V$ is defined as $min\\{d(v, x): x \\in P\\}$, and it is denoted by $d(v, P)$. An ordered partition $\\{P_1,P_2, ...,P_t\\}$ of vertices of a graph $G$, is a \\emph{resolving partition}of $G$, if all the distance vectors $(d(v,P_1),d(v,P_2),...,d(v,P_t))$ are different. The \\emph{partition dimension} of $G$, denoted by $pd(G)$, is the minimum number of sets in any resolving partition of $G$. In this article we study the partition dimension of Cartesian product graphs. More precisely, we show that for all pairs of connected graphs $G, H$, $pd(G\\times H)\\le pd(G)+pd(H)$ and $pd(G\\times H)\\le pd(G)+dim(H).$ Consequently, we show that $pd(G\\times H)\\le dim(G)+dim(H)+1.$
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
International Nuclear Information System (INIS)
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multi-core + SIMD - Single Instruction on Multiple Data) 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. (authors)
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...
Solus Secedo and Sapere Aude: Cartesian Meditation as Kantian Enlightenment
Directory of Open Access Journals (Sweden)
Suma Rajiva
2015-11-01
Full Text Available Recently Samuel Fleischacker has developed Kant’s model of enlightenment as a “minimalist enlightenment” in the tradition of a relatively thin proceduralism focused on the form of public debate and interaction. I want to discuss the possibility that such a minimalism, endorsed by Fleischacker, Habermas, Rawls, and others, benefits from a metaphysics of critical individual subjectivity as a prerequisite for the social proceduralism of the minimalist enlightenment. I argue that Kant’s enlightenment, metaphysically thicker than much contemporary proceduralism, constitutes a recovery and transformation of a subjective interiority deeply Cartesian in spirit and central to the reciprocity of the community of subjects in What is Enlightenment. This opens a space for a site of resistance to the social. Descartes’ solus secedo describes the analogical space of such a resistance for Kant’s sapere aude. The Meditations thus point forward implicitly to how a rational subject might achieve critical distance from tradition in its various forms, epistemic, ethical, moral, and political.
Tolerating Correlated Failures for Generalized Cartesian Distributions via Bipartite Matching
International Nuclear Information System (INIS)
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.
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 multilevel Cartesian non-uniform grid time domain algorithm
International Nuclear Information System (INIS)
A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at Ns observation locations from Ns collocated sources for Nt discrete time instances scales as O(NtNslogNs) and O(NtNslog2Ns) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.
Towards Efficient Viscous Modeling Based on Cartesian Methods for Automated Flow Simulation Project
National Aeronautics and Space Administration — The proposed work aims at developing techniques that will address the current limitations of Cartesian-based Navier-Stokes CFD schemes by exploring three promising...
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.
The Impact of Dutch Cartesian Medical Reformers in Early Enlightenment German Culture
Munt, A. H.
2005-01-01
This study analyses the reception and influence of Dutch Cartesian medical reformers in German culture during the Early Enlightenment period. The impact of their proposed reforms, involving the rejection of traditional Galenic-Aristotelian theory and practice, and placing medicine in an essentially new, mechanistic scienceoriented Cartesian philosophical framework, is discussed in the context of the large number of German translations of their works, published often in several ...
The impact of Dutch Cartesian medical reformers in early Enlightenment German culture (1680-1720).
Munt, A. H.
2005-01-01
This study analyses the reception and influence of Dutch Cartesian medical reformers in German culture during the Early Enlightenment period. The impact of their proposed reforms, involving the rejection of traditional Galenic-Aristotelian theory and practice, and placing medicine in an essentially new, mechanistic science-oriented Cartesian philosophical framework, is discussed in the context of the large number of German translations of their works, published often in several editions in va...
Choi, Cheol Ho
2004-02-22
A new way of generating the multipole moments of Cartesian Gaussian functions in spherical polar coordinates has been established, bypassing the intermediary of Cartesian moment tensors. A new set of recurrence relations have also been derived for the resulting analytic integral values. The new method furnishes a conceptually simple and numerically efficient evaluation procedure for the multipole moments. The advantages over existing methods are documented. The results are relevant for the linear scaling quantum theories based on the fast multipole method. PMID:15268515
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
Multiscale geometric modeling of macromolecules I: Cartesian representation
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
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
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
Analysis of Crustal Magnetisation in Cartesian Vector Harmonics
Gubbins, D.; Ivers, D.; Williams, S.
2015-12-01
We present a new set of functions, Vector Cartesian Harmonics (VCH), analogous to the Vector Spherical Harmonics that we have applied recently to global models of crustal and lithospheric magnetisation. Like their spherical counterpart, the VCH form a complete, orthogonal set: planar models of magnetisation can be expanded in them. There are 3 distinct types of VCH, one representing that part of the magnetisation which generates the potential magnetic field above the surface, another the potential magnetic field below the surface, and a toroidal function that generates only a non-potential field. One function therefore describes the magnetisation detected by observations of the magnetic anomaly while the other two describe the null space of an inversion of magnetic observations for magnetisation. The formalism is therefore ideal for analysing the results of inversions for magnetic structures in plane layers such as local or regional surveys where Earth's curvature can be ignored. The null space is in general very large, being an arbitrary combination of a doubly-infinite set of vector functions. However, in the absence of remanence and when the inducing field is uniform the null space reduces to only 2 types of structure, uniform susceptibility (Runcorn's Theorem) and a pattern of susceptibility induced by a uniform field, the null space is restricted to uniform magnetisation and 1D patterns of susceptibility aligned with a horizontal inducing field. Both these cases are already well known, but this analysis shows them to be the ONLY members of the null space. We also give results for familiar text-book structures to show the nature of the null space in each case. Curiously, inversion of the magnetic field from a buried dipole returns exactly half the correct magnitude plus a spurious distributed magnetisation. A more complex application is the topographic structure based on the Bishop formation in California (Fairhead and Williams, SEG exp. abstr. 25, 845, 2006
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.
Contrast sensitivity to angular frequency gratings is not higher than to Cartesian gratings
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Zana Y.
2004-01-01
Full Text Available When contrast sensitivity functions to Cartesian and angular gratings were compared in previous studies the peak sensitivity to angular stimuli was reported to be 0.21 log units higher. In experiments carried out to repeat this result, we used the same two-alternative forced-choice paradigm, but improved experimental control and precision by increasing contrast resolution from 8 to 12 bits, increasing the screen refresh rate from 30 Hz interlaced to 85 Hz non-interlaced, linearizing the voltage-luminance relation, modulating luminance in frequencies that minimize pixel aliasing, and improving control of the subject's exposure to the stimuli. The contrast sensitivity functions to Cartesian and angular gratings were similar in form and peak sensitivity (2.4 cycles per visual degree (c/deg and 32 c/360º, respectively to those reported in a previous study (3 c/deg and 32 c/360º, respectively, but peak sensitivity to angular stimuli was 0.13 log units lower than that to Cartesian stimuli. When the experiment was repeated, this time simulating the experimental control level used in the previous study, no difference between the peak sensitivity to Cartesian and angular stimuli was found. This result agrees with most current models that assume Cartesian filtering at the first visual processing stage. The discrepancy in the results is explained in part by differences in the degree of experimental control.
Geometry of Minimally Deformed Vortices and Domain Walls
Dobrowolski, Tomasz
2011-01-01
In this paper we consider relativistic models that contain in their spectra of solutions extended topological defects. We find the geometrical constrains that describe deformed vortices and domain walls of constant width. Analytical form of these solutions in co-moving coordinates is identical with analytical form of the appropriate static solutions in the laboratory Cartesian coordinates. The geometrical constrains presented in this report describe fully the shape and the evolution of the vo...
Experimental Decomposition of the Wave-Functions of Deformed Nuclear States into their Components
International Nuclear Information System (INIS)
Increasing experimental and theoretical evidence for the complexity of low-lying states in deformed nuclei suggests the need for a variety of experimental approaches. The available experimental methods are summarized with particular emphasis on multi-reaction spectroscopy as a method of separating various components in the structure of deformed nuclear states. Level structures and other experimental parameters of 162Dy, 177Hf, 175Lu and 177Lu agree well with the Nilsson Model and the calculations of Soloviev as is typical of the most strongly deformed nuclei. In this paper emphasis is placed on nuclei in the transition region between spherical and deformed nuclei where experiment is expected to test the theory most severely. Experimental data on 153Sm, 155Gd, 186Re and 181Hf indicate the presence of strong coriolis coupling, of mixing of principal harmonic oscillator shells (ΔN = 2 mixing) and of complex phonon admixtures in low-lying states which probably require more sophisticated theoretical analysis. (author)
Freitas, Andreia C.; Wylezinska, Marzena; Birch, Malcolm J.; Petersen, Steffen E.; Miquel, Marc E.
2016-01-01
Dynamic imaging of the vocal tract using real-time MRI has been an active and growing area of research, having demonstrated great potential to become routinely performed in the clinical evaluation of speech and swallowing disorders. Although many technical advances have been made in regards to acquisition and reconstruction methodologies, there is still no consensus in best practice protocols. This study aims to compare Cartesian and non-Cartesian real-time MRI sequences, regarding image quality and temporal resolution trade-off, for dynamic speech imaging. Five subjects were imaged at 1.5T, while performing normal phonation, in order to assess velar motion and velopharyngeal closure. Data was acquired using both Cartesian and non-Cartesian (spiral and radial) real-time sequences at five different spatial-temporal resolution sets, between 10 fps (1.7×1.7×10 mm3) and 25 fps (1.5×1.5×10 mm3). Only standard scanning resources provided by the MRI scanner manufacturer were used to ensure easy applicability to clinical evaluation and reproducibility. Data sets were evaluated by comparing measurements of the velar structure, dynamic contrast-to-noise ratio and image quality visual scoring. Results showed that for all proposed sequences, FLASH spiral acquisitions provided higher contrast-to-noise ratio, up to a 170.34% increase at 20 fps, than equivalent bSSFP Cartesian acquisitions for the same spatial-temporal resolution. At higher frame rates (22 and 25 fps), spiral protocols were optimal and provided higher CNR and visual scoring than equivalent radial protocols. Comparison of dynamic imaging at 10 and 22 fps for radial and spiral acquisitions revealed no significant difference in CNR performance, thus indicating that temporal resolution can be doubled without compromising spatial resolution (1.9×1.9 mm2) or CNR. In summary, this study suggests that the use of FLASH spiral protocols should be preferred over bSSFP Cartesian for the dynamic imaging of velopharyngeal
Freitas, Andreia C; Wylezinska, Marzena; Birch, Malcolm J; Petersen, Steffen E; Miquel, Marc E
2016-01-01
Dynamic imaging of the vocal tract using real-time MRI has been an active and growing area of research, having demonstrated great potential to become routinely performed in the clinical evaluation of speech and swallowing disorders. Although many technical advances have been made in regards to acquisition and reconstruction methodologies, there is still no consensus in best practice protocols. This study aims to compare Cartesian and non-Cartesian real-time MRI sequences, regarding image quality and temporal resolution trade-off, for dynamic speech imaging. Five subjects were imaged at 1.5T, while performing normal phonation, in order to assess velar motion and velopharyngeal closure. Data was acquired using both Cartesian and non-Cartesian (spiral and radial) real-time sequences at five different spatial-temporal resolution sets, between 10 fps (1.7×1.7×10 mm3) and 25 fps (1.5×1.5×10 mm3). Only standard scanning resources provided by the MRI scanner manufacturer were used to ensure easy applicability to clinical evaluation and reproducibility. Data sets were evaluated by comparing measurements of the velar structure, dynamic contrast-to-noise ratio and image quality visual scoring. Results showed that for all proposed sequences, FLASH spiral acquisitions provided higher contrast-to-noise ratio, up to a 170.34% increase at 20 fps, than equivalent bSSFP Cartesian acquisitions for the same spatial-temporal resolution. At higher frame rates (22 and 25 fps), spiral protocols were optimal and provided higher CNR and visual scoring than equivalent radial protocols. Comparison of dynamic imaging at 10 and 22 fps for radial and spiral acquisitions revealed no significant difference in CNR performance, thus indicating that temporal resolution can be doubled without compromising spatial resolution (1.9×1.9 mm2) or CNR. In summary, this study suggests that the use of FLASH spiral protocols should be preferred over bSSFP Cartesian for the dynamic imaging of velopharyngeal
Wu, C. S.; Young, D. L.; Chiu, C. L.
2013-12-01
This article aims to develop a Cartesian-grid-based numerical model to study the interaction between free-surface flow and stationary or oscillating immersed obstacle in a viscous fluid. To incorporate the effect of the free surface motion, an arbitrary Lagrangian-Eulerian (ALE) scheme is employed to accurately capture the configuration of free surface. To deal with the complex submerged obstacle in the fluid, a hybrid Cartesian/immersed boundary (HCIB) method is adopted, which allows easy implementation of the solid boundary conditions for a fixed structured grid. The two numerical techniques are combined to study the wave-structure interaction problems. The major merit of the proposed model is that the fluid grid is fixed throughout the computations during the transients, while the immersed body can move arbitrarily through the Cartesian grid. The meshes deform smoothly over the solid and free-surface boundaries, especially for representing sharp interface. There is no re-meshing process needed since this scheme only depends on the simple mesh generation to promote the efficiency of calculation. Some numerical examples are displayed respectively to validate the robustness and accuracy of the HCIB method, the ALE based finite-element scheme and their combinations. In addition, the other two numerical applications are carried out to simulate the wave-structure interaction with stationary and moving immersed body. In case studies some physical characteristics are also discussed for a range of amplitude of free-surface wave, Reynolds numbers and the proximity of structure under the liquid surface. The feasibility of the developed novel numerical model is shown through five numerical experiments.
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...
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...
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...
Parameter Studies, time-dependent simulations and design with automated Cartesian methods
Aftosmis, Michael
2005-01-01
Over the past decade, NASA has made a substantial investment in developing adaptive Cartesian grid methods for aerodynamic simulation. Cartesian-based methods played a key role in both the Space Shuttle Accident Investigation and in NASA's return to flight activities. The talk will provide an overview of recent technological developments focusing on the generation of large-scale aerodynamic databases, automated CAD-based design, and time-dependent simulations with of bodies in relative motion. Automation, scalability and robustness underly all of these applications and research in each of these topics will be presented.
A Cartesian Cut Cell Method for Rarefied Flow Simulations around Moving Obstacles
Dechristé, Guillaume
2015-01-01
For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian cells and various kind of cut cells by the same algorithm, with no need to identify the specific shape of each cut cell. This makes the implementation quite simple, and allows a direct extension to 3D problems. Such simulations are also made possible by using an adaptive mesh refinement technique and a hybrid parallel implementation. This is illustrated by several test cases, including a 3D unsteady simulation of the Crookes radiometer.
"Mens Sana in Corpore Sano": Cartesian Dualism and the Marginalisation of Sex Education
Paechter, Carrie
2004-01-01
Cartesian dualism has left a heavy legacy in terms of how we think about ourselves, so that we treat humans as minds within bodies rather than mind/body unities. This has far-reaching effects on our conceptualisation of the sex/gender distinction and on the relationship between bodies and identities. Related to this is a dualism that is embedded…
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...
A rhizome as a map of a rupture of the Cartesian dualism:
Cergolj Edwards, Katja
2008-01-01
This essay explores the potentiality of organizing the immediate reality of lived experience of modern individual through a construct of Deleuze' and Guattari's rhizome. This practice, claimed in this essay, negates the traditional construction of knowledge, based on Cartesian perspectivalism, and offers nomadic identities of postcolonial world prospective of active, performative construction of personal bricolages
Rapid Non-Cartesian Parallel Imaging Reconstruction on Commodity Graphics Hardware
DEFF Research Database (Denmark)
Sørensen, Thomas Sangild; Atkinson, David; Boubertakh, Redha;
2008-01-01
This presentation describes an implementation of non-Cartesian SENSE and kt-SENSE accelerated on commodity graphics hardware. This inexpensive hardware platform is now fully programmable and very suited for solving reconstruction problems. We show that for both SENSE and kt-SENSE the reconstruction...
Kapahi, A.; Sambasivan, S.; Udaykumar, H. S.
2013-05-01
This work presents a three-dimensional, Eulerian, sharp interface, Cartesian grid technique for simulating the response of elasto-plastic solid materials to hypervelocity impact, shocks and detonations. The mass, momentum and energy equations are solved along with evolution equations for deviatoric stress and plastic strain using a third-order finite difference scheme. Material deformation occurs with accompanying nonlinear stress wave propagation; in the Eulerian framework the boundaries of the deforming material are tracked in a sharp fashion using level-sets and the conditions on the immersed boundaries are applied by suitable modifications of a ghost fluid approach. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state and the Johnson-Cook model is employed to characterize the material response due to rate-dependent plastic deformation. Details are provided on the treatment of the deviatoric stress ghost state so that physically correct boundary conditions can be applied at the material interfaces. An efficient parallel algorithm is used to handle computationally intensive three-dimensional problems. The results demonstrate the ability of the method to simulate high-speed impact, penetration and fragmentation phenomena in three dimensions.
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...
International Nuclear Information System (INIS)
An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in Cartesian coordinates, which is considerably simpler. Under open boundary conditions, an expression for multipole moments of point dipoles in a cell is derived. These make the program appropriate for nanomagnetic simulations, including magnetic nanoparticles and ferrofluids. The performance is optimized in terms of cell size and parameter set (expansion order and opening angle) and the trade off between computing time and accuracy is quantitatively studied. A rule of thumb is proposed to decide the appropriate average number of dipoles in the smallest cells, and an optimal choice of parameter set is suggested. Finally, the superiority of Cartesian coordinate FMM is demonstrated by comparison to spherical harmonics FMM and FFT.
Qiu, Zhi-cheng
2012-07-01
A flexible Cartesian manipulator is a coupling system with a moving rigid body and flexible structures. Thus, vibration suppression problem must be solved to guarantee the stability and control accuracy. A characteristic model based nonlinear golden section adaptive control (CMNGSAC) algorithm is implemented to suppress the vibration of a flexible Cartesian smart material manipulator driven by a ballscrew mechanism using an AC servomotor. The system modeling is derived to recognize the dynamical characteristics. The closed loop stability is analyzed based on the model. Also, an experimental setup is constructed to verify the adopted method. Experimental comparison studies are conducted for modal frequencies' identification and active vibration control of the flexible manipulator. The active vibration control experiments include set-point vibration control responses, vibration suppression under resonant excitation and simultaneous translating and vibration suppression using different control methods. The experimental results demonstrate that the controller can suppress both the larger and the lower amplitude vibration near the equilibrium point effectively.
Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation
Buning, Pieter G.; Pulliam, Thomas H.
2011-01-01
An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.
A Cartesian Adaptive Level Set Method for Two-Phase Flows
Ham, F.; Young, Y.-N.
2003-01-01
In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.
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.
Aerodynamic Design of Complex Configurations Using Cartesian Methods and CAD Geometry
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
2003-01-01
The objective for this paper is to present the development of an optimization capability for the Cartesian inviscid-flow analysis package of Aftosmis et al. We evaluate and characterize the following modules within the new optimization framework: (1) A component-based geometry parameterization approach using a CAD solid representation and the CAPRI interface. (2) The use of Cartesian methods in the development Optimization techniques using a genetic algorithm. The discussion and investigations focus on several real world problems of the optimization process. We examine the architectural issues associated with the deployment of a CAD-based design approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute nodes. In addition, we study the influence of noise on the performance of optimization techniques, and the overall efficiency of the optimization process for aerodynamic design of complex three-dimensional configurations. of automated optimization tools. rithm and a gradient-based algorithm.
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.
Cartesian Stiffness Matrix Mapping of a Translational Parallel Mechanism with Elastic Joints
Maurizio Ruggiu
2012-01-01
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.
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.
Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates
Briggs, Andrew; Camblong, Horacio E.; Ordonez, Carlos R.
2011-01-01
The path-integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat spacetime geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.
Density functional calculation of many-electron systems in cartesian coordinate grid
Roy, Amlan K.
2010-01-01
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 investigati...
Nadal, E.; Ródenas, J. J.; Albelda, J.; Tur, M.; Tarancón, J. E.; Fuenmayor, F.J.
2013-01-01
This work presents an analysis methodology based on the use of the Finite Element Method (FEM) nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs). The proposed methodology, so-called cg-FEM (Cartesian grid FEM), has been implemented for fast and accurate numerical analysis of 2D linear elasticity problems. The traditional FEM uses geometry-conforming meshes; however, in cg-FEM the analysis mesh is not conformal to the geometry. This allows for defin...
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.
Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method
Nemec, Marian; Aftosmis, Michael J.
2004-01-01
Adjoint 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 optimization. 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 (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et 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 Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented
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...
Quantization of Floreanini-Jackiw chiral harmonic oscillator
Baleanu, D; Baleanu, Dumitru; Guler, Yurdahan
1999-01-01
The Floreanini-Jackiw formulation for the chiral quantum-mechanical system oscillator is a model of constrained theory with only second-class constraints. in the Dirac's classification.The covariant quantization needs an infinit number of auxiliary variables and a Wess-Zumino term. In this paper we investigate the path integral quatization of this model using $G\\ddot{u}ler's$ canonical formalism. All variables are gauge variables in the $G\\ddot{u}ler's$ formalism. The Siegel's action is obtained using Hamilton-Jacobi formulation of the systems with constraints.
Web-assisted tunneling in the kicked harmonic oscillator
Carvalho, A R R; Carvalho, Andr\\'e R. R.; Buchleitner, Andreas
2004-01-01
We show that heating of harmonically trapped ions by periodic delta kicks is dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these values, quasienergy eigenstates localized on island structures undergo avoided crossings with extended web-states.
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.
SU(1,1) perturbations of the simple harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Barut, A.O. [Bogazici Univ., Istanbul (Turkey). Physics Dept.; Beker, H. [Bogazici Univ., Istanbul (Turkey). Physics Dept.; Rador, T. [Bogazici Univ., Istanbul (Turkey). Physics Dept.
1995-09-04
A purely algebraic theory based on the dynamical group SU(1,1) is used to treat perturbations to the SHO problem. In particular potentials of the form 1/r{sup 2N} and r{sup 2N} are treated explicitly. (orig.).
Exact response of the non-relativistic harmonic oscillator
Pace, E.; Salme, G.; Rinat, A. S.
2014-01-01
Using Green$'$s function and operator techniques we give a closed expression for the response of a non-relativistic system interacting through confining, harmonic forces. The expression for the incoherent part permits rapid evaluation of coefficients in a 1/q expansion. A comparison is made with standard approximation methods.
Properties of infrared extrapolations in a harmonic oscillator basis
Coon, Sidney A.; Kruse, Michael K. G.
2016-02-01
The success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological NN and NNN interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as r2, considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods.
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.
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.
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
A second order Cartesian finite volume method for elliptic interface and embedded Dirichlet problems
International Nuclear Information System (INIS)
We present a finite volume method to solve elliptic equations with immersed interface conditions. This method allows discontinuities on the solution and its normal derivatives on an interface inside the domain on a Cartesian grid. The main idea is to use a piecewise polynomial representation of the solution on a dual grid that avoid distinctions between the different interface configurations. The method achieves second order accuracy with a compact nine-point stencil. Moreover, we show that this method applies to solve embedded Dirichlet and Neumann problems. (authors)
Three-dimensional multigroup diffusion code ANDEX based on nodal method for cartesian geometry
International Nuclear Information System (INIS)
An analytic polynomial nodal method using partial currents has been derived for the solution of multigroup neutron diffusion equations in three-dimensional (3-D) cartesian geometry. This method is characterized by expressing the source and leakage terms in an auxiliary 1-D diffusion equation by quadratic polynomials and solving it analytically. Based on this method, we have developed a 3-D multigroup diffusion code ANDEX, and applied to 2-D LWR and 3-D FBR models. The results of keff, power distributions and computing time have been compared with those of finite difference method calculations. (author)
Application of high-order diamond differencing schemes to 3D Cartesian geometries
International Nuclear Information System (INIS)
An innovative high-order discrete ordinate method for the resolution of the time-independent Boltzmann transport equation in 3D Cartesian geometries is presented. This approach consists in a generalization of the classical diamond differencing scheme to high-order spatial approximations. To insure convergence of the source iteration in presence of high diffusive and strong heterogeneous media, diffusion synthetic acceleration (DSA) has been implemented, conjugated with a Krylov subspace method, GMRES(m). We provide numerical comparisons of this 3D high-order SN method with SPn and Monte- Carlo reference calculations. (authors)
CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
2003-01-01
A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified nnd tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi-Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.
Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry
Nemec, Marian; Aftosmis,Michael J.
2006-01-01
Cartesian-mesh methods 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) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, 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 included 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 objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach
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.
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. PMID:27349179
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,...
The Cartesian Path Planning of Free- Floating Space Robot using Particle Swarm Optimization
Directory of Open Access Journals (Sweden)
Yangsheng Xu
2008-11-01
Full Text Available The Cartesian path planning of free-floating space robot is much more complex than that of fixed-based manipulators, since the end-effector pose (position and orientation is path dependent, and the position-level kinematic equations can not be used to determine the joint angles. In this paper, a method based on particle swarm optimization (PSO is proposed to solve this problem. Firstly, we parameterize the joint trajectory using polynomial functions, and then normalize the parameterized trajectory. Secondly, the Cartesian path planning is transformed to an optimization problem by integrating the differential kinematic equations. The object function is defined according to the accuracy requirement, and it is the function of the parameters to be defined. Finally, we use the Particle Swarm Optimization (PSO algorithm to search the unknown parameters. The approach has the following traits: 1 The limits on joint angles, rates and accelerations are included in the planning algorithm; 2 There exist not any kinematic and dynamic singularities, since only the direct kinematic equations are used; 3 The attitude singularities do not exist, for the orientation is represented by quaternion; 4 The optimization algorithm is not affected by the initial parameters. Simulation results verify the proposed method.
Applications of Space-Filling-Curves to Cartesian Methods for CFD
Aftosmis, M. J.; Murman, S. M.; Berger, M. J.
2003-01-01
This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.
Systematic and Deterministic Graph-Minor Embedding of Cartesian Products of Complete Graphs
Zaribafiyan, Arman; Marchand, Dominic J. J.; Changiz Rezaei, Seyed Saeed
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. The overhead of the widely used heuristic techniques is quickly proving to be a significant bottleneck for real-world applications. To alleviate this obstacle, we propose a systematic deterministic embedding method that exploits the structures of both the input graph of the specific combinatorial optimization problem and the quantum annealer. We focus on the specific case of the Cartesian product of two complete graphs, a regular structure that occurs in many problems. We first divide the problem by embedding one of the factors of the Cartesian product in a repeatable unit. The resulting simplified problem consists of placing copies of this unit and connecting them together appropriately. Aside from the obvious speed and efficiency advantages of a systematic deterministic approach, the embeddings produced can be easily scaled for larger processors and show desirable properties with respect to the number of qubits used and the chain length distribution.
Directory of Open Access Journals (Sweden)
E. Nadal
2013-01-01
Full Text Available This work presents an analysis methodology based on the use of the Finite Element Method (FEM nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs. The proposed methodology, so-called cg-FEM (Cartesian grid FEM, has been implemented for fast and accurate numerical analysis of 2D linear elasticity problems. The traditional FEM uses geometry-conforming meshes; however, in cg-FEM the analysis mesh is not conformal to the geometry. This allows for defining very efficient mesh generation techniques and using a robust integration procedure, to accurately integrate the domain’s geometry. The hierarchical data structure used in cg-FEM together with the Cartesian meshes allow for trivial data sharing between similar entities. The cg-FEM methodology uses advanced recovery techniques to obtain an improved solution of the displacement and stress fields (for which a discretization error estimator in energy norm is available that will be the output of the analysis. All this results in a substantial increase in accuracy and computational efficiency with respect to the standard FEM. cg-FEM has been applied in structural shape optimization showing robustness and computational efficiency in comparison with FEM solutions obtained with a commercial code, despite the fact that cg-FEM has been fully implemented in MATLAB.
Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft
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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.
Yamagami, M; Yamagami, Masayuki; Matsuyanagi, Kenichi
2000-01-01
High-spin yrast structure of 32S is investigated by means of the cranked Skyrme-Hartree-Fock method in the three-dimensional Cartesian-mesh representation without imposing restrictions on spatial symmetries. The result suggests that 1) a crossover from the superdeformed to the hyperdeformed-like configurations takes place on the yrast line at angular momentum $I \\simeq 24$, which corresponds to the ``band termination'' point in the cranked harmonic-oscillator model, and 2) non-axial octupole deformations of the $Y_{31}$ type play an important role in the yrast states in the range $5\\leq I
Yamagami, M
2000-01-01
The high-spin yrast structure of sup 3 sup 2 S is investigated by means of the cranked Skyrme-Hartree-Fock method in the three-dimensional Cartesian-mesh representation without imposing restrictions on spatial symmetries. The result suggests that (1) a crossover from the superdeformed to the hyperdeformed-like configurations takes place on the yrast line at angular momentum I approx =24, which corresponds to the 'band termination' point in the cranked harmonic-oscillator model, and (2) non-axial octupole deformations of the Y sub 3 sub 1 type play an important role in the yrast states in the range 5<=I<=13.
Semantyczne założenia sceptycyzmu kartezjańskiego (Semantic Presuppositions of Cartesian Skepticism
Directory of Open Access Journals (Sweden)
Krzysztof Posłajko
2010-12-01
Full Text Available The paper purports to show that in order to formulate the hypothesis that all our beliefs are collectively false – which is taken to be the core of Cartesian skepticism – one must accept the presumption that semantic properties of subject`s beliefs locally supervene on “internal” properties of said subject. In order to show that the responses to skepticism from semantic externalism, i.e. those formulated by Putnam and Davidson, are analyzed. It is argued that even though these arguments are controversial they indicate that Cartesian skeptic must assume that subject beliefs` semantic properties can remain the same in different surroundings, which is exactly what the supervenience thesis amounts to. Finally, it is pointed out that the skepticism introduced by Kripke in his discussion of rule-following is indeed more radical than traditional, Cartesian one, as the former denies the very thesis that the latter must assume.
International Nuclear Information System (INIS)
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
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
Lin, Dejun
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
Huang, He
In this thesis, I present the results of studies of the structural properties and phase transition of a charge neutral FCC Lattice Gas with Yukawa Interaction and discuss a novel fast calculation algorithm---Accelerated Cartesian Expansion (ACE) method. In the first part of my thesis, I discuss the results of Monte Carlo simulations carried out to understand the finite temperature (phase transition) properties and the ground state structure of a Yukawa Lattice Gas (YLG) model. In this model the ions interact via the potential q iqjexp(-kappar> ij)/rij where qi,j are the charges of the ions located at the lattice sites i and j with position vectors R i and Rj; rij = Ri-Rj, kappa is a measure of the range of the interaction and is called the screening parameter. This model approximates an interesting quaternary system of great current thermoelectric interest called LAST-m, AgSbPbmTem+2. I have also developed rapid calculation methods for the potential energy calculation in a lattice gas system with periodic boundary condition bases on the Ewald summation method and coded the algorithm to compute the energies in MC simulation. Some of the interesting results of the MC simulations are: (i) how the nature and strength of the phase transition depend on the range of interaction (Yukawa screening parameter kappa) (ii) what is the degeneracy of the ground state for different values of the concentration of charges, and (iii) what is the nature of two-stage disordering transition seen for certain values of x. In addition, based on the analysis of the surface energy of different nano-clusters formed near the transition temperature, the solidification process and the rate of production of these nano-clusters have been studied. In the second part of my thesis, we have developed two methods for rapidly computing potentials of the form R-nu. Both these methods are founded on addition theorems based on Taylor expansions. Taylor's series has a couple of inherent advantages: (i) it
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...
International Nuclear Information System (INIS)
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
Directory of Open Access Journals (Sweden)
Jeong Kwang-Leol
2014-06-01
Full Text Available The wave attenuation by floating breakwaters in high amplitude waves, which can lead to wave overtopping and breaking, is examined by numerical simulations. The governing equations, the Navier-Stokes equations and the continuity equation, are calculated in a fixed Cartesian grid system. The body boundaries are defined by the line segment connecting the points where the grid line and body surface meet. No-slip and divergence free conditions are satisfied at the body boundary cell. The nonlinear waves near the moving body is defined using the modified markerdensity method. To verify the present numerical method, vortex induced vibration on an elastically mounted cylinder and free roll decay are numerically simulated and the results are compared with those reported in the literature. Using the present numerical method, the wave attenuations by three kinds of floating breakwaters are simulated numerically in a regular wave to compare the performance.
International Nuclear Information System (INIS)
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 109 degrees of freedom within a few hours on a single shared-memory supercomputing node. This computation corresponds to a 26-group S8 3D PWR core model used to assess the SPN accuracy. At the pin level, the maximal error for the SP5 DIABOLO fission production rate is lower than 0.2% compared to the S8 DOMINO reference for this 3D PWR core model. (authors)
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)
Numerical Simulation of Rolling-Airframes Using a Multi-Level Cartesian Method
Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)
2002-01-01
A supersonic rolling missile with two synchronous canard control surfaces is analyzed using an automated, inviscid, Cartesian method. Sequential-static and time-dependent dynamic simulations of the complete motion are computed for canard dither schedules for level flight, pitch, and yaw maneuver. The dynamic simulations are compared directly against both high-resolution viscous simulations and relevant experimental data, and are also utilized to compute dynamic stability derivatives. The results show that both the body roll rate and canard dither motion influence the roll-averaged forces and moments on the body. At the relatively, low roll rates analyzed in the current work these dynamic effects are modest, however the dynamic computations are effective in predicting the dynamic stability derivatives which can be significant for highly-maneuverable missiles.
Validation of Inlet and Exhaust Boundary Conditions for a Cartesian Method
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted in aerodynamic simulations of aircraft due to the complexities involved in the modeling of engine details and flow physics. However, the omission is often improper since inlet or plume flows may have a substantial effect on vehicle aerodynamics. A method for modeling the effect of inlets and exhaust plumes using boundary conditions within an inviscid Cartesian flow solver is presented. This approach couples with both CAD systems and legacy geometry to provide an automated tool suitable for parameter studies. The method is validated using two and three-dimensional test problems which are compared with both theoretical and experimental results. The numerical results demonstrate excellent agreement with theory and available data, even for extremely strong jets and very sensitive inlets.
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...
ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach
Directory of Open Access Journals (Sweden)
M. Jähn
2014-07-01
Full Text Available In this work, the fully compressible, nonhydrostatic 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. An implicit time integration scheme ensures numerical stability around small cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid scale model, a two-moment bulk microphysics scheme, precipitation and vertical surface fluxes by a constant flux layer or a more complex soil model are implemented. Results for three benchmark test cases from the literature are shown. A sensitivity study regarding the development of a convective boundary layer together with island effects at Barbados is carried out to show the capability to perform real case simulations with ASAM.
Zhang, Wen
2008-01-01
An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in cartesian coordinates, which is considerably simpler. Under open boundary conditions, an expression for multipole moments of point dipoles in a cell is derived. These make the program appropriate for nanomagnetic simulations, including magnetic nanoparticles and ferrofluids. The performance is optimized in terms of cell size and parameter set (expansion order and opening angle) and trade off between computing time and accuracy is quantitatively studied. A rule of thumb is proposed to decide the average number of dipoles in the smallest cells, and an optimal choice of parameter set is suggested.
A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains
Energy Technology Data Exchange (ETDEWEB)
Johansen, H. [Univ. of California, Berkeley, CA (United States). Dept. of Mechanical Engineering; Colella, P. [Lawrence Berkeley National Lab., CA (United States). Center for Computational Sciences and Engineering
1997-01-31
The authors present a numerical method for solving Poisson`s equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. They treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservation differencing of second-order accurate fluxes, on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows them to use multi-grid iterations with a simple point relaxation strategy. They have combined this with an adaptive mesh refinement (AMR) procedure. They provide evidence that the algorithm is second-order accurate on various exact solutions, and compare the adaptive and non-adaptive calculations.
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...
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.
An adaptive p-refinement strategy applied to nodal expansion method in 3D Cartesian geometry
International Nuclear Information System (INIS)
Highlights: • An adaptive p-refinement approach is developed and implemented successfully in ACNEM. • The proposed strategy enhances the accuracy with regard to the uniform zeroth order solution. • Improvement of results is gained by less computation time relative to uniform high order solution. - Abstract: The aim of this work is to develop a coarse mesh treatment strategy using adaptive polynomial, p, refinement approach for average current nodal expansion method in order to solve the neutron diffusion equation. For performing the adaptive solution process, a posteriori error estimation scheme, i.e. flux gradient has been utilized for finding the probable numerical errors. The high net leakage in a node represents flux gradient existence between neighbor nodes and it may indicate the source of errors for the coarse mesh calculation. Therefore, the relative Cartesian directional net leakage of nodes is considered as an assessment criterion for mesh refinement in a sub-domain. In our proposed approach, the zeroth order nodal expansion solution is used along coarse meshes as large as fuel assemblies to treat neutron populations. Coarse nodes with high directional net leakage may be chosen for implementing higher order polynomial expansion in the corresponding direction, i.e. X and/or Y and/or Z Cartesian directions. Using this strategy, the computational cost and time are reduced relative to uniform high order polynomial solution. In order to demonstrate the efficiency of this approach, a computer program, APNEC, Adaptive P-refinement Nodal Expansion Code, has been developed for solving the neutron diffusion equation using various orders of average current nodal expansion method in 3D rectangular geometry. Some well-known benchmarks are investigated to compare the uniform and adaptive solutions. Results demonstrate the superiority of our proposed strategy in enhancing the accuracy of solution without using uniform high order solution throughout the domain and
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.
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
Adaptive control of nonlinear visual servoing systems for 3D cartesian tracking
Directory of Open Access Journals (Sweden)
Alessandro R. L. Zachi
2006-12-01
Full Text Available This paper presents a control strategy for robot manipulators to perform 3D cartesian tracking using visual servoing. Considering a fixed camera, the 3D cartesian motion is decomposed in a 2D motion on a plane orthogonal to the optical axis and a 1D motion parallel to this axis. An image-based visual servoing approach is used to deal with the nonlinear control problem generated by the depth variation without requiring direct depth estimation. Due to the lack of camera calibration, an adaptive control method is used to ensure both depth and planar tracking in the image frame. The depth feedback loop is closed by measuring the image area of a target object attached to the robot end-effector. Simulation and experimental results obtained with a real robot manipulator illustrate the viability of the proposed scheme.Este trabalho apresenta uma estratégia de controle para robôs manipuladores realizarem rastreamento cartesiano 3D utilizando servovisão. Considerando uma câmera fixa, o movimento cartesiano 3D é decomposto em um movimento 2D sobre um plano ortogonal ao eixo óptico e em outro movimento 1D paralelo ao mesmo eixo. Uma abordagem de servovisão baseada em imagem é utilizada para tratar o problema de controle não-linear, gerado pela variação de profundidade, sem a necessidade de estimar esta medida. Devido à ausência de calibração da câmera, um método de controle adaptativo é utilizado para assegurar rastreamento planar e de profundidade nas coordenadas da imagem. A malha de controle de profundidade é fechada através da medição da área da imagem de um objeto fixado no efetuador do robô. Simulação e resultados experimentais, obtidos com um robô manipulador real, ilustram a viabilidade do esquema proposto.
Directory of Open Access Journals (Sweden)
Zimmerman Peter A
2010-06-01
Full Text Available Abstract Background Diagnosis of infectious diseases now benefits from advancing technology to perform multiplex analysis of a growing number of variables. These advances enable simultaneous surveillance of markers characterizing species and strain complexity, mutations associated with drug susceptibility, and antigen-based polymorphisms in relation to evaluation of vaccine effectiveness. We have recently developed assays detecting single nucleotide polymorphisms (SNPs in the P. falciparum genome that take advantage of post-PCR ligation detection reaction and fluorescent microsphere labeling strategies. Data from these assays produce a spectrum of outcomes showing that infections result from single to multiple strains. Traditional methods for distinguishing true positive signal from background can cause false positive diagnoses leading to incorrect interpretation of outcomes associated with disease treatment. Results Following analysis of Plasmodium falciparum dihydrofolate reductase SNPs associated with resistance to a commonly used antimalarial drug, Fansidar (Sulfadoxine/pyrimethamine, and presumably neutral SNPs for parasite strain differentiation, we first evaluated our data after setting a background signal based on the mean plus three standard deviations for known negative control samples. Our analysis of single allelic controls suggested that background for the absent allele increased as the concentration of the target allele increased. To address this problem, we introduced a simple change of variables from customary (X,Y (Cartesian coordinates to planar polar coordinates (X = rcos(θ, Y = rsin(θ. Classification of multidimensional fluorescence signals based on histograms of angular and radial data distributions proved more effective than classification based on Cartesian thresholds. Comparison with known diallelic dilution controls suggests that histogram-based classification is effective for major:minor allele concentration ratios as
Development of a new two-dimensional Cartesian geometry nodal multigroup discrete-ordinates method
Energy Technology Data Exchange (ETDEWEB)
Pevey, R.E.
1982-07-01
The purpose of this work is the development and testing of a new family of methods for calculating the spatial dependence of the neutron density in nuclear systems described in two-dimensional Cartesian geometry. The energy and angular dependence of the neutron density is approximated using the multigroup and discrete ordinates techniques, respectively. The resulting FORTRAN computer code is designed to handle an arbitrary number of spatial, energy, and angle subdivisions. Any degree of scattering anisotropy can be handled by the code for either external source or fission systems. The basic approach is to (1) approximate the spatial variation of the neutron source across each spatial subdivision as an expansion in terms of a user-supplied set of exponential basis functions; (2) solve analytically for the resulting neutron density inside each region; and (3) approximate this density in the basis function space in order to calculate the next iteration flux-dependent source terms. In the general case the calculation is iterative due to neutron sources which depend on the neutron density itself, such as scattering interactions.
Viability of Bioprinted Cellular Constructs Using a Three Dispenser Cartesian Printer
Dennis, SG.; Trusk, T.; Richards, D.; Jia, J.; Tan, Y.; Mei, Y.; Fann, S.; Markwald, R.; Yost, M.
2016-01-01
Tissue engineering has centralized its focus on the construction of replacements for non-functional or damaged tissue. The utilization of three-dimensional bioprinting in tissue engineering has generated new methods for the printing of cells and matrix to fabricate biomimetic tissue constructs. The solid freeform fabrication (SFF) method developed for three-dimensional bioprinting uses an additive manufacturing approach by depositing droplets of cells and hydrogels in a layer-by-layer fashion. Bioprinting fabrication is dependent on the specific placement of biological materials into three-dimensional architectures, and the printed constructs should closely mimic the complex organization of cells and extracellular matrices in native tissue. This paper highlights the use of the Palmetto Printer, a Cartesian bioprinter, as well as the process of producing spatially organized, viable constructs while simultaneously allowing control of environmental factors. This methodology utilizes computer-aided design and computer-aided manufacturing to produce these specific and complex geometries. Finally, this approach allows for the reproducible production of fabricated constructs optimized by controllable printing parameters. PMID:26436877
International Nuclear Information System (INIS)
We describe hybrid spectral nodal methods for discrete ordinates (SN) eigenvalue problems in Cartesian geometry. These coarse-mesh methods are based on three ingredients: the use of the standard discretized spatial balance SN equations; the use of the non-standard spectral diamond (SD) auxiliary equations in the multiplying regions of the domain, e.g. fuel assemblies; and the use of the non-standard spectral Green's function (SGF) auxiliary equations in the non-multiplying regions of the domain, e.g., the reflector. In slab-geometry the hybrid SD-SGF method generates numerical results that are completely free of spatial truncation errors. In X,Y-geometry, we obtain a system of two 'slab-geometry' SN equations for the node-edge average angular fluxes by transverse-integrating the X,Y-geometry SN equations separately in the y- and then in the x-directions within an arbitrary node of the spatial grid set up on the domain. In this paper, we approximate the transverse leakage terms by constants. These are the only approximations considered in the SD-SGF-constant nodal method, as the source terms, that include scattering and eventually fission events, are treated exactly. We show numerical results to typical model problems to illustrate the accuracy of spectral nodal methods for coarse-mesh SN criticality calculations. (author)
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.
International Nuclear Information System (INIS)
The variational nodal method (VNM) has been generalized to three dimensions and used to solve a set of five criticality problems, in Cartesian, triangular, and hexagonal geometries. The code is implemented within the IDF 3D neutronics production code on a Cray-XMP. The first four benchmarks are taken from Takeda and Ikeda, and the last is a simplified sixth-core model of the Experimental Breeder Reactor II (EBR-II). Comparisons are made to various SN codes, the other nodal methods, and Monte Carlo reference solutions. The VNM is based on a variational principle whose Euler-Lagrange equation is the even-parity transport equation. Nodal balance is imposed through the odd-parity fluxes used as a Lagrange multiplier on nodal interfaces. Even- and odd-parity fluxes are expanded in a classical Ritz procedure with complete sets of orthogonal polynomials in space and angle. The VNM is cast in response matrix form, and the even- and odd-parity fluxes are replaced by partial current moments on the nodal interfaces
Ghysels, A.; Van Neck, D.; Waroquier, M.
2007-10-01
Partial optimization is a useful technique to reduce the computational load in simulations of extended systems. In such nonequilibrium structures, the accurate calculation of localized vibrational modes can be troublesome, since the standard normal mode analysis becomes inappropriate. In a previous paper [A. Ghysels et al., J. Chem. Phys. 126, 224102 (2007)], the mobile block Hessian (MBH) approach was presented to deal with the vibrational analysis in partially optimized systems. In the MBH model, the nonoptimized regions of the system are represented by one or several blocks, which can move as rigid bodies with respect to the atoms of the optimized region. In this way unphysical imaginary frequencies are avoided and the translational/rotational invariance of the potential energy surface is fully respected. In this paper we focus on issues concerning the practical numerical implementation of the MBH model. The MBH normal mode equations are worked out for several coordinate choices. The introduction of a consistent group-theoretical notation facilitates the treatment of both the case of a single block and the case of multiple blocks. Special attention is paid to the formulation in terms of Cartesian variables, in order to provide a link with the standard output of common molecular modeling programs.
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.; Nixon, David (Technical Monitor)
1998-01-01
The work presents a new method for on-the-fly domain decomposition technique for mapping grids and solution algorithms to parallel machines, and is applicable to both shared-memory and message-passing architectures. It will be demonstrated on the Cray T3E, HP Exemplar, and SGI Origin 2000. Computing time has been secured on all these platforms. The decomposition technique is an outgrowth of techniques used in computational physics for simulations of N-body problems and the event horizons of black holes, and has not been previously used by the CFD community. Since the technique offers on-the-fly partitioning, it offers a substantial increase in flexibility for computing in heterogeneous environments, where the number of available processors may not be known at the time of job submission. In addition, since it is dynamic it permits the job to be repartitioned without global communication in cases where additional processors become available after the simulation has begun, or in cases where dynamic mesh adaptation changes the mesh size during the course of a simulation. The platform for this partitioning strategy is a completely new Cartesian Euler solver tarcreted at parallel machines which may be used in conjunction with Ames' "Cart3D" arbitrary geometry simulation package.
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.
Platonism, cartesianism and Hegel’s thought in the Matrix Trilogy
Directory of Open Access Journals (Sweden)
Milidrag Predrag
2013-01-01
Full Text Available In this article I will try to interpret changes in Neo, the main character in The Matrix Trilogy, against the background of the ideas of Plato and Descartes, as well as Hegel’s from his Philosophy of History and The Phenomenology of Spirit. Although “philosophical” The Matrix Trilogy is not long-winded and boring film: instead of talking endlessly, the characters are working ceaselessly, and that work is changing them. Contrary to widespread opinion, this interpretation does not find the presence of Descartes’ hyperbolic doubt in the first part of trilogy, but first film sees as a pure Platonism. Nevertheless, there are the Cartesian motifs (e.g. dualism, freeing mind from preconceived opinions, acquiring different habits of belief. The result of the first film is the position of Hegelian unhappy consciousness. This is just a preparation for the key moment of whole Trilogy that is the dialogue between Neo and Architect. Neo’s decision to chose to save Trinity is interpreted in Hegel’s terms of the infinite right of the subject to satisfy himself in his activity and work; because of that, this, sixth Neo is new. After showing the differences in the objectives of Neo and Agent Smith, and transformations of the objectives of humans, the third part of the article analyzes the very end of the Matrix Revolutions, using Marx’s ideas, with some references to Plato and Nietzsche.
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...
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.
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.
Development of a new two-dimensional Cartesian geometry nodal multigroup discrete-ordinates method
International Nuclear Information System (INIS)
The purpose of this work is the development and testing of a new family of methods for calculating the spatial dependence of the neutron density in nuclear systems described in two-dimensional Cartesian geometry. The energy and angular dependence of the neutron density is approximated using the multigroup and discrete ordinates techniques, respectively. The resulting FORTRAN computer code is designed to handle an arbitrary number of spatial, energy, and angle subdivisions. Any degree of scattering anisotropy can be handled by the code for either external source or fission systems. The basic approach is to (1) approximate the spatial variation of the neutron source across each spatial subdivision as an expansion in terms of a user-supplied set of exponential basis functions; (2) solve analytically for the resulting neutron density inside each region; and (3) approximate this density in the basis function space in order to calculate the next iteration flux-dependent source terms. In the general case the calculation is iterative due to neutron sources which depend on the neutron density itself, such as scattering interactions
On the Use of CAD and Cartesian Methods for Aerodynamic Optimization
Nemec, M.; Aftosmis, M. J.; Pulliam, T. H.
2004-01-01
The objective for this paper is to present the development of an optimization capability for Curt3D, a Cartesian inviscid-flow analysis package. We present the construction of a new optimization framework and we focus on the following issues: 1) Component-based geometry parameterization approach using parametric-CAD models and CAPRI. A novel geometry server is introduced that addresses the issue of parallel efficiency while only sparingly consuming CAD resources; 2) The use of genetic and gradient-based algorithms for three-dimensional aerodynamic design problems. The influence of noise on the optimization methods is studied. Our goal is to create a responsive and automated framework that efficiently identifies design modifications that result in substantial performance improvements. In addition, we examine the architectural issues associated with the deployment of a CAD-based approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute engines. We demonstrate the effectiveness of the framework for a design problem that features topology changes and complex geometry.
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...
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
International Nuclear Information System (INIS)
In this work we report an analytical solution for the time-dependent one-dimensional neutron transport equation in cartesian geometry for bounded and unbounded domain. The main idea consists in the application of the Laplace transform technique in time variable, solution of the resulting equation by the LTSN method and reconstruction of the angular flux in time-variable by numerical inversion scheme. We report numerical simulations and results validations with the ones of literature. (author)
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. PMID:27586772
Shooshtary, S; Solbach, K
2015-08-01
A 7 Tesla Magnetic Resonance Imaging (MRI) system with parallel transmission (pTx) for 32 near-magnet Cartesian feedback loop power amplifiers (PA) with output power of 1kW is under construction at Erwin L. Hahn Institute for Magnetic Resonance Imaging. Variation of load impedance due to mutual coupling of neighborhood coils in the array may lead to instability of the Cartesian feedback loop amplifier. MRI safety requires unconditional stability of the PAs at any load. In order to avoid instability in the pTx system, conditions and limits of stability have to be investigated for every possible excitation mode for the coil array. In this work, an efficient method of stability check for an array of two transmit channels (Tx) with Cartesian feedback loop amplifier and a selective excitation mode for the coil array is proposed which allows extension of stability investigations to a large pTx array with any arbitrary excitation mode for the coil array. PMID:26736573
A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity
International Nuclear Information System (INIS)
In 3 + 1 numerical simulations of dynamic black-hole spacetimes, it is 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 are too slow to be practically usable at each time step. Here I present a new AH finder, AHFINDERDIRECT, which is very fast and accurate: at typical resolutions it takes only a few seconds to find an AH ∼ 10-5m accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlkoerper ('star-shaped region') with respect to some local origin, and so parametrize the AH shape by r = h(angle) for some single-valued function h:S2 → R2. The AH equation then becomes a nonlinear elliptic PDE in h on S2, whose coefficients are algebraic functions of gij, Kij, and the Cartesian-coordinate spatial derivatives of gij. I discretize S2 using six angular patches (one each in the neighbourhood of the ±x, ± y, and ±z axes) to avoid coordinate singularities, and finite difference the AH equation in the angular coordinates using fourth-order finite differencing. I solve the resulting system of nonlinear algebraic equations (for h at the angular grid points) by Newton's method, using a 'symbolic differentiation' technique to compute the Jacobian matrix. AHFINDERDIRECT is implemented as a thorn in the CACTUS computational toolkit, and is freely available by anonymous CVS checkout
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.
Deformed Dynamics of Q-Deformed Systems
International Nuclear Information System (INIS)
Quantum algebras have been the subject of an intensively research in the last years. Particularly, after the works of Macfarlane and Biedenharn on the q-deformed oscillators, a great effort has been devoted to the application and generalization of q-deformed systems in chemistry and physics. In quantum optics, q-bosons have been used to generalized fundamental models such as, the Jaynes-Cummings and Dicke models. Besides, using generalized deformed oscillators several versions of the Jaynes-Cummings Hamiltonian have found a unified description. In the present work, we study the dynamical properties of q-deformed oscillators and their relationship to the anharmonic oscillators by means of a Lie-algebraic approach. In doing so, we find that an infinite dimensional set of 'q-deformed relevant operators' close a 'partial q-deformed Lie algebra' under commutation with the Arik-Coon Hamiltonian. We show that the dynamics of the s?stem can be described in terms of the multi commutator of the type [H,... , [H, 0] . . .]. Eve also obtain, that the multi commutator can be expressed for q > 1 as an operator average with respect to the ('Binomial distribution' which depends on[g on the deformation parameter q, and for the general case (i.e. q - R) as a 'power law'. As a consequence of the power law dependence, we find that the dynamics of the infinite-dimensional q-deformed Lie-algebra scale, i.e. the temporal evolution for the whole set of relevant operators collapse on a single curve. We calculate and analyze, the temporal evolution of the set of relevant operators for the q-deformed and the anharmonic oscillator when the initial conditions are a q-coherent and coherent states respectively. We obtain that the dynamics of both models is governed by a weighted average with respect to the 'q-deformed Poisson' and the 'standard Poisson' distributions respectively. Finally, we find the conditions under which the dynamics of the relevant operators of both oscillators are
Branduardi, Davide; Faraldo-Gómez, José D
2013-09-10
The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string. PMID
International Nuclear Information System (INIS)
ABCXYZ is a computer code for obtaining the Cartesian components of the vector potential and the magnetic field on an observed grid from an arrangement of current-carrying wires. Arbitrary combinations of straight line segments, arcs, and loops are allowed in the specification of the currents. Arbitrary positions and orientations of the current-carrying elements are also allowed. Specification of the wire diameter permits the computation of well-defined fields, even in the interiors of the conductors. An optical feature generates magnetic field lines. Extensive graphical and printed output is available to the user including contour, grid-line, and field-line plots. 12 figures, 1 table
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.
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.
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...
International Nuclear Information System (INIS)
This paper presents a Cartesian method for the simultaneous fitting of the bathymetry and shorelines in a three-dimensional, hydrodynamic model for free-surface flows. The model, named LESS3D (Lake and Estuarine Simulation System in Three Dimensions), solves flux-based finite difference equations in the Cartesian-coordinate system (x,y,z). It uses a bilinear bottom to fit the bottom topography and keeps track the dynamic position of the shoreline. The resulting computational cells are hybrid: interior cells are regular Cartesian grid cells with six rectangular faces, and boundary/bottom cells (at least one face is the water-solid interface) are unstructured cells whose faces are generally not rectangular. With the bilinear interpolation, the shape of a boundary/bottom cell can be determined at each time step. This allows the Cartesian coordinate model to accurately track the dynamic position of the shorelines. The method was tested with a laboratory experiment of a Tsunami runup case on a circular island. It was also tested for an estuary in Florida, USA. Both model applications demonstrated that the Cartesian method is quite robust. Because the present method does not require any coordinate transformation, it can be an attractive alternative to curvilinear grid model
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.
Arzano, Michele
2016-01-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of kappa-deformations of the Poincare 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 kappa to be derived via precision measurements of discrete symmetries and CPT.
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...... triangles/tetrahedra marked as outside from those marked as inside. Such an approach allows for robust topological adaptivity. Among other advantages of the deformable simplicial complexes there are: space adaptivity, ability to handle and preserve sharp features, possibility for topology control. We...
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.
Deformations of algebroid stacks
DEFF Research Database (Denmark)
Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris
2011-01-01
In this paper we consider deformations of an algebroid stack on an étale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of ...
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
Neves, J C S
2015-01-01
In this work, we have deformed regular black holes which possess a general mass term described by a function which generalizes the Bardeen and Hayward mass terms. Using linear constraints in the energy-momentum tensor, the solutions are either regular or singular. That is, with this approach, it is possible to generate singular black holes from regular black holes and vice versa. Moreover, contrary to the Bardeen and Hayward regular solutions, the regular deformed metrics may violate the weak energy condition despite the presence of the spherical symmetry. Some comments on accretion of deformed black holes in cosmological scenarios are made.
Gillies, Val; Harden, Angela; Johnson, Katherine; Reavey, Paula; Strange, Vicki; Willig, Carla
2004-03-01
The research presented in this paper uses memory work as a method to explore six women's collective constructions of two embodied practices, sweating and pain. The paper identifies limitations in the ways in which social constructionist research has theorized the relationship between discourse and materiality, and it proposes an approach to the study of embodiment which enjoins, rather than bridges, the discursive and the non-discursive. The paper presents an analysis of 25 memories of sweating and pain which suggests that Cartesian dualism is central to the women's accounts of their experiences. However, such dualism does not operate as a stable organizing principle. Rather, it offers two strategies for the performance of a split between mind and body. The paper traces the ways in which dualism can be both functional and restrictive, and explores the tensions between these two forms. The paper concludes by identifiying opportunities and limitations associated with memory work as a method for studying embodiment. PMID:15035700
Vandewalle, Kristof; Festjens, Nele; Plets, Evelyn; Vuylsteke, Marnik; Saeys, Yvan; Callewaert, Nico
2015-01-01
Reverse genetics research approaches require the availability of methods to rapidly generate specific mutants. Alternatively, where these methods are lacking, the construction of pre-characterized libraries of mutants can be extremely valuable. However, this can be complex, expensive and time consuming. Here, we describe a robust, easy to implement parallel sequencing-based method (Cartesian Pooling-Coordinate Sequencing or CP-CSeq) that reports both on the identity as well as on the location of sequence-tagged biological entities in well-plate archived clone collections. We demonstrate this approach using a transposon insertion mutant library of the Mycobacterium bovis BCG vaccine strain, providing the largest resource of mutants in any strain of the M. tuberculosis complex. The method is applicable to any entity for which sequence-tagged identification is possible. PMID:25960123
Energy Technology Data Exchange (ETDEWEB)
Crockett, Robert; Graves, Daniel; Colella, Phillip
2009-10-23
We present a method for solving Poisson and heat equations with discon- tinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materi- als, as described in Johansen& Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 106, thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.
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
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 ...
Directory of Open Access Journals (Sweden)
Mohd E. Rasul
2015-12-01
Full Text Available Sprengel shoulder is a rare congenital deformity of one or both scapulae that is usually detected at birth. It occurs due to failure of the scapula to descend during intrauterine development. Although the deformity appears randomly most of the time, familial cases have been reported. Sprengel shoulder is often associated with Klippel-Feil syndrome and other congenital skeletal deformities. Anteroposterior X-ray imaging can accurately diagnose Sprengel deformity. However, computed tomography and magnetic resonance scans with three-dimensional reconstruction are nowadays used in everyday practice in order to diagnose concomitant abnormalities, study in detail the anatomy of the affected shoulder(s, and plan appropriate management. We present here our imaging experience from one pediatric case with Sprengel shoulder and take the opportunity to discuss this rare entity, which is, nevertheless, the commonest congenital defect of the scapula. [Int J Res Med Sci 2015; 3(12.000: 3869-3871
Canonical Infinitesimal Deformations
Ran, Ziv
1998-01-01
This paper gives a canonical construction, in terms of additive cohomological functors, of the universal formal deformation of a compact complex manifold without vector fields (more generally of a faithful $g$-module, where $g$ is a sheaf of Lie algebras without sections). The construction is based on a certain (multivariate) Jacobi complex $J(g)$ associatd to $g$: indeed ${\\mathbb C}\\oplus {\\mathbb H}^0(J(g))^*$ is precisely the base ring of the universal deformation.
Poirot, Jordan; De Luna, Paolo; Rainer, Gregor
2016-04-01
We comprehensively characterize spiking and visual evoked potential (VEP) activity in tree shrew V1 and V2 using Cartesian, hyperbolic, and polar gratings. Neural selectivity to structure of Cartesian gratings was higher than other grating classes in both visual areas. From V1 to V2, structure selectivity of spiking activity increased, whereas corresponding VEP values tended to decrease, suggesting that single-neuron coding of Cartesian grating attributes improved while the cortical columnar organization of these neurons became less precise from V1 to V2. We observed that neurons in V2 generally exhibited similar selectivity for polar and Cartesian gratings, suggesting that structure of polar-like stimuli might be encoded as early as in V2. This hypothesis is supported by the preference shift from V1 to V2 toward polar gratings of higher spatial frequency, consistent with the notion that V2 neurons encode visual scene borders and contours. Neural sensitivity to modulations of polarity of hyperbolic gratings was highest among all grating classes and closely related to the visual receptive field (RF) organization of ON- and OFF-dominated subregions. We show that spatial RF reconstructions depend strongly on grating class, suggesting that intracortical contributions to RF structure are strongest for Cartesian and polar gratings. Hyperbolic gratings tend to recruit least cortical elaboration such that the RF maps are similar to those generated by sparse noise, which most closely approximate feedforward inputs. Our findings complement previous literature in primates, rodents, and carnivores and highlight novel aspects of shape representation and coding occurring in mammalian early visual cortex. PMID:26843607
Vaporization of Deforming Droplets
Wang, Yanxing; Chen, Xiaodong; Ma, Dongjun; Yang, Vigor
2012-11-01
Droplet deformation is one of the most important factors influencing the evaporation rate. In the present study, high-fidelity numerical simulations of single evaporating droplets with deformation are carried out over a wide range of the Reynolds and Weber numbers. The formulation is based on a complete set of conservation equations for both the liquid and surrounding gas phases. A modified volume-of-fluid (VOF) technique that takes into account heat and mass transfer is used to track the behavior of the liquid/gas interface. Special attention is given to the property conservation, which can be realized by using an iterative algorithm that enforces a divergence constraint in cells containing the interface. The effect of the ambient flow on droplet dynamics and evaporation are investigated systematically. Various underlying mechanisms dictating the droplet characteristics in different deformation regimes are identified. Correlations for the droplet evaporation rate are established in terms of the Reynolds and Weber numbers.
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...
Crustal deformation and earthquakes
Cohen, S. C.
1984-01-01
The manner in which the Earth's surface deforms during the cycle of stress accumulation and release along major faults is investigated. In an investigation of the crustal deformation associated with a thin channel asthenosphere displacements are reduced from those computed for a half space asthenosphere. A previous finding by other workers that displacements are enhanced when flow is confined to a thin channel is based on several invalid approximations. The major predictions of the finite element model are that the near field postseismic displacements and strain rates are less than those for a half space asthenosphere and that the postseismic strain rates at intermediate distances are greater (in magnitude). The finite width of the asthenosphere ceases to have a significant impact on the crustal deformation pattern when its magnitude exceeds about three lithosphere thicknesses.
Agrawal, Ashish; Agrawal, Rahul; Singh, Rajat; Agrawal, Romi; Agrawal, Seema
2014-01-01
Endogenous erythroid colony (EEC) syndrome comprise of three cardinal features, i.e. ectrodactyly, ectodermal dysplasia and cleft lip. EEC itself has three different forms. Ectrodactyly (absence of one or more digits) can be present with clefting in the proximal portion of hand or foot known as split hand foot malformation (SHFM) or lobster claw deformity. SHFM can be of four types depending upon the different responsible chromosomal loci. SHFM-4 can be present as pure limb malformation (non-syndromic form). In this article, describes a rare case report of lobster claw deformity patient. PMID:24992861
Directory of Open Access Journals (Sweden)
Ashish Agrawal
2014-01-01
Full Text Available Endogenous erythroid colony (EEC syndrome comprise of three cardinal features, i.e. ectrodactyly, ectodermal dysplasia and cleft lip. EEC itself has three different forms. Ectrodactyly (absence of one or more digits can be present with clefting in the proximal portion of hand or foot known as split hand foot malformation (SHFM or lobster claw deformity. SHFM can be of four types depending upon the different responsible chromosomal loci. SHFM-4 can be present as pure limb malformation (non-syndromic form. In this article, describes a rare case report of lobster claw deformity patient.
Joining by plastic deformation
DEFF Research Database (Denmark)
Mori, Ken-ichiro; Bay, Niels; Fratini, Livan;
2013-01-01
As the scale and complexity of products such as aircraft and cars increase, demand for new functional processes to join mechanical parts grows. The use of plastic deformation for joining parts potentially offers improved accuracy, reliability and environmental safety as well as creating opportuni......As the scale and complexity of products such as aircraft and cars increase, demand for new functional processes to join mechanical parts grows. The use of plastic deformation for joining parts potentially offers improved accuracy, reliability and environmental safety as well as creating...
Nail Deformities and Injuries.
Tucker, James Rory J
2015-12-01
A variety of nail deformities commonly presents in the primary care office. An understanding of nail anatomy coupled with inspection of the nails at routine office visits can reveal undetected disorders. Some problems are benign, and treatment should be attempted by the primary care provider, such as onychomycosis, paronychia, or ingrown toenails. For conditions such as benign melanonychia, longitudinal ridges, isolated Beau lines, and onycholysis, clinicians may offer reassurance to patients who are concerned about the change in their nails. For deformities such as early pterygium or clubbing, a thorough evaluation and referral to an appropriate specialist may be warranted. PMID:26612379
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.
Deforming Geometric Transitions
Rossi, Michele
2013-01-01
After a quick review of the wild structure of the complex moduli space of Calabi-Yau threefolds and the role of geometric transitions in this context (the Calabi-Yau web) the concept of "deformation equivalence" for geometric transitions is introduced to understand the arrows of the Gross-Reid Calabi-Yau web as deformation-equivalence classes of geometric transitions. Then the focus will be on some results and suitable examples to understand under which conditions it is possible to get "simpl...
Universal deformation formulas
Czech Academy of Sciences Publication Activity Database
Remm, E.; Markl, Martin
2015-01-01
Roč. 43, č. 11 (2015), s. 4711-4734. ISSN 0092-7872 Institutional support: RVO:67985840 Keywords : algebra * deformation * twisting Subject RIV: BA - General Mathematics Impact factor: 0.388, year: 2014 http://www.tandfonline.com/doi/abs/10.1080/00927872.2014.949729
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....
Diffeomorphic Statistical Deformation Models
DEFF Research Database (Denmark)
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
manifold and that the distance between two deformations are given by the metric introduced by the L2-norm in the parameter space. The chosen L2-norm is shown to have a clear and intuitive interpretation on the usual nonlinear manifold. Our model is validated on a set of MR images of corpus callosum with...
Nienhuys, Han-Wen
2003-01-01
Virtual reality simulations of surgical procedures allow such procedures to be practiced on computers instead of patients and test-animals. The core of such a system is a soft tissue simulation, that has to react very quickly but be realistic at the same time. This thesis discusses how deformable
Formation and subdivision of deformation structures during plastic deformation
DEFF Research Database (Denmark)
Jakobsen, B.; Poulsen, H.F.; Lienert, U.;
2006-01-01
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...
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.
Aftosmis, M. J.; Berger, M. J.; Murman, S. M.; Kwak, Dochan (Technical Monitor)
2002-01-01
The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.