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.
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.
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
An application of the 3-dimensional q-deformed harmonic oscillator to the nuclear shell model
Raychev, P P; Lo-Iudice, N; Terziev, P A
1998-01-01
An analysis of the construction of a q-deformed version of the 3-dimensional harmonic oscillator, which is based on the application of q-deformed algebras, is presented. The results together with their applicability to the shell model are compared with the predictions of the modified harmonic oscillator.
Cooper pair of superconductivity in the coordinate representation and q-deformed harmonic oscillator
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2016-06-01
In this work we study the similarity between the wave functions of q -deformed harmonic oscillator and wave functions of Cooper pair. The wave functions of Cooper pairs in coordinate-space have an “onion-like” layered structure with exponent decay (Boltzmann) envelope modulation. The ground state wave function of q -deform harmonic oscillator has the form of oscillate functions with Gaussian decay envelope modulation. The corresponding between Boltzmann and Gaussian forms of envelope functions and their quantum similarity are discussed.
Braid group representations from a deformation of the harmonic oscillator algebra
Tarlini, Marco
2016-01-01
We describe a new technique to obtain representations of the braid group B_n from the R-matrix of a quantum deformed algebra of the one dimensional harmonic oscillator. We consider the action of the R-matrix not on the tensor product of representations of the algebra, that in the harmonic oscillator case are infinite dimensional, but on the subspace of the tensor product corresponding to the lowest weight vectors.
The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters
Bonatsos, Dennis; Raychev, P P; Roussev, R P; Terziev, P A; Bonatsos, Dennis
1999-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of alkali metal clusters.
An application of the three-dimensional q-deformed harmonic oscillator to the shell model
Energy Technology Data Exchange (ETDEWEB)
Raychev, P.P. [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Monte S Angelo, via Cintia, I-80125 Napoli (Italy); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, BG-1784 Sofia (Bulgaria); Roussev, R.P.; Terziev, P.A. [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, BG-1784 Sofia (Bulgaria); Lo Iudice, N. [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Monte S Angelo, via Cintia, I-80125 Napoli (Italy)
1998-10-01
A procedure for the construction of a q-deformed version of the Hamiltonian of the three-dimensional harmonic oscillator (HO), based on the application of q-deformed algebras, is presented. The spectrum of this Hamiltonian is not degenerated in the quantum number of the q-deformed angular momentum. The results together with their applicability to the shell model are compared with the predictions of the modified HO. (author)
Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2003-01-01
The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).
Deformed Relativistic Hartree Theory in Coordinate Space and in Harmonic Oscillator Basis
Institute of Scientific and Technical Information of China (English)
ZHOU Shan-Gui; MENG Jie; Shuhei YAMAJI; YANG Si-Chun
2000-01-01
The deformed relativistic Hartree theory (DRH) is solved both in coordinate space (DRH-c) and in harmonic oscillator basis (DRH-o). Results obtained from these two methods are compared in details. The DRH-c and DRH-o calculations give similar total binding energies, deformation, level structures and radii for nitrogen iso topes, while their descriptions on the density distributions for drip-line nuclei are very different. The large spatiai istributions of nucleon densities, which is crucial to understand a weakly bound system, can only be obtained by DRH-c calculations. This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.
Bonatsos, Dennis; Lenis, D; Raychev, P P; Roussev, R P; Terziev, P A
2000-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry ...
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.
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.
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, ...
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.
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...
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.
Quantum dynamics of the damped harmonic oscillator
Philbin, T G
2012-01-01
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
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.
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.
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.
Quantum harmonic oscillator with superoscillating initial datum
Energy Technology Data Exchange (ETDEWEB)
Buniy, R. V.; Struppa, D. C. [Schmid College of Science and Technology, Chapman University, Orange, California 92866 (United States); Colombo, F.; Sabadini, I. [Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi 9, 20133 Milano (Italy)
2014-11-15
In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.
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.
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
DEFF Research Database (Denmark)
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting...... U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...
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 means of numerical integration of the appropriate differential equations....
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.
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
Institute of Scientific and Technical Information of China (English)
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
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.
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.
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.
Bound states of two-dimensional relativistic harmonic oscillators
Institute of Scientific and Technical Information of China (English)
Qiang Wen-Chao
2004-01-01
We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.
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)
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...
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)
The relativistic bound states for a new ring-shaped harmonic oscillator
Institute of Scientific and Technical Information of China (English)
Zhou Yan; Guo Jian-You
2008-01-01
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.
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.
Institute of Scientific and Technical Information of China (English)
LIN Bing-Sheng; HENG Tai-Hua
2011-01-01
We use the invariant eigen-operator method to study the higher-dimensional harmonic oscillator in a type of generalized noncommutative phase space,and obtain the explicit expression of the energy spectra of the noncommutative harmonic oscillator in arbitrary dimension.It is found that the energy spectra of the higher-dimensional noncommutative harmonic oscillator are equal to the sum of the energy spectra of some 1D harmonic oscillators and some 2D noncommutative harmonic oscillators. We believe that the properties of the harmonic oscillator may reflect some essence of the noncommutative phase space.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...
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.
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…
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…
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 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.
Simulating Harmonic Oscillator and Electrical Circuits: A Didactical Proposal
Albano, Giovannina; D'Apice, Ciro; Tomasiello, Stefania
2002-01-01
A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…
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.
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.
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
Nita, Gelu M.
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
The harmonic oscillator, dimensional analysis and inflationary solutions
San Costa, S
2002-01-01
In this work, focused on the production of exact inflationary solutions using dimensional analysis, it is shown how to explain inflation from a pragmatic and basic point of view, in a step-by-step process, starting from the one-dimensional harmonic oscillator.
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
Equity prices as a simple harmonic oscillator with noise
Ataullah, Ali; Tippett, Mark
2007-08-01
The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.
An analogue of the Berry phase for simple harmonic oscillators
Suslov, S. K.
2013-03-01
We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.
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.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber
2009-04-01
This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.
Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
Kim, Y S; Noz, Marilyn E.
2004-01-01
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$...
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Elementary derivation of the quantum propagator for the harmonic oscillator
Shao, Jiushu
2016-10-01
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
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.
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...
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Chou, Chia-Chun
2016-10-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
Earl, Boyd L.
2008-01-01
A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…
Institute of Scientific and Technical Information of China (English)
CHEN CHANG-YUAN
2000-01-01
In this paper, the general formulas and the recurrence formulas for radial matrix elements of N-dimensional isotropic harmonic oscillator are obtained. The relevant results of 2- dimensional and 3- dimensiona] isotropic harmonic oscillators reported in the reference papers are contained in a more general equations derived in this paper as special cases.
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
Amitava Choudhuri; Subrata Ghosh; B Talukdar
2008-04-01
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.
Chiral potential renormalized in harmonic-oscillator space
Yang, C -J
2016-01-01
We renormalize the chiral effective field theory (EFT) potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultra-violet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J-matrix method to reproduce the nucleon-nucleon (NN) scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy $T_{lab}=100$ MeV with number of HO basis $n_{max}$ as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. Our work serves as the input to perform ab-initio calculations.
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.
Ecological optimization of an irreversible harmonic oscillators Carnot heat engine
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A model of an irreversible quantum Carnot heat engine with heat resistance,internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach,equations of some important performance parameters,such as power output,efficiency,exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.
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.
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)
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.
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
Singh, Manu Pratap; Rajput, B. S.
2016-10-01
Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.
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 ...
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.
Entanglement dynamics for a conditionally kicked harmonic oscillator
Arrais, Eric G.; Sales, J. S.; de Almeida, N. G.
2016-08-01
The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0, the so-called Lamb-Dicke parameter η whose square is proportional to the effective Planck constant {{\\hslash }}{{eff}}, and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting {{\\hslash }}{{eff}} become negligible. In this paper we investigate how the ratio T, considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or {{\\hslash }}{{eff}} parameters.
Entangled Harmonic Oscillators and Space-Time Entanglement
Directory of Open Access Journals (Sweden)
Sibel Başkal
2016-06-01
Full Text Available 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 the 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 the S p ( 4 group, which serves as the basic language for two-mode squeezed states. Since the S p ( 4 symmetry contains both rotations and squeezes, one interesting case is the combination of rotation and squeeze, resulting in a shear. While the current literature is mostly on the entanglement based on squeeze along the normal coordinates, the shear transformation is an interesting future possibility. The mathematical issues on this problem are clarified.
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...
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.
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...
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.
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...
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.
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.
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.
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
Institute of Scientific and Technical Information of China (English)
刘宇峰; 曾谨言
1997-01-01
The factorization of the radial Schrodinger equation of n-dimensional (n≥2) hydrogen atoms and isotropic harmonic oscillators was investigated and four kinds of raising and lowering operators were derived.The relation between n -dimensional (n≥2) and one-dimensional hydrogen atoms and harmonic oscillators was discussed.
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.
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
su(2) Lie algebra approach for the Feynman propagator of the one-dimensional harmonic oscillator
Martínez, D.; Avendaño, C. G.
2014-04-01
We evaluate the Feynman propagator for the harmonic oscillator in one dimension. Considering the ladder operators for the Hamiltonian of this system, we construct a set of operators which satisfy the su(2) Lie algebra to obtain Mehler’s formula.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M
2001-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M
2004-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, Miguel
2001-07-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Institute of Scientific and Technical Information of China (English)
JINShuo; XIEBing-Hao; ZHANGHong-Biao; GEMo-Lin
2004-01-01
Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2) squeezed number states respectively. Some statistical properties of these states are also discussed.
Institute of Scientific and Technical Information of China (English)
JIN Shuo; XIE Bing-Hao; ZHANG Hong-Biao; GE Mo-Lin
2004-01-01
Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2)squeezed number states respectively. Some statistical properties of these states are also discussed.
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
2010-01-01
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...
The Adiabatic Invariant of the n-Degree-of-Freedom Harmonic Oscillator
Devaud, M.; Leroy, V.; Bacri, J.-C.; Hocquet, T.
2008-01-01
In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with…
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.
Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space
Das, Saurya; Walton, Mark A
2016-01-01
We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.
Bonatsos, Dennis; Kolokotronis, P; Lenis, D; Bonatsos, Dennis
1994-01-01
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems.
Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp(4, R) Lie Algebra
Institute of Scientific and Technical Information of China (English)
PAN Feng; DAI LianRong
2001-01-01
Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).``
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.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... to the extent that it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes the effects...
López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.
2012-08-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
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.
Saha, Anirban
2015-01-01
We investigate the quantum mechanical transitions, induced by the combined effect of Gravitational wave (GW) and noncommutative (NC) structure of space, among the states of a 2-dimensional harmonic oscillator. The phonon modes excited by the passing GW within the resonant bar-detector are formally identical to forced harmonic oscillator and they represent a length variation of roughly the same order of magnitude as the characteristic length-scale of spatial noncommutativity estimated from the phenomenological upper bound of the NC parameter. This motivates our present work. We employ a number of different GW wave-forms that are typically expected from possible astronomical sources. We find that the transition probablities are quite sensitive to the nature of polarization of the GW. We further elaborate on the particular type of sources of GW radiation which can induce transitions that can be used as effective probe of the spatial noncommutative structure.
Energy Technology Data Exchange (ETDEWEB)
Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)
2011-09-19
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.
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
Directory of Open Access Journals (Sweden)
Sameer M. Ikhdair
2013-01-01
Full Text Available The Klein-Gordon (KG equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0 and AB flux field (ξ=0 cases. Effect of external fields on the nonrelativistic energy eigenvalues and wave function solutions is also precisely presented. Some special cases like harmonic oscillator and Coulombic fields are also studied.
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...
Institute of Scientific and Technical Information of China (English)
Shi-Qi Jiang; Bo Wu; Tian-Xiang Gu
2007-01-01
The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper By using the random average method and ShapiroLoginov formula, the exact solution of the average output amplitude gain (OAG) is obtained. Numerical results show that OAG depends nonmonotonically on the noise characteristics: intensity, correlation time and asymmetry.The maximum OAG can be achieved by tuning the noise asymmetry and or the noise correlation time.
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.
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, ...
Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams
Steely, Sidney L.
1993-01-01
The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.
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...
Institute of Scientific and Technical Information of China (English)
WEI Gao-Feng; LONG Chao-Yun; LONG Zheng-Wen; QIN Shui-Jie
2008-01-01
In this paper,the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space;the corresponding exact energy is obtained,and the analytic eigenfunction is presented in terms of the confluent hypergeometric function.It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.
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
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.
Pupasov-Maksimov, Andrey M.
2015-12-01
It is shown that fundamental solutions Kσ(x , y ; t) = of the non-stationary Schrödinger equation (Green functions, or propagators) for the rational extensions of the Harmonic oscillator Hσ =Hosc + ΔVσ are expressed in terms of elementary functions only. An algorithm to calculate explicitly Kσ for an arbitrary increasing sequence of positive integers σ is given, and compact expressions for K { 1 , 2 } and K { 2 , 3 } are presented. A generalization of Mehler's formula to the case of exceptional Hermite polynomials is given.
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.
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.
A least squares finite element scheme for transonic flow around harmonically oscillating airfoils
Cox, C. L.; Fix, G. J.; Gunzburger, M. D.
1983-01-01
The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.
Guo, Feng; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Li, Heng
2016-10-01
Stochastic resonance in a fractional harmonic oscillator with random mass and signal-modulated noise is investigated. Applying linear system theory and the characteristics of the noises, the analysis expression of the mean output-amplitude-gain (OAG) is obtained. It is shown that the OAG varies non-monotonically with the increase of the intensity of the multiplicative dichotomous noise, with the increase of the frequency of the driving force, as well as with the increase of the system frequency. In addition, the OAG is a non-monotonic function of the system friction coefficient, as a function of the viscous damping coefficient, as a function of the fractional exponent.
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-Gr ̈uneisen EOS developed for an atomic solid, the specific heat and Gr ̈uneisen coefficient depend on both density and temperature.
Rosu, H. C.; Khmelnytskaya, K. V.
2011-09-01
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned.
Rosu, H C
2010-01-01
Previous research made us consider a simple but curious problem related to the kind of oscillators that are produced in the usual supersymmetric scheme when one introduces a constant shift of the Riccati solution R(t)=-omega _0 tan(omega _0t) of the classical harmonic oscillator. The corresponding mathematical scheme is presented in detail showing that at least some of these oscillators could be of physical nature. We give the solutions of the resulting second-order differential equations obtaining the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry
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....
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-07-01
We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number.
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...
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.
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.
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./.
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.
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.
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.
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.
Use of videos for students to see the effect of changing gravity on harmonic oscillators
Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber
2010-03-01
In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.
Institute of Scientific and Technical Information of China (English)
Sameer M.Ikhdair; Majid Hamzavi
2012-01-01
We study the effects of the perpendicular magnetic and Aharonov Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein-Gordon (KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator (PHO).We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter,magnetic field strength,AB flux field,and magnetic quantum number by means of the Nikiforov-Uvarov (NU) method.The non-relativistic limit,PHO,and harmonic oscillator solutions in the existence and absence of external fields are also obtained.
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
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System
Directory of Open Access Journals (Sweden)
Lock Yue Chew
2014-04-01
Full Text Available In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state.
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015), 10.1103/PhysRevE.91.012920] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
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.
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.
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
2016-09-01
In this work, we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore, the motion is periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.
Time operator for the quantum harmonic oscillator resolution of an apparent paradox
Granik, A; Granik, Alex
2000-01-01
An apparent paradox is resolved that concerns the existence of time operators which have been derived for the quantum harmonic oscillator. There is an apparent paradox because, although a time operator is canonically conjugate to the Hamiltonian, it has been asserted that no operator exists that is canonically conjugate to the Hamiltonian. In order to resolve the apparent paradox, we work in a representation where the phase operator is diagonal. The boundary condition on wave functions is such that they be periodic in the phase variable, which is related to the (continuous) eigenvalue of the time operator. Matrix elements of the commutator of the time operator with the Hamiltonian involve the phase variable itself in addition to periodic functions of the phase variable. The Hamiltonian is not hermitian when operating in space that includes the phase variable itself. The apparent paradox is resolved when this non-hermeticity is taken into account correctly in the evaluation of matrix elements of the commutatio...
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.
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.
Bose–Einstein condensation in a two-component Bose gas with harmonic oscillator interaction
Abulseoud, A. A.; Abbas, A. H.; Galal, A. A.; El-Sherbini, Th M.
2016-07-01
In this article a system containing two species of identical bosons interacting via a harmonic oscillator potential is considered. It is assumed that the number of bosons of each species is the same and that bosons belonging to the same species repel each other while those belonging to different species attract. The Hamiltonian is diagonalized and the energy spectrum of the system is written down. The behaviour of the system in the thermodynamic limit is studied within the framework of the grand canonical ensemble, and thermodynamic parameters, such as the internal energy, entropy and specific heat capacity are calculated. It is shown that the system exhibits a single species Bose–Einstein condensation when the coupling strengths are equal and a dual species condensation when they are different.
Directory of Open Access Journals (Sweden)
V. Mohammadi
2015-01-01
Full Text Available We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, the SO(3 group generators of the Schrödinger-like equation with the Kepler-Coulomb potential are represented. In addition, by Levi-Civita transformation, the Schrödinger-like equation with harmonic oscillator which is dual to the Kepler-Coulomb potential and the SU(2 group generators of associated system are studied. Also, we construct the quadratic algebra of the hyperboloid superintegrable system. Then, we obtain the corresponding Casimir operators and the structure functions and the relativistic energy spectra of the corresponding quasi-Hamiltonians by using the quadratic algebra approach.
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.
The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
Schliemann, John
2013-01-01
It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only neighboring states of its standard basis, and (ii) its matrix elements show a unique maximum as a function of internal angular momentum quantum numbers. These quantum numbers, considered as a continuous variable, are the coordinate of the oscillator describing its quadratic potential, while the corresponding derivative defines a momentum operator. We also analyze the scaling properties of the oscillator parameters as a function of the size of the tetrahedron, and the role of different angular momentum coupling schemes.
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 ...
Evolution of a quantum harmonic oscillator coupled to a minimal thermal environment
Vidiella-Barranco, A.
2016-10-01
In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled A), prepared in a coherent state. The environment itself consists of a second oscillator (labelled B), initially in a thermal state. Two types of interaction Hamiltonians are considered, and the time-evolution of the reduced density operator of oscillator A is compared to the one obtained from the usual master equation approach, i.e., assuming that oscillator A is coupled to a large reservoir. An analysis of the linear entropy evolution of oscillator A shows that simplified models may be able to describe important features related to the phenomenon of decoherence, such as the rapid growth of the linear entropy, as well as its dependence on the effective temperature of the environment.
Andrews, David L.; Romero, Luciana C. Davila
2009-01-01
The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…
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.
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.
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
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
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.
Directory of Open Access Journals (Sweden)
Cornelia A. Bulucea
2012-03-01
Full Text Available Over the last several decades, it has become increasingly accepted that the term xenobiotic relates to environmental impact, since environmental xenobiotics are understood to be substances foreign to a biological system, which did not exist in nature before their synthesis by humans. In this context, xenobiotics are persistent pollutants such as dioxins and polychlorinated biphenyls, as well as plastics and pesticides. Dangerous and unstable situations can result from the presence of environmental xenobiotics since their harmful effects on humans and ecosystems are often unpredictable. For instance, the immune system is extremely vulnerable and sensitive to modulation by environmental xenobitics. Various experimental assays could be performed to ascertain the immunotoxic potential of environmental xenobiotics, taking into account genetic factors, the route of xenobiotic penetration, and the amount and duration of exposure, as well as the wave shape of the xenobiotic. In this paper, we propose an approach for the analysis of xenobiotic metabolism using mathematical models and corresponding methods. This study focuses on a pattern depicting mathematically modeled processes of resonant absorption of a xenobiotic harmonic oscillation by an organism modulated as an absorbing oscillator structure. We represent the xenobiotic concentration degree through a spatial concentration vector, and we model and simulate the oscillating regime of environmental xenobiotic absorption. It is anticipated that the results could be used to facilitate the assessment of the processes of environmental xenobiotic absorption, distribution, biotransformation and removal within the framework of compartmental analysis, by establishing appropriate mathematical models and simulations.
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.
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...
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
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.
Le Yaouanc, A; Morénas, V; Oliver, L; Pène, O; Raynal, J C
2000-01-01
The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $\\delta m/m_b^2$.
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.
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
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)
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)
A new look at the quantum mechanics of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
Energy Technology Data Exchange (ETDEWEB)
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Mendez, D.I. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Marini, S. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-08-03
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
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
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
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.
Institute of Scientific and Technical Information of China (English)
ZHAI Zhi-Yuan; YANG Tao; PAN Xiao-Yin
2012-01-01
The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated. Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.%The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated.Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.
Energy Technology Data Exchange (ETDEWEB)
Thantu, Napoleon; McMorrow, D.; Melinger, J. S.; Kleiman, V.; Lotshaw, W. T.
2001-07-01
The apparently-multicomponent subpicosecond intermolecular dynamics of carbon disulfide liquid are addressed in a unified manner in terms of an inhomogeneously broadened quantum mechanical harmonic oscillator model for a single vibrational coordinate. For an inhomogeneously broadened (Gaussian) distribution of oscillators, the model predicts naturally the bimodal character of the subpicosecond intermolecular dynamics of carbon disulfide liquid, and also the spectral evolution effects (spectral narrowing and saturation) that are observed for solutions of carbon disulfide in weakly interacting alkane solvents. The unique dynamical signature of these low-frequency vibrational coordinates is determined largely by the physical constraints on the coordinates (near equality of oscillator frequency, dephasing frequency, and inhomogeneous bandwidth), such that constructive and destructive interference effects play a dominant role in shaping the experimental observable.
Directory of Open Access Journals (Sweden)
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.
Structure and Behavior of the Edge Harmonic Oscillation in Quiescent H-Mode Plasmas on DIII-D
McKee, G. R.; Yan, Z.; Burrell, K. H.; Garofalo, A. M.; Grierson, B. A.; Solomon, W. M.
2013-10-01
The edge harmonic oscillation (EHO) is a steady-state, pedestal-localized instability that is observed in high-performance, ELM-free Quiescent H-mode plasmas. The spatiotemporal characteristics of the EHO have been measured in QH-mode plasmas with a 2D BES array that measures low-k density fluctuations. The skewness of the fluctuation distribution increases radially from -0.5 to +1 near the separatrix, consistent with the radially varying and highly non-sinusoidal harmonic structure. These fluctuation characteristics are qualitatively consistent with an outward particle transport driven by the EHO. The density fluctuation (ñ / n) profile peaks inside the pedestal, near ρ = 0.90-0.95, and is observed from ρ = 0 . 85 to the separatrix; the fundamental frequency is typically in the range of 5-15 kHz. The radial structure of the oscillation has a monotonically varying phase shift of approximately 180 degrees across the outer plasma region that changes direction with plasma current, suggesting that the mode structure is impacted by the high edge toroidal rotation velocity. Work supported by the US Department of Energy under DE-FG02-08ER54999, DE-FC02-04ER54698, and DE-AC02-09CH11466.
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Directory of Open Access Journals (Sweden)
Marcin Salamaga
2013-09-01
Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.
Institute of Scientific and Technical Information of China (English)
Liu Li; Zhang Liang-Ying; Cao Li
2009-01-01
The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ_3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Orustein-Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3)Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.
Graham Hoover, William; Clinton Sprott, Julien; Griswold Hoover, Carol
2016-10-01
We describe the application of adaptive (variable time step) integrators to stiff differential equations encountered in many applications. Linear harmonic oscillators subject to nonlinear thermal constraints can exhibit either stiff or smooth dynamics. Two closely related examples, Nosé's dynamics and Nosé-Hoover dynamics, are both based on Hamiltonian mechanics and generate microstates consistent with Gibbs' canonical ensemble. Nosé's dynamics is stiff and can present severe numerical difficulties. Nosé-Hoover dynamics, although it follows exactly the same trajectory, is smooth and relatively trouble-free. We emphasize the power of adaptive integrators to resolve stiff problems such as the Nosé dynamics for the harmonic oscillator. The solutions also illustrate the power of computer graphics to enrich numerical solutions.
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
用光电鼠标做传感器显示振动图像%Using optical mouse as sensor to display simple harmonic oscillation image
Institute of Scientific and Technical Information of China (English)
霍金胜
2014-01-01
Using wireless optical mouse as sensor ,the simple harmonic oscillation image was dis-played by Flash program .The experimental results were explored .%介绍了用无线光电鼠标做传感器，通过Flash程序显示物体做简谐振动的图像的实验方法，并探究了该方法的实验效果。
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...
Sobhani, Hadi; Hassanabadi, Hassan
2016-08-01
This paper contains study of Bohr Hamiltonian considering time-dependent form of two important and famous nuclear potentials and harmonic oscillator. Dependence on time in interactions is considered in general form. In order to investigate this system, a powerful mathematical method has been employed, so-called Lewis-Riesenfeld dynamical invariant method. Appropriate dynamical invariant for considered system has been constructed. Then its eigen functions and the wave function are derived. At the end, we discussed about physical meaning of the results.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Neipp, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Belendez, T [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-02-15
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.
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.
Cartesian product of hypergraphs: properties and algorithms
Directory of Open Access Journals (Sweden)
Alain Bretto
2009-09-01
Full Text Available Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspects of Cartesian products of hypergraphs. We also extend a classical prime factorization algorithm initially designed for graphs to connected conformal hypergraphs using 2-sections of hypergraphs.
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...
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.
Cartesian Grid Method for Gas Kinetic Scheme
Chen, Songze; Li, Zhihui
2015-01-01
A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four different categories, the fluid point, the solid point, the drop point, and the interpolation point. The boundaries are represented by a set of direction-oriented boundary points. A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points. Different boundary conditions, including isothermal boundary, adiabatic boundary, and Euler slip boundary, are presented by different interpolation strategies. We also propose a simplified gas kinetic scheme as the flux solver for both subsonic and supersonic flow computations. The methodology of constructing a simplified kinetic flux function can be extended to other flow systems. A few numerical examples are used to validate the Cartesian grid method and the simplified flux func...
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.
Caligiuri, Luigi Maxmilian
2015-01-01
The question regarding the potential biological and adverse health effects of non-ionizing electromagnetic fields on living organisms is of primary importance in biophysics and medicine. Despite the several experimental evidences showing such occurrence in a wide frequency range from extremely low frequency to microwaves, a definitive theoretical model able to explain a possible mechanism of interaction between electromagnetic fields and living matter, especially in the case of weak and very weak intensities, is still missing. In this paper it has been suggested a possible mechanism of interaction involving the resonant absorption of electromagnetic radiation by microtubules. To this aim these have been modeled as non-dissipative forced harmonic oscillators characterized by two coupled "macroscopic" degrees of freedom, respectively describing longitudinal and transversal vibrations induced by the electromagnetic field. We have shown that the proposed model, although at a preliminary stage, is able to explain the ability of even weak electromagnetic radiating electromagnetic fields to transfer high quantities of energy to living systems by means of a resonant mechanism, so capable to easily damage microtubules structure.
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.
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
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.
Conversion of contours to cartesian grids
DEFF Research Database (Denmark)
Mann, Jakob; Broe, Brian Riget
A robust and efficient method of calculating a cartesian grid of heights or roughnesses from contour line maps is developed. The purpose of the grids is to serve as input for atmospheric flow solvers such as WAsP Engineering or EllipSys3D. The method builds on Delaunay triangulation constrained t...... to include all contour segments in the triangulation. It is furthermore refined to avoid spurious flat areas produced by the Delaunay triangulation. Robust ways to extrapolate beyond the convex hull of the map points are provided....
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.
Masood, Syed; Zaz, Zaid; Ali, Ahmed Farag; Raza, Jamil; Shah, Mushtaq B
2016-01-01
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by space fractional quantum mechanics and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
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.
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.
Cartesian Trajectory Tracking for Manipulators Using Optimal Control Theory
Directory of Open Access Journals (Sweden)
Olav Egeland
1987-07-01
Full Text Available A Cartesian trajectory tracking system for manipulators is developed using optimal control theory. By including the Cartesian position in the state vector, transformation of the trajectory from Cartesian space to manipulator joint space is avoided, and the Jacobian matrix need not be inverted. The tracking system may also be applied to kinematically redundant manipulators. For this type of manipulator, singularities are avoided by choosing a suitable performance index in the optimal control problem. Simulation using a simple kinematically redundant manipulator shows that a small tracking error can be achieved with low motor torques.
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 ...
An adaptive phase alignment algorithm for cartesian feedback loops
Gimeno-Martin, A.; Pardo-Martin, J.; Ortega-Gonzalez, F.
2010-01-01
An adaptive algorithm to correct phase misalignments in Cartesian feedback linearization loops for power amplifiers has been presented. It yields an error smaller than 0.035 rad between forward and feedback loop signals once convergence is reached. Because this algorithm enables a feedback system to process forward and feedback samples belonging to almost the same algorithm iteration, it is suitable to improve the performance not only of power amplifiers but also any other digital feedback system for communications systems and circuits such as all digital phase locked loops. Synchronizing forward and feedback paths of Cartesian feedback loops takes a small period of time after the system starts up. The phase alignment algorithm needs to converge before the feedback Cartesian loop can start its ideal behavior. However, once the steady state is reached, both paths can be considered synchronized, and the Cartesian feedback loop will only depend on the loop parameters (open-loop gain, loop bandwidth, etc.). It means that the linearization process will also depend only on these parameters since the misalignment effect disappears. Therefore, this algorithm relieves the power amplifier linearizer circuit design of any task required for solving phase misalignment effects inherent to Cartesian feedback systems. Furthermore, when a feedback Cartesian loop has to be designed, the designer can consider that forward and feedback paths are synchronized, since the phase alignment algorithm will do this task. This will reduce the simulation complexity. Then, all efforts are applied to determining the suitable loop parameters that will make the linearization process more efficient.
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.
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.
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…
Virtual Prototyping through Co-simulation of a Cartesian Plotter
Groothuis, M.A.; Damstra, A.S.; Broenink, J.F.
2008-01-01
This paper shows a model-based design trajectory for the development of real-time embedded control software using virtual prototyping. As a test case, a Cartesian plotter is designed. Functional correctness of the plotter software has been ensured by means of co-simulation using a virtual prototype
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...
The Approach to Steady State Using Homogeneous and Cartesian Coordinates
Directory of Open Access Journals (Sweden)
D. F. Gochberg
2013-01-01
Full Text Available Repeating an arbitrary sequence of RF pulses and magnetic field gradients will eventually lead to a steady-state condition in any magnetic resonance system. While numerical methods can quantify this trajectory, analytic analysis provides significantly more insight and a means for faster calculation. Recently, an analytic analysis using homogeneous coordinates was published. The current work further develops this line of thought and compares the relative merits of using a homogeneous or a Cartesian coordinate system.
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.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Hegel's Solution to Cartesian Dualism of Mind and Body
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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.
Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.
Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H
2013-05-01
In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction.
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.
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.
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...
[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...
Neural Network Schemes in Cartesian Space Control of Robot Manipulators
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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.
Optimal online robot trajectory generation in Cartesian space
Bazaz, Shafat A.; Tondu, Bertrand
1997-12-01
We propose the use of cubic quadratic cubic squared (CQCS) spline for the trajectory generation in Cartesian space. Use of CQCS spline gives simple analytical solution to minimum time trajectory generation with velocity and acceleration constraints. The expressions for wandering time and wandering acceleration are also calculated. A straight line path with constant maximum allowed speed in minimum time can be generated with this method. This property leads to interpolate two position points by constant speed straight line motion with smooth transition. The advantage of this method is that the trajectory thus obtained is traversed in minimum time while passing through the given intermediate points. The simplicity of this method makes its on-line computation possible.
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.
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.
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.
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.
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.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-06-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.
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.
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...
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.
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.
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...
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
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...
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.
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.
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...
Directory of Open Access Journals (Sweden)
O. A. Domínguez-Ramírez
2006-01-01
Full Text Available Perception and interaction with virtual surfaces, through kinaesthetic sensation and visual stimuli, is the basic issue of a haptic interface. When the virtual or real object is in a remote location, and guidance is required to perceive kinaesthetic feedback, a haptic guidance scheme is required. In this document, with purpose of haptic-guided exploration, a new scheme for simultaneous control of force and cartesian position is proposed without using inverse kinematics, and without using the dynamic model of PHANToM, though a strict stability analysis includes the dynamic model of PHANToM. We rely on our previously proposed results to propose a new haptic cartesian controller to reduce the burden of computing cartesian forces in PHANToM. Furthermore, a time base generator for finite-time tracking is also proposed to achieve very fast tracking and high precision, which translated into high fidelity kinaesthetic feedback.
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...
Euler solution using adaptive Cartesian grid with a gridless boundary treatment
Institute of Scientific and Technical Information of China (English)
Liang Xiang; Guowei Yang
2009-01-01
A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid.First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indicate the developed method is reasonable for complex flows.
Piecewise oblique boundary treatment for the elastic-plastic wave equation on a cartesian grid
Giese, Guido
2009-11-01
Numerical schemes for hyperbolic conservation laws in 2-D on a Cartesian grid usually have the advantage of being easy to implement and showing good computational performances, without allowing the simulation of “real-world” problems on arbitrarily shaped domains. In this paper a numerical treatment of boundary conditions for the elastic-plastic wave equation is developed, which allows the simulation of problems on an arbitrarily shaped physical domain surrounded by a piece-wise smooth boundary curve, but using a PDE solver on a rectangular Cartesian grid with the afore-mentioned advantages.
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.
[Odontology and the beginning of cartesianism (1673--1650) (Rene Descartes)].
Gysel, C
1979-01-01
In the seventeenth century the universities of the Netherlands underwent the influence of Descartes in all the faculties. In medicine three periods can be distinguished: in the first, pathology and therapy are still galenic; the second, by the application of the cartesian method, triumphs in physiology; and the third, corrected by the views of Newton is integrated in a moderate biomechanism.
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...
Embodying Learning: Post-Cartesian Pedagogy and the Academic Study of Religion
Lelwica, Michelle Mary
2009-01-01
This paper explores the concept and practice of "embodied pedagogy" as an alternative to the Cartesian approach to knowledge that is tacitly embedded in traditional modes of teaching and learning about religion. My analysis highlights a class I co-teach that combines the study of Aikido (a Japanese martial art) with seminar-style discussions of…
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...
Adjacent Vertex Distinguishing Incidence Coloring of the Cartesian Product of Some Graphs
Institute of Scientific and Technical Information of China (English)
Qian WANG; Shuang Liang TIAN
2011-01-01
An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors. We obtain the adjacent vertex distinguishing incidence chromatic number of the Cartesian product of a path and a path, a path and a wheel, a path and a fan, and a path and a star.
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.
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.
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.
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.
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...
Continuous Genetic Algorithms for Collision-Free Cartesian Path Planning of Robot Manipulators
Directory of Open Access Journals (Sweden)
Za'er S. Abo-Hammour
2011-12-01
Full Text Available A novel continuous genetic algorithm (CGA along with distance algorithm for solving collisions‐free path planning problem for robot manipulators is presented in this paper. Given the desired Cartesian path to be followed by the manipulator, the robot configuration as described by the D‐H parameters, and the available stationary obstacles in the workspace of the manipulator, the proposed approach will autonomously select a collision free path for the manipulator that minimizes the deviation between the generated and the desired Cartesian path, satisfy the joints limits of the manipulator, and maximize the minimum distance between the manipulator links and the obstacles. One of the main features of the algorithm is that it avoids the manipulator kinematic singularities due to the inclusion of forward kinematics model in the calculations instead of the inverse kinematics. The new robot path planning approach has been applied to two different robot configurations; 2R and PUMA 560, as non‐ redundant manipulators. Simulation results show that the proposed CGA will always select the safest path avoiding obstacles within the manipulator workspace regardless of whether there is a unique feasible solution, in terms of joint limits, or there are multiple feasible solutions. In addition to that, the generated path in Cartesian space will be of very minimal deviation from the desired one.
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
DEFF Research Database (Denmark)
Hansen, N.; Huang, X.; Hughes, D.A.
2004-01-01
Microstructural characterization and modeling has shown that a variety of metals deformed by different thermomechanical processes follows a general path of grain subdivision, by dislocation boundaries and high angle boundaries. This subdivision has been observed to very small structural scales of...
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.
A Twist (with Pike) for the Simple Harmonic Oscillator
Filewood, G
2003-01-01
Extension of the formalism of Q.M. to resolve mathematical anomalies in the structure of anti-unitary operators; implications for vacuum structure and spin-statistics arising from an analysis applied to the S.H.O. Outline of the derived properties of the S.M. Higgs boson.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...
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.
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.
Fara, Patricia
2008-12-01
Few original portraits exist of René Descartes, yet his theories of vision were central to Enlightenment thought. French philosophers combined his emphasis on sight with the English approach of insisting that ideas are not innate, but must be built up from experience. In particular, Denis Diderot criticised Descartes's views by describing how Nicholas Saunderson--a blind physics professor at Cambridge--relied on touch. Diderot also made Saunderson the mouthpiece for some heretical arguments against the existence of God.
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
KNOT POINT PLANNING FOR CARTESIAN TRAJECTORY GENERATION BASED ON INHERITANCE BISECTION ALGORITHM
Institute of Scientific and Technical Information of China (English)
Yan Bo; Yan Guozheng
2005-01-01
The computation algorithm of knot point planning for Cartesian trajectory generation of manipulator is investigated. A novel inheritance bisection algorithm (IBA) based on conventional bisection algorithm (BA) is proposed. IBA has two steps. The first step is the 1st knot point planning under lower set position accuracy; the second step is the 2nd knot point planning that inherits the results of the 1st planning under higher set position accuracy. The simulation results reveal that the number of inverse kinematical calculation (IKC) caused by IBA is decreased compared with BA. IBA is more efficient to plan knot points.
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.
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
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 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.
The Numerical Simulation of Ship Waves Using Cartesian Grid Methods with Adaptive Mesh Refinement
Dommermuth, Douglas G; Beck, Robert F; O'Shea, Thomas T; Wyatt, Donald C; Olson, Kevin; MacNeice, Peter
2014-01-01
Cartesian-grid methods with Adaptive Mesh Refinement (AMR) are ideally suited for simulating the breaking of waves, the formation of spray, and the entrainment of air around ships. As a result of the cartesian-grid formulation, minimal input is required to describe the ships geometry. A surface panelization of the ship hull is used as input to automatically generate a three-dimensional model. No three-dimensional gridding is required. The AMR portion of the numerical algorithm automatically clusters grid points near the ship in regions where wave breaking, spray formation, and air entrainment occur. Away from the ship, where the flow is less turbulent, the mesh is coarser. The numerical computations are implemented using parallel algorithms. Together, the ease of input and usage, the ability to resolve complex free-surface phenomena, and the speed of the numerical algorithms provide a robust capability for simulating the free-surface disturbances near a ship. Here, numerical predictions, with and without AMR,...
Darwin's evolution theory, brain oscillations, and complex brain function in a new "Cartesian view".
Başar, Erol; Güntekin, Bahar
2009-01-01
Comparatively analyses of electrophysiological correlates across species during evolution, alpha activity during brain maturation, and alpha activity in complex cognitive processes are presented to illustrate a new multidimensional "Cartesian System" brain function. The main features are: (1) The growth of the alpha activity during evolution, increase of alpha during cognitive processes, and decrease of the alpha entropy during evolution provide an indicator for evolution of brain cognitive performance. (2) Human children younger than 3 years are unable to produce higher cognitive processes and do not show alpha activity till the age of 3 years. The mature brain can perform higher cognitive processes and demonstrates regular alpha activity. (3) Alpha activity also is significantly associated with highly complex cognitive processes, such as the recognition of facial expressions. The neural activity reflected by these brain oscillations can be considered as constituent "building blocks" for a great number of functions. An overarching statement on the alpha function is presented by extended analyzes with multiple dimensions that constitute a "Cartesian Hyperspace" as the basis for oscillatory function. Theoretical implications are considered.
Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft
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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.
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.
Darwin's evolution theory, brain oscillations, and complex brain function in a new "Cartesian view".
Başar, Erol; Güntekin, Bahar
2009-01-01
Comparatively analyses of electrophysiological correlates across species during evolution, alpha activity during brain maturation, and alpha activity in complex cognitive processes are presented to illustrate a new multidimensional "Cartesian System" brain function. The main features are: (1) The growth of the alpha activity during evolution, increase of alpha during cognitive processes, and decrease of the alpha entropy during evolution provide an indicator for evolution of brain cognitive performance. (2) Human children younger than 3 years are unable to produce higher cognitive processes and do not show alpha activity till the age of 3 years. The mature brain can perform higher cognitive processes and demonstrates regular alpha activity. (3) Alpha activity also is significantly associated with highly complex cognitive processes, such as the recognition of facial expressions. The neural activity reflected by these brain oscillations can be considered as constituent "building blocks" for a great number of functions. An overarching statement on the alpha function is presented by extended analyzes with multiple dimensions that constitute a "Cartesian Hyperspace" as the basis for oscillatory function. Theoretical implications are considered. PMID:18805445
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
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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.
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
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Lin, Dejun, E-mail: dejun.lin@gmail.com [Department of Biochemistry and Biophysics, University of Rochester Medical Center, Rochester, New York 14642 (United States)
2015-09-21
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
Indian Academy of Sciences (India)
A K De
2014-10-01
A discrete forcing based Cartesian grid method is presented. The nonstaggered arrangement of velocity and pressure is considered. The pressure gradient in localized discrete form is added separately with the velocity making them explicitly coupled. The governing equation is time-integrated implicitly with both linearized and non-linear forms are investigated. Both linear and bi-linear reconstruction techniques are tested for extrapolation of velocity near a complex boundary. The present method is tested for vortical flow in an inclined cavity, flow past circular and inclined square cylinder. Both homogeneous and non-homogeneous Dirichlet forcing problems are tested. The parallelized version of the method is applied to 2D-to-3D transitional flow behind a single and multiple circular cylinders. The present numerical results compare well with the previously documented results.
Best of Both Worlds: Uniform sampling in Cartesian and Cayley Molecular Assembly Configuration Space
Ozkan, Aysegul
2014-01-01
EASAL (efficient atlasing and sampling of assembly landscapes) is a recently reported geometric method for representing, visualizing, sampling and computing integrals over the potential energy landscape tailored for small molecular assemblies. EASAL's efficiency arises from the fact that small assembly landscapes permit the use of so-called Cayley parameters (inter-atomic distances) for geometric representation and sampling of the assembly configuration space regions; this results in their isolation, convexification, customized sampling and systematic traversal using a comprehensive topological roadmap, ensuring reasonable coverage of crucial but narrow regions of low effective dimension. However, this alone is inadequate for accurate computation of configurational entropy and other integrals, required for estimation of both free energy and kinetics - where it is essential to obtain uniform sampling in appropriate cartesian or moduli space parameterization. Standard adjustment of Cayley sampling via the Jacob...
ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach
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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.
A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains
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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...
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.
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
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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
Path Planning of Free-Floating Robot in Cartesian Space Using Direct Kinematics
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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.
López-Muñoz, Francisco; Rubio, Gabriel; Molina, Juan D; Alamo, Cecilio
2011-04-25
The relationship between the "passions" (emotions or feelings) and psychopathology has been a constant throughout the history of medicine. In this context, melancholy was considered a perversion of the soul (corruption of the passions). One of the most influential authors on this subject was René Descartes, who discussed it in his work The Treatise on the Passions of the Soul (1649). Descartes believed that "passions" were sensitive movements that the soul experienced due to its union with the body (res extensa). According to this theory, the soul was located in the pineal gland, where it was actively involved in overseeing the functions of the "human machine" and kept its dysfunctions under control, by circulating animal spirits. Descartes described sadness as one of "the six primitive passions of the soul", which leads to melancholy if not remedied. Cartesian theories had a great deal of influence on the way that mental pathologies were considered throughout the entire 17th century (Spinoza, Willis, Pitcairn) and during much of the 18th century (Le Cat, Tissot). From the 19th century onwards, emotional symptomatology finally began to be used in diagnostic criteria for mood disorders.
A novel 3D Cartesian random sampling strategy for Compressive Sensing Magnetic Resonance Imaging.
Valvano, Giuseppe; Martini, Nicola; Santarelli, Maria Filomena; Chiappino, Dante; Landini, Luigi
2015-01-01
In this work we propose a novel acquisition strategy for accelerated 3D Compressive Sensing Magnetic Resonance Imaging (CS-MRI). This strategy is based on a 3D cartesian sampling with random switching of the frequency encoding direction with other K-space directions. Two 3D sampling strategies are presented. In the first strategy, the frequency encoding direction is randomly switched with one of the two phase encoding directions. In the second strategy, the frequency encoding direction is randomly chosen between all the directions of the K-Space. These strategies can lower the coherence of the acquisition, in order to produce reduced aliasing artifacts and to achieve a better image quality after Compressive Sensing (CS) reconstruction. Furthermore, the proposed strategies can reduce the typical smoothing of CS due to the limited sampling of high frequency locations. We demonstrated by means of simulations that the proposed acquisition strategies outperformed the standard Compressive Sensing acquisition. This results in a better quality of the reconstructed images and in a greater achievable acceleration.
Modelling rapid mass movements using the shallow water equations in Cartesian coordinates
Hergarten, S.; Robl, J.
2015-03-01
We propose a new method to model rapid mass movements on complex topography using the shallow water equations in Cartesian coordinates. These equations are the widely used standard approximation for the flow of water in rivers and shallow lakes, but the main prerequisite for their application - an almost horizontal fluid table - is in general not satisfied for avalanches and debris flows in steep terrain. Therefore, we have developed appropriate correction terms for large topographic gradients. In this study we present the mathematical formulation of these correction terms and their implementation in the open-source flow solver GERRIS. This novel approach is evaluated by simulating avalanches on synthetic and finally natural topographies and the widely used Voellmy flow resistance law. Testing the results against analytical solutions and the proprietary avalanche model RAMMS, we found a very good agreement. As the GERRIS flow solver is freely available and open source, it can be easily extended by additional fluid models or source areas, making this model suitable for simulating several types of rapid mass movements. It therefore provides a valuable tool for assisting regional-scale natural hazard studies.
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.
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...
ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach
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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.
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.
Extending a CAD-Based Cartesian Mesh Generator for the Lattice Boltzmann Method
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Cantrell, J Nathan [ORNL; Inclan, Eric J [ORNL; Joshi, Abhijit S [ORNL; Popov, Emilian L [ORNL; Jain, Prashant K [ORNL
2012-01-01
This paper describes the development of a custom preprocessor for the PaRAllel Thermal Hydraulics simulations using Advanced Mesoscopic methods (PRATHAM) code based on an open-source mesh generator, CartGen [1]. PRATHAM is a three-dimensional (3D) lattice Boltzmann method (LBM) based parallel flow simulation software currently under development at the Oak Ridge National Laboratory. The LBM algorithm in PRATHAM requires a uniform, coordinate system-aligned, non-body-fitted structured mesh for its computational domain. CartGen [1], which is a GNU-licensed open source code, already comes with some of the above needed functionalities. However, it needs to be further extended to fully support the LBM specific preprocessing requirements. Therefore, CartGen is being modified to (i) be compiler independent while converting a neutral-format STL (Stereolithography) CAD geometry to a uniform structured Cartesian mesh, (ii) provide a mechanism for PRATHAM to import the mesh and identify the fluid/solid domains, and (iii) provide a mechanism to visually identify and tag the domain boundaries on which to apply different boundary conditions.
Directory of Open Access Journals (Sweden)
Goran Lešaja
2011-02-01
Full Text Available We present an interior point method for Cartesian P*(k-Linear Complementarity Problems over Symmetric Cones (SCLCPs. The Cartesian P*(k-SCLCPs have been recently introduced as the generalization of the more commonly known and more widely used monotone SCLCPs. The IPM is based on the barrier functions that are defined by a large class of univariate functions called eligible kernel function which have recently been successfully used to design new IPMs for various optimization problems. Eligible barrier (kernel functions are used in calculating the Nesterov-Todd search directions and the default step-size which leads to a very good complexity results for the method. For some specific eligilbe kernel functions we match the best known iteration bound for the long-step methods while for the short-step methods the best iteration bound is matched for all cases.
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
Sato, Norikazu; Takeuchi, Shintaro; Kajishima, Takeo; Inagaki, Masahide; Horinouchi, Nariaki
2016-09-01
A new discretization scheme on Cartesian grids, namely, a "consistent direct discretization scheme", is proposed for solving incompressible flows with convective and conjugate heat transfer around a solid object. The Navier-Stokes and the pressure Poisson equations are discretized directly even in the immediate vicinity of a solid boundary with the aid of the consistency between the face-velocity and the pressure gradient. From verifications in fundamental flow problems, the present method is found to significantly improve the accuracy of the velocity and the wall shear stress. It is also confirmed that the numerical results are less sensitive to the Courant number owing to the consistency between the velocity and pressure fields. The concept of the consistent direct discretization scheme is also explored for the thermal field; the energy equations for the fluid and solid phases are discretized directly while satisfying the thermal relations that should be valid at their interface. It takes different forms depending on the thermal boundary conditions: Dirichlet (isothermal) and Neumann (adiabatic/iso-heat-flux) boundary conditions for convective heat transfer and a fluid-solid thermal interaction for conjugate heat transfer. The validity of these discretizations is assessed by comparing the simulated results with analytical solutions for the respective thermal boundary conditions, and it is confirmed that the present schemes also show high accuracy for the thermal field. A significant improvement for the conjugate heat transfer problems is that the second-order spatial accuracy and numerical stability are maintained even under severe conditions of near-practical physical properties for the fluid and solid phases.
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.
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.
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.
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
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
Martini, M; Hilaire, S; Goriely, S; Lechaftois, F
2016-01-01
Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we present large-scale calculations of the $E1$ $\\gamma$-ray strength function obtained in the framework of the axially-symmetric deformed QRPA based on the finite-range Gogny force. This approach is applied to even-even nuclei, the strength function for odd nuclei being derived by interpolation. The convergence with respect to the adopted number of harmonic oscillator shells and the cut-off energy introduced in the 2-quasiparticle (2-$qp$) excitation space is analyzed. The calculations performed with two different Gogny interactions, namely D1S and D1M, are compared. A systematic energy shift of the $E1$ strength is found for D1M relative to D1S, leading to a lower energy centroid and a smaller energy-weighted sum rule for D1M. When comparing with experimental photoabsorption data, the Gogny-QRPA predictions are found to...
Indian Academy of Sciences (India)
Ramaswamy Jaganathan; Sudeshna Sinha
2005-03-01
Motivated by studies on -deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the concept of -deformed nonlinear maps is introduced. As a specific example, a -deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family of -logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors – a phenomenon rare in one-dimensional maps.
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; 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.
The Spherical Deformation Model
DEFF Research Database (Denmark)
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...
Deformations of Superconformal Theories
Cordova, Clay; Intriligator, Kenneth
2016-01-01
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \\geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and non-central charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformat...
Deformation mechanisms in experimentally deformed Boom Clay
Desbois, Guillaume; Schuck, Bernhard; Urai, Janos
2016-04-01
Bulk mechanical and transport properties of reference claystones for deep disposal of radioactive waste have been investigated since many years but little is known about microscale deformation mechanisms because accessing the relevant microstructure in these soft, very fine-grained, low permeable and low porous materials remains difficult. Recent development of ion beam polishing methods to prepare high quality damage free surfaces for scanning electron microscope (SEM) is opening new fields of microstructural investigation in claystones towards a better understanding of the deformation behavior transitional between rocks and soils. We present results of Boom Clay deformed in a triaxial cell in a consolidated - undrained test at a confining pressure of 0.375 MPa (i.e. close to natural value), with σ1 perpendicular to the bedding. Experiments stopped at 20 % strain. As a first approximation, the plasticity of the sample can be described by a Mohr-Coulomb type failure envelope with a coefficient of cohesion C = 0.117 MPa and an internal friction angle ϕ = 18.7°. After deformation test, the bulk sample shows a shear zone at an angle of about 35° from the vertical with an offset of about 5 mm. We used the "Lamipeel" method that allows producing a permanent absolutely plane and large size etched micro relief-replica in order to localize and to document the shear zone at the scale of the deformed core. High-resolution imaging of microstructures was mostly done by using the BIB-SEM method on key-regions identified after the "Lamipeel" method. Detailed BIB-SEM investigations of shear zones show the following: the boundaries between the shear zone and the host rock are sharp, clay aggregates and clastic grains are strongly reoriented parallel to the shear direction, and the porosity is significantly reduced in the shear zone and the grain size is smaller in the shear zone than in the host rock but there is no evidence for broken grains. Comparison of microstructures
Verma, Siddhartha; Novati, Guido; Koumoutsakos, Petros
2016-01-01
The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self-propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers, and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body-fitted grids are used. Alternatively, such simulations may employ penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow- induced forces on the surface of both rigid and deforming bodies, in simulations using re-...
Cerezo, Javier; Zúñiga, José; Requena, Alberto; Ávila Ferrer, Francisco J; Santoro, Fabrizio
2013-11-12
When large structural displacements take place between the ground state (GS) and excited state (ES) minima of polyatomic molecules, the choice of a proper set of coordinates can be crucial for a reliable simulation of the vibrationally resolved absorption spectrum. In this work, we study two carotenoids that undergo structural displacements from GS to ES minima of different magnitude, from small displacements for violaxanthin to rather large ones for β-carotene isomers. Their finite-temperature (77 and 300 K) spectra are simulated at the harmonic level, including Duschinsky effect, by time-dependent (TD) and time-independent (TI) approaches, using (TD)DFT computed potential energy surfaces (PES). We adopted two approaches to construct the harmonic PES, the Adiabatic (AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate frames: Cartesian and valence internal coordinates. Our results show that when large displacements take place, Cartesian coordinates dramatically fail to describe curvilinear displacements and to account for the Duschinsky matrix, preventing a realistic simulation of the spectra within the AH model, where the GS and ES PESs are quadratically expanded around their own equilibrium geometry. In contrast, internal coordinates largely amend such deficiencies and deliver reasonable spectral widths. As expected, both coordinate frames give similar results when small displacements occur. The good agreement between VH and experimental line shapes indicates that VH model, in which GS and ES normal modes are both evaluated at the GS equilibrium geometry, is a good alternative to deal with systems exhibiting large displacements. The use of this model can be, however, problematic when imaginary frequencies arise. The extent of the nonorthogonality of the Dushinsky matrix in internal coordinates and its correlation with the magnitude of the displacement of the GS and ES geometries is analyzed in detail.
Blanc, Emilie; Chiavassa, Guillaume; Lombard, Bruno
2014-10-01
A time-domain numerical modeling of transversely isotropic Biot poroelastic waves is proposed in two dimensions. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency. In the time-domain, these coefficients introduce shifted fractional derivatives of order 1/2, involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations, resulting in the Biot-DA (diffusive approximation) model. The properties of both the Biot-JKD and the Biot-DA models are analyzed: hyperbolicity, decrease of energy, dispersion. To determine the coefficients of the diffusive approximation, two approaches are analyzed: Gaussian quadratures and optimization methods in the frequency range of interest. The nonlinear optimization is shown to be the better way of determination. A splitting strategy is then applied to approximate numerically the Biot-DA equations. The propagative part is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. An immersed interface method is implemented to take into account heterogeneous media on a Cartesian grid and to discretize the jump conditions at interfaces. Numerical experiments are presented. Comparisons with analytical solutions show the efficiency and the accuracy of the approach, and some numerical experiments are performed to investigate wave phenomena in complex media, such as multiple scattering across a set of random scatterers.
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 ....... One particular advantage of DSC is the fact that as an alternative to topology adaptivity, topology control is also possible. This is exploited in the construction of cut loci on tori where a front expands from a single point on a torus and stops when it self-intersects....
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.
Martini, M.; Péru, S.; Hilaire, S.; Goriely, S.; Lechaftois, F.
2016-07-01
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 E 1 γ -ray strength function obtained in the framework of the axially symmetric deformed quasiparticle random-phase approximation based on the finite-range Gogny force. This approach is applied to even-even nuclei, the strength function for odd nuclei being derived by interpolation. The convergence with respect to the adopted number of harmonic oscillator shells and the cutoff energy introduced in the 2-quasiparticle (2 -q p ) excitation space is analyzed. The calculations performed with two different Gogny interactions, namely D1S and D1M, are compared. A systematic energy shift of the E 1 strength is found for D1M relative to D1S, leading to a lower energy centroid and a smaller energy-weighted sum rule for D1M. When comparing with experimental photoabsorption data, the Gogny-QRPA predictions are found to overestimate the giant dipole energy by typically ˜2 MeV. Despite the microscopic nature of our self-consistent Hartree-Fock-Bogoliubov plus QRPA calculation, some phenomenological corrections need to be included to take into account the effects beyond the standard 2 -q p QRPA excitations and the coupling between the single-particle and low-lying collective phonon degrees of freedom. For this purpose, three prescriptions of folding procedure are considered and adjusted to reproduce experimental photoabsorption data at best. All of them are shown to lead to somewhat similar predictions of the E 1 strength, both at low energies and for exotic neutron-rich nuclei. Predictions of γ -ray strength functions and Maxwellian-averaged neutron capture rates for the whole Sn isotopic chain are also discussed and compared with previous theoretical calculations.
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 ...
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
Deformation quantization of principal bundles
Aschieri, Paolo
2016-01-01
We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles, and more in general to the deformation of Hopf-Galois extensions. First we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next we twist deform a subgroup of the group of authomorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations we obtain noncommutative principal bundles with noncommutative fiber and base space as well.
Diffeomorphic Statistical Deformation Models
DEFF Research Database (Denmark)
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al. Th...... with ground truth in form of manual expert annotations, and compared to Cootes's model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes.......In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al...... 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...
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...
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
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.
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.
Low-dimensional model of turbulent Rayleigh-Benard convection in a Cartesian cell with square domain
Bailon-Cuba, Jorge
2011-01-01
A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The empirical eigenfunctions are obtained from a joint Proper Orthogonal Decomposition (POD) of the velocity and temperature fields using the Snapshot Method on the basis of a direct numerical simulation (DNS). The resulting LDM is a quadratic inhomogeneous system of coupled ordinary differential equations which we use to describe the long-time temporal evolution of the large-scale mode amplitudes for a Rayleigh number of 1e5 and a Prandtl number of 0.7. The truncation to a finite number of degrees of freedom, that does not exceed a number of 310 for the present, requires the additional implementation of an eddy viscosity-diffusivity to capture the missing dissipation of the small-scale modes. The magnitude of this additional dissipation mechanism is determined by requiring statis...
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Azmy, Yousry Y., E-mail: snschune@ncsu.edu, E-mail: yyazmy@ncsu.edu [Department of Nuclear Engineering, North Carolina State University, Raleigh, NC (United States); Fournier, Damien; Le Tellier, Romain, E-mail: damien.fournier@cea.fr, E-mail: romain.le-tellier@cea.fr [CEA, DEN, DER/SPRC/LEPh, Cadarache, Saint Paul-lez-Durance (France)
2011-07-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen's benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semi analytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation. (author)
Energy Technology Data Exchange (ETDEWEB)
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
Lyra, W; Klahr, H; Piskunov, N
2007-01-01
We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to show that Cartesian codes are comparable to cylindrical and spherical ones in handling the magnetohydrodynamics of the disk simulations, as the disk-in-a-box models presented here develop and sustain MHD turbulence. We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure. The turbulent stresses depend on the thermal pressure obeying a power law of 0.24+/-0.03, compatible with the value of 0.25 found in shearing box calculations. The ratio of stresses decreased with increasing temperature. We also study the dynamics of boulders in the hydromagnetic turbulence. The vertical turbulent diffusion of the embedded boulders is comparable to the...
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.
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....
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
Sawada, Ryohto; Ishikawa, Kenichi L
2016-01-01
We report a three-dimensional numerical implementation of multiconfiguration time-dependent Hartree-Fock (MCTDHF) based on a multi-resolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully compute high-harmonic generation (HHG) of H2 and H2O. The present implementation will open a way to the first-principle theoretical study of intense-field and attosecond-pulse induced ultrafast phenomena in general molecules.
Chen, Zhaopeng; Lii, Neal Y.; Wimböck, Thomas; Shaowei, Fan; Hong, Liu
2011-01-01
This paper presents impedance controllers with adaptive friction compensation for the five-finger dexterous robot hand DLR-HIT II in both joint and Cartesian space. A FPGAbased control hardware and software architecture with real-time communication is designed to fulfill the requirements of the impedance controller. Modeling of the robot finger with exible joints and mechanical couplings in the differential gear-box are described in this paper. In order to address the friction due to t...
McGavin, Dennis G; Tennant, W Craighead
2009-06-17
In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS(3) and BS(5). Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, [Formula: see text] Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present. PMID:21693947
Kalinić, Hrvoje; Mihanović, Hrvoje; Cosoli, Simone; Vilibić, Ivica
2015-11-01
In this paper, the Self-Organizing Map (SOM) method was applied to the surface currents data obtained between February and November 2008 by a network of high-frequency (HF) radars in the northern Adriatic. The sensitivity of the derived SOM solutions was tested in respect to the change of coordinate system of the data introduced to the SOM. In one experiment the original radial data measurements were used, and in the other experiment the Cartesian (total) current vectors derived from original radar data were analyzed. Although the computation of SOM solutions was not a demanding task, comparing both neural lattices yielded the nondeterministic polynomial time (NP) problem for which is difficult to propose a solution that will be globally optimal. Thus, we suggested utilizing the greedy algorithm with underlying assumption of 1-to-1 mapping between lattices. The results suggested that such solution could be local, but not global optimum and that the latter assumption could lower the obtained correlations between the patterns. However, without the assumption of 1-to-1 mapping between lattices, correlation between the derived SOM patterns was quite high, indicating that SOM mapping introduced to the radial current vectors and subsequent transformation into Cartesian coordinate system does not significantly affect obtained patterns in comparison to the SOM mapping done on the derived Cartesian current vectors. The documented similarity corroborates the use of total current vectors in various oceanographic studies, as being representative derivative of original radial measurements.
Deformation quantization of bosonic strings
International Nuclear Information System (INIS)
Deformation quantization of bosonic strings is considered. We show that the light-cone gauge is the most convenient classical description to perform the quantization of bosonic strings in the deformation quantization formalism. Similar to the field theory case, the oscillator variables greatly facilitates the analysis. The mass spectrum, propagators and the Virasoro algebra are finally described within this deformation quantization scheme. (author)
Rotational Deformation of Neutron Stars
Institute of Scientific and Technical Information of China (English)
WEN De-Hua; CHEN Wei; LIU Liang-Gang
2005-01-01
@@ The rotational deformations of two kinds of neutron stars are calculated by using Hartle's slow-rotation formulism.The results show that only the faster rotating neutron star gives an obvious deformation. For the slow rotating neutron star with a period larger than hundreds of millisecond, the rotating deformation is very weak.
Cosmetic and Functional Nasal Deformities
... nasal complaints. Nasal deformity can be categorized as “cosmetic” or “functional.” Cosmetic deformity of the nose results in a less ... taste , nose bleeds and/or recurrent sinusitis . A cosmetic or functional nasal deformity may occur secondary to ...
[Babies with cranial deformity].
Feijen, Michelle M W; Claessens, Edith A W M Habets; Dovens, Anke J Leenders; Vles, Johannes S; van der Hulst, Rene R W J
2009-01-01
Plagiocephaly was diagnosed in a baby aged 4 months and brachycephaly in a baby aged 5 months. Positional or deformational plagio- or brachycephaly is characterized by changes in shape and symmetry of the cranial vault. Treatment options are conservative and may include physiotherapy and helmet therapy. During the last two decades the incidence of positional plagiocephaly has increased in the Netherlands. This increase is due to the recommendation that babies be laid on their backs in order to reduce the risk of sudden infant death syndrome. We suggest the following: in cases of positional preference of the infant, referral to a physiotherapist is indicated. In cases of unacceptable deformity of the cranium at the age 5 months, moulding helmet therapy is a possible treatment option. PMID:19857299
Localization of plastic deformation
Energy Technology Data Exchange (ETDEWEB)
Rice, J R
1976-04-01
The localization of plastic deformation into a shear band is discussed as an instability of plastic flow and a precursor to rupture. Experimental observations are reviewed, a general theoretical framework is presented, and specific calculations of critical conditions are carried out for a variety of material models. The interplay between features of inelastic constitutive description, especially deviations from normality and vertex-like yielding, and the onset of localization is emphasized.
Ashish Agrawal; Rahul Agrawal; Rajat Singh; Romi Agrawal; Seema Agrawal
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-...
Deformations of fractured rock
International Nuclear Information System (INIS)
Results of the DBM and FEM analysis in this study indicate that a suitable rock mass for repository of radioactive waste should be moderately jointed (about 1 joint/m2) and surrounded by shear zones of the first order. This allowes for a gentle and flexible deformation under tectonic stresses and prevent the development of large cross-cutting failures in the repository area. (author)
Muralidharan, Balaji; Menon, Suresh
2016-09-01
A new adaptive finite volume conservative cut-cell method that is third-order accurate for simulation of compressible viscous flows is presented. A high-order reconstruction approach using cell centered piecewise polynomial approximation of flow quantities, developed in the past for body-fitted grids, is now extended to the Cartesian based cut-cell method. It is shown that the presence of cut-cells of very low volume results in numerical oscillations in the flow solution near the embedded boundaries when standard small cell treatment techniques are employed. A novel cell clustering approach for polynomial reconstruction in the vicinity of the small cells is proposed and is shown to achieve smooth representation of flow field quantities and their derivatives on immersed interfaces. It is further shown through numerical examples that the proposed clustering method achieves the design order of accuracy and is fairly insensitive to the cluster size. Results are presented for canonical flow past a single cylinder and a sphere at different flow Reynolds numbers to verify the accuracy of the scheme. Investigations are then performed for flow over two staggered cylinders and the results are compared with prior data for the same configuration. All the simulations are carried out with both quadratic and cubic reconstruction, and the results indicate a clear improvement with the cubic reconstruction. The new cut-cell approach with cell clustering is able to predict accurate results even at relatively low resolutions. The ability of the high-order cut-cell method in handling sharp geometrical corners and narrow gaps is also demonstrated using various examples. Finally, three-dimensional flow interactions between a pair of spheres in cross flow is investigated using the proposed cut-cell scheme. The results are shown to be in excellent agreement with past studies, which employed body-fitted grids for studying this complex case.
Sunvisson, Helena; Habermann, Barbara; Weiss, Sara; Benner, Patricia
2009-10-01
Using three paradigm cases of persons living with Parkinson's Disease (PD) the authors make a case for augmenting and enriching a Cartesian medical account of the pathophysiology of PD with an enriched understanding of the lived body experience of PD, the lived implications of PD for a particular person's concerns and coping with the illness. Linking and adding a thick description of the lived experience of PD can enrich caregiving imagination and attunement to the patient's possibilities, concerns and constraints. The work of Merleau-Ponty is used to articulate the middle terms of the lived experience of dwelling in a lifeworld. Examining lived experience of embodied intentionality, skilled bodily capacities as highlighted in Merleau-Ponty's non-mechanistic physiology opens new therapeutic, coping and caregiving possibilities. Matching temporal rhythms can decrease the stress of being assisted with activities of daily living. For example, caregivers and patients alike can be taught strategies for extending their lived bodily capacities by altering rhythms, by shifting hyperactivity to different parts of the body and other strategies that change the perceptual experience associated with walking in different environment. A medical account of the pathophysiology of PD is nessessary and useful, but not sufficient for designing caregiving in ways that enrich and extend the existential skills of dwelling of persons with PD. The dominance of mechanistic physiology makes caregivers assume that it is the 'real discourse' about the disease, causing researchers and caregivers alike to overlook the equally real lived experience of the patient which requires different descriptive discourses and different sources of understanding. Lack of dialogue between the two discourses is tragic for patients because caregivers need both in order to provide attuned, effective caregiving.
Institute of Scientific and Technical Information of China (English)
GAO Lin; ZHANG GuoXin; LAI YuKun
2012-01-01
Shape deformation is a fundamental tool in geometric modeling.Existing methods consider preserving local details by minimizing some energy functional measuring local distortions in the L2 norm.This strategy distributes distortions quite uniformly to all the vertices and penalizes outliers.However,there is no unique answer for a natural deformation as it depends on the nature of the objects.Inspired by recent sparse signal reconstruction work with non L2 norm,we introduce general Lp norms to shape deformation; the positive parameter p provides the user with a flexible control over the distribution of unavoidable distortions.Compared with the traditional L2 norm,using smaller p,distortions tend to be distributed to a sparse set of vertices,typically in feature regions,thus making most areas less distorted and structures better preserved. On the other hand,using larger p tends to distribute distortions more evenly across the whole model.This flexibility is often desirable as it mimics objects made up with different materials.By specifying varying p over the shape,more flexible control can be achieved.We demonstrate the effectiveness of the proposed algorithm with various examples.
Strauss, Karl F.; Sheldon, Douglas J.
2011-01-01
Several missions and instruments in the conceptual design phase rely on the technique of interferometry to create detectable fringe patterns. The intimate emplacement of reflective material upon electron device cells based upon chalcogenide material technology permits high-speed, predictable deformation of the reflective surface to a subnanometer or finer resolution with a very high degree of accuracy. In this innovation, a layer of reflective material is deposited upon a wafer containing (perhaps in the millions) chalcogenic memory cells with the reflective material becoming the front surface of a mirror and the chalcogenic material becoming a means of selectively deforming the mirror by the application of heat to the chalcogenic material. By doing so, the mirror surface can deform anywhere from nil to nanometers in spots the size of a modern day memory cell, thereby permitting realtime tuning of mirror focus and reflectivity to mitigate aberrations caused elsewhere in the optical system. Modern foundry methods permit the design and manufacture of individual memory cells having an area of or equal to the Feature (F) size of the design (assume 65 nm). Fabrication rules and restraints generally require the instantiation of one memory cell to another no closer than 1.5 F, or, for this innovation, 90 nm from its neighbor in any direction. Chalcogenide is a semiconducting glass compound consisting of a combination of chalcogen ions, the ratios of which vary according to properties desired. It has been shown that the application of heat to cells of chalcogenic material cause a large alteration in resistance to the range of 4 orders of magnitude. It is this effect upon which chalcogenidebased commercial memories rely. Upon removal of the heat source, the chalcogenide rapidly cools and remains frozen in the excited state. It has also been shown that the chalcogenide expands in volume because of the applied heat, meaning that the coefficient of expansion of chalcogenic
Sadolah Nasiri; Samira Bahrami
2008-01-01
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 Schr\\"odinger 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-Jacob...
Lomineishvili, S N; Zhelyazkov, I; Tevzadze, A G
2014-01-01
Previous works indicate that the frequency ratio of second and first harmonics of kink oscillations has tendency towards 3 in the case of prominence threads. We aim to study the magnetohydrodynamic oscillations of longitudinally inhomogeneous prominence threads and to shed light on the problem of frequency ratio. Classical Sturm--Liouville problem is used for the threads with longitudinally inhomogeneous plasma density. We show that the spatial variation of total pressure perturbations along the thread is governed by the stationary Schr\\"{o}dinger equation, where the longitudinal inhomogeneity of plasma density stands for the potential energy. Consequently, the equation has bounded solutions in terms of Hermite polynomials. Boundary conditions at the thread surface lead to transcendental dispersion equation with Bessel functions. Thin flux tube approximation of the dispersion equation shows that the frequency of kink waves is proportional to the expression \\alpha(2n+1), where \\alpha is the density inhomogenei...
Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Brouard, S; Sokolovski, D
2010-01-01
We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a `coherent' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power law) or rapid (Gaussian) decoherence of the mean values themselves.
Forced harmonic oscillations of the Euler-Bernoulli beam with resistance forces
Directory of Open Access Journals (Sweden)
Yuriy S. Krutiy
2015-12-01
Full Text Available The important issue in the oscillation theory is the study of resistance impact on oscillatory processes. Unlike the calculations of free oscillations, that reside in determination of natural frequencies and waveshapes and unlike the calculations of forced oscillations far away from resonance, that are performing without reference to friction, the oscillations researches in vicinity of resonance need accounting of friction forces. Special attention is paid to forced transverse fluctuations in beams as an important technical problem for engineering and building. Aim: The aim of the work is constructing of analytical solution of the problem of forced transverse vibrations of a straight rod with constant cross-section, which is under the influence of the harmonic load taking into account external and internal resistances. Materials and Methods: The internal resistance is taken into account using the corrected hypothesis of Kelvin-Voigt which reflects the empirically proven fact about the frequency-independent internal friction in the material. The external friction is also considered as frequency-independent. Results: An analytical solution is built for the differential equation of forced transverse oscillations of a straight rod with constant cross-section which is under the influence of the harmonic load taking into account external and internal resistances. As a result, analytically derived formulae are presented which describe the forced dynamic oscillations and the dynamic internal forces due to the harmonic load applied to the rod thus reducing the problem with any possible fixed ends to the search of unknown integration constants represented in a form of initial parameters.
Castro-Palacio, Juan Carlos; Gimenez, Marcos H; Monsoriu, Juan A
2012-01-01
The mobile acceleration sensor has been used to in Physics experiments on free and damped oscillations. Results for the period, frequency, spring constant and damping constant match very well to measurements obtained by other methods. The Accelerometer Monitor application for Android has been used to get the outputs of the sensor. Perspectives for the Physics laboratory have also been discussed.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
Institute of Scientific and Technical Information of China (English)
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are dis-cussed in brief.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
Institute of Scientific and Technical Information of China (English)
WANG JianHui; HE JiZhou; MAO ZhiYuan
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are discussed in brief.
Durisen, R. H.
1978-01-01
The structure and stability of Maclaurin spheroids embedded in rigid uniform-density oblate spheroidal halos are determined by the tensor virial-equation method. These spheroid-halo systems can be thought of as crude fluid analogs of disk galaxies with halos. The halos are assumed to have the same center, the same axis of symmetry, and the same equatorial radius as the Maclaurin spheroids. Only halos with lower eccentricity than the Maclaurin spheroids are considered. The dynamic instability of the toroidal (barlike) modes is suppressed when m, the ratio of the halo mass to Maclaurin spheroid mass, is greater than 3 pi/8 for spherical halos and when m is greater than 1/2 for halos congruent to the Maclaurin spheroids. Intermediate halo flattenings yield intermediate critical m-values. On the other hand, a neutral point of the toroidal modes in the rotating and inertial frames occurs for all m and for all allowed halo flattenings. Growth rates for secular instability beyond the neutral point are calculated, and the eigenfrequencies of all second-harmonic modes are given for select cases. The Ostriker-Peebles (1973) conjecture concerning the stability of disk galaxies against barlike perturbations appears to be incorrect.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
2009-01-01
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
The phase of the Riemann zeta function and the inverted harmonic oscillator
Bhaduri, R K; Law, J; Avinash Khare
1994-01-01
The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. This leads to the analogy with the scattering amplitude, and an approximate rule for the location of the zeros. The smooth phase of the Zeta function along the line of the zeros is related to the quantum density of states of an inverted oscillator.
The Phase of the Riemann Zeta Function and the Inverted Harmonic Oscillator
Bhaduri, R. K.; Khare, Avinash; Law, J.
1994-01-01
The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. This leads to the analogy with the scattering amplitude, and an approximate rule for the location of the zeros. The smooth phase of the Zeta function along the line of the zeros is related to the quantum density of states of an inverted oscillator.
Phase of the Riemann ζ function and the inverted harmonic oscillator
Bhaduri, R. K.; Khare, Avinash; Law, J.
1995-07-01
The Argand diagram is used to display some characteristics of the Riemann ζ function. The zeros of the ζ function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. The behavior of the phase of the ζ function on and off the line of zeros is studied. Up to some distance from the line of the complex zeros, the phase angle is shown to still retain their memory. The Argand plots also lead to an analogy with the scattering amplitude and an approximate rule for the location of the zeros. The smooth phase of the ζ function along the line of the zeros is related to the quantum density of states of an inverted oscillator.
Demonstration of double EIT using coupled harmonic oscillators and RLC circuits
Harden, Joshua; Serna, Juan D
2010-01-01
Single and double electromagnetically induced transparency in a medium (EIT), consisting of four-level atoms in the inverted-Y configuration, are discussed by using mechanical and electrical analogies. A spring-mass system subject to damping and driven by an external force is used to represent mechanically the four-level atom. The equations of motion of this system are solved analytically, and the revealed single and double EIT studied numerically. On the other hand, three coupled RLC circuits are used, as the electrical analog, to explore and demonstrate experimentally single and double EIT. The simplicity of these two models makes this experiment appropriate for undergraduate students and easy to incorporate into a college physics laboratory.
Vector constants of motion for time-dependent Kepler and isotropic harmonic oscillator potentials
Ritter, O. M.; Santos, F. C.; Tort, A C
2000-01-01
A method of obtaining vector constants of motion for time-independent as well as time-dependent central fields is discussed. Some well-established results are rederived in this alternative way and new ones obtained.
Kagan, Mikhail
2011-01-01
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely powerful problem-solving tool. While the former idea is typically discussed in the context of Newton's Laws, the latter starts with introducing conservation of energy even later. This work presents an elegant example of implementing both aforementioned ideas in the kinematical context, thus providing a "warm-up" introduction to the standard tools used later on in dynamics. Both the choice of the (non-orthogonal) reference frame and the conserved quantities are rather non-standard, yet at the same time quite intuitive to the problem at hand. Two such problems are discussed in detail with two alternative approaches. The first approach does not even require knowledge of calculus. In the appendix, I also present the brute-force solution involving a coupled system of differential equat...
Quantizing Earth surface deformations
Directory of Open Access Journals (Sweden)
C. O. Bowin
2015-03-01
Full Text Available The global analysis of Bowin (2010 used the global 14 absolute Euler pole set (62 Myr history from Gripp and Gordon (1990 and demonstrated that plate tectonics conserves angular momentum. We herein extend that analysis using the more detailed Bird (2003 52 present-day Euler pole set (relative to a fixed Pacific plate for the Earth's surface, after conversion to absolute Euler poles. Additionally, new analytical results now provide new details on upper mantle mass anomalies in the outer 200 km of the Earth, as well as an initial quantizing of surface deformations.
Directory of Open Access Journals (Sweden)
Emílio Borges
2007-04-01
Full Text Available A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational analysis. Examples are given for diatomic and triatomic molecules.
Energy Technology Data Exchange (ETDEWEB)
Anderson, D.V.; Breazeal, J.; Finan, C.H.; Johnston, B.M.
1976-09-14
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.
Götze, Jan P; Karasulu, Bora; Thiel, Walter
2013-12-21
We address the effects of using Cartesian or internal coordinates in the adiabatic Franck-Condon (AFC) and vertical Franck-Condon (VFC) approaches to electronic spectra. The adopted VFC approach is a simplified variant of the original approach [A. Hazra, H. H. Chang, and M. Nooijen, J. Chem. Phys. 151, 2125 (2004)], as we omit any contribution from normal modes with imaginary frequency. For our test molecules ranging from ethylene to flavin compounds, VFC offers several advantages over AFC, especially by preserving the properties of the FC region and by avoiding complications arising from the crossing of excited-state potential surfaces or from the failure of the harmonic approximation. The spectral quality for our target molecules is insensitive to the chosen approach. We also explore the effects of Duschinsky rotation and relate the need for internal coordinates to the absence of symmetry elements. When using Duschinsky rotation and treating larger systems without planar symmetry, internal coordinates are found to outperform Cartesian coordinates in the AFC spectral calculations.
Directory of Open Access Journals (Sweden)
Kuczyński Paweł
2014-06-01
Full Text Available The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD. The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.
Static multipole deformations in nuclei
International Nuclear Information System (INIS)
The physics of static multipole deformations in nuclei is reviewed. Nuclear static moments result from the delicate balance between the vibronic Jahn-Teller interaction (particle-vibration coupling) and the residual interaction (pairing force). Examples of various permanent nuclear deformations are discussed
Plastic Deformation of Metal Surfaces
DEFF Research Database (Denmark)
Hansen, Niels; Zhang, Xiaodan; Huang, Xiaoxu
2013-01-01
Plastic deformation of metal surfaces by sliding and abrasion between moving parts can be detrimental. However, when the plastic deformation is controlled for example by applying different peening techniques hard surfaces can be produced which can increase the fracture resistance and fatigue life...
Curved Space-Times from Strict Deformations?
Much, Albert
2016-01-01
We use a deformed differential structure and the Rieffel deformation to obtain a curved metric by deforming the flat space-time. In particular, a deformed Friedmann-Robertson-Walker and an ultra-static space-time emerge from this strict deformation scheme.
Deformation of Man Made Objects
Ibrahim, Mohamed
2012-07-01
We introduce a framework for 3D object deformation with primary focus on man-made objects. Our framework enables a user to deform a model while preserving its defining characteristics. Moreover, our framework enables a user to set constraints on a model to keep its most significant features intact after the deformation process. Our framework supports a semi-automatic constraint setting environment, where some constraints could be automatically set by the framework while others are left for the user to specify. Our framework has several advantages over some state of the art deformation techniques in that it enables a user to add new features to the deformed model while keeping its general look similar to the input model. In addition, our framework enables the rotation and extrusion of different parts of a model.
Involvement of valgus hindfoot deformity in hallux valgus deformity in rheumatoid arthritis.
Yamada, Shutaro; Hirao, Makoto; Tsuboi, Hideki; Akita, Shosuke; Matsushita, Masato; Ohshima, Shiro; Saeki, Yukihiko; Hashimoto, Jun
2014-09-01
The involvement of valgus hindfoot deformity in hallux valgus deformity was confirmed in a rheumatoid arthritis case with a destructive valgus hindfoot deformity. Correction of severe valgus, calcaneal lateral offset, and pronated foot deformity instantly normalized hallux valgus deformities postoperatively. Thus, careful hindfoot status evaluation is important when assessing forefoot deformity, including hallux valgus, in rheumatoid arthritis cases.
Inelastic deformation in crystalline rocks
Rahmani, H.; Borja, R. I.
2011-12-01
The elasto-plastic behavior of crystalline rocks, such as evaporites, igneous rocks, or metamorphic rocks, is highly dependent on the behavior of their individual crystals. Previous studies indicate that crystal plasticity can be one of the dominant micro mechanisms in the plastic deformation of crystal aggregates. Deformation bands and pore collapse are examples of plastic deformation in crystalline rocks. In these cases twinning within the grains illustrate plastic deformation of crystal lattice. Crystal plasticity is governed by the plastic deformation along potential slip systems of crystals. Linear dependency of the crystal slip systems causes singularity in the system of equations solving for the plastic slip of each slip system. As a result, taking the micro-structure properties into account, while studying the overall behavior of crystalline materials, is quite challenging. To model the plastic deformation of single crystals we use the so called `ultimate algorithm' by Borja and Wren (1993) implemented in a 3D finite element framework to solve boundary value problems. The major advantage of this model is that it avoids the singularity problem by solving for the plastic slip explicitly in sub steps over which the stress strain relationship is linear. Comparing the results of the examples to available models such as Von Mises we show the significance of considering the micro-structure of crystals in modeling the overall elasto-plastic deformation of crystal aggregates.
Coirier, William John
1994-01-01
A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a
Impact between deformable bodies
International Nuclear Information System (INIS)
The bodies are represented by constant strain finite elements so that the element internal forces can most easily be calculated, especially after yielding has taken place when the stress and strain increments are related in accordance with the Prandtl-Reuss theory. In the case of axisymmetrical problems triangular axisymmetrical elements are used whose properties are approximately calculated by sampling at the centroid of the cross-section. The external applied forces arise from the impact and contact forces at the interfaces, and the inertia forces are obtained from lumped mass matrices. The equation of motion is solved by a central difference explicit scheme in small incremental time steps. This enables the stress propagation as well as the history of plastic deformation in the bodies to be traced throughout the duration of impact. The material law is idealised to be piecewise linear, with an initial elastic portion followed by one linear hardening segment. Perfect plasticity (zero hardening) can also be allowed. A simple procedure deals with the case of loading from an elastic initial state to a final plastic state in one time step. The program has been applied to the investigation of a number of axisymmetrical problems. The three dimensional version of the program is now being coded. Examples: impact of a falling fuel stringer in a storage tube; impact of a cylinder on a rigid boundary; supported circular plate loaded by uniformly distributed impulses; impact of a non-return valve in a pipe rupture; impact of a cylindrical fuel-waste flask; impact of a conical missile on a rigid surface. (orig./HP)
Nuclear deformation of lutetium isotopes
Ekström, C
1974-01-01
For odd-A lutetium isotopes the ground-state equilibrium deformations ( epsilon , epsilon /sub 4/) and the Nilsson model Z=71 single proton levels in an ( epsilon , epsilon /sub 4/)-representation are considered.
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
Variable focal length deformable mirror
Headley, Daniel; Ramsey, Marc; Schwarz, Jens
2007-06-12
A variable focal length deformable mirror has an inner ring and an outer ring that simply support and push axially on opposite sides of a mirror plate. The resulting variable clamping force deforms the mirror plate to provide a parabolic mirror shape. The rings are parallel planar sections of a single paraboloid and can provide an on-axis focus, if the rings are circular, or an off-axis focus, if the rings are elliptical. The focal length of the deformable mirror can be varied by changing the variable clamping force. The deformable mirror can generally be used in any application requiring the focusing or defocusing of light, including with both coherent and incoherent light sources.
ROCK DEFORMATION. Final Progress Report
Energy Technology Data Exchange (ETDEWEB)
None
2002-05-24
The Gordon Research Conference (GRC) on ROCK DEFORMATION was held at II Ciocco from 5/19/02 thru 5/24/02. Emphasis was placed on current unpublished research and discussion of the future target areas in this field.
Deformed Mittag-Leffler Polynomials
Miomir S. Stankovic; Marinkovic, Sladjana D.; Rajkovic, Predrag M.
2010-01-01
The starting point of this paper are the Mittag-Leffler polynomials introduced by H. Bateman [1]. Based on generalized integer powers of real numbers and deformed exponential function, we introduce deformed Mittag-Leffler polynomials defined by appropriate generating function. We investigate their recurrence relations, differential properties and orthogonality. Since they have all zeros on imaginary axes, we also consider real polynomials with real zeros associated to them.
Bilateral cleft lip nasal deformity
Singh Arun; Nandini R.
2009-01-01
Bilateral cleft lip nose deformity is a multi-factorial and complex deformity which tends to aggravate with growth of the child, if not attended surgically. The goals of primary bilateral cleft lip nose surgery are, closure of the nasal floor and sill, lengthening of the columella, repositioning of the alar base, achieving nasal tip projection, repositioning of the lower lateral cartilages, and reorienting the nares from horizontal to oblique position. The multiplicity of procedures in the li...
Energy Technology Data Exchange (ETDEWEB)
Borges, Volnei; Vilhena, Marco Tullio, E-mail: borges@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Fernandes, Julio Cesar Lombaldo, E-mail: julio.lombaldo@ufrgs.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada
2011-07-01
In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two dimensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTS{sub N} method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTS{sub N} nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature. (author)
摩擦补偿下基于关节力矩的笛卡尔阻抗控制%Joint torque-based Cartesian impedance control with friction compensations
Institute of Scientific and Technical Information of China (English)
刘业超; 金明河; 刘宏
2008-01-01
In order to investigate the joint torque-based Cartesian impedance control strategies and the influence of compensations for friction, an experimental study on the identification of friction parameters, friction compensation and the Cartesian impedance control are developed for the harmonic drive robot, by using the sensors available in the joint itself. Different from the conventional Cartesian impedance control schemes which are mostly based on the robot end force/torque information, five joint torque-based Cartesian impedance control schemes are considered, including the force-based schemes in Cartesian/joint space, the position-based ,schemes in Cartesian/joint space and the stiffness control. Four of them are verified by corresponding experiments with/without friction compensations. By comparison, it is found that the force-based impedance control strategy is more suitable than the position-based one for the robot based on joint torque feedback and the friction has even a positive effect on Cartesian impedance control stability.%为了研究基于关节力矩信息的笛卡尔阻抗控制策略及摩擦补偿的影响,利用关节本身具有的传感器,进行了辨识谐波驱动摩擦参数、摩擦补偿和笛卡尔阻抗控制的实验研究.与传统的基于机器人末端力/力矩信息的笛卡尔阻抗控制方案不同,考虑了5种基于关节力矩的笛卡尔阻抗控制方案,包括笛卡尔空间/关节空间基于力的、笛卡尔空间/关节空间基于位置的方案和刚度控制.其中,前4种方案分别在有/无摩擦补偿的条件下进行了相应的实验验证.实验比较结果表明:对于基于关节力矩信息来实现笛卡尔阻抗控制的机器人,基于力的阻抗控制策略比基于位置的策略更适合,并且摩擦对这类笛卡尔阻抗控制的稳定性有积极影响.
Interactive Character Deformation Using Simplified Elastic Models
Luo, Z.
2016-01-01
This thesis describes the results of our research into realistic skin and model deformation methods aimed at the field of character deformation and animation. The main contributions lie in the properties of our deformation scheme. Our approach preserves the volume of the deformed object while retain
Bilateral cleft lip nasal deformity
Directory of Open Access Journals (Sweden)
Singh Arun
2009-01-01
Full Text Available Bilateral cleft lip nose deformity is a multi-factorial and complex deformity which tends to aggravate with growth of the child, if not attended surgically. The goals of primary bilateral cleft lip nose surgery are, closure of the nasal floor and sill, lengthening of the columella, repositioning of the alar base, achieving nasal tip projection, repositioning of the lower lateral cartilages, and reorienting the nares from horizontal to oblique position. The multiplicity of procedures in the literature for correction of this deformity alludes to the fact that no single procedure is entirely effective. The timing for surgical intervention and its extent varies considerably. Early surgery on cartilage may adversely affect growth and development; at the same time, allowing the cartilage to grow in an abnormal position and contributing to aggravation of deformity. Some surgeons advocate correction of deformity at an early age. However, others like the cartilages to grow and mature before going in for surgery. With peer pressure also becoming an important consideration during the teens, the current trend is towards early intervention. There is no unanimity in the extent of nasal dissection to be done at the time of primary lip repair. While many perform limited nasal dissection for the fear of growth retardation, others opt for full cartilage correction at the time of primary surgery itself. The value of naso-alveolar moulding (NAM too is not universally accepted and has now more opponents than proponents. Also most centres in the developing world have neither the personnel nor the facilities for the same. The secondary cleft nasal deformity is variable and is affected by the extent of the original abnormality, any prior surgeries performed and alteration due to nasal growth. This article reviews the currently popular methods for correction of nasal deformity associated with bilateral cleft lip, it′s management both at the time of cleft lip repair
Some Results of the Cartesian Composition of Fuzzy Finite State Machines%模糊有限状态机笛卡尔合成的一些结果
Institute of Scientific and Technical Information of China (English)
杨京开
2012-01-01
In this paper, some properties of the cartesian composition of fuzzy finite state machines are discussed utilizing algebraic techniques, the cartesian composition of fuzzy finite state machines satisfy commutative law and associative law in the sense of strong isomorphism are obtained, the similar properties between the cartesian composition of fuzzy finite state machines and the factors in subsystem (strong subsystem), free subset, basis and so on are discussed, a decomposition theorem for the cartesian composition of fuzzy finite state machines in terms of primary submachines is given, the admissible relation of the cartesian composition of fuzzy finite state machines under the projection mapping is the factors's admissible relations is proved.%讨论了模糊有限状态机的笛卡尔合成的一些性质,得到了模糊有限状态机的笛卡尔合成在强同构意义下满足交换律,结合律,讨论了模糊有限状态机的笛卡尔合成与其因子在子系统(强子系统),自由子集,基等方面的相似的结构性质,给出了模糊有限状态机的笛卡尔合成的准素子机分解,证明了模糊有限状态机的笛卡尔合成的容许关系的投影是其因子的容许关系.
q-Deformed Dynamics and Virial Theorem
Zhang, Jian-zu
2002-01-01
In the framework of the q-deformed Heisenberg algebra the investigation of $q$-deformation of Virial theorem explores that q-deformed quantum mechanics possesses better dynamical property. It is clarified that in the case of the zero potential the theoretical framework for the q-deformed Virial theorem is self-consistent. In the selfadjoint states the q-deformed uncertainty relation essentially deviates from the Heisenberg one.
Quadrupole Deformation of Barium Isotopes
Sugita, M; Furuno, K
1998-01-01
The B(E2:0_1^+ -> 2_1^+) values of the Ba isotopes (Z=56) exhibit a sharp increase in deformation as the neutron numbers approach the mid-shell value of N=66. This behavior is anomalous because the 2_1^+ level energies are very similar to those of the neighboring isotopes. By means of the axially-symmetric deformed Woods-Saxon (WS) hamiltonian plus the BCS method, we investigated the systematics of B(E2) of the Ba isotopes. We showed that 15% of the B(E2) values at N=66 was due to the level crossing, occurring at the deformation with beta being nearly 0.3, between the proton orbits originating from the orbits Omega=1/2^-(h11/2) and 9/2^+(g9/2) at zero deformation. The latter of these two was an intruder orbit originating from below the energy gap at Z=50, rising higher in energy with the deformation and intruding the Z=50-82 shell. These two orbits have the largest magnitude of the quadrupole moment with a different sign among the orbits near and below the Fermi surface. Occupancy and non-occupancy of these o...
Mixing of discontinuously deforming media
Smith, L. D.; Rudman, M.; Lester, D. R.; Metcalfe, G.
2016-02-01
Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations—such as shear banding or wall slip—creates new mechanisms for mixing and transport beyond those predicted by classical dynamical systems theory. Here, we show how a novel mixing mechanism combining stretching with cutting and shuffling yields exponential mixing rates, quantified by a positive Lyapunov exponent, an impossibility for systems with cutting and shuffling alone or bounded systems with stretching alone, and demonstrate it in a fluid flow. While dynamical systems theory provides a framework for understanding mixing in smoothly deforming media, a theory of discontinuous mixing is yet to be fully developed. New methods are needed to systematize, explain, and extrapolate measurements on systems with discontinuous deformations. Here, we investigate "webs" of Lagrangian discontinuities and show that they provide a template for the overall transport dynamics. Considering slip deformations as the asymptotic limit of increasingly localised smooth shear, we also demonstrate exactly how some of the new structures introduced by discontinuous deformations are analogous to structures in smoothly deforming systems.
Ooguri, H; Ooguri, Hirosi; Vafa, Cumrun
2003-01-01
We study F-terms describing coupling of the supergravity to N=1 supersymmetric gauge theories which admit large N expansions. We show that these F-terms are given by summing over genus one non-planar diagrams of the large N expansion of the associated matrix model (or more generally bosonic gauge theory). The key ingredient in this derivation is the observation that the chiral ring of the gluino fields is deformed by the supergravity fields, generalizing the C-deformation which was recently introduced. The gravity induced part of the C-deformation can be derived from the Bianchi identities of the supergravity, but understanding gravitational corrections to the F-terms requires a non-traditional interpretation of these identities.
Phonon operators in deformed nuclei
International Nuclear Information System (INIS)
For the description of the excited states in deformed nuclei new phonon operators are introduced, which depend on the sign of the angular momentum projection onto the symmetry axis of a deformed nucleus. In the calculations with new phonons the Pauli principle is correctly taken into account in the two-phonon components of the wave functions. There is a difference in comparison with the calculation with phonons independent of the sign of the angular momentum projection. The new phonons should be used in deformed nuclei if the Pauli principle is consistently taken into account and in the calculations with the excited state wave functions having the components with more than one phonon operator
Finite Deformation of Magnetoelastic Film
Energy Technology Data Exchange (ETDEWEB)
Barham, Matthew Ian [Univ. of California, Berkeley, CA (United States)
2011-05-31
A nonlinear two-dimensional theory is developed for thin magnetoelastic lms capable of large deformations. This is derived directly from three-dimensional theory. Signi cant simpli cations emerge in the descent from three dimensions to two, permitting the self eld generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers with two material models. First weak magnetization is investigated leading to a free energy where magnetization and deformation are un-coupled. The second closely couples the magnetization and deformation. Numerical solutions are obtained to equilibrium boundary-value problems in which the membrane is subjected to lateral pressure and an applied magnetic eld. An instability is inferred and investigated for the weak magnetization material model.
On deformations of triangulated models
De Deken, Olivier
2012-01-01
This paper is the first part of a project aimed at understanding deformations of triangulated categories, and more precisely their dg and A infinity models, and applying the resulting theory to the models occurring in the Homological Mirror Symmetry setup. In this first paper, we focus on models of derived and related categories, based upon the classical construction of twisted objects over a dg or $A_{\\infty}$-algebra. For a Hochschild 2 cocycle on such a model, we describe a corresponding "curvature compensating" deformation which can be entirely understood within the framework of twisted objects. We unravel the construction in the specific cases of derived A infinity and abelian categories, homotopy categories, and categories of graded free qdg-modules. We identify a purity condition on our models which ensures that the structure of the model is preserved under deformation. This condition is typically fulfilled for homotopy categories, but not for unbounded derived categories.
Mixing of discontinuously deforming media
Smith, Lachlan D; Lester, Daniel R; Metcalfe, Guy
2016-01-01
Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations - such as shear banding or wall slip - creates new mechanisms for mixing and transport beyond those predicted by classical dynamical systems theory. Here we show how a novel mixing mechanism combining stretching with cutting and shuffling yields exponential mixing rates, quantified by a positive Lyapunov exponent, an impossibility for systems with cutting and shuffling alone or bounded systems with stretching alone, and demonstrate it in a fluid flow. While dynamical systems theory provides a framework for understanding mixing in smoothly deforming media, a theory of discontinuous mixing is yet to be fully developed. New methods are needed to systematize, explain and extrapolate measurements on systems with discontinuous deformations. Here we investigate 'webs' of Lagrangian discontinuities and show that they provide a template for the overall transport dynamics. Considering sl...
Phonon operators for deformed nuclei
International Nuclear Information System (INIS)
The mathematical formalism with the phonon operators independent of the signature of the angular momentum projection turns out to be inadequate for describing excited states of deformed nuclei. New phonon operators are introduced which depend on the signature of the angular momentum projection on the symmetry axis of a deformed nucleus. It is shown that the calculations with the new phonons take correctly into account the Pauli principle in two-phonon components of wave functions. The results obtained differ from those given by the phonons independent of the signature of the angular momentum projection. The new phonons must be used in deformed nuclei at taking systematically the Pauli principle into account and in calculations involving wave functions of excited states having components with more than one-phonon operator
Deforming baryons into confining strings
Hartnoll, S A; Hartnoll, Sean A.; Portugues, Ruben
2004-01-01
We find explicit probe D3-brane solutions in the infrared of the Maldacena-Nunez background. The solutions describe deformed baryon vertices: q external quarks are separated in spacetime from the remaining N-q. As the separation is taken to infinity we recover known solutions describing infinite confining strings in ${\\mathcal{N}}=1$ gauge theory. We present results for the mass of finite confining strings as a function of length. We also find probe D2-brane solutions in a confining type IIA geometry, the reduction of a G_2 holonomy M theory background. The interpretation of these solutions as deformed baryons/confining strings is not as straightforward.
Computing layouts with deformable templates
Peng, Chihan
2014-07-27
In this paper, we tackle the problem of tiling a domain with a set of deformable templates. A valid solution to this problem completely covers the domain with templates such that the templates do not overlap. We generalize existing specialized solutions and formulate a general layout problem by modeling important constraints and admissible template deformations. Our main idea is to break the layout algorithm into two steps: a discrete step to lay out the approximate template positions and a continuous step to refine the template shapes. Our approach is suitable for a large class of applications, including floorplans, urban layouts, and arts and design. Copyright © ACM.
Cavity coalescence in superplastic deformation
Energy Technology Data Exchange (ETDEWEB)
Stowell, M.J.; Livesey, D.W.; Ridley, N.
1984-01-01
An analysis of the probability distribution function of particles randomly dispersed in a solid has been applied to cavitation during superplastic deformation and a method of predicting cavity coalescence developed. Cavity size distribution data were obtained from two microduplex nickel-silver alloys deformed superplastically to various extents at elevated temperature, and compared to theoretical predictions. Excellent agreement occurred for small void sizes but the model underestimated the number of voids in the largest size groups. It is argued that the discrepancy results from a combination of effects due to non-random cavity distributions and to enhanced growth rates and incomplete spheroidization of the largest cavities.
Numerical Modelling of Overburden Deformations
Directory of Open Access Journals (Sweden)
J. Barták
2002-01-01
Full Text Available This paper focuses on the application and verification of mathematical models of the effect of supporting measures on the reduction of overburden deformations. The study of the behaviour of the models is divided into three parts: reduction of the tunnelling effects on the Minorit monastery by means of a jet-grouting curtain; the behaviour of the Hvížďalka backfilled tunnel and a numerical analysis of the supporting measures affecting the tunnel deformations of the Mrázovka tunnel in Prague.
Neutron scattering on deformed nuclei
International Nuclear Information System (INIS)
Measurements of neutron elastic and inelastic differential cross sections around 14 MeV for 9Be, C, 181Ta, 232Th, 238U and 239Pu have been analyzed using a coupled channel (CC) formalism for deformed nuclei and phenomenological global optical model potentials (OMP). For the actinide targets these results are compared with the predictions of a semi-microscopic calculation using Jeukenne, Lejeune and Mahaux (JLM) microscopic OMP and a deformed ground state nuclear density. The overall agreement between calculations and the measurements is reasonable good even for the very light nuclei, where the quality of the fits is better than those obtained with spherical OMP
Formation and subdivision of deformation structures during plastic deformation
DEFF Research Database (Denmark)
Jakobsen, B.; Poulsen, H.F.; Lienert, U.;
2006-01-01
During plastic deformation of metals and alloys, dislocations arrange in ordered patterns. How and when these self-organization processes take place have remained elusive, because in situ observations have not been feasible. We present an x-ray diffraction method that provided data on the dynamics...
A Deformation of Quantum Dynamics through the Phase Space Path Integral
Govaerts, Jan
2008-01-01
Using a regularised construction of the phase space path integral due to Ingrid Daubechies and John Klauder which involves a time scale ultimately taken to vanish, and motivated by the general programme towards a noncommutative space(time) geometry, physical consequences of assuming this time parameter to provide rather a new fundamental time scale are explored in the context of the one dimensional harmonic oscillator. Some tantalising results are achieved, which raise intriguing prospects when extrapolated to the quantum field theory and gravitational contexts.
Space-based monitoring of ground deformation
Nobakht Ersi, Fereydoun; Safari, Abdolreza; Gamse, Sonja
2016-07-01
Ground deformation monitoring is valuable to understanding of the behaviour of natural phenomena. Space-Based measurement systems such as Global Positioning System are useful tools for continuous monitoring of ground deformation. Ground deformation analysis based on space geodetic techniques have provided a new, more accurate, and reliable source of information for geodetic positioning which is used to detect deformations of the Ground surface. This type of studies using displacement fields derived from repeated measurments of space-based geodetic networks indicates how crucial role the space geodetic methods play in geodynamics. The main scope of this contribution is to monitor of ground deformation by obtained measurements from GPS sites. We present ground deformation analysis in three steps: a global congruency test on daily coordinates of permanent GPS stations to specify in which epochs deformations occur, the localization of the deformed GPS sites and the determination of deformations.
Directory of Open Access Journals (Sweden)
Jiran L.
2016-06-01
Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.
Deformable Models for Eye Tracking
DEFF Research Database (Denmark)
Vester-Christensen, Martin; Leimberg, Denis; Ersbøll, Bjarne Kjær;
2005-01-01
A deformable template method for eye tracking on full face images is presented. The strengths of the method are that it is fast and retains accuracy independently of the resolution. We compare the me\\$\\backslash\\$-thod with a state of the art active contour approach, showing that the heuristic...
Hamilton, Nicholas; Cal, Raúl Bayoán
2015-01-01
A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean
Directory of Open Access Journals (Sweden)
Monica Fernandes Abreu
2010-09-01
Full Text Available Esta reflexão pretende mostrar o discurso racional cartesiano na segunda prova da existência de Deus. Para tanto, Descartes se depara com uma pergunta central: qual a causa da existência da res cogitans que é finita e possui a ideia de infinito? A resposta é encontrada na desproporcionalidade ontológica entre o finito e o infinito. Essa desproporcionalidade é elucidada mediante dois conceitos: o princípio de causalidade que determina que a causa deve ser igual ou superior a coisa causada e o princípio de criação contínua em que a causa que criou o ser não é menor do que aquela que o conserva em sua existência. As objeções destacadas no texto contra os argumentos cartesianos foram escolhas deliberadas que servem para elucidar a importância da racionalidade como fundamento para a prova da existência de Deus. A relação entre o entendimento e a liberdade, apresentada no texto sucintamente, justifica a impossibilidade da res cogitans ser causa de si mesma.Palavras-chave: Infinito; finito; causalidade; criação contínua AbstractThis essay aims to show the rational Cartesian discourse on the second proof of God’s existence. In order to do so, Descartes faces a core question: which is the cause for the existence of the res cogitans that is finite in front of the idea of the infinite? The answer is found in the ontological disproportionality between the finite and the infinite. This disproportionality is elucidated through a couple crucial concepts: the principle of causality, which determines that the cause must be equal or superior to the caused thing and the principle of continuous creation, in which the cause that created the being is not inferior than the one that preserves its existence. The objections highlighted in the text against the Cartesian arguments were deliberated choices, to elucidate the relevance of rationality as the foundation for the proof of God’s existence. The relation between the understanding
Highly deformable bones: unusual deformation mechanisms of seahorse armor.
Porter, Michael M; Novitskaya, Ekaterina; Castro-Ceseña, Ana Bertha; Meyers, Marc A; McKittrick, Joanna
2013-06-01
Multifunctional materials and devices found in nature serve as inspiration for advanced synthetic materials, structures and robotics. Here, we elucidate the architecture and unusual deformation mechanisms of seahorse tails that provide prehension as well as protection against predators. The seahorse tail is composed of subdermal bony plates arranged in articulating ring-like segments that overlap for controlled ventral bending and twisting. The bony plates are highly deformable materials designed to slide past one another and buckle when compressed. This complex plate and segment motion, along with the unique hardness distribution and structural hierarchy of each plate, provide seahorses with joint flexibility while shielding them against impact and crushing. Mimicking seahorse armor may lead to novel bio-inspired technologies, such as flexible armor, fracture-resistant structures or prehensile robotics.
2-D geometrical analysis of deformation
International Nuclear Information System (INIS)
Engineering structures such as dams, bridges, high rise buildings, etc. are subject to deformation. Deformation survey is therefore necessary to determine the magnitude and direction of such movements for the purpose of safety assessment. In this study, a strategy for two-step analyses for deformation survey rising the two dimensional (2-D) geodetic method has been developed, consisting of independent least squares estimation (LSE) of each epoch followed by deformation detection. Important aspects on LSE include global and local testing. In deformation detection, the following aspects were implemented; datum definition by the user. determination of stable datum points, geometrical analysis of deformation and graphic presentation. The developed strategy has been implemented in three computer programs, COMPUT, DEFORM and STRANS. Tests carried out with simulated and known data show that the developed strategy and programs are applicable for 2-D geometrical detection of deformation. (Author)
Prediction of deformity in spinal tuberculosis
Jutte, Paul; Wuite, Sander; The, Bertram; van Altena, Richard; Veldhuizen, Albert
2007-01-01
Tuberculosis of the spine may cause kyphosis, which may in turn cause late paraplegia, respiratory compromise, and unsightly deformity. Surgical correction therefore may be considered for large or progressive deformities. We retrospectively analyzed clinical and radiographic parameters to predict th
Kedia, Kushal S.; Safta, Cosmin; Ray, Jaideep; Najm, Habib N.; Ghoniem, Ahmed F.
2014-09-01
In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A “buffer zone” methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed.
Directory of Open Access Journals (Sweden)
Yufei Liu
2015-01-01
Full Text Available Flexible Cartesian robotic arms (CRAs are typical multicoupling systems. Considering the elastic effects of bolted joints and the motion disturbances, this paper investigates the dynamic and stability of the flexible CRA. With the kinetic energy and potential energy of the comprising components, Hamilton’s variational principle and Duhamel integral are utilized to derive the dynamic equation and vibration differential equation. Based on the proposed elastic restraint model of the bolted joints, boundary conditions and mode equations of the flexible CRA are determined with using the principle of virtual work. According to the mode frequencies and sensitivities analysis, it reveals that the connecting stiffness of the bolted joints has significant influences, and the mode frequencies are more sensitive to the tensional stiffness. Moreover, describing the motion displacement of the driving base as combination of an average motion displacement and a harmonic disturbance, the vibration responses of the system are studied. The result indicates that the motion disturbance has obvious influence on the vibration responses, and the influence enhances under larger accelerating operations. The multiple scales method is introduced to analyze the parametric stability of the system, as well as the influences of the tensional stiffness and the end-effector on the stability.
Directory of Open Access Journals (Sweden)
Wen-hua Wang
2014-01-01
Full Text Available In order to study the interactions between fluid and elastic structure (such as marine lifeboat falling down and ship, this paper presents a new CFD method on hydroelastic water-entry problem of free-falling elastic wedge, which can more conveniently handle moving solid boundaries. In the CFD solver, a surface capturing method and the Cartesian cut cell mesh are employed to deal with the moving free surface and solid boundaries, respectively. On the other hand, in structural analysis, the finite element method and lath-beam structural model are introduced to calculate the elastic response. Furthermore, based on the current CFD and structural solver, a particular data transfer method and coupling strategy are presented for the fluid-structure interaction. Finally, by comparing numerical results with experimental data, the present method is validated to be available and feasible for hydroelastic water-entry problem and further successfully adopted to analyze the motion characteristics of free-falling elastic wedge.
Polkowski, Marcin
2016-04-01
Seismic wave travel time calculation is the most common numerical operation in seismology. The most efficient is travel time calculation in 1D velocity model - for given source, receiver depths and angular distance time is calculated within fraction of a second. Unfortunately, in most cases 1D is not enough to encounter differentiating local and regional structures. Whenever possible travel time through 3D velocity model has to be calculated. It can be achieved using ray calculation or time propagation in space. While single ray path calculation is quick it is complicated to find the ray path that connects source with the receiver. Time propagation in space using Fast Marching Method seems more efficient in most cases, especially when there are multiple receivers. In this presentation a Python module pySeismicFMM is presented - simple and very efficient tool for calculating travel time from sources to receivers. Calculation requires regular 2D or 3D velocity grid either in Cartesian or geographic coordinates. On desktop class computer calculation speed is 200k grid cells per second. Calculation has to be performed once for every source location and provides travel time to all receivers. pySeismicFMM is free and open source. Development of this tool is a part of authors PhD thesis. National Science Centre Poland provided financial support for this work via NCN grant DEC-2011/02/A/ST10/00284.
Kedia, Kushal S.
2014-09-01
In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A "buffer zone" methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed. © 2014 Elsevier Inc.
Deformable hybrid approach for haptic interaction
Susín Sánchez, Antonio; Mero, Máximo G.
2006-01-01
A new hybrid approach for deformable models is presented here and carried out in a virtual reality environment, achieving real time performance with haptic interactions. Our implementation consists in using two approaches for the deformable model. The deformation is modelled using simultaneously a Finite Element Method and a Mesh Free Method. With this Mesh Free method, particles are used to simulate large deformations in the volume region near the surface of the object. The remaining inte...
Foot Deformities in Patients with Cerebral Palsy
E Ameri; A. Yeganeh
2007-01-01
Introduction & Objective: In patients with cerebral palsy (CP) the most common presentation is lower extremity deformity specially foot deformity. Inability to ambulation is the one of the most important disabilities, that dependent to the variety of factors such as severity of disease, kind of CP, etc. This study was aimed to assess prevalence of kinds of foot deformity in CP and communication between kind of CP and foot deformity and another hand inability to ambulation.Materials & Methods...
Arithmetic Deformation Theory of Lie Algebras
Rastegar, Arash
2012-01-01
This paper is devoted to deformation theory of graded Lie algebras over $\\Z$ or $\\Z_l$ with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artin local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations. In the second part, we use a version of Schlessinger criteria for functors on the Artinian cat...
Airborne Repeat Pass Interferometry for Deformation Measurements
Groot, J.; Otten, M.; Halsema, E. van
2000-01-01
In ground engineering the need for deformation measurements is urgent. SAR interferometry can be used to measure small (sub-wavelength) deformations. An experiment to investigate this for dike deformations was set up, using the C-band SAR system PHARUS (PHased ARray Universal SAR). This paper descri
Formal connections in deformation quantization
DEFF Research Database (Denmark)
Masulli, Paolo
The field of this thesis is deformation quantization, and we consider mainly symplectic manifolds equipped with a star product. After reviewing basics in complex geometry, we introduce quantization, focusing on geometric quantization and deformation quantization. The latter is defined as a star...... manifold. Gammelgaard gave an explicit formula for a class of star products in this setting. We review his construction, which is combinatorial and based on a certain family of graphs and extend it, to provide the graph formalism with the notions of composition and differentiation. We shall focus our...... products. Afterwards we study the problem of trivializing a formal connection, that is to define a differential operator on the manifold which makes any section of the bundle parallel with respect to the connection. To approach the problem we use the graph formalism described above to encode it in graph...
Making Deformable Template Models Operational
DEFF Research Database (Denmark)
Fisker, Rune
2000-01-01
Deformable template models are a very popular and powerful tool within the field of image processing and computer vision. This thesis treats this type of models extensively with special focus on handling their common difficulties, i.e. model parameter selection, initialization and optimization. A...... estimation of the model parameters, which applies a combination of a maximum likelihood and minimum distance criterion. Another contribution is a very fast search based initialization algorithm using a filter interpretation of the likelihood model. These two methods can be applied to most deformable template...... models making a non-expert user able to use the model. A comparative study of a number of optimization algorithms is also reported. In addition a general polygon-based model, an ellipse model and a textile model are proposed and a number of applications have been solved. Finally the Grenander model and...