Gauge equivalence of the Gross Pitaevskii equation and the equivalent Heisenberg spin chain

Science.gov (United States)

Radha, R.; Kumar, V. Ramesh

2007-11-01

In this paper, we construct an equivalent spin chain for the Gross-Pitaevskii equation with quadratic potential and exponentially varying scattering lengths using gauge equivalence. We have then generated the soliton solutions for the spin components S3 and S-. We find that the spin solitons for S3 and S- can be compressed for exponentially growing eigenvalues while they broaden out for decaying eigenvalues.

Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

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Ying Wang

2014-06-01

Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.

Global solutions for 3D nonlocal Gross-Pitaevskii equations with rough data

Directory of Open Access Journals (Sweden)

Hartmut Pecher

2012-10-01

Full Text Available We study the Cauchy problem for the Gross-Pitaevskii equation with a nonlocal interaction potential of Hartree type in three space dimensions. If the potential is even and positive definite or a positive function and its Fourier transform decays sufficiently rapidly the problem is shown to be globally well-posed for large rough data which not necessarily have finite energy and also in a situation where the energy functional is not positive definite. The proof uses a suitable modification of the I-method.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates.

Science.gov (United States)

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F =1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

One-dimensional reduction of the three-dimenstional Gross-Pitaevskii equation with two- and three-body interactions

International Nuclear Information System (INIS)

Cardoso, W. B.; Avelar, A. T.; Bazeia, D.

2011-01-01

We deal with the three-dimensional Gross-Pitaevskii equation which is used to describe a cloud of dilute bosonic atoms that interact under competing two- and three-body scattering potentials. We study the case where the cloud of atoms is strongly confined in two spatial dimensions, allowing us to build an unidimensional nonlinear equation,controlled by the nonlinearities and the confining potentials that trap the system along the longitudinal coordinate. We focus attention on specific limits dictated by the cubic and quintic coefficients, and we implement numerical simulations to help us to quantify the validity of the procedure.

Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Cherny, A.Yu.; Brand, J.

2004-01-01

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g., in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behavior of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, crossover regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial

Numerically exact dynamics of the interacting many-body Schroedinger equation for Bose-Einstein condensates. Comparison to Bose-Hubbard and Gross-Pitaevskii theory

Energy Technology Data Exchange (ETDEWEB)

Sakmann, Kaspar

2010-07-21

In this thesis, the physics of trapped, interacting Bose-Einstein condensates is analyzed by solving the many-body Schroedinger equation. Particular emphasis is put on coherence, fragmentation and reduced density matrices. First, the ground state of a trapped Bose-Einstein condensate and its correlation functions are obtained. Then the dynamics of a bosonic Josephson junction is investigated by solving the time-dependent many-body Schroedinger equation numerically exactly. These are the first exact results in literature in this context. It is shown that the standard approximations of the field, Gross-Pitaevskii theory and the Bose-Hubbard model fail at weak interaction strength and within their range of expected validity. For stronger interactions the dynamics becomes strongly correlated and a new equilibration phenomenon is discovered. By comparison with exact results it is shown that a symmetry of the Bose- Hubbard model between attractive and repulsive interactions must be considered an artefact of the model. A conceptual innovation of this thesis are time-dependent Wannier functions. Equations of motion for time-dependent Wannier functions are derived from the variational principle. By comparison with exact results it is shown that lattice models can be greatly improved at little computational cost by letting the Wannier functions of a lattice model become time-dependent. (orig.)

Control of the dynamics of coupled atomic-molecular Bose-Einstein condensates: Modified Gross-Pitaevskii approach

International Nuclear Information System (INIS)

Gupta, Moumita; Dastidar, Krishna Rai

2009-01-01

We study the dynamics of the atomic and molecular Bose-Einstein condensates (BECs) of 87 Rb in a spherically symmetric trap coupled by stimulated Raman photoassociation process. Considering the higher order nonlinearity in the atom-atom interaction we analyze the dynamics of the system using coupled modified Gross-Pitaevskii (MGP) equations and compare it with mean-field coupled Gross-Pitaevskii (GP) dynamics. Considerable differences in the dynamics are obtained in these two approaches at large scattering length, i.e., for large values of peak-gas parameter x pk ≥10 -3 . We show how the dynamics of the coupled system is affected when the atom-molecule and molecule-molecule interactions are considered together with the atom-atom interaction and also when the strengths of these three interactions are increased. The effect of detuning on the efficiency of conversion of atomic fractions into molecules is demonstrated and the feasibility of maximum molecular BEC formation by varying the Raman detuning parameter at different values of time is explored. Thus by varying the Raman detuning and the scattering length for atom-atom interaction one can control the dynamics of the coupled atomic-molecular BEC system. We have also solved coupled Gross-Pitaevskii equations for atomic to molecular condensate formation through magnetic Feshbach resonance in a BEC of 85 Rb. We found similar features for oscillations between atomic and molecular condensates noted in previous theoretical study and obtained fairly good agreement with the evolution of total atomic condensate observed experimentally.

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

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Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively

Motions in a Bose condensate: X. New results on stability of axisymmetric solitary waves of the Gross-Pitaevskii equation

OpenAIRE

Berloff, Natalia G.; Roberts, Paul H.

2004-01-01

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linea...

Periodic, complexiton solutions and stability for a (2+1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation

Science.gov (United States)

Yin, Hui-Min; Tian, Bo; Zhao, Xin-Chao

2018-06-01

This paper presents an investigation of a (2 + 1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation. Periodic and complexiton solutions are obtained. Solitons solutions are also gotten through the periodic solutions. Numerical solutions via the split step method are stable. Effects of the weak and strong modulation instability on the solitons are shown: the weak modulation instability permits an observable soliton, and the strong one overwhelms its development.

Gap solitons in elongated geometries: The one-dimensional Gross-Pitaevskii equation and beyond

International Nuclear Information System (INIS)

Mateo, A. Munoz; Delgado, V.; Malomed, Boris A.

2011-01-01

We report results of a systematic analysis of matter-wave gap solitons (GSs) in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded into a combination of a cigar-shaped trap and axial optical-lattice (OL) potential. Basic cases of the strong, intermediate, and weak radial (transverse) confinement are considered, as well as settings with shallow and deep OL potentials. Only in the case of the shallow lattice combined with tight radial confinement, which actually has little relevance to realistic experimental conditions, does the usual one-dimensional (1D) cubic Gross-Pitaevskii equation (GPE) furnish a sufficiently accurate description of GSs. However, the effective 1D equation with the nonpolynomial nonlinearity, derived in Ref. [Phys. Rev. A 77, 013617 (2008)], provides for quite an accurate approximation for the GSs in all cases, including the situation with weak transverse confinement, when the soliton's shape includes a considerable contribution from higher-order transverse modes, in addition to the usual ground-state wave function of the respective harmonic oscillator. Both fundamental GSs and their multipeak bound states are considered. The stability is analyzed by means of systematic simulations. It is concluded that almost all the fundamental GSs are stable, while their bound states may be stable if the underlying OL potential is deep enough.

Analysis of the Complex Gross-Pitaevskii Equation for the Bose-Einstein Condensation of Exciton-Polaritons

KAUST Repository

Núñez, Jesus

2011-08-01

Considered as a fundamental step for the development of the atomic laser and quantum computing, as well as the theoretical explanation of super fluidity, the Bose- Einstein condensate (BEC) has emerged as one of the most important topics in modern physics. This project is devoted to the analysis of a condensate based on exciton-polaritons. This BEC is characterized by a high critical temperature of condensation (about 20 K) and non-equilibrium dynamics. A mathematical model called complex Gross- Pitaevskii equation (cGPE) is used to describe its behavior. The steady state solutions of the cGPE are studied and a numerical method based on a collocation method is proposed in order to find these solutions. Once the steady state solutions are found, a linear stability analysis is performed, demonstrating that the steady state solutions become unstable as the pumping spot radius increases. Finally, the manifestations of these instabilities are analyzed by direct simulation of the cGPE, using a second order time-splitting spectral method. As a result, it is possible to see the formation of quantum vortices, which increase in number as the pumping spot radius increases.

Mathematical and physical aspects of controlling the exact solutions of the 3D Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Fedele, Renato; Jovanovic, Dusan; De Nicola, Sergio; Eliasson, Bengt; Shukla, Padma K.

2010-01-01

The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schroedinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schroedinger equation coupled with a 1D nonlinear Schroedinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.

OpenMP GNU and Intel Fortran programs for solving the time-dependent Gross-Pitaevskii equation

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Young-S., Luis E.; Muruganandam, Paulsamy; Adhikari, Sadhan K.; Lončar, Vladimir; Vudragović, Dušan; Balaž, Antun

2017-11-01

We present Open Multi-Processing (OpenMP) version of Fortran 90 programs for solving the Gross-Pitaevskii (GP) equation for a Bose-Einstein condensate in one, two, and three spatial dimensions, optimized for use with GNU and Intel compilers. We use the split-step Crank-Nicolson algorithm for imaginary- and real-time propagation, which enables efficient calculation of stationary and non-stationary solutions, respectively. The present OpenMP programs are designed for computers with multi-core processors and optimized for compiling with both commercially-licensed Intel Fortran and popular free open-source GNU Fortran compiler. The programs are easy to use and are elaborated with helpful comments for the users. All input parameters are listed at the beginning of each program. Different output files provide physical quantities such as energy, chemical potential, root-mean-square sizes, densities, etc. We also present speedup test results for new versions of the programs. Program files doi:http://dx.doi.org/10.17632/y8zk3jgn84.2 Licensing provisions: Apache License 2.0 Programming language: OpenMP GNU and Intel Fortran 90. Computer: Any multi-core personal computer or workstation with the appropriate OpenMP-capable Fortran compiler installed. Number of processors used: All available CPU cores on the executing computer. Journal reference of previous version: Comput. Phys. Commun. 180 (2009) 1888; ibid.204 (2016) 209. Does the new version supersede the previous version?: Not completely. It does supersede previous Fortran programs from both references above, but not OpenMP C programs from Comput. Phys. Commun. 204 (2016) 209. Nature of problem: The present Open Multi-Processing (OpenMP) Fortran programs, optimized for use with commercially-licensed Intel Fortran and free open-source GNU Fortran compilers, solve the time-dependent nonlinear partial differential (GP) equation for a trapped Bose-Einstein condensate in one (1d), two (2d), and three (3d) spatial dimensions for

Exact soliton-like solutions of the radial Gross–Pitaevskii equation

International Nuclear Information System (INIS)

Toikka, L A; Hietarinta, J; Suominen, K-A

2012-01-01

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e. radial) Gross–Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlevé transcendent. In each case the potential can be chosen to be time independent. (paper)

Motions in a Bose condensate: X. New results on the stability of axisymmetric solitary waves of the Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Berloff, Natalia G; Roberts, Paul H

2004-01-01

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The implicitly restarted Arnoldi method for banded matrices with shift-invert is used to solve the linearized spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linearly stable. The growth rates of the instabilities on the upper branch are so small that an arbitrarily specified initial perturbation of a rarefaction wave at first usually evolves towards the upper branch as it acoustically radiates away its excess energy. This is demonstrated through numerical integrations of the GP equation starting from an initial state consisting of an unstable rarefaction wave and random non-axisymmetric noise. The resulting solution evolves towards, and remains for a significant time in the vicinity of, an unperturbed unstable rarefaction wave. It is shown however that, ultimately (or for an initial state extremely close to the upper branch), the solution evolves onto the lower branch or is completely dissipated as sound. It is shown how density depletions in uniform and trapped condensates can generate rarefaction waves, and a simple method is suggested by which such waves can be created in the laboratory

Motions in a Bose condensate: X. New results on the stability of axisymmetric solitary waves of the Gross-Pitaevskii equation

Energy Technology Data Exchange (ETDEWEB)

Berloff, Natalia G [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Roberts, Paul H [Department of Mathematics, University of California, Los Angeles, CA, 90095 (United States)

2004-11-26

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The implicitly restarted Arnoldi method for banded matrices with shift-invert is used to solve the linearized spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linearly stable. The growth rates of the instabilities on the upper branch are so small that an arbitrarily specified initial perturbation of a rarefaction wave at first usually evolves towards the upper branch as it acoustically radiates away its excess energy. This is demonstrated through numerical integrations of the GP equation starting from an initial state consisting of an unstable rarefaction wave and random non-axisymmetric noise. The resulting solution evolves towards, and remains for a significant time in the vicinity of, an unperturbed unstable rarefaction wave. It is shown however that, ultimately (or for an initial state extremely close to the upper branch), the solution evolves onto the lower branch or is completely dissipated as sound. It is shown how density depletions in uniform and trapped condensates can generate rarefaction waves, and a simple method is suggested by which such waves can be created in the laboratory.

Effective evolution equations from many-body quantum mechanics

International Nuclear Information System (INIS)

Benedikter, Niels Patriz

2014-01-01

Systems of interest in physics often consist of a very large number of interacting particles. In certain physical regimes, effective non-linear evolution equations are commonly used as an approximation for making predictions about the time-evolution of such systems. Important examples are Bose-Einstein condensates of dilute Bose gases and degenerate Fermi gases. While the effective equations are well-known in physics, a rigorous justification is very difficult. However, a rigorous derivation is essential to precisely understand the range and the limits of validity and the quality of the approximation. In this thesis, we prove that the time evolution of Bose-Einstein condensates in the Gross-Pitaevskii regime can be approximated by the time-dependent Gross-Pitaevskii equation, a cubic non-linear Schroedinger equation. We then turn to fermionic systems and prove that the evolution of a degenerate Fermi gas can be approximated by the time-dependent Hartree-Fock equation (TDHF) under certain assumptions on the semiclassical structure of the initial data. Finally, we extend the latter result to fermions with relativistic kinetic energy. All our results provide explicit bounds on the error as the number of particles becomes large. A crucial methodical insight on bosonic systems is that correlations can be modeled by Bogolyubov transformations. We construct initial data appropriate for the Gross-Pitaevskii regime using a Bogolyubov transformation acting on a coherent state, which amounts to studying squeezed coherent states. As a crucial insight for fermionic systems, we point out a semiclassical structure in states close to the ground state of fermions in a trap. As a convenient language for studying the dynamics of fermionic systems, we use particle-hole transformations.

On the numerical solution of the Gross–Pitaevskii equation | Laoye ...

African Journals Online (AJOL)

The Gross–Pitaevskii equation is solved using an approach developed for the solution of the Bogoliubov–de Gennes equations for type II superconductivity. The solution is compared with others in the literature and is shown to be easily adapted to the study of an isolated vortex recently discovered in Bose-Einstein ...

Energy cascade with small-scale thermalization, counterflow metastability, and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Krstulovic, Giorgio; Brachet, Marc

2011-01-01

The statistical equilibria of the (conservative) dynamics of the Gross-Pitaevskii equation (GPE) with a finite range of spatial Fourier modes are characterized using a new algorithm, based on a stochastically forced Ginzburg-Landau equation (SGLE), that directly generates grand-canonical distributions. The SGLE-generated distributions are validated against finite-temperature GPE-thermalized states and exact (low-temperature) results obtained by steepest descent on the (grand-canonical) partition function. A standard finite-temperature second-order λ transition is exhibited. A mechanism of GPE thermalization through a direct cascade of energy is found using initial conditions with mass and energy distributed at large scales. A long transient with partial thermalization at small scales is observed before the system reaches equilibrium. Vortices are shown to disappear as a prelude to final thermalization and their annihilation is related to the contraction of vortex rings due to mutual friction. Increasing the amount of dispersion at the truncation wave number is shown to slow thermalization and vortex annihilation. A bottleneck that produces spontaneous effective self-truncation with partial thermalization is characterized in the limit of large dispersive effects. Metastable counterflow states, with nonzero values of momentum, are generated using the SGLE algorithm. Spontaneous nucleation of the vortex ring is observed and the corresponding Arrhenius law is characterized. Dynamical counterflow effects on vortex evolution are investigated using two exact solutions of the GPE: traveling vortex rings and a motionless crystal-like lattice of vortex lines. Longitudinal effects are produced and measured on the crystal lattice. A dilatation of vortex rings is obtained for counterflows larger than their translational velocity. The vortex ring translational velocity has a dependence on temperature that is an order of magnitude above that of the crystal lattice, an effect

Dynamics of Bose-Einstein condensates in a time-dependent trap

International Nuclear Information System (INIS)

Kumar, V. Ramesh; Radha, R.; Panigrahi, Prasanta K.

2008-01-01

In this paper, we generate the Lax pair for the one-dimensional Gross-Pitaevskii equation with time-dependent scattering length in the presence of a confining or expulsive harmonic time-dependent trap. We then exploit the Lax pair profitably to construct multisoliton solutions using gauge transformation from a trivial input solution. In particular, we have investigated the effect of both expulsive and confining traps on soliton interaction. Even though we find that the amplitude of the bright soliton relies upon the time-dependent scattering length and the external time-dependent trap with the velocity being dictated by the external trap alone, the observation of interdependence of the scattering length on the trap shows that the bright solitons not only can be compressed into a desirable width and amplitude but also can be remote controlled and driven anywhere in the plane by suitably maneuvering the external time-dependent trap alone

Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential

International Nuclear Information System (INIS)

Liang, Z.X.; Zhang, Z.D.; Liu, W.M.

2005-01-01

We present a family of exact solutions of the one-dimensional nonlinear Schroedinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background

Radio pulsar glitches as a state-dependent Poisson process

Science.gov (United States)

Fulgenzi, W.; Melatos, A.; Hughes, B. D.

2017-10-01

Gross-Pitaevskii simulations of vortex avalanches in a neutron star superfluid are limited computationally to ≲102 vortices and ≲102 avalanches, making it hard to study the long-term statistics of radio pulsar glitches in realistically sized systems. Here, an idealized, mean-field model of the observed Gross-Pitaevskii dynamics is presented, in which vortex unpinning is approximated as a state-dependent, compound Poisson process in a single random variable, the spatially averaged crust-superfluid lag. Both the lag-dependent Poisson rate and the conditional distribution of avalanche-driven lag decrements are inputs into the model, which is solved numerically (via Monte Carlo simulations) and analytically (via a master equation). The output statistics are controlled by two dimensionless free parameters: α, the glitch rate at a reference lag, multiplied by the critical lag for unpinning, divided by the spin-down rate; and β, the minimum fraction of the lag that can be restored by a glitch. The system evolves naturally to a self-regulated stationary state, whose properties are determined by α/αc(β), where αc(β) ≈ β-1/2 is a transition value. In the regime α ≳ αc(β), one recovers qualitatively the power-law size and exponential waiting-time distributions observed in many radio pulsars and Gross-Pitaevskii simulations. For α ≪ αc(β), the size and waiting-time distributions are both power-law-like, and a correlation emerges between size and waiting time until the next glitch, contrary to what is observed in most pulsars. Comparisons with astrophysical data are restricted by the small sample sizes available at present, with ≤35 events observed per pulsar.

On the Gross–Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stability

KAUST Repository

Sierra Nunez, Jesus Alfredo; Kasimov, Aslan R.; Markowich, Peter A.; Weishä upl, Rada Maria

2015-01-01

We investigate the behavior of solutions of the complex Gross–Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose–Einstein condensates. The stationary radially symmetric solutions of the equation are studied, and their linear stability with respect to two-dimensional perturbations is analyzed. Using numerical continuation, we calculate not only the ground state of the system, but also a number of excited states. Accurate numerical integration is employed to study the general nonlinear evolution of the system from the unstable stationary solutions to the formation of stable vortex patterns.

On the Gross–Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stability

KAUST Repository

Sierra Nunez, Jesus Alfredo

2015-02-11

We investigate the behavior of solutions of the complex Gross–Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose–Einstein condensates. The stationary radially symmetric solutions of the equation are studied, and their linear stability with respect to two-dimensional perturbations is analyzed. Using numerical continuation, we calculate not only the ground state of the system, but also a number of excited states. Accurate numerical integration is employed to study the general nonlinear evolution of the system from the unstable stationary solutions to the formation of stable vortex patterns.

Fragmented metastable states exist in an attractive bose-einstein condensate for atom numbers well above the critical number of the Gross-Pitaevskii theory.

Science.gov (United States)

Cederbaum, Lorenz S; Streltsov, Alexej I; Alon, Ofir E

2008-02-01

It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number N(cr)(GP) of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above N(cr)(GP). The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.

Fractional Bhatnagar-Gross-Krook kinetic equation

Science.gov (United States)

Goychuk, Igor

2017-11-01

The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover

Science.gov (United States)

Simonucci, S.; Strinati, G. C.

2014-02-01

We derive a nonlinear differential equation for the gap parameter of a superfluid Fermi system by performing a suitable coarse graining of the Bogoliubov-de Gennes (BdG) equations throughout the BCS-BEC crossover, with the aim of replacing the time-consuming solution of the original BdG equations by the simpler solution of this novel equation. We perform a favorable numerical test on the validity of this new equation over most of the temperature-coupling phase diagram, by an explicit comparison with the full solution of the original BdG equations for an isolated vortex. We also show that the new equation reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling close to the critical temperature and to the Gross-Pitaevskii equation for composite bosons in strong coupling at low temperature.

A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates

KAUST Repository

Sierra Nunez, Jesus Alfredo

2018-05-16

The Schrödinger equations have had a profound impact on a wide range of fields of modern science, including quantum mechanics, superfluidity, geometrical optics, Bose-Einstein condensates, and the analysis of dispersive phenomena in the theory of PDE. The main purpose of this thesis is to explore two Schrödinger-type equations appearing in the so-called Bohmian formulation of quantum mechanics and in the study of exciton-polariton condensates. For the first topic, the linear Schrödinger equation is the starting point in the formulation of a phase-space model proposed in [1] for the Bohmian interpretation of quantum mechanics. We analyze this model, a nonlinear Vlasov-type equation, as a Hamiltonian system defined on an appropriate Poisson manifold built on Wasserstein spaces, the aim being to establish its existence theory. For this purpose, we employ results from the theory of PDE, optimal transportation, differential geometry and algebraic topology. The second topic of the thesis is the study of a nonlinear Schrödinger equation, called the complex Gross-Pitaevskii equation, appearing in the context of Bose-Einstein condensation of exciton-polaritons. This model can be roughly described as a driven-damped Gross-Pitaevskii equation which shares some similarities with the complex Ginzburg-Landau equation. The difficulties in the analysis of this equation stem from the fact that, unlike the complex Ginzburg-Landau equation, the complex Gross-Pitaevskii equation does not include a viscous dissipation term. Our approach to this equation will be in the framework of numerical computations, using two main tools: collocation methods and numerical continuation for the stationary solutions and a time-splitting spectral method for the dynamics. After performing a linear stability analysis on the computed stationary solutions, we are led to postulate the existence of radially symmetric stationary ground state solutions only for certain values of the parameters in the

Vortex nucleation in Bose-Einstein condensates in time-dependent traps

International Nuclear Information System (INIS)

Lundh, Emil; Martikainen, J.-P.; Suominen, Kalle-Antti

2003-01-01

Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. In the case of a rotating, slightly anisotropic harmonic potential, the numerical results reproduce experimental findings, thereby showing that finite temperatures are not necessary for vortex excitation below the quadrupole frequency. In the case of a condensate subject to stirring by a narrow rotating potential, the process of vortex excitation is described by a classical model that treats the multitude of vortices created by the stirrer as a continuously distributed vorticity at the center of the cloud, but retains a potential flow pattern at large distances from the center

Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit

International Nuclear Information System (INIS)

Suárez, Abril; Chavanis, Pierre-Henri

2015-01-01

Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with an arbitrary potential of the form V(|ϕ| 2 ). We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrodinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c → +∞. (paper)

Introduction to numerical methods for time dependent differential equations

CERN Document Server

Kreiss, Heinz-Otto

2014-01-01

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t

Dynamics and decoherence of two cold bosons in a one-dimensional harmonic trap

International Nuclear Information System (INIS)

Sowinski, Tomasz; Brewczyk, Miroslaw; Gajda, Mariusz; RzaPzewski, Kazimierz

2010-01-01

We study dynamics of two interacting ultracold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the δ-like potential, we study the time evolution of an initially separable state of two particles. The corresponding time-dependent single-particle density matrix is obtained and diagonalized, and single-particle orbitals are found. This allows us to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled, then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit.

Wave Functions for Time-Dependent Dirac Equation under GUP

Science.gov (United States)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

The time-dependent simplified P2 equations: Asymptotic analyses and numerical experiments

International Nuclear Information System (INIS)

Shin, U.; Miller, W.F. Jr.

1998-01-01

Using an asymptotic expansion, the authors found that the modified time-dependent simplified P 2 (SP 2 ) equations are robust, high-order, asymptotic approximations to the time-dependent transport equation in a physical regime in which the conventional time-dependent diffusion equation is the leading-order approximation. Using diffusion limit analysis, they also asymptotically compared three competitive time-dependent equations (the telegrapher's equation, the time-dependent SP 2 equations, and the time-dependent simplified even-parity equation). As a result, they found that the time-dependent SP 2 equations contain higher-order asymptotic approximations to the time-dependent transport equation than the other competitive equations. The numerical results confirm that, in the vast majority of cases, the time-dependent SP 2 solutions are significantly more accurate than the time-dependent diffusion and the telegrapher's solutions. They have also shown that the time-dependent SP 2 equations have excellent characteristics such as rotational invariance (which means no ray effect), good diffusion limit behavior, guaranteed positivity in diffusive regimes, and significant accuracy, even in deep-penetration problems. Through computer-running-time tests, they have shown that the time-dependent SP 2 equations can be solved with significantly less computational effort than the conventionally used, time-dependent S N equations (for N > 2) and almost as fast as the time-dependent diffusion equation. From all these results, they conclude that the time-dependent SP 2 equations should be considered as an important competitor for an improved approximately transport equations solver. Such computationally efficient time-dependent transport models are important for problems requiring enhanced computational efficiency, such as neutronics/fluid-dynamics coupled problems that arise in the analyses of hypothetical nuclear reactor accidents

Vortices in atomic Bose-Einstein condensates in the large-gas-parameter region

International Nuclear Information System (INIS)

Nilsen, J.K.; Mur-Petit, J.; Guilleumas, M.; Polls, A.; Hjorth-Jensen, M.

2005-01-01

In this work we compare the results of the Gross-Pitaevskii and modified Gross-Pitaevskii equations with ab initio variational Monte Carlo calculations for Bose-Einstein condensates of atoms in axially symmetric traps. We examine both the ground state and excited states having a vortex line along the z axis at high values of the gas parameter and demonstrate an excellent agreement between the modified Gross-Pitaevskii and ab initio Monte Carlo methods, both for the ground and vortex states

Stochastic Landau equation with time-dependent drift

International Nuclear Information System (INIS)

Swift, J.B.; Hohenberg, P.C.; Ahlers, G.

1991-01-01

The stochastic differential equation τ 0 ∂ tA =ε(t)A-g 3 A 3 +bar f(t), where bar f(t) is Gaussian white noise, is studied for arbitrary time dependence of ε(t). In particular, cases are considered where ε(t) goes through the bifurcation of the deterministic system, which occurs at ε=0. In the limit of weak noise an approximate analytic expression generalizing earlier work of Suzuki [Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) Suppl. 64, 402 (1978)] is obtained for the time-dependent distribution function P(A,t). The results compare favorably with a numerical simulation of the stochastic equation for the case of a linear ramp (both increasing and decreasing) and for a periodic time dependence of ε(t). The procedure can be generalized to an arbitrary deterministic part ∂ tA =D(A,t)+bar f(t), but the deterministic equation may then have to be solved numerically

The relation between the Gross-Pitaevskii and Bogoliubov descriptions of a dilute Bose gas

International Nuclear Information System (INIS)

Leggett, A J

2003-01-01

I formulate a 'pseudo-paradox' in the theory of a dilute Bose gas with repulsive interactions: the standard expression for the ground state energy within the Gross-Pitaevskii (GP) approximation is lower than that in the Bogoliubov approximation, and hence, by the standard variational argument, the former should prima facie be a better approximation than the latter to the true ground state - a conclusion which is of course opposite to the established wisdom concerning this problem. It is shown that the pseudo-paradox is (unsurprisingly) resolved by a correct transcription of the two-body scattering theory to the many-body case; however, contrary to what appears to be a widespread belief, the resolution has nothing to do with any spurious ultraviolet divergences which result from the replacement of the true interatomic potential by a delta-function pseudopotential. Rather, it relates to an infrared divergence which has the consequence that (a) the most obvious form of the GP 'approximation' actually does not correspond to any well-defined ansatz for the many-body wavefunction, and (b) that the 'best shot' at such a wavefunction always produces an energy which exceeds, or at best equals, that calculated in the Bogoliubov approximation. In fact, the necessity of the latter may be seen as a consequence of the need to reduce the Fock term in the energy, which is absent in the two-particle problem but dominant in the many-body case; it does this by increasing the density correlations, at distances less than or approximately equal to the correlation length ξ, above the value extrapolated from the two-body case. As a by-product I devise an alternative formulation of the Bogoliubov approximation which does not require the explicit replacement of the true interatomic potential by a delta-function pseudopotential

The relation between the Gross-Pitaevskii and Bogoliubov descriptions of a dilute Bose gas

Energy Technology Data Exchange (ETDEWEB)

Leggett, A J [Department of Physics, University of Illinois at Urbana-Champaign, IL 61801-3080 (United States)

2003-07-01

I formulate a 'pseudo-paradox' in the theory of a dilute Bose gas with repulsive interactions: the standard expression for the ground state energy within the Gross-Pitaevskii (GP) approximation is lower than that in the Bogoliubov approximation, and hence, by the standard variational argument, the former should prima facie be a better approximation than the latter to the true ground state - a conclusion which is of course opposite to the established wisdom concerning this problem. It is shown that the pseudo-paradox is (unsurprisingly) resolved by a correct transcription of the two-body scattering theory to the many-body case; however, contrary to what appears to be a widespread belief, the resolution has nothing to do with any spurious ultraviolet divergences which result from the replacement of the true interatomic potential by a delta-function pseudopotential. Rather, it relates to an infrared divergence which has the consequence that (a) the most obvious form of the GP 'approximation' actually does not correspond to any well-defined ansatz for the many-body wavefunction, and (b) that the 'best shot' at such a wavefunction always produces an energy which exceeds, or at best equals, that calculated in the Bogoliubov approximation. In fact, the necessity of the latter may be seen as a consequence of the need to reduce the Fock term in the energy, which is absent in the two-particle problem but dominant in the many-body case; it does this by increasing the density correlations, at distances less than or approximately equal to the correlation length {xi}, above the value extrapolated from the two-body case. As a by-product I devise an alternative formulation of the Bogoliubov approximation which does not require the explicit replacement of the true interatomic potential by a delta-function pseudopotential.

Time-dependent restricted-active-space self-consistent-field theory for bosonic many-body systems

International Nuclear Information System (INIS)

Lévêque, Camille; Madsen, Lars Bojer

2017-01-01

We develop an ab initio time-dependent wavefunction based theory for the description of a many-body system of cold interacting bosons. Like the multi-configurational time-dependent Hartree method for bosons (MCTDHB), the theory is based on a configurational interaction Ansatz for the many-body wavefunction with time-dependent self-consistent-field orbitals. The theory generalizes the MCTDHB method by incorporating restrictions on the active space of the orbital excitations. The restrictions are specified based on the physical situation at hand. The equations of motion of this time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory are derived. The similarity between the formal development of the theory for bosons and fermions is discussed. The restrictions on the active space allow the theory to be evaluated under conditions where other wavefunction based methods due to exponential scaling in the numerical effort cannot, and to clearly identify the excitations that are important for an accurate description, significantly beyond the mean-field approach. For ground state calculations we find it to be important to allow a few particles to have the freedom to move in many orbitals, an insight facilitated by the flexibility of the restricted-active-space Ansatz . Moreover, we find that a high accuracy can be obtained by including only even excitations in the many-body self-consistent-field wavefunction. Time-dependent simulations of harmonically trapped bosons subject to a quenching of their noncontact interaction, show failure of the mean-field Gross-Pitaevskii approach within a fraction of a harmonic oscillation period. The TD-RASSCF theory remains accurate at much reduced computational cost compared to the MCTDHB method. Exploring the effect of changes of the restricted-active-space allows us to identify that even self-consistent-field excitations are mainly responsible for the accuracy of the method. (paper)

Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation

CERN Document Server

Qin, Hong

2005-01-01

Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

Riccati and Ermakov Equations in Time-Dependent and Time-Independent Quantum Systems

Directory of Open Access Journals (Sweden)

Dieter Schuch

2008-05-01

Full Text Available The time-evolution of the maximum and the width of exact analytic wave packet (WP solutions of the time-dependent Schrödinger equation (SE represents the particle and wave aspects, respectively, of the quantum system. The dynamics of the maximum, located at the mean value of position, is governed by the Newtonian equation of the corresponding classical problem. The width, which is directly proportional to the position uncertainty, obeys a complex nonlinear Riccati equation which can be transformed into a real nonlinear Ermakov equation. The coupled pair of these equations yields a dynamical invariant which plays a key role in our investigation. It can be expressed in terms of a complex variable that linearizes the Riccati equation. This variable also provides the time-dependent parameters that characterize the Green's function, or Feynman kernel, of the corresponding problem. From there, also the relation between the classical and quantum dynamics of the systems can be obtained. Furthermore, the close connection between the Ermakov invariant and the Wigner function will be shown. Factorization of the dynamical invariant allows for comparison with creation/annihilation operators and supersymmetry where the partner potentials fulfil (real Riccati equations. This provides the link to a nonlinear formulation of time-independent quantum mechanics in terms of an Ermakov equation for the amplitude of the stationary state wave functions combined with a conservation law. Comparison with SUSY and the time-dependent problems concludes our analysis.

Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation

KAUST Repository

Hadj Selem, Fouad; Hajaiej, Hichem; Markowich, Peter A.; Trabelsi, Saber

2014-01-01

This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schrödinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We

Dynamics of partial differential equations

CERN Document Server

Wayne, C Eugene

2015-01-01

This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation.   The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...

Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation

KAUST Repository

Hadj Selem, Fouad

2014-08-26

This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schrödinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We also prove the orbital stability of such solutions referred to as standing waves and characterize the associated orbit. In the last section, we illustrate our results with few numerical simulations. © 2014 Springer Basel.

The accuracy of time dependent transport equation ergodic approximation

International Nuclear Information System (INIS)

Stancic, V.

1995-01-01

In order to predict the accuracy of the ergodic approximation for solving the time dependent transport equation, a comparison with respect to multiple collision and time finite difference methods, has been considered. (author)

Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation

Science.gov (United States)

Charalampidis, E. G.; Kevrekidis, P. G.; Farrell, P. E.

2018-01-01

In this work we employ a recently proposed bifurcation analysis technique, the deflated continuation algorithm, to compute steady-state solitary waveforms in a one-component, two-dimensional nonlinear Schrödinger equation with a parabolic trap and repulsive interactions. Despite the fact that this system has been studied extensively, we discover a wide variety of previously unknown branches of solutions. We analyze the stability of the newly discovered branches and discuss the bifurcations that relate them to known solutions both in the near linear (Cartesian, as well as polar) and in the highly nonlinear regimes. While deflated continuation is not guaranteed to compute the full bifurcation diagram, this analysis is a potent demonstration that the algorithm can discover new nonlinear states and provide insights into the energy landscape of complex high-dimensional Hamiltonian dynamical systems.

Similarity solutions of the Fokker–Planck equation with time-dependent coefficients

International Nuclear Information System (INIS)

Lin, W.-T.; Ho, C.-L.

2012-01-01

In this work, we consider the solvability of the Fokker–Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker–Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulting ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker–Planck equations are presented, and their properties analyzed. - Highlights: ► Scaling form of the Fokker–Planck equation with time-dependent drift and diffusion coefficients is derived. ► Exact similarity solution of the Fokker–Planck equation is given in closed forms. ► New examples of Fokker–Planck equations exactly solvable by similarity methods are discussed.

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

International Nuclear Information System (INIS)

Guo, Ran; Du, Jiulin

2015-01-01

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

Energy Technology Data Exchange (ETDEWEB)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.

Relativistic Photoionization Computations with the Time Dependent Dirac Equation

Science.gov (United States)

2016-10-12

Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6795--16-9698 Relativistic Photoionization Computations with the Time Dependent Dirac... Photoionization Computations with the Time Dependent Dirac Equation Daniel F. Gordon and Bahman Hafizi Naval Research Laboratory 4555 Overlook Avenue, SW...Unclassified Unlimited Unclassified Unlimited 22 Daniel Gordon (202) 767-5036 Tunneling Photoionization Ionization of inner shell electrons by laser

Propagators for the time-dependent Kohn-Sham equations

International Nuclear Information System (INIS)

Castro, Alberto; Marques, Miguel A. L.; Rubio, Angel

2004-01-01

In this paper we address the problem of the numerical integration of the time-dependent Schroedinger equation i∂ t φ=Hφ. In particular, we are concerned with the important case where H is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrically on the time-dependent density, H is in general time dependent, even in the absence of an external time-dependent field. The present analysis also holds for the description of the excited state dynamics of a many-electron system under the influence of arbitrary external time-dependent electromagnetic fields. Our discussion is separated in two parts: (i) First, we look at several algorithms to approximate exp(A), where A is a time-independent operator [e.g., A=-iΔtH(τ) for some given time τ]. In particular, polynomial expansions, projection in Krylov subspaces, and split-operator methods are investigated. (ii) We then discuss different approximations for the time-evolution operator, such as the midpoint and implicit rules, and Magnus expansions. Split-operator techniques can also be modified to approximate the full time-dependent propagator. As the Hamiltonian is time dependent, problem (ii) is not equivalent to (i). All these techniques have been implemented and tested in our computer code OCTOPUS, but can be of general use in other frameworks and implementations

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

International Nuclear Information System (INIS)

Soffer, A.; Weinstein, M.I.

2005-01-01

A theory of time-dependent nonlinear dispersive equations of the Schroedinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, 'selection of the ground state', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides

Spin-zero DKP equation with two time-dependent interactions

Energy Technology Data Exchange (ETDEWEB)

Saeedi, K.; Hassanabadi, H. [Shahrood University of Technology, Physics Department, Shahrood (Iran, Islamic Republic of); Zarrinkamar, S. [Islamic Azad University, Department of Basic Sciences, Garmsar Branch, Garmsar (Iran, Islamic Republic of)

2016-11-15

The Duffin-Kemmer-Petiau equation for spin-zero bosons is considered in (1 + 1) - and (2 + 1) -dimensional space-time. Some time-dependent interactions are considered within the framework and quasi-exact solutions are provided. The results are discussed via various figures. (orig.)

Optimal moving grids for time-dependent partial differential equations

Science.gov (United States)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Numerical simulation of trapped dipolar quantum gases: Collapse studies and vortex dynamics

KAUST Repository

Sparber, Christof; Markowich, Peter; Huang, Zhongyi

2010-01-01

We numerically study the three dimensional Gross-Pitaevskii equation for dipolar quantum gases using a time-splitting algorithm. We are mainly concerned with numerical investigations of the possible blow-up of solutions, i.e. collapse of the condensate, and the dynamics of vortices. © American Institute of Mathematical Sciences.

Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

Energy Technology Data Exchange (ETDEWEB)

Xin, Zhou [Wisconsin Univ., Madison (USA). Dept. of Mathematics

1990-03-01

For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.).

Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

International Nuclear Information System (INIS)

Zhou Xin

1990-01-01

For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.)

The time dependent Schrodinger equation revisited I: quantum field and classical Hamilton-Jacobi routes to Schrodinger's wave equation

International Nuclear Information System (INIS)

Scully, M O

2008-01-01

The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation

Symmetries and invariants of the oscillator and envelope equations with time-dependent frequency

Directory of Open Access Journals (Sweden)

Hong Qin

2006-05-01

Full Text Available The single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant, a fundamental concept in accelerator physics, is fundamentally a result of the corresponding symmetry admitted by the harmonic oscillator equation with linear time-dependent frequency. It is demonstrated that the Lie algebra of the symmetry group for the oscillator equation with time-dependent frequency is eight dimensional, and is composed of four independent subalgebras. A detailed analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. As an application to accelerator physics, the symmetries of the envelope equation enable a fast numerical algorithm for finding matched solutions without using the conventional iterative Newton’s method, where the envelope equation needs to be numerically integrated once for every iteration, and the Jacobi matrix needs to be calculated for the envelope perturbation.

A multi scale approximation solution for the time dependent Boltzmann-transport equation

International Nuclear Information System (INIS)

Merk, B.

2004-03-01

The basis of all transient simulations for nuclear reactor cores is the reliable calculation of the power production. The local power distribution is generally calculated by solving the space, time, energy and angle dependent neutron transport equation known as Boltzmann equation. The computation of exact solutions of the Boltzmann equation is very time consuming. For practical numerical simulations approximated solutions are usually unavoidable. The objective of this work is development of an effective multi scale approximation solution for the Boltzmann equation. Most of the existing methods are based on separation of space and time. The new suggested method is performed without space-time separation. This effective approximation solution is developed on the basis of an expansion for the time derivative of different approximations to the Boltzmann equation. The method of multiple scale expansion is used for the expansion of the time derivative, because the problem of the stiff time behaviour can't be expressed by standard expansion methods. This multiple scale expansion is used in this work to develop approximation solutions for different approximations of the Boltzmann equation, starting from the expansion of the point kinetics equations. The resulting analytic functions are used for testing the applicability and accuracy of the multiple scale expansion method for an approximation solution with 2 delayed neutron groups. The results are tested versus the exact analytical results for the point kinetics equations. Very good agreement between both solutions is obtained. The validity of the solution with 2 delayed neutron groups to approximate the behaviour of the system with 6 delayed neutron groups is demonstrated in an additional analysis. A strategy for a solution with 4 delayed neutron groups is described. A multiple scale expansion is performed for the space-time dependent diffusion equation for one homogenized cell with 2 delayed neutron groups. The result is

Double parametric resonance for matter-wave solitons in a time-modulated trap

International Nuclear Information System (INIS)

Baizakov, Bakhtiyor; Salerno, Mario; Filatrella, Giovanni; Malomed, Boris

2005-01-01

We analyze the motion of solitons in a self-attractive Bose-Einstein condensate, loaded into a quasi-one-dimensional parabolic potential trap, which is subjected to time-periodic modulation with an amplitude ε and frequency Ω. First, we apply the variational approximation, which gives rise to decoupled equations of motion for the center-of-mass coordinate of the soliton, ξ(t), and its width a(t). The equation for ξ(t) is the ordinary Mathieu equation (ME) (it is an exact equation that does not depend on the adopted ansatz), the equation for a(t) being a nonlinear generalization of the ME. Both equations give rise to the same map of instability zones in the (ε,Ω) plane, generated by the parametric resonances (PRs), if the instability is defined as the onset of growth of the amplitude of the parametrically driven oscillations. In this sense, the double PR is predicted. Direct simulations of the underlying Gross-Pitaevskii equation give rise to a qualitatively similar but quantitatively different stability map for oscillations of the soliton's width a(t). In the direct simulations, we identify the soliton dynamics as unstable if the instability (again, realized as indefinite growth of the amplitude of oscillations) can be detected during a time comparable with, or smaller than, the lifetime of the condensate (therefore accessible to experimental detection). Two-soliton configurations are also investigated. It is concluded that multiple collisions between solitons are elastic, and they do not affect the instability borders

Exact solutions to the supply chain equations for arbitrary, time-dependent demands

DEFF Research Database (Denmark)

Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn

2014-01-01

, so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP......We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate...

Finite moments approach to the time-dependent neutron transport equation

International Nuclear Information System (INIS)

Kim, Sang Hyun

1994-02-01

Currently, nodal techniques are widely used in solving the multidimensional diffusion equation because of savings in computing time and storage. Thanks to the development of computer technology, one can now solve the transport equation instead of the diffusion equation to obtain more accurate solution. The finite moments method, one of the nodal methods, attempts to represent the fluxes in the cell and on cell surfaces more rigorously by retaining additional spatial moments. Generally, there are two finite moments schemes to solve the time-dependent transport equation. In one, the time variable is treated implicitly with finite moments method in space variable (implicit finite moments method), the other method uses finite moments method in both space and time (space-time finite moments method). In this study, these two schemes are applied to two types of time-dependent neutron transport problems. One is a fixed source problem, the other a heterogeneous fast reactor problem with delayed neutrons. From the results, it is observed that the two finite moments methods give almost the same solutions in both benchmark problems. However, the space-time finite moments method requires a little longer computing time than that of the implicit finite moments method. In order to reduce the longer computing time in the space-time finite moments method, a new iteration strategy is exploited, where a few time-stepwise calculation, in which original time steps are grouped into several coarse time divisions, is performed sequentially instead of performing iterations over the entire time steps. This strategy results in significant reduction of the computing time and we observe that 2-or 3-stepwise calculation is preferable. In addition, we propose a new finite moments method which is called mixed finite moments method in this thesis. Asymptotic analysis for the finite moments method shows that accuracy of the solution in a heterogeneous problem mainly depends on the accuracy of the

The large discretization step method for time-dependent partial differential equations

Science.gov (United States)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Time-dependent field equations for paraxial relativistic electron beams: Beam Research Program

International Nuclear Information System (INIS)

Sharp, W.M.; Yu, S.S.; Lee, E.P.

1987-01-01

A simplified set of field equations for a paraxial relativistic electron beam is presented. These equations for the beam electrostatic potential phi and pinch potential Phi identical to A/sub z/ - phi retain previously neglected time-dependent terms and for axisymmetric beams reduce exactly to Maxwell's equations

Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models, and stimulated Raman adiabatic passage

International Nuclear Information System (INIS)

Graefe, E. M.; Korsch, H. J.; Witthaut, D.

2006-01-01

We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning

Spectral methods for time dependent partial differential equations

Science.gov (United States)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

Science.gov (United States)

Zhou, Xin

1990-03-01

For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.

Non-integrability of time-dependent spherically symmetric Yang-Mills equations

Energy Technology Data Exchange (ETDEWEB)

Matinyan, S G; Prokhorenko, E B; Savvidy, G K

1988-03-07

The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. It is shown that the motion of this system is ergodic, while the system itself is non-integrable, i.e. manifests dynamical chaos.

Exact solutions of time-dependent Dirac equations and the quantum-classical correspondence

International Nuclear Information System (INIS)

Zhang Zhiguo

2006-01-01

Exact solutions to the Dirac equations with a time-dependent mass and a static magnetic field or a time-dependent linear potential are given. Matrix elements of the coordinate, momentum and velocity operator are calculated. In the large quantum number limit, these matrix elements give the classical solution

Inertial-range structure of Gross–Pitaevskii turbulence within a spectral closure approximation

International Nuclear Information System (INIS)

Yoshida, Kyo; Arimitsu, Toshihico

2013-01-01

The inertial-range structure of turbulence obeying the Gross–Pitaevskii equation, the equation of motion for quantum fluids, is analyzed by means of a spectral closure approximation. It is revealed that, for the energy-transfer range, the spectrum of the order parameter field ψ obeys k −2 law for k ≪ k * and k −1 law for k ≫ k * , where k * is the wavenumber where the characteristic timescales associated with linear and nonlinear terms are of the same order. It is also shown that, for the particle-number-transfer range, the spectrum obeys k −1 law for k ≪ k *, n and k −1/3 law for k ≫ k *,n , where k *,n is the wavenumber corresponding to k * in the particle-number-transfer range. (paper)

Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping

Directory of Open Access Journals (Sweden)

Jieqiong Wu

2015-09-01

Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.

Form-preserving Transformations for the Time-dependent Schroedinger Equation in (n + 1) Dimensions

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2006-01-01

We define a form-preserving transformation (also called point canonical transformation) for the time-dependent Schroedinger equation (TDSE) in (n+1) dimensions. The form-preserving transformation is shown to be invertible and to preserve L 2 -normalizability. We give a class of time-dependent TDSEs that can be mapped onto stationary Schroedinger equations by our form-preserving transformation. As an example, we generate a solvable, time-dependent potential of Coulombic ring-shaped type together with the corresponding exact solution of the TDSE in (3+1) dimensions. We further consider TDSEs with position-dependent (effective) masses and show that there is no form-preserving transformation between them and the conventional TDSEs, if the spatial dimension of the system is higher than one

Simulation of Time-Dependent P3 Equations Using a Semi-Analog Medium

International Nuclear Information System (INIS)

Hadad, K.; Pirouzmand, A.; Suh, Kune Y.

2010-01-01

A wide variety of numerical methods have been introduced to solve the neutron transport equation for reactor calculations. With the state-of-the-art computer technology, successful implementation of higher-order approximation of transport methods (P N , S N , MOC, etc.) may now be feasible. Although these methods have been adaptable to code parallelization techniques, the computational expense remains a significant obstacle and thwarts their implementation in a whole-core, time-dependent methodology. A novel method to remove this problem is based on the method of cellular neural networks (CNN) coupling with the PN method. Parallel data processing in CNN reduces the processing time and makes it possible to solve the time dependent models of neutron transport equation in real time

The master symmetry and time dependent symmetries of the differential–difference KP equation

International Nuclear Information System (INIS)

Khanizadeh, Farbod

2014-01-01

We first obtain the master symmetry of the differential–difference KP equation. Then we show how this master symmetry, through sl(2,C)-representation of the equation, can construct generators of time dependent symmetries. (paper)

Application of Trotter approximation for solving time dependent neutron transport equation

International Nuclear Information System (INIS)

Stancic, V.

1987-01-01

A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)

An elementary solution of the Maxwell equations for a time-dependent source

International Nuclear Information System (INIS)

Rivera, R; Villarroel, D

2002-01-01

We present an elementary solution of the Maxwell equations for a time-dependent source consisting of an infinite solenoid with a current density that increases linearly with time. The geometrical symmetries and the time dependence of the current density make possible a mathematical treatment that does not involve the usual technical difficulties, thus making this presentation suitable for students that are taking a first course in electromagnetism. We also show that the electric field generated by the solenoid can be used to construct an exact solution of the relativistic equation of motion of the electron that takes into account the effect of the radiation. In particular, we derive, in an almost trivial way, the formula for the radiation rate of an electron in circular motion

Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons

Science.gov (United States)

Lekala, M. L.; Chakrabarti, B.; Das, T. K.; Rampho, G. J.; Sofianos, S. A.; Adam, R. M.; Haldar, S. K.

2017-05-01

We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (˜ 3) to very large (˜ 10^7) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter C6. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

Integral equation approach to time-dependent kinematic dynamos in finite domains

International Nuclear Information System (INIS)

Xu Mingtian; Stefani, Frank; Gerbeth, Gunter

2004-01-01

The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α 2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples - the α 2 dynamo model with radially varying α and the Bullard-Gellman model - illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α 2 dynamo in rectangular domains

Time-dependent potential-functional embedding theory

International Nuclear Information System (INIS)

Huang, Chen; Libisch, Florian; Peng, Qing; Carter, Emily A.

2014-01-01

We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na 4 cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na 4 cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods

Integration of the time-dependent heat equation in the fuel rod performance program IAMBUS

International Nuclear Information System (INIS)

West, G.

1982-01-01

An iterative numerical method for integration of the time-dependent heat equation is described. No presuppositions are made for the dependency of the thermal conductivity and heat capacity on space, time and temperature. (orig.) [de

Non-integrability of time-dependent spherically symmetric Yang-Mills equations

International Nuclear Information System (INIS)

Matinyan, S.G.; Prokhorenko, E.V.; Savvidy, G.K.

1986-01-01

The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. The phase space of this system is shown to have no quasi-periodic motion specific for integrable systems. In particular, the well-known Wu-Yang static solution is unstable, so its vicinity in phase is the stochasticity region

On time transformations for differential equations with state-dependent delay

Czech Academy of Sciences Publication Activity Database

Rezunenko, Oleksandr

2014-01-01

Roč. 12, č. 2 (2014), s. 298-307 ISSN 1895-1074 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : differential equations * state-dependent delay * time transformations Subject RIV: BD - Theory of Information Impact factor: 0.578, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/rezunenko-0429130.pdf

The time-dependent Hartree-Fock equations with Coulomb two-body interaction

International Nuclear Information System (INIS)

Chadam, J.M.; Glassey, R.T.

1975-06-01

The existence and uniqueness of global solutions to the Cauchy problem is proved in the space of ''smooth'' density matrices for the time-dependent Hartree-Fock equations describing the motion of finite Fermi systems interacting via a Coulomb two-body potential [fr

Time-Dependent Heat Conduction Problems Solved by an Integral-Equation Approach

International Nuclear Information System (INIS)

Oberaigner, E.R.; Leindl, M.; Antretter, T.

2010-01-01

Full text: A classical task of mathematical physics is the formulation and solution of a time dependent thermoelastic problem. In this work we develop an algorithm for solving the time-dependent heat conduction equation c p ρ∂ t T-kT, ii =0 in an analytical, exact fashion for a two-component domain. By the Green's function approach the formal solution of the problem is obtained. As an intermediate result an integral-equation for the temperature history at the domain interface is formulated which can be solved analytically. This method is applied to a classical engineering problem, i.e. to a special case of a Stefan-Problem. The Green's function approach in conjunction with the integral-equation method is very useful in cases were strong discontinuities or jumps occur. The initial conditions and the system parameters of the investigated problem give rise to two jumps in the temperature field. Purely numerical solutions are obtained by using the FEM (finite element method) and the FDM (finite difference method) and compared with the analytical approach. At the domain boundary the analytical solution and the FEM-solution are in good agreement, but the FDM results show a signicant smearing effect. (author)

Modulated amplitude waves in Bose-Einstein condensates

International Nuclear Information System (INIS)

Porter, Mason A.; Cvitanovic, Predrag

2004-01-01

We analyze spatiotemporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent structure ansatz yields a parametrically forced nonlinear oscillator, to which we apply Lindstedt's method and multiple-scale perturbation theory to determine the dependence of the intensity of periodic orbits ('modulated amplitude waves') on their wave number. We explore BEC band structure in detail using Hamiltonian perturbation theory and supporting numerical simulations

Schemes for loading a Bose-Einstein condensate into a two-dimensional dipole trap

International Nuclear Information System (INIS)

Colombe, Yves; Kadio, Demascoth; Olshanii, Maxim; Mercier, Brigitte; Lorent, Vincent; Perrin, Helene

2003-01-01

We propose two loading mechanisms of a degenerate Bose gas into a surface trap. This trap relies on the dipole potential produced by two evanescent optical waves far detuned from the atomic resonance, yielding a strongly anisotropic trap with typical frequencies 40 Hz x 65 Hz x 30 kHz. We present numerical simulations based on the time-dependent Gross-Pitaevskii equation of the transfer process from a conventional magnetic trap into the surface trap. We show that, despite a large discrepancy between the oscillation frequencies along one direction in the initial and final traps, a loading time of a few tens of milliseconds would lead to an adiabatic transfer. Preliminary experimental results are presented

AIREK-MOD, Time Dependent Reactor Kinetics with Feedback Differential Equation

International Nuclear Information System (INIS)

Tamagnini, C.

1984-01-01

1 - Nature of physical problem solved: Solves the reactor kinetic equations with respect to time. A standard form for the reactivity behaviour has been introduced in which the reactivity is given by the sum of a polynomial, sine, cosine and exponential expansion. Tabular form is also included. The presence of feedback differential equations in which the dependence on variables different from the considered one is considered enables many heat-exchange problems to be dealt with. 2 - Method of solution: The method employed for the solution of the differential equations is the one developed by E.R. Cohen (Geneva Conference, 1958). 3 - Restrictions on the complexity of the problem: The maximum number of differential equations that can be solved simultaneously is 50. Within this limitation there may be n delayed neutron groups (n less than or equal to 25), on m other linear feedback equations (n+m less than or equal to 49). CDC 1604 version was offered by EIR (Institut Federal de Recherches en matiere de reacteurs, Switzerland)

1-Soliton solution of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and time-dependent coefficients

International Nuclear Information System (INIS)

Biswas, Anjan

2009-01-01

In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

Science.gov (United States)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Time dependent solutions of the Fokker-Planck equation for fast fusion ions

International Nuclear Information System (INIS)

Gnavi, G.; Gratton, F.T.; Heyn, M.

1990-01-01

Approximate time dependent solutions for the Fokker-Planck equation for fast fusion ions from an isotropic, monoenergetic source are presented, for the problem of D - T - He 3 reactions. The equations include the effect of diffusion, which is particularly noticeable in the distribution of particles of lower energy and in the formation of a tail of particles with energy higher than that of the source. (Author)

Engineering bright solitons to enhance the stability of two-component Bose-Einstein condensates

Science.gov (United States)

Radha, R.; Vinayagam, P. S.; Sudharsan, J. B.; Liu, Wu-Ming; Malomed, Boris A.

2015-12-01

We consider a system of coupled Gross-Pitaevskii (GP) equations describing a binary quasi-one-dimensional Bose-Einstein condensate (BEC) with intrinsic time-dependent attractive interactions, placed in a time-dependent expulsive parabolic potential, in a special case when the system is integrable (a deformed Manakov's system). Since the nonlinearity in the integrable system which represents binary attractive interactions exponentially decays with time, solitons are also subject to decay. Nevertheless, it is shown that the robustness of bright solitons can be enhanced in this system, making their respective lifetime longer, by matching the time dependence of the interaction strength (adjusted with the help of the Feshbach-resonance management) to the time modulation of the strength of the parabolic potential. The analytical results, and their stability, are corroborated by numerical simulations. In particular, we demonstrate that the addition of random noise does not impact the stability of the solitons.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

Science.gov (United States)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Time-dependent Hartree approximation and time-dependent harmonic oscillator model

International Nuclear Information System (INIS)

Blaizot, J.P.

1982-01-01

We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schroedinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory. (orig.)

Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

International Nuclear Information System (INIS)

Cao Rui; Zhang Jian

2013-01-01

In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions. (general)

Bright matter wave solitons and their collision in Bose-Einstein condensates

International Nuclear Information System (INIS)

Radha, R.; Ramesh Kumar, V.

2007-01-01

We obtain the bright matter wave solitons in Bose-Einstein condensates from a trivial input solution by solving the time dependent Gross-Pitaevskii (GP) equation with quadratic potential and exponentially varying scattering length. We observe that the matter wave density of bright soliton increases with time by virtue of the exponentially increasing scattering length. We also understand that the matter wave densities of bright soliton trains remain finite despite the exchange of atoms during interaction and they travel along different trajectories (diverge) after interaction. We also observe that their amplitudes continue to fluctuate with time. For exponentially decaying scattering lengths, instability sets in the condensates. However, the scattering length can be suitably manipulated without causing the explosion or the collapse of the condensates

Time-dependent simplified PN approximation to the equations of radiative transfer

International Nuclear Information System (INIS)

Frank, Martin; Klar, Axel; Larsen, Edward W.; Yasuda, Shugo

2007-01-01

The steady-state simplified P N approximation to the radiative transport equation has been successfully applied to many problems involving radiation. This paper presents the derivation of time-dependent simplified P N (SP N ) equations (up to N = 3) via two different approaches. First, we use an asymptotic analysis, similar to the asymptotic derivation of the steady-state SP N equations. Second, we use an approach similar to the original derivation of the steady-state SP N equations and we show that both approaches lead to similar results. Special focus is put on the well-posedness of the equations and the question whether it can be guaranteed that the solution satisfies the correct physical bounds. Several numerical test cases are shown, including an analytical benchmark due to Su and Olson [B. Su, G.L. Olson, An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium, Ann. Nucl. Energy 24 (1997) 1035-1055.

Solution of the time-dependent, three-dimensional resistive magnetohydrodynamic equations

International Nuclear Information System (INIS)

Finan, C.H. III; Killeen, J.; California Univ., Davis

1981-01-01

Resistive magnetohydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are expressed as conservation laws, the momentum and energy equations are nonconservative. This is to: (1) provide enhanced numerical stability by eliminating errors introduced by the nonvanishing of nabla x B on the finite difference mesh; and, (2) allow the simulation of low β plasmas. The resulting finite difference equations are a coupled system of nonlinear algebraic equations which are solved by the Newton-Raphson iteration technique. We apply our model to a number of problems of importance in magnetic fusion research. Ideal and resistive internal kink instabilities are simulated in a Cartesian geometry. Growth rates and nonlinear saturation amplitudes are found to be in agreement with previous analytic and numerical predictions. We also simulate these instabilities in a torus, which demonstrates the versatility of the orthogonal curvilinear coordinate representation. (orig.)

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

Energy Technology Data Exchange (ETDEWEB)

Ho, C.-L. [Department of Physics, Tamkang University, Tamsui 25137, Taiwan (China); Lee, C.-C., E-mail: chieh.no27@gmail.com [Center of General Education, Aletheia University, Tamsui 25103, Taiwan (China)

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Electron scattering from the deuteron using the Gross equation

Energy Technology Data Exchange (ETDEWEB)

J.W. Van Orden; N. Devine; F. Gross

1996-01-01

The elastic electromagnetic form factors for the deuteron are calculated in the context of a one-boson-exchange model using the Gross or Spectator equation [1]. The formalism is manifestly covariant and gauge invariant. Results are shown for the impulse approximation and for pxy exchange currents. The impulse approximation results are quite close to the available data which suggests that only a relatively small exchange current contribution is required. It is shown that by using a soft form factor for the exchange current, the model provides a very good representation of the data.

Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

OpenAIRE

Li, Zhiyuan; Huang, Xinchi; Yamamoto, Masahiro

2018-01-01

In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion L...

On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients

Directory of Open Access Journals (Sweden)

Kilic Bulent

2016-01-01

Full Text Available This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE with time dependent coefficients.

Mean-field model for the interference of matter-waves from a three-dimensional optical trap

International Nuclear Information System (INIS)

Adhikari, Sadhan K.; Muruganandam, Paulsamy

2003-01-01

Using the mean-field time-dependent Gross-Pitaevskii equation we study the formation of a repulsive Bose-Einstein condensate on a combined optical and harmonic traps in two and three dimensions and subsequent generation of the interference pattern upon the removal of the combined traps as in the experiment by Greiner et al. [Nature (London) 415 (2002) 39]. For optical traps of moderate strength, interference pattern of 27 (9) prominent bright spots is found to be formed in three (two) dimensions on a cubic (square) lattice in agreement with experiment. Similar interference pattern can also be formed upon removal of the optical lattice trap only. The pattern so formed can oscillate for a long time in the harmonic trap which can be observed experimentally

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

Science.gov (United States)

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Time Dependent Hartree Fock Equation: Gateway to Nonequilibrium Plasmas

International Nuclear Information System (INIS)

Dufty, James W.

2007-01-01

This is the Final Technical Report for DE-FG02-2ER54677 award 'Time Dependent Hartree Fock Equation - Gateway to Nonequilibrium Plasmas'. Research has focused on the nonequilibrium dynamics of electrons in the presence of ions, both via basic quantum theory and via semi-classical molecular dynamics (MD) simulation. In addition, fundamental notions of dissipative dynamics have been explored for models of grains and dust, and for scalar fields (temperature) in turbulent edge plasmas. The specific topics addressed were Quantum Kinetic Theory for Metallic Clusters, Semi-classical MD Simulation of Plasmas , and Effects of Dissipative Dynamics.

A Derivation of Source-based Kinetics Equation with Time Dependent Fission Kernel for Reactor Transient Analyses

International Nuclear Information System (INIS)

Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho; Pyeon, Cheol Ho

2015-01-01

In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r g , E g , t g ) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the neutron sources

Stability of BEC galactic dark matter halos

Energy Technology Data Exchange (ETDEWEB)

Guzmán, F.S.; Lora-Clavijo, F.D.; González-Avilés, J.J.; Rivera-Paleo, F.J., E-mail: guzman@ifm.umich.mx, E-mail: fadulora@ifm.umich.mx, E-mail: javiles@ifm.umich.mx, E-mail: friverap@ifm.umich.mx [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Cd. Universitaria, 58040 Morelia, Michoacán (Mexico)

2013-09-01

In this paper we show that spherically symmetric BEC dark matter halos, with the sin r/r density profile, that accurately fit galactic rotation curves and represent a potential solution to the cusp-core problem are unstable. We do this by introducing back the density profiles into the fully time-dependent Gross-Pitaevskii-Poisson system of equations. Using numerical methods to track the evolution of the system, we found that these galactic halos lose mass at an approximate rate of half of its mass in a time scale of dozens of Myr. We consider this time scale is enough as to consider these halos are unstable and unlikely to be formed. We provide some arguments to show that this behavior is general and discuss some other drawbacks of the model that restrict its viability.

Competing role of interactions in synchronisation of exciton-polariton condensates

Science.gov (United States)

Khan, Saeed A.; Türeci, Hakan E.

2017-10-01

We present a theoretical study of synchronisation dynamics of incoherently pumped exciton-polariton condensates in coupled polariton traps. Our analysis is based on a coupled-mode theory for the generalised Gross-Pitaevskii equation, which employs an expansion in non-Hermitian, pump-dependent modes appropriate for the pumped geometry. We find that polariton-polariton and reservoir-polariton interactions play competing roles and lead to qualitatively different synchronised phases of the coupled polariton modes as pumping power is increased. Crucially, these interactions can also act against each other to hinder synchronisation. We map out a phase diagram and discuss the general characteristics of these phases using a generalised Adler equation.

Boundary-integral equation formulation for time-dependent inelastic deformation in metals

Energy Technology Data Exchange (ETDEWEB)

Kumar, V; Mukherjee, S

1977-01-01

The mathematical structure of various constitutive relations proposed in recent years for representing time-dependent inelastic deformation behavior of metals at elevated temperatues has certain features which permit a simple formulation of the three-dimensional inelasticity problem in terms of real time rates. A direct formulation of the boundary-integral equation method in terms of rates is discussed for the analysis of time-dependent inelastic deformation of arbitrarily shaped three-dimensional metallic bodies subjected to arbitrary mechanical and thermal loading histories and obeying constitutive relations of the kind mentioned above. The formulation is based on the assumption of infinitesimal deformations. Several illustrative examples involving creep of thick-walled spheres, long thick-walled cylinders, and rotating discs are discussed. The implementation of the method appears to be far easier than analogous BIE formulations that have been suggested for elastoplastic problems.

Time-dependent embedding

OpenAIRE

Inglesfield, J. E.

2007-01-01

A method of solving the time-dependent Schr\\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an embedding term added on to the Hamiltonian. This time-dependent embedding term is derived from the Fourier transform of the energy-dependent embedding potential, which embeds the time-independent Schr\\"odinger equation. Results are presented for a one-dimensi...

Numerical method for solving the three-dimensional time-dependent neutron diffusion equation

International Nuclear Information System (INIS)

Khaled, S.M.; Szatmary, Z.

2005-01-01

A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)

Stability of the Filter Equation for a Time-Dependent Signal on Rd

International Nuclear Information System (INIS)

Stannat, Wilhelm

2005-01-01

Stability of the pathwise filter equation for a time-dependent signal process induced by a d-dimensional stochastic differential equation and a linear observation is studied, using a variational approach. A lower bound for the rate of stability is identified in terms of the mass-gap of a parabolic ground state transform associated with the generator of the signal process and the square of the observation. The lower bound can be easily calculated a priori and provides hints on how precisely to measure the signal in order to reach a certain rate of stability. Ergodicity of the signal process is not needed

A Derivation of Source-based Kinetics Equation with Time Dependent Fission Kernel for Reactor Transient Analyses

Energy Technology Data Exchange (ETDEWEB)

Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho [Hanyang University, Seoul (Korea, Republic of); Pyeon, Cheol Ho [Kyoto University, Osaka (Japan)

2015-10-15

In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r{sub g}, E{sub g}, t{sub g}) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the

Solution of the time-dependent inertial-frame equation of radiative transfer in moving media to O(v/c)

International Nuclear Information System (INIS)

Mihalas, D.; Klein, R.I.

1982-01-01

A stable and efficient mixed-frame method has been formulated for the solution of the time-dependent equation of radiative transfer with full retention of all velocity dependent terms to O(ν/c). The method retains the simplicity of the differential operator found in the inertial frame while transforming the absorption and emission coefficients to the comoving frame keeping them isotropic. The method is ideally suited to continuum calculations. To correctly treat the time dependence of the radiation field over fluid-flow time increments, the velocity-dependent terms on the right-hand side of both the transfer and moment equations must be retained for consistency

Time-dependent density functional theory for open quantum systems with unitary propagation.

Science.gov (United States)

Yuen-Zhou, Joel; Tempel, David G; Rodríguez-Rosario, César A; Aspuru-Guzik, Alán

2010-01-29

We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.

Solitons in a hard-core bosonic system: Gross–Pitaevskii type and ...

Indian Academy of Sciences (India)

2015-10-20

Oct 20, 2015 ... Solitons in a hard-core bosonic system: Gross–Pitaevskii type and beyond ... the corresponding class of magnetic solitons in Heisenberg spin chains with different types of anisotropy. ... Pramana – Journal of Physics | News.

Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing

Directory of Open Access Journals (Sweden)

Lianbing She

2018-01-01

Full Text Available This paper deals with pullback dynamics for the weakly damped Schrödinger equation with time-dependent forcing. An increasing, bounded, and pullback absorbing set is obtained if the forcing and its time-derivative are backward uniformly integrable. Also, we obtain the forward absorption, which is only used to deduce the backward compact-decay decomposition according to high and low frequencies. Based on a new existence theorem of a backward compact pullback attractor, we show that the nonautonomous Schrödinger equation has a pullback attractor which is compact in the past. The method of energy, high-low frequency decomposition, Sobolev embedding, and interpolation are quite involved in calculating a priori pullback or forward bound.

Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

KAUST Repository

Said-Houari, Belkacem

2012-03-01

In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.

Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

KAUST Repository

Said-Houari, Belkacem

2012-01-01

In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.

Matter-wave interference, Josephson oscillation and its disruption in a Bose-Einstein condensate on an optical lattice

International Nuclear Information System (INIS)

Adhikari, Sadhan K.

2004-01-01

Using the axially-symmetric time-dependent mean-field Gross-Pitaevskii equation we study the Josephson oscillation in a repulsive Bose-Einstein condensate trapped by a harmonic plus an one-dimensional optical-lattice potential to describe the experiments by Cataliotti et al. [Science 293 (2001) 843, New J. Phys. 5 (2003) 71.1]. After a study of the formation of matter-wave interference upon releasing the condensate from the optical trap, we directly investigate the alternating atomic superfluid Josephson current upon displacing the harmonic trap along the optical axis. The Josephson current is found to be disrupted upon displacing the harmonic trap through a distance greater than a critical distance signaling a superfluid to a classical insulator transition in the condensate

Time-dependent integral transport equation kernels, leakage rates and collision rates for plane and spherical geometry

International Nuclear Information System (INIS)

Henderson, D.L.

1987-01-01

Time-dependent integral transport equation flux and current kernels for plane and spherical geometry are derived for homogeneous media. Using the multiple collision formalism, isotropic sources that are delta distributions in time are considered for four different problems. The plane geometry flux kernel is applied to a uniformly distributed source within an infinite medium and to a surface source in a semi-infinite medium. The spherical flux kernel is applied to a point source in an infinite medium and to a point source at the origin of a finite sphere. The time-dependent first-flight leakage rates corresponding to the existing steady state first-flight escape probabilities are computed by the Laplace transform technique assuming a delta distribution source in time. The case of a constant source emitting neutrons over a time interval, Δt, for a spatially uniform source is obtained for a slab and a sphere. Time-dependent first-flight leakage rates are also determined for the general two region spherical medium problem for isotropic sources with a delta distribution in time uniformly distributed throughout both the inner and outer regions. The time-dependent collision rates due to the uncollided neutrons are computed for a slab and a sphere using the time-dependent first-flight leakage rates and the time-dependent continuity equation. The case of a constant source emitting neutrons over a time interval, Δt, is also considered

Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice

International Nuclear Information System (INIS)

Kevrekidis, P. G.; Carretero-Gonzalez, R.; Theocharis, G.; Frantzeskakis, D. J.; Malomed, B. A.

2003-01-01

We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis is based on both the full Gross-Pitaevskii equation and its tight-binding approximation counterpart (discrete nonlinear Schroedinger equation). We find that DSs are subject to weak instabilities with an onset of instability mainly governed by the period and amplitude of the OL. The instability, if present, sets in at large times and it is characterized by quasiperiodic oscillations of the DS about the minimum of the parabolic trap

Application of the multigrid amplitude function method for time-dependent transport equation using MOC

International Nuclear Information System (INIS)

Tsujita, K.; Endo, T.; Yamamoto, A.

2013-01-01

An efficient numerical method for time-dependent transport equation, the mutigrid amplitude function (MAF) method, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, efficient kinetic calculation method for MOC is still desirable since it requires significant computation time. Various efficient numerical methods for solving the space-dependent kinetic equation, e.g., the improved quasi-static (IQS) and the frequency transform methods, have been developed so far mainly for diffusion calculation. These calculation methods are known as effective numerical methods and they offer a way for faster computation. However, they have not been applied to the kinetic calculation method using MOC as the authors' knowledge. Thus, the MAF method is applied to the kinetic calculation using MOC aiming to reduce computation time. The MAF method is a unified numerical framework of conventional kinetic calculation methods, e.g., the IQS, the frequency transform, and the theta methods. Although the MAF method is originally developed for the space-dependent kinetic calculation based on the diffusion theory, it is extended to transport theory in the present study. The accuracy and computational time are evaluated though the TWIGL benchmark problem. The calculation results show the effectiveness of the MAF method. (authors)

Space-time Dependency of the Time and its Effect on the Relativistic Classical Equation of the String Theory

Science.gov (United States)

Gholibeigian, Hassan; Amirshahkarami, Abdolazim; Gholibeigian, Kazem

2017-01-01

In special relativity theory, time dilates in velocity of near light speed. Also based on ``Substantial motion'' theory of Sadra, relative time (time flux); R = f (mv , σ , τ) , for each atom is momentum of its involved fundamental particles, which is different from the other atoms. In this way, for modification of the relativistic classical equation of string theory and getting more precise results, we should use effect of dilation and contraction of time in equation. So we propose to add two derivatives of the time's flux to the equation as follows: n.tp∂/R ∂ τ +∂2Xμ/(σ , τ) ∂τ2 = n .tp (∂/R ∂ σ ) +c2∂2Xμ/(σ , τ) ∂σ2 In which, Xμ is space-time coordinates of the string, σ & τ are coordinates on the string world sheet, respectively space and time along the string, string's mass m , velocity of string's motion v , factor n depends on geometry of each hidden extra dimension which relates to its own flux time, and tp is Planck's time. AmirKabir University of Technology, Tehran, Iran.

Solution to the monoenergetic time-dependent neutron transport equation with a time-varying source

International Nuclear Information System (INIS)

Ganapol, B.D.

1986-01-01

Even though fundamental time-dependent neutron transport problems have existed since the inception of neutron transport theory, it has only been recently that a reliable numerical solution to one of the basic problems has been obtained. Experience in generating numerical solutions to time-dependent transport equations has indicated that the multiple collision formulation is the most versatile numerical technique for model problems. The formulation coupled with a moment reconstruction of each collided flux component has led to benchmark-quality (four- to five-digit accuracy) numerical evaluation of the neutron flux in plane infinite geometry for any degree of scattering anisotropy and for both pulsed isotropic and beam sources. As will be shown in this presentation, this solution can serve as a Green's function, thus extending the previous results to more complicated source situations. Here we will be concerned with a time-varying source at the center of an infinite medium. If accurate, such solutions have both pedagogical and practical uses as benchmarks against which other more approximate solutions designed for a wider class of problems can be compared

The truncated Wigner method for Bose-condensed gases: limits of validity and applications

International Nuclear Information System (INIS)

Sinatra, Alice; Lobo, Carlos; Castin, Yvan

2002-01-01

We study the truncated Wigner method applied to a weakly interacting spinless Bose-condensed gas which is perturbed away from thermal equilibrium by a time-dependent external potential. The principle of the method is to generate an ensemble of classical fields ψ(r) which samples the Wigner quasi-distribution function of the initial thermal equilibrium density operator of the gas, and then to evolve each classical field with the Gross-Pitaevskii equation. In the first part of the paper we improve the sampling technique over our previous work (Sinatra et al 2000 J. Mod. Opt. 47 2629-44) and we test its accuracy against the exactly solvable model of the ideal Bose gas. In the second part of the paper we investigate the conditions of validity of the truncated Wigner method. For short evolution times it is known that the time-dependent Bogoliubov approximation is valid for almost pure condensates. The requirement that the truncated Wigner method reproduces the Bogoliubov prediction leads to the constraint that the number of field modes in the Wigner simulation must be smaller than the number of particles in the gas. For longer evolution times the nonlinear dynamics of the noncondensed modes of the field plays an important role. To demonstrate this we analyse the case of a three-dimensional spatially homogeneous Bose-condensed gas and we test the ability of the truncated Wigner method to correctly reproduce the Beliaev-Landau damping of an excitation of the condensate. We have identified the mechanism which limits the validity of the truncated Wigner method: the initial ensemble of classical fields, driven by the time-dependent Gross-Pitaevskii equation, thermalizes to a classical field distribution at a temperature T class which is larger than the initial temperature T of the quantum gas. When T class significantly exceeds T a spurious damping is observed in the Wigner simulation. This leads to the second validity condition for the truncated Wigner method, T class - T

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

Science.gov (United States)

Zhu, Ying; Herbert, John M.

2018-01-01

The "real time" formulation of time-dependent density functional theory (TDDFT) involves integration of the time-dependent Kohn-Sham (TDKS) equation in order to describe the time evolution of the electron density following a perturbation. This approach, which is complementary to the more traditional linear-response formulation of TDDFT, is more efficient for computation of broad-band spectra (including core-excited states) and for systems where the density of states is large. Integration of the TDKS equation is complicated by the time-dependent nature of the effective Hamiltonian, and we introduce several predictor/corrector algorithms to propagate the density matrix, one of which can be viewed as a self-consistent extension of the widely used modified-midpoint algorithm. The predictor/corrector algorithms facilitate larger time steps and are shown to be more efficient despite requiring more than one Fock build per time step, and furthermore can be used to detect a divergent simulation on-the-fly, which can then be halted or else the time step modified.

Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods.

Science.gov (United States)

Gómez Pueyo, Adrián; Marques, Miguel A L; Rubio, Angel; Castro, Alberto

2018-05-09

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

Collision of bright vector solitons in two-component Bose-Einstein condensates

International Nuclear Information System (INIS)

Ramesh Kumar, V.; Radha, R.; Wadati, Miki

2010-01-01

We investigate the coupled Gross-Pitaevskii equation describing the dynamics of two hyperfine states of Bose-Einstein condensates and deduce the integrability condition for the propagation of bright vector solitons. We show how the transient trap and scattering length can be suitably tailored to bring about fascinating collisional dynamics of vector solitons.

Angular distribution of scission neutrons studied with time-dependent Schrödinger equation

Science.gov (United States)

Wada, Takahiro; Asano, Tomomasa; Carjan, Nicolae

2018-03-01

We investigate the angular distribution of scission neutrons taking account of the effects of fission fragments. The time evolution of the wave function of the scission neutron is obtained by integrating the time-dependent Schrodinger equation numerically. The effects of the fission fragments are taken into account by means of the optical potentials. The angular distribution is strongly modified by the presence of the fragments. In the case of asymmetric fission, it is found that the heavy fragment has stronger effects. Dependence on the initial distribution and on the properties of fission fragments is discussed. We also discuss on the treatment of the boundary to avoid artificial reflections

Time-dependent density functional theory for multi-component systems

International Nuclear Information System (INIS)

Tiecheng Li; Peiqing Tong

1985-10-01

The Runge-Gross version of Hohenberg-Kohn-Sham's density functional theory is generalized to multi-component systems, both for arbitrary time-dependent pure states and for arbitrary time-dependent ensembles. (author)

Multi-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients

International Nuclear Information System (INIS)

Liao Cui-Cui; Cui Jin-Chao; Liang Jiu-Zhen; Ding Xiao-Hua

2016-01-01

In this paper, we propose a variational integrator for nonlinear Schrödinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrödinger equations with variable coefficients, cubic nonlinear Schrödinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space. (paper)

Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.

Science.gov (United States)

Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht

2013-09-21

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.

Time-dependent Schroedinger equations with effective mass in (2 + 1) dimensions: intertwining relations and Darboux operators

International Nuclear Information System (INIS)

Cobian, Hector; Schulze-Halberg, Axel

2011-01-01

We construct Darboux transformations for time-dependent Schroedinger equations with position-dependent mass in (2 + 1) dimensions. Several examples illustrate our results, which complement and generalize former findings for the constant mass case in two spatial variables (Schulze-Halberg 2010 J. Math. Phys. 51 033521).

Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations

Directory of Open Access Journals (Sweden)

Matt Challacombe

2014-03-01

Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.

Optimal conversion of an atomic to a molecular Bose-Einstein condensate

International Nuclear Information System (INIS)

Hornung, Thomas; Gordienko, Sergei; Vivie-Riedle, Regina de; Verhaar, Boudewijn J.

2002-01-01

The work in this article extends the optimal control framework of variational calculus to optimize the conversion of a Bose-Einstein condensate of atoms to one of molecules. It represents the derivation of the closed form optimal control equations for a system governed by a nonlinear Schroedinger equation and its successful application. It was necessary to derive a density matrix formulation of the coupled Gross-Pitaevskii equations to optimize STIRAP-like Raman light fields, to overcome dissipation

Determination of parameters for a stress-strain constitutive equation considering time-dependent behavior of Toki granite

International Nuclear Information System (INIS)

Hirano, Toru; Seno, Yasuhiro; Nakama, Shigeo; Okubo, Seisuke

2008-01-01

Toki granite was tested to obtain parameters for the constitutive equation. The testing method was uniaxial compressive loading at the moderate a constant strain rate that is decreased after yielding to obtain the complete stress-strain curve. In addition, two kinds of the strain rate were alternately switched to obtain the parameter n from one specimen. The n represents the strength time-dependence in the constitutive equation. The second parameter m can be obtained by fitting the experimental stress-strain curve to the calculated curve. The m accounts for the behavior after yielding. According to the results, Toki granite has n=52 and m=60, showing relatively weak time-dependence of creep failure. (author)

Quantum trajectories for time-dependent adiabatic master equations

Science.gov (United States)

Yip, Ka Wa; Albash, Tameem; Lidar, Daniel A.

2018-02-01

We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension N instead of a complex density matrix of dimension N2, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor N advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor N2 is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for 8-qubit quantum annealing examples. We also apply the quantum trajectories method to a 16-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.

Solution of time dependent atmospheric diffusion equation with a proposed diffusion coefficient

International Nuclear Information System (INIS)

Mayhoub, A.B.; Essa, KH.S.M.; Aly, SH.

2004-01-01

One-dimensional model for the dispersion of passive atmospheric contaminant (not included chemical reactions) in the atmospheric boundary layer is considered. On the basis of the gradient transfer theory (K-theory), the time dependent diffusion equation represents the dispersion of the pollutants is solved analytically. The solution depends on diffusion coefficient K', which is expressed in terms of the friction velocity 'u the vertical coordinate -L and the depth of the mixing layer 'h'. The solution is obtained to either the vertical coordinate 'z' is less or greater than the mixing height 'h'. The obtained solution may be applied to study the atmospheric dispersion of pollutants

A Solution of Time Dependent Schrodinger Equation by Quantum Walk

International Nuclear Information System (INIS)

Sekino, Hideo; Kawahata, Masayuki; Hamada, Shinji

2012-01-01

Time Dependent Schroedinger Equation (TDSE) with an initial Gaussian distribution, is solved by a discrete time/space Quantum Walk (QW) representing consecutive operations corresponding to a dot product of Pauli matrix and momentum operators. We call it as Schroedinger Walk (SW). Though an Hadamard Walk (HW) provides same dynamics of the probability distribution for delta-function-like initial distributions as that of the SW with a delta-function-like initial distribution, the former with a Gaussian initial distribution leads to a solution for advection of the probability distribution; the initial distribution splits into two distinctive distributions moving in opposite directions. Both mechanisms are analysed by investigating the evolution of the both amplitude components. Decoherence of the oscillating amplitudes in central region is found to be responsible for the splitting of the probability distribution in the HW.

Delay differential equations and the dose-time dependence of early radiotherapy reactions

International Nuclear Information System (INIS)

Fenwick, John D.

2006-01-01

The dose-time dependence of early radiotherapy reactions impacts on the design of accelerated fractionation schedules--oral mucositis, for example, can be dose limiting for short treatments designed to avoid tumor repopulation. In this paper a framework for modeling early reaction dose-time dependence is developed. Variation of stem cell number with time after the start of a radiation schedule is modeled using a first-order delay differential equation (DDE), motivated by experimental observations linking the speed of compensatory proliferation in early reacting tissues to the degree of tissue damage. The modeling suggests that two types of early reaction radiation response are possible, stem cell numbers either monotonically approaching equilibrium plateau levels or overshooting before returning to equilibrium. Several formulas have been derived from the delay differential equation, predicting changes in isoeffective total radiation dose with schedule duration for different types of fractionation scheme. The formulas have been fitted to a wide range of published animal early reaction data, the fits all implying a degree of overshoot. Results are presented illustrating the scope of the delay differential model: most of the data are fitted well, although the model struggles with a few datasets measured for schedules with distinctive dose-time patterns. Ways of extending the current model to cope with these particular dose-time patterns are briefly discussed. The DDE approach is conceptually more complex than earlier descriptive dose-time models but potentially more powerful. It can be used to study issues not addressed by simpler models, such as the likely effects of increasing or decreasing the dose-per-day over time, or of splitting radiation courses into intense segments separated by gaps. It may also prove useful for modeling the effects of chemoirradiation

Delay differential equations and the dose-time dependence of early radiotherapy reactions.

Science.gov (United States)

Fenwick, John D

2006-09-01

The dose-time dependence of early radiotherapy reactions impacts on the design of accelerated fractionation schedules--oral mucositis, for example, can be dose limiting for short treatments designed to avoid tumor repopulation. In this paper a framework for modeling early reaction dose-time dependence is developed. Variation of stem cell number with time after the start of a radiation schedule is modeled using a first-order delay differential equation (DDE), motivated by experimental observations linking the speed of compensatory proliferation in early reacting tissues to the degree of tissue damage. The modeling suggests that two types of early reaction radiation response are possible, stem cell numbers either monotonically approaching equilibrium plateau levels or overshooting before returning to equilibrium. Several formulas have been derived from the delay differential equation, predicting changes in isoeffective total radiation dose with schedule duration for different types of fractionation scheme. The formulas have been fitted to a wide range of published animal early reaction data, the fits all implying a degree of overshoot. Results are presented illustrating the scope of the delay differential model: most of the data are fitted well, although the model struggles with a few datasets measured for schedules with distinctive dose-time patterns. Ways of extending the current model to cope with these particular dose-time patterns are briefly discussed. The DDE approach is conceptually more complex than earlier descriptive dose-time models but potentially more powerful. It can be used to study issues not addressed by simpler models, such as the likely effects of increasing or decreasing the dose-per-day over time, or of splitting radiation courses into intense segments separated by gaps. It may also prove useful for modeling the effects of chemoirradiation.

Effective equations for matter-wave gap solitons in higher-order transversal states.

Science.gov (United States)

Mateo, A Muñoz; Delgado, V

2013-10-01

We demonstrate that an important class of nonlinear stationary solutions of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) exhibiting nontrivial transversal configurations can be found and characterized in terms of an effective one-dimensional (1D) model. Using a variational approach we derive effective equations of lower dimensionality for BECs in (m,n(r)) transversal states (states featuring a central vortex of charge m as well as n(r) concentric zero-density rings at every z plane) which provides us with a good approximate solution of the original 3D problem. Since the specifics of the transversal dynamics can be absorbed in the renormalization of a couple of parameters, the functional form of the equations obtained is universal. The model proposed finds its principal application in the study of the existence and classification of 3D gap solitons supported by 1D optical lattices, where in addition to providing a good estimate for the 3D wave functions it is able to make very good predictions for the μ(N) curves characterizing the different fundamental families. We have corroborated the validity of our model by comparing its predictions with those from the exact numerical solution of the full 3D GPE.

Alternating-direction implicit numerical solution of the time-dependent, three-dimensional, single fluid, resistive magnetohydrodynamic equations

Energy Technology Data Exchange (ETDEWEB)

Finan, C.H. III

1980-12-01

Resistive magnetohydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are solved simultaneously to avoid syncronization errors.

Darboux transformations for the time-dependent nonhomogeneous Burgers equation in (1+1) dimensions

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; Manuel Carballo Jimenez, Juan

2009-01-01

We extend the formalism of nth order Darboux transformations to the time-dependent nonhomogeneous Burgers equation (NBE) in (1+1) dimensions. Similar to the Schroedinger case, our Darboux transformation retains the form of the NBE, while changing the nonhomogeneous term. The transformed solution of the NBE and the corresponding transformed nonhomogeneity are given in closed form. Furthermore, properties of the transformation are discussed and an application is given.

Time dependent resonating Hartree-Bogoliubov theory

International Nuclear Information System (INIS)

Nishiyama, Seiya; Fukutome, Hideo.

1989-01-01

Very recently, we have developed a theory of excitations in superconducting Fermion systems with large quantum fluctuations that can be described by resonance of time dependent non-orthogonal Hartree-Bogoliubov (HB) wave functions with different correlation structures. We have derived a new kind of variation equation called the time dependent Resonating HB equation, in order to determine both the time dependent Resonating HB wave functions and coefficients of a superposition of the HB wave functions. Further we have got a new approximation for excitations from time dependent small fluctuations of the Resonating HB ground state, i.e., the Resonating HB RPA. The Res HB RPA equation is represented in a given single particle basis. It, however, has drawbacks that the constraints for the Res HB RPA amplitudes are not taken into account and the equation contains equations which are not independent. We shall derive another form of the Res HB RPA equation eliminating these drawbacks. The Res HB RPA gives a unified description of the vibrons and resonons and their interactions. (author)

Vortex lattices in binary mixtures of repulsive superfluids

Science.gov (United States)

Mingarelli, Luca; Keaveny, Eric E.; Barnett, Ryan

2018-04-01

We present an extension of the framework introduced in previous work [L. Mingarelli, E. E. Keaveny, and R. Barnett, J. Phys.: Condens. Matter 28, 285201 (2016), 10.1088/0953-8984/28/28/285201] to treat multicomponent systems, showing that new degrees of freedom are necessary in order to obtain the desired boundary conditions. We then apply this extended framework to the coupled Gross-Pitaevskii equations to investigate the ground states of two-component systems with equal masses, thereby extending previous work in the lowest Landau limit [E. J. Mueller and T.-L. Ho, Phys. Rev. Lett. 88, 180403 (2002), 10.1103/PhysRevLett.88.180403] to arbitrary interactions within Gross-Pitaevskii theory. We show that away from the lowest Landau level limit, the predominant vortex lattice consists of two interlaced triangular lattices. Finally, we derive a linear relation which accurately describes the phase boundaries in the strong interacting regimes.

Uniform in N global well-posedness of the time-dependent Hartree-Fock-Bogoliubov equations in R^{1+1}

Science.gov (United States)

Chong, Jacky Jia Wei

2018-04-01

We prove the global well-posedness of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations in R^{1+1} with two-body interaction potential of the form N^{-1}v_N(x) = N^{β -1} v(N^β x) where v≥0 is a sufficiently regular radial function, i.e., v \\in L^1(R)\\cap C^∞ (R) . In particular, using methods of dispersive PDEs similar to the ones used in Grillakis and Machedon (Commun Partial Differ Equ 42:24-67, 2017), we are able to show for any scaling parameter β >0 the TDHFB equations are globally well-posed in some Strichartz-type spaces independent of N, cf. (Bach et al. in The time-dependent Hartree-Fock-Bogoliubov equations for Bosons, 2016. arXiv:1602.05171).

Thermalization of a quenched Bose-Josephson junction

Energy Technology Data Exchange (ETDEWEB)

Posazhennikova, Anna [Royal Holloway, University of London (United Kingdom); Trujillo-Martinez, Mauricio; Kroha, Johann [Universitaet Bonn (Germany)

2015-07-01

The experimental realization and control of quantum systems isolated from the environment, in ultracold atomic gases relaunched the interest in the fundamental non-equilibrium problem of how a finite system approaches thermal equilibrium. Despite intensive research there is still no conclusive answer to this question. We investigate theoretically how a quenched Bose-Josephson junction, where the Josephson coupling is switched on instantaneously, approaches its stationary state. We use the field theoretical approach for bosons out of equilibrium in a trap with discrete levels, developed by us previously. In this approach the operators for Bose-Einstein condensate (BEC) particles are treated on mean-field level, while excitations of the Bose gas in higher trap levels are treated fully quantum-mechanically. This leads to coupled equations of motion for the BEC amplitudes (Gross-Pitaevskii equation) and the quasiparticle propagators. The inelastic quasiparticle collisions responsible for the system relaxation during the time-dependent evolution are described within self-consistent second-order approximation.

Onto the stability analysis of hyperbolic secant-shaped Bose-Einstein condensate

Science.gov (United States)

Sabari, S.; Murali, R.

2018-05-01

We analyze the stability of the hyperbolic secant-shaped attractive Bose-Einstein condensate in the absence of external trapping potential. The appropriate theoretical model for the system is described by the nonlinear mean-field Gross-Pitaevskii equation with time varying two-body interaction effects. Using the variational method, the stability of the system is analyzed under the influence of time varying two-body interactions. Further we confirm that the stability of the attractive condensate increases by considering the hyperbolic secant-shape profile instead of Gaussian shape. The analytical results are compared with the numerical simulation by employing the split-step Crank-Nicholson method.

Component separation in harmonically trapped boson-fermion mixtures

DEFF Research Database (Denmark)

Nygaard, Nicolai; Mølmer, Klaus

1999-01-01

We present a numerical study of mixed boson-fermion systems at zero temperature in isotropic and anise tropic harmonic traps. We investigate the phenomenon of component separation as a function of the strength ut the interparticle interaction. While solving a Gross-Pitaevskii mean-field equation ...... for the boson distribution in the trap, we utilize two different methods to extract the density profile of the fermion component; a semiclassical Thomas-Fermi approximation and a quantum-mechanical Slater determinant Schrodinger equation....

Global existence of solutions to the Cauchy problem for time-dependent Hartree equations

International Nuclear Information System (INIS)

Chadam, J.M.; Glassey, R.T.

1975-01-01

The existence of global solutions to the Cauchy problem for time-dependent Hartree equations for N electrons is established. The solution is shown to have a uniformly bounded H 1 (R 3 ) norm and to satisfy an estimate of the form two parallel PSI (t) two parallel/sub H 2 ; less than or equal to c exp(kt). It is shown that ''negative energy'' solutions do not converge uniformly to zero as t → infinity. (U.S.)

Rhodium SPND's Error Reduction using Extended Kalman Filter combined with Time Dependent Neutron Diffusion Equation

International Nuclear Information System (INIS)

Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su

2014-01-01

The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core

Rhodium SPND's Error Reduction using Extended Kalman Filter combined with Time Dependent Neutron Diffusion Equation

Energy Technology Data Exchange (ETDEWEB)

Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su [FNC Technology Co., Ltd., Yongin (Korea, Republic of)

2014-05-15

The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core.

An implicit fast Fourier transform method for integration of the time dependent Schrodinger or diffusion equation

International Nuclear Information System (INIS)

Ritchie, A.B.; Riley, M.E.

1997-06-01

The authors have found that the conventional exponentiated split operator procedure is subject to difficulties in energy conservation when solving the time-dependent Schrodinger equation for Coulombic systems. By rearranging the kinetic and potential energy terms in the temporal propagator of the finite difference equations, one can find a propagation algorithm for three dimensions that looks much like the Crank-Nicholson and alternating direction implicit methods for one- and two-space-dimensional partial differential equations. They report comparisons of this novel implicit split operator procedure with the conventional exponentiated split operator procedure on hydrogen atom solutions. The results look promising for a purely numerical approach to certain electron quantum mechanical problems

State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

Science.gov (United States)

Korayem, M H; Nekoo, S R

2015-07-01

This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

A stable computational scheme for stiff time-dependent constitutive equations

International Nuclear Information System (INIS)

Shih, C.F.; Delorenzi, H.G.; Miller, A.K.

1977-01-01

Viscoplasticity and creep type constitutive equations are increasingly being employed in finite element codes for evaluating the deformation of high temperature structural members. These constitutive equations frequently exhibit stiff regimes which makes an analytical assessment of the structure very costly. A computational scheme for handling deformation in stiff regimes is proposed in this paper. By the finite element discretization, the governing partial differential equations in the spatial (x) and time (t) variables are reduced to a system of nonlinear ordinary differential equations in the independent variable t. The constitutive equations are expanded in a Taylor's series about selected values of t. The resulting system of differential equations are then integrated by an implicit scheme which employs a predictor technique to initiate the Newton-Raphson procedure. To examine the stability and accuracy of the computational scheme, a series of calculations were carried out for uniaxial specimens and thick wall tubes subjected to mechanical and thermal loading. (Auth.)

Spectral fitting method for the solution of time-dependent Schroedinger equations: Applications to atoms in intense laser fields

International Nuclear Information System (INIS)

Qiao Haoxue; Cai Qingyu; Rao Jianguo; Li Baiwen

2002-01-01

A spectral fitting method for solving the time-dependent Schroedinger equation has been developed and applied to the atom in intense laser fields. This method allows us to obtain a highly accurate time-dependent wave function with a contribution from the high-order term of Δt. Moreover, the time-dependent wave function is determined on a small number of discrete mesh points, thus making calculations simple and accurate. This method is illustrated by computing wave functions and harmonic generation spectra of a model atom in laser fields

Producing superfluid circulation states using phase imprinting

Science.gov (United States)

Kumar, Avinash; Dubessy, Romain; Badr, Thomas; De Rossi, Camilla; de Goër de Herve, Mathieu; Longchambon, Laurent; Perrin, Hélène

2018-04-01

We propose a method to prepare states of given quantized circulation in annular Bose-Einstein condensates (BEC) confined in a ring trap using the method of phase imprinting without relying on a two-photon angular momentum transfer. The desired phase profile is imprinted on the atomic wave function using a short light pulse with a tailored intensity pattern generated with a spatial light modulator. We demonstrate the realization of "helicoidal" intensity profiles suitable for this purpose. Due to the diffraction limit, the theoretical steplike intensity profile is not achievable in practice. We investigate the effect of imprinting an intensity profile smoothed by a finite optical resolution onto the annular BEC with a numerical simulation of the time-dependent Gross-Pitaevskii equation. This allows us to optimize the intensity pattern for a given target circulation to compensate for the limited resolution.

From Feshbach-resonance managed Bose-Einstein condensates to anisotropic universes: Applications of the Ermakov-Pinney equation with time-dependent nonlinearity

International Nuclear Information System (INIS)

Herring, G.; Kevrekidis, P.G.; Williams, F.; Christodoulakis, T.; Frantzeskakis, D.J.

2008-01-01

In this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov-Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to 'engineer' trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how similar time-dependent EP equations may arise in the description of anisotropic scalar field cosmologies

From Feshbach-resonance managed Bose-Einstein condensates to anisotropic universes: Applications of the Ermakov-Pinney equation with time-dependent nonlinearity

International Nuclear Information System (INIS)

Herring, G.; Kevrekidis, P.G.; Williams, F.; Christodoulakis, T.; Frantzeskakis, D.J.

2007-01-01

In this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov-Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to 'engineer' trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how similar time-dependent EP equations may arise in the description of anisotropic scalar field cosmologies

Dissipation-Managed Bright Soliton in a 1D Bose-Einstein Condensate in an Optical-Lattice Potential

International Nuclear Information System (INIS)

Zhou Zheng; Yu Huiyou; Ao Shengmei; Yan Jiaren

2010-01-01

We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate by including an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross-Pitaevskii equation, trapped in a shallow optical-lattice potential. Based on the direct approach of perturbation theory for the nonlinear Schroedinger equation, we demonstrate that the height (as well as width) of bright soliton may have little change through selecting experimental parameters. (general)

LUCKY-TD code for solving the time-dependent transport equation with the use of parallel computations

Energy Technology Data Exchange (ETDEWEB)

Moryakov, A. V., E-mail: sailor@orc.ru [National Research Centre Kurchatov Institute (Russian Federation)

2016-12-15

An algorithm for solving the time-dependent transport equation in the P{sub m}S{sub n} group approximation with the use of parallel computations is presented. The algorithm is implemented in the LUCKY-TD code for supercomputers employing the MPI standard for the data exchange between parallel processes.

Critique of the foundations of time-dependent density-functional theory

International Nuclear Information System (INIS)

Schirmer, J.; Dreuw, A.

2007-01-01

The general expectation that, in principle, the time-dependent density-functional theory (TDDFT) is an exact formulation of the time evolution of an interacting N-electron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on four theorems by Runge and Gross (RG) [Phys. Rev. Lett. 52, 997 (1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B 15, 1969 (2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the Kohn-Sham (KS) concept has been introduced, in which the ground-state density is obtained from a single KS equation for one spatial (spinless) orbital. The time-dependent (TD) form of this radical Kohn-Sham (rKS) scheme, which has the same validity status as the ordinary KS version, has proved to be a valuable tool for analysis. The rKS concept is used to clarify also the alternative nonvariational formulation of TD KS theory. We argue that it is just a formal theory, allowing one to reproduce but not predict the time development of the exact density of the interacting N-electron system. Besides the issue of the formal exactness of TDDFT, it is shown that both the static and time-dependent KS linear response equations neglect the particle-particle (p-p) and hole-hole (h-h) matrix elements of the perturbing operator. For a local (multiplicative) operator this does not lead to a loss of information due to a remarkable general property of local operators. Accordingly, no logical inconsistency arises with respect to DFT, because DFT requires any external potential to be local. For a general nonlocal operator the error resulting from the neglected matrix elements is of second order in the electronic repulsion

Anomaly detection in real-time gross payment data

NARCIS (Netherlands)

Triepels, Ron; Daniels, Hennie; Heijmans, R.; Camp, Olivier; Filipe, Joaquim

2017-01-01

We discuss how an autoencoder can detect system-level anomalies in a real-time gross settlement system by reconstructing a set of liquidity vectors. A liquidity vector is an aggregated representation of the underlying payment network of a settlement system for a particular time interval.

On Forecasting Macro-Economic Indicators with the Help of Finite-Difference Equations and Econometric Methods

Directory of Open Access Journals (Sweden)

Polshkov Yulian M.

2013-11-01

Full Text Available The article considers data on the gross domestic product, consumer expenditures, gross investments and volume of foreign trade for the national economy. It is assumed that time is a discrete variable with one year iteration. The article uses finite-difference equations. It considers models with a high degree of the regulatory function of the state with respect to the consumer market. The econometric component is based on the hypothesis that each of the above said macro-economic indicators for this year depends on the gross domestic product for the previous time periods. Such an assumption gives a possibility to engage the least-squares method for building up linear models of the pair regression. The article obtains the time series model, which allows building point and interval forecasts for the gross domestic product for the next year based on the values of the gross domestic product for the current and previous years. The article draws a conclusion that such forecasts could be considered justified at least in the short-term prospect. From the mathematical point of view the built model is a heterogeneous finite-difference equation of the second order with constant ratios. The article describes specific features of such equations. It illustrates graphically the analytical view of solutions of the finite-difference equation. This gives grounds to differentiate national economies as sustainable growth economies, one-sided, weak or being in the stage of successful re-formation. The article conducts comparison of the listed types with specific economies of modern states.

Helicity conservation under quantum reconnection of vortex rings.

Science.gov (United States)

Zuccher, Simone; Ricca, Renzo L

2015-12-01

Here we show that under quantum reconnection, simulated by using the three-dimensional Gross-Pitaevskii equation, self-helicity of a system of two interacting vortex rings remains conserved. By resolving the fine structure of the vortex cores, we demonstrate that the total length of the vortex system reaches a maximum at the reconnection time, while both writhe helicity and twist helicity remain separately unchanged throughout the process. Self-helicity is computed by two independent methods, and topological information is based on the extraction and analysis of geometric quantities such as writhe, total torsion, and intrinsic twist of the reconnecting vortex rings.

Magnetic resonance, especially spin echo, in spinor Bose-Einstein condensates

International Nuclear Information System (INIS)

Yasunaga, Masashi; Tsubota, Makoto

2009-01-01

Magnetic resonance, especially NMR and ESR, has been studied in magnetic materials for a long time, having been used in various fields. Spin echo is typical phenomenon in magnetic resonance. The magnetic resonance should be applied to spinor Bose-Einstein condensates (BECs). We numerically study spin echo of a spinor BEC in a gradient magnetic field by calculating the spin-1 two-dimensional Gross-Pitaevskii equations, obtaining the recovery of the signal of the spins, which is called spin echo. We will discuss the relation between the spin echo and the Stern-Gelrach separation in the system.

Interference patterns of Bose-condensed gases in a two-dimensional optical lattice

International Nuclear Information System (INIS)

Liu Shujuan; Xiong Hongwei; Xu Zhijun; Huang Guoxiang

2003-01-01

For a Bose-condensed gas confined in a magnetic trap and in a two-dimensional (2D) optical lattice, the non-uniform distribution of atoms in different lattice sites is considered based on the Gross-Pitaevskii equation. A propagator method is used to investigate the time evolution of 2D interference patterns after (i) only the optical lattice is switched off, and (ii) both the optical lattice and the magnetic trap are switched off. An analytical description on the motion of side peaks in the interference patterns is presented by using the density distribution in a momentum space

Bose-Einstein condensate collapse: A comparison between theory and experiment

International Nuclear Information System (INIS)

Savage, C.M.; Robins, N.P.; Hope, J.J.

2003-01-01

We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed with Bose-Einstein condensates of 85 Rb, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. In addition to the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally

Stationary states and rotational properties of spin-orbit-coupled Bose-Einstein condensates held under a toroidal trap

Science.gov (United States)

He, Zhang-Ming; Zhang, Xiao-Fei; Kato, Masaya; Han, Wei; Saito, Hiroki

2018-06-01

We consider a pseudospin-1/2 Bose-Einstein condensate with Rashba spin-orbit coupling in a two-dimensional toroidal trap. By solving the damped Gross-Pitaevskii equations for this system, we show that the system exhibits a rich variety of stationary states, such as vehicle wheel and flower-petal stripe patterns. These stationary states are stable against perturbation with thermal energy and can survive for a long time. In the presence of rotation, our results show that the rotating systems have exotic vortex configurations. These phenomenon originates from the interplay among spin-orbit coupling, trap geometry, and rotation.

Derivation and solution of a time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter

International Nuclear Information System (INIS)

Esrick, M.A.

1981-01-01

A time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter is derived from the Gor'kov equations. Three types of traveling wave solutions of the equation are discussed. The phases and amplitudes of these solutions propagate at different speeds. The first type of solution has an amplitude that propagates as a soliton and it is suggested that this solution might correspond to the recently observed propagating collective modes of the order parameter. The amplitude of the second type of solution propagates as a periodic disturbance in space and time. It is suggested that this type of solution might explain the recently observed multiple values of the superconductor energy gap as well as the spatially inhomogenous superconducting state. The third type of solution, which is of a more general character, might provide some insight into non-periodic, inhomogeneous states occuring in superconductors. It is also proposed that quasiparticle injection and microwave irradiation might generate soliton-like disturbances in superconductors

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

International Nuclear Information System (INIS)

Lo, C.F.

2009-01-01

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)

Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice

International Nuclear Information System (INIS)

Cheng Yongshan; Adhikari, S. K.

2010-01-01

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method, we study different aspects of the localization of a cigar-shaped interacting binary (two-component) Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)]. We consider two types of localized states: (i) when both localized components have a maximum of density at the origin x=0, and (ii) when the first component has a maximum of density and the second a minimum of density at x=0. In the noninteracting case, the density profiles are symmetric around x=0. We numerically study the breakdown of this symmetry due to interspecies and intraspecies interactions acting on the two components. Where possible, we have compared the numerical results with a time-dependent variational analysis. We also demonstrate the stability of the localized symmetry-broken BEC states under small perturbation.

Simple waves in a two-component Bose-Einstein condensate

Science.gov (United States)

Ivanov, S. K.; Kamchatnov, A. M.

2018-04-01

We study the dynamics of so-called simple waves in a two-component Bose-Einstein condensate. The evolution of the condensate is described by Gross-Pitaevskii equations which can be reduced for these simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fluid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between interspecies and intraspecies nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.

Time-dependent massless Dirac fermions in graphene

Energy Technology Data Exchange (ETDEWEB)

Khantoul, Boubakeur, E-mail: bobphys@gmail.com [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Department of Physics, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel (Algeria); Fring, Andreas, E-mail: a.fring@city.ac.uk [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom)

2015-10-30

Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians. - Highlights: • An explicit analytical solution for a massless 2+1 dimensional time-dependent Dirac equation is found. • All steps of the Lewis–Riesenfeld method have been carried out.

Time-dependent magnetization of a type-II superconductor numerically calculated by using the flux-creep equation

International Nuclear Information System (INIS)

Lee, J. H.; Park, I. S.; Ahmad, D.; Kim, D.; Kim, Y. C.; Ko, R. K.; Jeong, D. Y.

2012-01-01

The macroscopic magnetic behaviors of a type-II superconductor, such as the field- or the temperature-dependent magnetization, have been described by using critical state models. However, because the models are time-independent, the magnetic relaxation in a type-II superconductor cannot be described by them, and the time dependence of the magnetization can affect the field or the temperature-dependent magnetization curve described by the models. In order to avoid the time independence of critical state models, we try the numerical calculation used by Qin et al., who mainly calculated the temperature dependence of the ac susceptibility χ(T). Their calculation showed that the frequency-dependent χ(T) could be obtained by using the flux-creep equation. We calculated the field-dependent magnetization and magnetic relaxation by using a numerical method. The calculated field-dependent magnetization M(H) curves shows the shapes of a typical type-II superconductor. The calculated magnetic relaxation do not show a logarithmic decay of the magnetization, but the addition of a surface barrier to the relaxation calculation caused a clear logarithmic decay of the magnetization, producing a crossover at a mid-time. This means that the logarithmic magnetic relaxation is caused by not only flux creep but also a combination of flux creep and a surface barrier.

Matter-wave dark solitons in optical lattices

International Nuclear Information System (INIS)

Louis, Pearl J Y; Ostrovskaya, Elena A; Kivshar, Yuri S

2004-01-01

We analyse the Floquet-Bloch spectrum of matter waves in Bose-Einstein condensates loaded into single-periodic optical lattices and double-periodic superlattices. In the framework of the Gross-Pitaevskii equation, we describe the structure and analyse the mobility properties of matter-wave dark solitons residing on backgrounds of extended nonlinear Bloch-type states. We demonstrate that interactions between dark solitons can be effectively controlled in optical superlattices

Numerical solution of the time dependent neutron transport equation by the method of the characteristics

International Nuclear Information System (INIS)

Talamo, Alberto

2013-01-01

This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps

Numerical solution of the time dependent neutron transport equation by the method of the characteristics

Energy Technology Data Exchange (ETDEWEB)

Talamo, Alberto, E-mail: alby@anl.gov [Nuclear Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439 (United States)

2013-05-01

This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems

Science.gov (United States)

Kang, Yan-Mei

2016-09-01

For a physically realistic type of time-dependent time fractional Fokker-Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker-Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed.

Solitary wave dynamics in time-dependent potentials

International Nuclear Information System (INIS)

Abou Salem, Walid K.

2008-01-01

The long time dynamics of solitary wave solutions of the nonlinear Schroedinger equation in time-dependent external potentials is rigorously studied. To set the stage, the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schroedinger equation with time-dependent nonlinearities and potential is established. Afterward, the dynamics of NLS solitary waves in time-dependent potentials is studied. It is shown that in the space-adiabatic regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. Finally, two physical applications are discussed: the first is adiabatic transportation of solitons and the second is the Mathieu instability of trapped solitons due to time-periodic perturbations

A Generalized Estimating Equations Approach to Model Heterogeneity and Time Dependence in Capture-Recapture Studies

Directory of Open Access Journals (Sweden)

Akanda Md. Abdus Salam

2017-03-01

Full Text Available Individual heterogeneity in capture probabilities and time dependence are fundamentally important for estimating the closed animal population parameters in capture-recapture studies. A generalized estimating equations (GEE approach accounts for linear correlation among capture-recapture occasions, and individual heterogeneity in capture probabilities in a closed population capture-recapture individual heterogeneity and time variation model. The estimated capture probabilities are used to estimate animal population parameters. Two real data sets are used for illustrative purposes. A simulation study is carried out to assess the performance of the GEE estimator. A Quasi-Likelihood Information Criterion (QIC is applied for the selection of the best fitting model. This approach performs well when the estimated population parameters depend on the individual heterogeneity and the nature of linear correlation among capture-recapture occasions.

Simulating transient dynamics of the time-dependent time fractional Fokker–Planck systems

Energy Technology Data Exchange (ETDEWEB)

Kang, Yan-Mei, E-mail: ymkang@mail.xjtu.edu.cn

2016-09-16

For a physically realistic type of time-dependent time fractional Fokker–Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker–Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed. - Highlights: • An iteration method is proposed for the transient dynamics of time-dependent time fractional Fokker–Planck equations. • The method is based on Fourier Series solution and the multi-step transition probability formula. • With the time-modulated subdiffusion on finite interval as example, the polarized motion orientation is disclosed. • With the time-modulated subdiffusion within a confined potential as example, the death of dynamic response is observed.

Simulating transient dynamics of the time-dependent time fractional Fokker–Planck systems

International Nuclear Information System (INIS)

Kang, Yan-Mei

2016-01-01

For a physically realistic type of time-dependent time fractional Fokker–Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker–Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed. - Highlights: • An iteration method is proposed for the transient dynamics of time-dependent time fractional Fokker–Planck equations. • The method is based on Fourier Series solution and the multi-step transition probability formula. • With the time-modulated subdiffusion on finite interval as example, the polarized motion orientation is disclosed. • With the time-modulated subdiffusion within a confined potential as example, the death of dynamic response is observed.

Use of a theoretical equation of state to interpret time-dependent free volume in polymer glasses

International Nuclear Information System (INIS)

Curro, J.G.; Lagasse, R.R.; Simha, R.

1981-01-01

Many physical properties of polymer glasses change spontaneously during isothermal aging by a process commonly modeled as collapse of free volume. The model has not been verified rigorously because free volume cannot be unambiguously measured. In the present investigation we tentatively identify the free-volume fraction with the fraction of empty sites in the equation of state of Simha and Somcynsky. With this theory, volume recovery measurements can be analyzed to yield directly the time-dependent, free-volume fraction. Using this approach, recent volume measurements on poly(methyl methacrylate) are analyzed. The resulting free-volume fractions are then used in the Doolittle equation to predict the shift in stress relaxation curves at 23 0 C. These predicted shift factors agree with the experimental measurements of Cizmecioglu et al. In addition, it is shown that previous assumptions concerning temperature dependence of free volume are inconsistent with the theory

Solution of the atmospheric diffusion equation with a realistic diffusion coefficient and time dependent mixing height

International Nuclear Information System (INIS)

Mayhoub, A.B.; Etman, S.M.

1997-01-01

One dimensional model for the dispersion of a passive atmospheric contaminant (neglecting chemical reactions) in the atmospheric boundary layer is introduced. The differential equation representing the dispersion of pollutants is solved on the basis of gradient-transfer theory (K- theory). The present approach deals with a more appropriate and realistic profile for the diffusion coefficient K, which is expressed in terms of the friction velocity U, the vertical coordinate z and the depth of the mixing layer h, which is taken time dependent. After some mathematical simplification, the equation analytic obtained solution can be easily applied to case study concerning atmospheric dispersion of pollutants

Relativistic Gross-Pitaevskii equation and the cosmological Bose Einstein Condensation-Quantum Structure in Universe

International Nuclear Information System (INIS)

Fukuyama, Takeshi; Morikawa, Masahiro

2006-01-01

We do not know 96% of the total matter in the universe. A model is proposed in which Dark Energy is identified as Bose-Einstein Condensation. Global cosmic acceleration and rapid local collapse into black holes (Dark Matter) are examined. We also propose a novel mechanism of inflation due to the steady flow of condensation, which is free from slow-roll conditions for the potential

Two routes to the one-dimensional discrete nonpolynomial Schroedinger equation

International Nuclear Information System (INIS)

Gligoric, G.; Hadzievski, Lj.; Maluckov, A.; Salasnich, L.; Malomed, B. A.

2009-01-01

The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schroedinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce 'model 1' (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. 'Model 2,' which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2--in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.

Optimized effective potential in real time: Problems and prospects in time-dependent density-functional theory

International Nuclear Information System (INIS)

Mundt, Michael; Kuemmel, Stephan

2006-01-01

The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential is analyzed

Effect of interactions on the localization of a Bose-Einstein condensate in a quasi-periodic lattice

OpenAIRE

Lye, J. E.; Fallani, L.; Fort, C.; Guarrera, V.; Modugno, M.; Wiersma, D. S.; Inguscio, M.

2006-01-01

The transport properties of a Bose-Einstein condensate in a 1D incommensurate bichromatic lattice are investigated both theoretically and experimentally. We observe a blockage of the center of mass motion with low atom number, and a return of motion when the atom number is increased. Solutions of the Gross-Pitaevskii equation show how the localization due to the quasi-disorder introduced by the incommensurate bichromatic lattice is affected by the interactions.

Bouncing cosmologies from quantum gravity condensates

Science.gov (United States)

Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward

2017-02-01

We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

Direct measurements of the light dependence of gross photosynthesis and oxygen consumption in the ocean

Science.gov (United States)

Bailleul, B.; Park, J.; Brown, C. M.; Bidle, K. D.; Lee, S.; Falkowski, P. G.

2016-02-01

For decades, a lack of understanding of how respiration is influenced by light has been stymying our ability to quantitatively analyze how phytoplankton allocate carbon in situ and the biological mechanisms that participate to the fate of blooms. Using membrane inlet mass spectrometry (MIMS), the light dependencies of gross photosynthesis and oxygen uptake rates were measured during the bloom demises of two prymnesiophytes, in two open ocean regions. In the North Atlantic, dominated by Emiliania huxleyi, respiration was independent of irradiance and was higher than the gross photosynthetic rate at all irradiances. In the Amundsen Sea (Antarctica), dominated by Phaeocystis antarctica, the situation was very different. Dark respiration was one order of magnitude lower than the maximal gross photosynthetic rate. ut the oxygen uptake rate increased by 10 fold at surface irradiances, where it becomes higher than gross photosynthesis. Our results suggest that the light dependence of oxygen uptake in P. antarctica has two sources: one is independent of photosynthesis, and is possibly associated with the photo-reduction of O2 mediated by dissolved organic matter; the second reflects the activity of an oxidase fueled in the light with photosynthetic electron flow. Interestingly, these dramatic light-dependent changes in oxygen uptake were not reproduced in nutrient-replete P. antarctica cultures, in the laboratory. Our measurements highlight the importance of improving our understanding of oxygen consuming reactions in the euphotic zone, which is critical to investigating the physiology of phytoplankton and tracing the fate of phytoplankton blooms.

The semi-classical limit of the time dependent Hartree-Fock equation. II. The Wick symbol of the solution

OpenAIRE

Amour, Laurent; Khodja, Mohamed; Nourrigat, Jean

2011-01-01

We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem for observables that are not pseudo-differential operators.

Exact norm-conserving stochastic time-dependent Hartree-Fock

International Nuclear Information System (INIS)

Tessieri, Luca; Wilkie, Joshua; Cetinbas, Murat

2005-01-01

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method, we calculate the low energy spectrum of helium. An extension of the method to bosons is outlined

Structural equation modeling of motor impairment, gross motor function, and the functional outcome in children with cerebral palsy.

Science.gov (United States)

Park, Eun-Young; Kim, Won-Ho

2013-05-01

Physical therapy intervention for children with cerebral palsy (CP) is focused on reducing neurological impairments, improving strength, and preventing the development of secondary impairments in order to improve functional outcomes. However, relationship between motor impairments and functional outcome has not been proved definitely. This study confirmed the construct of motor impairment and performed structural equation modeling (SEM) between motor impairment, gross motor function, and functional outcomes of regarding activities of daily living in children with CP. 98 children (59 boys, 39 girls) with CP participated in this cross-sectional study. Mean age was 11 y 5 mo (SD 1 y 9 mo). The Manual Muscle Test (MMT), the Modified Ashworth Scale (MAS), range of motion (ROM) measurement, and the selective motor control (SMC) scale were used to assess motor impairments. Gross motor function and functional outcomes were measured using the Gross Motor Function Measure (GMFM) and the Functional Skills domain of the Pediatric Evaluation of Disability Inventory (PEDI) respectively. Measurement of motor impairment was consisted of strength, spasticity, ROM, and SMC. The construct of motor impairment was confirmed though an examination of a measurement model. The proposed SEM model showed good fit indices. Motor impairment effected gross motor function (β=-.0869). Gross motor function and motor impairment affected functional outcomes directly (β=0.890) and indirectly (β=-0.773) respectively. We confirmed that the construct of motor impairment consist of strength, spasticity, ROM, and SMC and it was identified through measurement model analysis. Functional outcomes are best predicted by gross motor function and motor impairments have indirect effects on functional outcomes. Copyright © 2013 Elsevier Ltd. All rights reserved.

Soliton solutions of some nonlinear evolution equations with time ...

Indian Academy of Sciences (India)

Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...

Separation of massive field equation of arbitrary spin in Robertson-Walker space-time

International Nuclear Information System (INIS)

Zecca, A.

2006-01-01

The massive spin-(3/2) field equation is explicitly integrated in the Robertson-Walker space-time by the Newman Penrose formalism. The solution is obtained by extending a separation procedure previously used to solve the spin-1 equation. The separated time dependence results in two coupled equations depending on the cosmological background evolution. The separated angular equations are explicitly integrated and the eigenvalues determined. The separated radial equations are integrated in the flat space-time case. The separation method of solution is then generalized, by induction, to prove the main result, that is the separability of the massive field equations of arbitrary spin in the Robertson-Walker space-time

Exact solution of a quantum forced time-dependent harmonic oscillator

Science.gov (United States)

Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN

1992-01-01

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Finite difference solution of the time dependent neutron group diffusion equations

International Nuclear Information System (INIS)

Hendricks, J.S.; Henry, A.F.

1975-08-01

In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods

State-dependent neutral delay equations from population dynamics.

Science.gov (United States)

Barbarossa, M V; Hadeler, K P; Kuttler, C

2014-10-01

A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.

On an nth-order infinitesimal generator and time-dependent operator differential equation with a strongly almost periodic solution

Directory of Open Access Journals (Sweden)

Aribindi Satyanarayan Rao

2002-01-01

Full Text Available In a Banach space, if u is a Stepanov almost periodic solution of a certain nth-order infinitesimal generator and time-dependent operator differential equation with a Stepanov almost periodic forcing function, then u,u′,…,u (n−2 are all strongly almost periodic and u (n−1 is weakly almost periodic.

On the time evolution operator for time-dependent quadratic Hamiltonians

International Nuclear Information System (INIS)

Fernandez, F.M.

1989-01-01

The Schroedinger equation with a time-dependent quadratic Hamiltonian is investigated. The time-evolution operator is written as a product of exponential operators determined by the Heisenberg equations of motion. This product operator is shown to be global in the occupation number representation when the Hamiltonian is Hermitian. The success of some physical applications of the product-form representation is explained

A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

Science.gov (United States)

Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

2018-05-01

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

Generalization of uncertainty relation for quantum and stochastic systems

Science.gov (United States)

Koide, T.; Kodama, T.

2018-06-01

The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.

On the initial conditions of time-dependent mean-field equations of evolution. Pt. 2

International Nuclear Information System (INIS)

Troudet, T.; Paris-11 Univ., 91 - Orsay

1986-01-01

We analyze the problem so far untouched of determining the initial mean-field wavefunction in the context of zero-temperature mean-field descriptions of time-dependent expectation values and quantum fluctuations of nuclear observables. The nucleus, at zero temperature, is taken to be in a low-lying excited many-body eigenstate and is approximated by the corresponding RPA wavefunction as a continuous superposition of coherent states (i.e. Slater determinants). A generating function Gsub(A)(lambda) for time-dependent expectation values and quantum fluctuations is constructed within the formalism of functional integration. By applying the saddle-point method to the functional action of Gsub(A)(lambda) and then taking its lambda-derivatives, we recover the well-known TDHF theory and propose a simple determination of the initial Slater determinant for an appropriate mean-field description of time-dependent expectation values. The analog mean-field description of quadratic-quantum fluctuations proceeds similarly and in addition includes the contribution of the uncorrelated TDHF-RPA phonons coupled to collective excitations of the initial (static) mean-field configuration. When the collective TDHF-RPA excitations are solely taken into account, we obtain an improved version of the Balian-Veneroni dispersion formula by showing how to determine the initial mean-field wavefunction. By first taking the lambda-derivatives of Gsub(A)(lambda) before applying the saddle-point method, the initial mean-field wavefunction is found to be non-linearly coupled to the mean-field dynamics themselves. In return, and in contrast to the first quantization scheme, these both depend non-trivially upon the observable A being measured so that approximations must be proposed to simplify the resulting mean-field equations. (orig.)

Time evolution of some quantum-mechanical systems. Wavefunction cloning in evolving rotating systems. Finite range boundary conditions for time dependent Schroedinger Equation

International Nuclear Information System (INIS)

Arvieu, R.; Carbonell, J.; Gignoux, C.; Mangin-Brinet, M.; Rozmej, P.

1997-01-01

The time evolution of coherent rotational wave packets associated to a diatomic molecule or to a deformed nucleus has been studied. Assuming a rigid body dynamics the J(J+1) law leads to a mechanism of cloning: the way function is divided into wave packets identical to the initial one at specific time. Applications are studied for a nuclear wave packed formed by Coulomb excitation. Exact boundary conditions at finite distance for the solution of the time-dependent Schroedinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples. (authors)

Cellular neural networks (CNN) simulation for the TN approximation of the time dependent neutron transport equation in slab geometry

International Nuclear Information System (INIS)

Hadad, Kamal; Pirouzmand, Ahmad; Ayoobian, Navid

2008-01-01

This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the time dependent one-speed neutron transport equation in slab geometry. We use a neutron angular flux in terms of the Chebyshev polynomials (T N ) of the first kind and then we attempt to implement the equations in an equivalent electrical circuit. We apply this equivalent circuit to analyze the T N moments equation in a uniform finite slab using Marshak type vacuum boundary condition. The validity of the CNN results is evaluated with numerical solution of the steady state T N moments equations by MATLAB. Steady state, as well as transient simulations, shows a very good comparison between the two methods. We used our CNN model to simulate space-time response of total flux and its moments for various c (where c is the mean number of secondary neutrons per collision). The complete algorithm could be implemented using very large-scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for neutron transport calculations

Solution of the linearised Vlasov equation for collisionless plasmas evolving in external fields of arbitrary spatial and time dependence: Pt. 2

International Nuclear Information System (INIS)

Skarka, V.; Coveney, P.V.

1990-01-01

We solve perturbatively the linearised Vlasov equation describing inhomogeneous collisionless plasmas evolving in time-dependent external fields. The method employs an explicitly time-dependent formalism and is facilitated by the used of diagrammatic techniques. It leads to a straightforward algorithm for computing the contribution to the solution, order by order in the external field. In the previous paper we provided the solution to first order; higher orders are described in the present paper. (author)

Dynamics of second order in time evolution equations with state-dependent delay

Czech Academy of Sciences Publication Activity Database

Chueshov, I.; Rezunenko, Oleksandr

123-124, č. 1 (2015), s. 126-149 ISSN 0362-546X R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Second order evolution equations * State dependent delay * Nonlinear plate * Finite-dimensional attractor Subject RIV: BD - Theory of Information Impact factor: 1.125, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444708.pdf

Application of Trotter approximation for solving time dependent neutron transport equation; Primena Trotterove aproksimacije za resavanje vremenski zavisne transportne jednacine neutrona

Energy Technology Data Exchange (ETDEWEB)

Stancic, V [Institut za nuklearne nauke Boris Kidric, Vinca, Beograd (Yugoslavia)

1987-07-01

A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)

The constrained discrete-time state-dependent Riccati equation technique for uncertain nonlinear systems

Science.gov (United States)

Chang, Insu

The objective of the thesis is to introduce a relatively general nonlinear controller/estimator synthesis framework using a special type of the state-dependent Riccati equation technique. The continuous time state-dependent Riccati equation (SDRE) technique is extended to discrete-time under input and state constraints, yielding constrained (C) discrete-time (D) SDRE, referred to as CD-SDRE. For the latter, stability analysis and calculation of a region of attraction are carried out. The derivation of the D-SDRE under state-dependent weights is provided. Stability of the D-SDRE feedback system is established using Lyapunov stability approach. Receding horizon strategy is used to take into account the constraints on D-SDRE controller. Stability condition of the CD-SDRE controller is analyzed by using a switched system. The use of CD-SDRE scheme in the presence of constraints is then systematically demonstrated by applying this scheme to problems of spacecraft formation orbit reconfiguration under limited performance on thrusters. Simulation results demonstrate the efficacy and reliability of the proposed CD-SDRE. The CD-SDRE technique is further investigated in a case where there are uncertainties in nonlinear systems to be controlled. First, the system stability under each of the controllers in the robust CD-SDRE technique is separately established. The stability of the closed-loop system under the robust CD-SDRE controller is then proven based on the stability of each control system comprising switching configuration. A high fidelity dynamical model of spacecraft attitude motion in 3-dimensional space is derived with a partially filled fuel tank, assumed to have the first fuel slosh mode. The proposed robust CD-SDRE controller is then applied to the spacecraft attitude control system to stabilize its motion in the presence of uncertainties characterized by the first fuel slosh mode. The performance of the robust CD-SDRE technique is discussed. Subsequently

Boundary layer phenomena for differential-delay equations with state-dependent time lags: III

Science.gov (United States)

Mallet-Paret, John; Nussbaum, Roger D.

We consider a class of singularly perturbed delay-differential equations of the form ɛ ẋ(t)=f(x(t),x(t-r)), where r= r( x( t)) is a state-dependent delay. We study the asymptotic shape, as ɛ→0, of slowly oscillating periodic solutions. In particular, we show that the limiting shape of such solutions can be explicitly described by the solution of a pair of so-called max-plus equations. We are able thereby to characterize both the regular parts of the solution graph and the internal transition layers arising from the singular perturbation structure.

Bose-Einstein condensates in optical lattices: Band-gap structure and solitons

International Nuclear Information System (INIS)

Louis, Pearl J. Y.; Kivshar, Yuri S.; Ostrovskaya, Elena A.; Savage, Craig M.

2003-01-01

We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions

Dark and bright solitons in a quasi-one-dimensional Bose-Einstein condensate

International Nuclear Information System (INIS)

Wang, Shun-Jin; Jia, Cheng-Long; An, Jun-Hong; Zhao, Dun; Luo, Hong-Gang

2003-01-01

The analytical dark and bright soliton solutions of the one-dimensional Gross-Pitaevskii equation with a confining potential are obtained. For the bright soliton, the recent experimental finding is studied, and the particle number of the soliton and the window of the particle numbers for the bright soliton to occur are estimated analytically and in good agreement with the experimental data. The existence of dark soliton for the attractive interaction and bright soliton for the repulsive interaction is predicted under proper conditions

Velocity form of the Kohn-Sham frequency-dependent polarizability equations

International Nuclear Information System (INIS)

Bartolotti, L.J.

1987-01-01

A single equation is derived for the determination of the first-order correction to the frequency-dependent density, due to the perturbation of a time-varying electric field. This new expression for the first-order correction to the frequency-dependent Kohn-Sham amplitudes depends explicitly upon the velocity form of the dipole-moment operator and the square of the Kohn-Sham Hamiltonian

A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

Science.gov (United States)

Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.

2016-10-01

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

Analytic solutions of the multigroup space-time reactor kinetics equations

International Nuclear Information System (INIS)

Lee, C.E.; Rottler, S.

1986-01-01

The development of analytical and numerical solutions to the reactor kinetics equations is reviewed. Analytic solutions of the multigroup space-time reactor kinetics equations are developed for bare and reflected slabs and spherical reactors for zero flux, zero current and extrapolated endpoint boundary conditions. The material properties of the reactors are assumed constant in space and time, but spatially-dependent source terms and initial conditions are investigated. The system of partial differential equations is reduced to a set of linear ordinary differential equations by the Laplace transform method. These equations are solved by matrix Green's functions yielding a general matrix solution for the neutron flux and precursor concentration in the Laplace transform space. The detailed pole structure of the Laplace transform matrix solutions is investigated. The temporally- and spatially-dependent solutions are determined from the inverse Laplace transform using the Cauchy residue theorem, the theorem of Frobenius, a knowledge of the detailed pole structure and matrix operators. (author)

Time-Dependent Mean-Field Games in the Subquadratic Case

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard A.; Sá nchez-Morgado, Hé ector

2014-01-01

In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.

Time-Dependent Mean-Field Games in the Subquadratic Case

KAUST Repository

Gomes, Diogo A.

2014-10-14

In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Time dependent drift Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1982-04-01

The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

Science.gov (United States)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

Functional approach to a time-dependent self-consistent field theory

International Nuclear Information System (INIS)

Reinhardt, H.

1979-01-01

The time-dependent Hartree-Fock approximation is formulated within the path integral approach. It is shown that by a suitable choice of the collective field the classical equation of motion of the collective field coincides with the time-dependent Hartree (TDH) equation. The consideration is restricted to the TDH equation, since the exchange terms do not appear in the functional approach on the same footing as the direct terms

Exact wavefunctions for a time-dependent Coulomb potential

International Nuclear Information System (INIS)

Menouar, S; Maamache, M; Saadi, Y; Choi, J R

2008-01-01

The one-dimensional Schroedinger equation associated with a time-dependent Coulomb potential is studied. The invariant operator method (Lewis and Riesenfeld) and unitary transformation approach are employed to derive quantum solutions of the system. We obtain an ordinary second-order differential equation whose analytical exact solution has been unknown. It is confirmed that the form of this equation is similar to the radial Schroedinger equation for the hydrogen atom in a (arbitrary) strong magnetic field. The qualitative properties for the eigenstates spectrum are described separately for the different values of the parameter ω 0 appearing in the x 2 term, x being the position, i.e., ω 0 > 0, ω 0 0 = 0. For the ω 0 = 0 case, the eigenvalue equation of invariant operator reduces to a solvable form and, consequently, we have provided exact eigenstates of the time-dependent Hamiltonian system

Faraday waves in Bose-Einstein condensates

International Nuclear Information System (INIS)

Nicolin, Alexandru I.; Carretero-Gonzalez, R.; Kevrekidis, P. G.

2007-01-01

Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation of the strength of the transverse confinement. We offer a fully analytical explanation of the observed parametric resonance, based on a Mathieu-type analysis of the non-polynomial Schroedinger equation. The theoretical prediction for the pattern periodicity versus the driving frequency is directly compared to the experimental data, yielding good qualitative and quantitative agreement between the two. These results are corroborated by direct numerical simulations of both the one-dimensional non-polynomial Schroedinger equation and of the fully three-dimensional Gross-Pitaevskii equation

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

Science.gov (United States)

Na, D.-Y.; Moon, H.; Omelchenko, Y. A.; Teixeira, F. L.

2018-01-01

Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

On the time-dependent Aharonov–Bohm effect

Directory of Open Access Journals (Sweden)

Jian Jing

2017-11-01

Full Text Available The Aharonov–Bohm effect in the background of a time-dependent vector potential is re-examined for both non-relativistic and relativistic cases. Based on the solutions to the Schrodinger and Dirac equations which contain the time-dependent magnetic vector potential, we find that contrary to the conclusions in a recent paper (Singleton and Vagenas 2013 [4], the interference pattern will be altered with respect to time because of the time-dependent vector potential.

On the reduced dynamics of a subset of interacting bosonic particles

Science.gov (United States)

Gessner, Manuel; Buchleitner, Andreas

2018-03-01

The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an N-particle system produces a hierarchical expansion for the subdynamics of M ≤ N particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross-Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction-induced decoherence in form of a nonlinear Lindblad-type master equation.

Measurement and Quantification of Gross Human Shoulder Motion

Directory of Open Access Journals (Sweden)

Jeremy T. Newkirk

2013-01-01

Full Text Available The shoulder girdle plays an important role in the large pointing workspace that humans enjoy. The goal of this work was to characterize the human shoulder girdle motion in relation to the arm. The overall motion of the human shoulder girdle was characterized based on motion studies completed on test subjects during voluntary (natural/unforced motion. The collected data from the experiments were used to develop surface fit equations that represent the position and orientation of the glenohumeral joint for a given humeral pointing direction. These equations completely quantify gross human shoulder girdle motion relative to the humerus. The equations are presented along with goodness-of-fit results that indicate the equations well approximate the motion of the human glenohumeral joint. This is the first time the motion has been quantified for the entire workspace, and the equations provide a reference against which to compare future work.

Attainable conditions and exact invariant for the time-dependent harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)

2006-09-22

The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.

Attainable conditions and exact invariant for the time-dependent harmonic oscillator

International Nuclear Information System (INIS)

Guasti, Manuel Fernandez

2006-01-01

The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system

Association Between Gross-Motor and Executive Function Depends on Age and Motor Task Complexity

DEFF Research Database (Denmark)

Spedden, Meaghan E; Malling, Anne Sofie B; Andersen, Ken K

2017-01-01

The objective was to examine associations between motor and executive function across the adult lifespan and to investigate the role of motor complexity in these associations. Young, middle-aged and older adults (n = 82; 19-83y) performed two gross-motor tasks with different levels of complexity...... and a Stroop-like computer task. Performance was decreased in older adults. The association between motor and cognitive performance was significant for older adults in the complex motor task (p = 0.03, rs = -0.41), whereas no significant associations were found for young or middle-aged groups, suggesting...... that the link between gross-motor and executive function emerges with age and depends on motor complexity....

Construction of an exact solution of time-dependent Ginzburg ...

Indian Academy of Sciences (India)

time-dependent Ginzburg–Landau (TDGL) equations we have calculated the ... The prototype of such equations is the parabolic reaction diffusion equation [7,8] ..... It may be possible to compare the above results with suitable experiments, ...

Time-dependent problems and difference methods

CERN Document Server

Gustafsson, Bertil; Oliger, Joseph

2013-01-01

Praise for the First Edition "". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations."" -SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-de

Time-dependent deterministic transport on parallel architectures using PARTISN

International Nuclear Information System (INIS)

Alcouffe, R.E.; Baker, R.S.

1998-01-01

In addition to the ability to solve the static transport equation, the authors have also incorporated time dependence into the parallel S N code PARTISN. Using a semi-implicit scheme, PARTISN is capable of performing time-dependent calculations for both fissioning and pure source driven problems. They have applied this to various types of problems such as shielding and prompt fission experiments. This paper describes the form of the time-dependent equations implemented, their solution strategies in PARTISN including iteration acceleration, and the strategies used for time-step control. Results are presented for a iron-water shielding calculation and a criticality excursion in a uranium solution configuration

Introducing time-dependent molecular fields: a new derivation of the wave equations

Science.gov (United States)

Baer, Michael

2018-02-01

This article is part of a series of articles trying to establish the concept molecular field. The theory that induced us to introduce this novel concept is based on the Born-Huang expansion as applied to the Schroedinger equation that describes the interaction of a molecular system with an external electric field. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from a single spatial curl equation, two space-time curl equations and one single space-time divergent equation to a pair of decoupled wave equations usually encountered within the theory of fields. In the present study, just like in the previous study [see Baer et al., Mol. Phys. 114, 227 (2016)] the wave equations are derived for an electric field having two features: (a) its intensity is high enough; (b) its duration is short enough. Although not all the findings are new the derivation, in the present case, is new, straightforward, fluent and much friendlier as compared to the previous one and therefore should be presented again. For this situation the study reveals that the just described interaction creates two fields that coexist within a molecule: one is a novel vectorial field formed via the interaction of the electric field with the Born-Huang non-adiabatic coupling terms (NACTs) and the other is an ordinary, scalar, electric field essentially identical to the original electric field. Section 4 devoted to the visualization of the outcomes via two intersecting Jahn-Teller cones which contain NACTs that become singular at the intersection point of these cones. Finally, the fact that eventually we are facing a kind of a cosmic situation may bring us to speculate that singular NACTs are a result of cosmic phenomena. Thus, if indeed this singularity is somehow connected to reality then, like other singularities in physics, it is formed at (or immediately after) the Big Bang and consequently, guarantees the formation of molecules.

Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations

International Nuclear Information System (INIS)

Dong, B; Ding, G H; Lei, X L

2015-01-01

A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime. (paper)

A vortex filament tracking method for the Gross–Pitaevskii model of a superfluid

International Nuclear Information System (INIS)

Villois, Alberto; Proment, Davide; Salman, Hayder; Krstulovic, Giorgio

2016-01-01

We present an accurate and robust numerical method to track quantised vortex lines in a superfluid described by the Gross–Pitaevskii equation. By utilising the pseudo-vorticity field of the associated complex scalar order parameter of the superfluid, we are able to track the topological defects of the superfluid and reconstruct the vortex lines which correspond to zeros of the field. Throughout, we assume our field is periodic to allow us to make extensive use of the Fourier representation of the field and its derivatives in order to retain spectral accuracy. We present several case studies to test the precision of the method which include the evaluation of the curvature and torsion of a torus vortex knot, and the measurement of the Kelvin wave spectrum of a vortex line and a vortex ring. The method we present makes no a priori assumptions on the geometry of the vortices and is therefore applicable to a wide range of systems such as a superfluid in a turbulent state that is characterised by many vortex rings coexisting with sound waves. This allows us to track the positions of the vortex filaments in a dense turbulent vortex tangle and extract statistical information about the distribution of the size of the vortex rings and the inter-vortex separations. In principle, the method can be extended to track similar topological defects arising in other physical systems. (paper)

Integrable Time-Dependent Quantum Hamiltonians

Science.gov (United States)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Motivation for Using Generalized Geometry in the Time Dependent Transport Code TDKENO

Energy Technology Data Exchange (ETDEWEB)

Dustin Popp; Zander Mausolff; Sedat Goluoglu

2016-04-01

We are proposing to use the code, TDKENO, to model TREAT. TDKENO solves the time dependent, three dimensional Boltzmann transport equation with explicit representation of delayed neutrons. Instead of directly integrating this equation, the neutron flux is factored into two components – a rapidly varying amplitude equation and a slowly varying shape equation and each is solved separately on different time scales. The shape equation is solved using the 3D Monte Carlo transport code KENO, from Oak Ridge National Laboratory’s SCALE code package. Using the Monte Carlo method to solve the shape equation is still computationally intensive, but the operation is only performed when needed. The amplitude equation is solved deterministically and frequently, so the solution gives an accurate time-dependent solution without having to repeatedly We have modified TDKENO to incorporate KENO-VI so that we may accurately represent the geometries within TREAT. This paper explains the motivation behind using generalized geometry, and provides the results of our modifications. TDKENO uses the Improved Quasi-Static method to accomplish this. In this method, the neutron flux is factored into two components. One component is a purely time-dependent and rapidly varying amplitude function, which is solved deterministically and very frequently (small time steps). The other is a slowly varying flux shape function that weakly depends on time and is only solved when needed (significantly larger time steps).

The quantum computer game: citizen science

Science.gov (United States)

Damgaard, Sidse; Mølmer, Klaus; Sherson, Jacob

2013-05-01

Progress in the field of quantum computation is hampered by daunting technical challenges. Here we present an alternative approach to solving these by enlisting the aid of computer players around the world. We have previously examined a quantum computation architecture involving ultracold atoms in optical lattices and strongly focused tweezers of light. In The Quantum Computer Game (see http://www.scienceathome.org/), we have encapsulated the time-dependent Schrödinger equation for the problem in a graphical user interface allowing for easy user input. Players can then search the parameter space with real-time graphical feedback in a game context with a global high-score that rewards short gate times and robustness to experimental errors. The game which is still in a demo version has so far been tried by several hundred players. Extensions of the approach to other models such as Gross-Pitaevskii and Bose-Hubbard are currently under development. The game has also been incorporated into science education at high-school and university level as an alternative method for teaching quantum mechanics. Initial quantitative evaluation results are very positive. AU Ideas Center for Community Driven Research, CODER.

Time-dependent 2-stream particle transport

International Nuclear Information System (INIS)

Corngold, Noel

2015-01-01

Highlights: • We consider time-dependent transport in the 2-stream or “rod” model via an attractive matrix formalism. • After reviewing some classical problems in homogeneous media we discuss transport in materials with whose density may vary. • There we achieve a significant contraction of the underlying Telegrapher’s equation. • We conclude with a discussion of stochastics, treated by the “first-order smoothing approximation.” - Abstract: We consider time-dependent transport in the 2-stream or “rod” model via an attractive matrix formalism. After reviewing some classical problems in homogeneous media we discuss transport in materials whose density may vary. There we achieve a significant contraction of the underlying Telegrapher’s equation. We conclude with a discussion of stochastics, treated by the “first-order smoothing approximation.”

Time dependent mean-field games

KAUST Repository

Gomes, Diogo A.

2014-01-06

We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.

Vortices in spin-orbit-coupled Bose-Einstein condensates

International Nuclear Information System (INIS)

Radic, J.; Sedrakyan, T. A.; Galitski, V.; Spielman, I. B.

2011-01-01

Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to nonequilibrium behavior described by an intrinsically time-dependent Hamiltonian. We propose here the following alternative methods to induce thermodynamically stable static vortex configurations: (i) to rotate both the lasers and the anisotropic trap and (ii) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. Effective Hamiltonians for spin-orbit condensates under such perturbations are derived for most currently known realistic laser schemes that induce synthetic spin-orbit couplings. The Gross-Pitaevskii equation is solved for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates, the appearance of unusual vortex arrangements, and parity effects in vortex nucleation where the topological excitations are predicted to appear in pairs. All these phenomena are shown to be highly nonuniversal and depend strongly on a specific laser scheme and system parameters.

Bose-Einstein condensates in atomic gases: simple theoretical results

International Nuclear Information System (INIS)

Castin, Y.

2001-01-01

The author presents the theory of the Bose-Einstein condensation along with a discussion of experimental tests. The author deals successively with the following topics: - the ideal Bose gas in a trap (first in a harmonic trap and then in a more general trap), - a model for the atomic interaction, - interacting Bose gas in the Hartree-Fock approximation, - properties of the condensate wavefunction, - the Gross-Pitaevskii equation, - Bogoliubov approach and thermodynamical stability, - phase coherence properties at the Bose-Einstein condensate, and - symmetry-breaking description of condensates. (A.C.)

Lattice solitons in Bose-Einstein condensates

International Nuclear Information System (INIS)

Efremidis, Nikolaos K.; Christodoulides, Demetrios N.

2003-01-01

We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs

Depletion of superfluidity in a disordered non-equilibrium quantum condensate

Energy Technology Data Exchange (ETDEWEB)

Janot, Alexander; Rosenow, Bernd [Institut fuer Theoretische Physik, Universitaet Leipzig, 04009 Leipzig (Germany); Hyart, Timo [Institute of Physics, Leiden University, Niels Bohrweg 2, 2333 CA Leiden (Netherlands); Eastham, Paul [School of Physics, Trinity College, Dublin 2 (Ireland)

2013-07-01

Observations of quantum coherence in driven systems, e.g. polariton condensates, have strongly stimulated experimental as well as theoretical efforts during the last decade. We analyze the superfluid stiffness of a non-equilibrium quantum-condensate in a disordered environment taking gain and loss of particles into account. To this end a modified effective Gross-Pitaevskii equation is employed. We find that the disorder-driven depletion of superfluidity is strongly enhanced due to the gain-loss mechanism. It turns out that the condensate remains stiff at finite length scales only.

Magnus force in discrete and continuous two-dimensional superfluids

International Nuclear Information System (INIS)

Gecse, Z.; Khlebnikov, S.

2005-01-01

Motion of vortices in two-dimensional superfluids in the classical limit is studied by solving the Gross-Pitaevskii equation numerically on a uniform lattice. We find that, in the presence of a superflow directed along one of the main lattice periods, vortices move with the superflow on fine lattices but perpendicular to it on coarse ones. We interpret this result as a transition from the full Magnus force in a Galilean-invariant limit to vanishing effective Magnus force in a discrete system, in agreement with the existing experiments on vortex motion in Josephson junction arrays

Scenario of strongly nonequilibrated Bose-Einstein condensation

International Nuclear Information System (INIS)

Berloff, Natalia G.; Svistunov, Boris V.

2002-01-01

Large scale numerical simulations of the Gross-Pitaevskii equation are used to elucidate the self-evolution of a Bose gas from a strongly nonequilibrium initial state. The stages of the process confirm and refine the theoretical scenario of Bose-Einstein condensation developed by Svistunov and co-workers [J. Mosc. Phys. Soc. 1, 373 (1991); Sov. Phys. JETP 75, 387 (1992); 78, 187 (1994)]: the system evolves from the regime of weak turbulence to superfluid turbulence via states of strong turbulence in the long-wavelength region of energy space

Linear and nonlinear optical signals in probability and phase-space representations

International Nuclear Information System (INIS)

Man'ko, Margarita A

2006-01-01

Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schroedinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schroedinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies - symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed

Time-dependent, Bianchi II, rotating universe

International Nuclear Information System (INIS)

Reboucas, M.J.

1981-01-01

An exact cosmological solution of Einstein's equations which has time-dependent rotation is presented. The t-constant sections are of Bianchi type II. The source of this geometry is a fluid which has not been thermalized. (Author) [pt

Variational derivation of a time-dependent Hartree-Fock Hamiltonian

International Nuclear Information System (INIS)

Lichtner, P.C.; Griffin, J.J.; Schultheis, H.; Schultheis, R.; Volkov, A.B.

1979-01-01

The variational derivation of the time-dependent Hartree-Fock equation is reviewed. When norm-violating variations are included, a unique time-dependent Hartree-Fock Hamiltonian, which differs from that customarily used in time-dependent Hartree-Fock analyses, is implied. This variationally ''true'' Hartree-Fock Hamiltonian has the same expectation value as the exact Hamiltonian, equal to the average energy of the system. Since this quantity remains constant under time-dependent Hartree-Fock time evolution, we suggest the label ''constant '' for this form of time-dependent Hartree-Fock theory

A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

Energy Technology Data Exchange (ETDEWEB)

Ohsuga, Ken; Takahashi, Hiroyuki R. [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)

2016-02-20

We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.

An “Airy gun”: Self-accelerating solutions of the time-dependent Schrödinger equation in vacuum

International Nuclear Information System (INIS)

Mahalov, Alex; Suslov, Sergei K.

2012-01-01

We consider generalizations of the Berry and Balazs nonspreading and accelerating solution of the time-dependent Schrödinger equation in empty space, which has been experimentally demonstrated in paraxial optics. In particular, we show that the original nonspreading wave packet is unstable. An explicit variation of the initial Airy-state evolves into the self-accelerating and self-compressing solution presented here. Quasi-diffraction-free finite energy Airy beams that are more realistic for experimental study are obtained by analytic continuation and their Wigner function is evaluated. Nonlinear generalizations related to second Painlevé transcendents are briefly discussed.

Capillary waves at the interface of two Bose–Einstein condensates. Long wavelengths asymptotic by trial function approach

International Nuclear Information System (INIS)

Mishonov, T.M.

2015-01-01

The dispersion relation for capillary waves at the boundary of two different Bose condensates is investigated using a trial wave-function approach applied to the Gross-Pitaevskii (GP) equations. The surface tension is expressed by the parameters of the GP equations. In the long wave-length limit the usual dispersion relation is re-derived while for wavelengths comparable to the healing length we predict significant deviations from the ω ∝ k 3/2 law which can be experimentally observed. We approximate the wave variables by a frozen order parameter, i.e. the wave function is frozen in the superfluid analogous to the magnetic field in highly conductive space plasmas. PACS codes: 67.85.Jk

Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity

Directory of Open Access Journals (Sweden)

Hee Chul Pak

2012-01-01

Full Text Available A blow-up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow-up time is presented. It is pointed out that the upper bound of the first blow-up time depends on the support of the initial datum.

Time dependent variational method in quantum mechanics

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1987-01-01

Using the fact that the solutions to the time-dependent Schodinger equation can be obtained from a variational principle, by restricting the evolution of the state vector to some surface in the corresponding Hilbert space, approximations to the exact solutions can be obtained, which are determined by equations similar to Hamilton's equations. It is shown that, in order for the approximate evolution to be well defined on a given surface, the imaginary part of the inner product restricted to the surface must be non-singular. (author)

Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative

Directory of Open Access Journals (Sweden)

José Francisco Gómez Aguilar

2014-01-01

Full Text Available An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as 0<β, γ≤1 for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters σx and σt are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters β and γ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.

Isostable reduction with applications to time-dependent partial differential equations.

Science.gov (United States)

Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

The Q2-Dependence of the Gross-Llewellyn Smith Sum Rule and of the Parton Distributions

International Nuclear Information System (INIS)

Kataev, A.L.; AN SSSR, Moscow; Sidorov, A.V.

1994-01-01

We describe the results of our recent work on the determination of the value of the parameter Λ and of the Q 2 -dependence of the Gross-Llewellyn Smith (GLS) sum rule from the experimental data of the CCFR collaboration on neutrino-nucleon deep inelastic scattering, using the Jacobi polynomials QCD analysis. The new information on the Q 2 -dependence of the parton distributions is presented. 37 refs., 3 figs., 3 tabs

Subdiffusive master equation with space-dependent anomalous exponent and structural instability

Science.gov (United States)

Fedotov, Sergei; Falconer, Steven

2012-03-01

We derive the fractional master equation with space-dependent anomalous exponent. We analyze the asymptotic behavior of the corresponding lattice model both analytically and by Monte Carlo simulation. We show that the subdiffusive fractional equations with constant anomalous exponent μ in a bounded domain [0,L] are not structurally stable with respect to the nonhomogeneous variations of parameter μ. In particular, the Gibbs-Boltzmann distribution is no longer the stationary solution of the fractional Fokker-Planck equation whatever the space variation of the exponent might be. We analyze the random distribution of μ in space and find that in the long-time limit, the probability distribution is highly intermediate in space and the behavior is completely dominated by very unlikely events. We show that subdiffusive fractional equations with the nonuniform random distribution of anomalous exponent is an illustration of a “Black Swan,” the low probability event of the small value of the anomalous exponent that completely dominates the long-time behavior of subdiffusive systems.

Time-dependent Kohn-Sham approach to quantum electrodynamics

International Nuclear Information System (INIS)

Ruggenthaler, M.; Mackenroth, F.; Bauer, D.

2011-01-01

We prove a generalization of the van Leeuwen theorem toward quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. We circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external four-potential and four-current of the Kohn-Sham system are uniquely defined and that the effective four-current takes a very simple form. Further we rederive the Runge-Gross theorem for quantum electrodynamics.

The Harmonic Potential Theorem for a Quantum System with Time-Dependent Effective Mass

International Nuclear Information System (INIS)

Lai Meng-Yun; Xiao Duan-Liang; Pan Xiao-Yin

2015-01-01

We investigate the many-body wave function of a quantum system with time-dependent effective mass, confined by a harmonic potential with time-dependent frequency, and perturbed by a time-dependent spatially homogeneous electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the harmonic potential theorem wave function when both the effective mass and frequency are static. An example of application is also given. (paper)

A time-dependent neutron transport method of characteristics formulation with time derivative propagation

Energy Technology Data Exchange (ETDEWEB)

Hoffman, Adam J., E-mail: adamhoff@umich.edu; Lee, John C., E-mail: jcl@umich.edu

2016-02-15

A new time-dependent Method of Characteristics (MOC) formulation for nuclear reactor kinetics was developed utilizing angular flux time-derivative propagation. This method avoids the requirement of storing the angular flux at previous points in time to represent a discretized time derivative; instead, an equation for the angular flux time derivative along 1D spatial characteristics is derived and solved concurrently with the 1D transport characteristic equation. This approach allows the angular flux time derivative to be recast principally in terms of the neutron source time derivatives, which are approximated to high-order accuracy using the backward differentiation formula (BDF). This approach, called Source Derivative Propagation (SDP), drastically reduces the memory requirements of time-dependent MOC relative to methods that require storing the angular flux. An SDP method was developed for 2D and 3D applications and implemented in the computer code DeCART in 2D. DeCART was used to model two reactor transient benchmarks: a modified TWIGL problem and a C5G7 transient. The SDP method accurately and efficiently replicated the solution of the conventional time-dependent MOC method using two orders of magnitude less memory.

A time-dependent neutron transport method of characteristics formulation with time derivative propagation

International Nuclear Information System (INIS)

Hoffman, Adam J.; Lee, John C.

2016-01-01

A new time-dependent Method of Characteristics (MOC) formulation for nuclear reactor kinetics was developed utilizing angular flux time-derivative propagation. This method avoids the requirement of storing the angular flux at previous points in time to represent a discretized time derivative; instead, an equation for the angular flux time derivative along 1D spatial characteristics is derived and solved concurrently with the 1D transport characteristic equation. This approach allows the angular flux time derivative to be recast principally in terms of the neutron source time derivatives, which are approximated to high-order accuracy using the backward differentiation formula (BDF). This approach, called Source Derivative Propagation (SDP), drastically reduces the memory requirements of time-dependent MOC relative to methods that require storing the angular flux. An SDP method was developed for 2D and 3D applications and implemented in the computer code DeCART in 2D. DeCART was used to model two reactor transient benchmarks: a modified TWIGL problem and a C5G7 transient. The SDP method accurately and efficiently replicated the solution of the conventional time-dependent MOC method using two orders of magnitude less memory.

Characterizing the development of sectoral gross domestic product composition

Science.gov (United States)

Lutz, Raphael; Spies, Michael; Reusser, Dominik E.; Kropp, Jürgen P.; Rybski, Diego

2013-07-01

We consider the sectoral composition of a country's gross domestic product (GDP), i.e., the partitioning into agrarian, industrial, and service sectors. Exploring a simple system of differential equations, we characterize the transfer of GDP shares between the sectors in the course of economic development. The model fits for the majority of countries providing four country-specific parameters. Relating the agrarian with the industrial sector, a data collapse over all countries and all years supports the applicability of our approach. Depending on the parameter ranges, country development exhibits different transfer properties. Most countries follow three of eight characteristic paths. The types are not random but show distinct geographic and development patterns.

Exactly solvable position dependent mass schroedinger equation

International Nuclear Information System (INIS)

Koc, R.; Tuetuencueler, H.; Koercuek, E.

2002-01-01

Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems

''Free-space'' boundary conditions for the time-dependent wave equation

International Nuclear Information System (INIS)

Lindman, E.L.

1975-01-01

Boundary conditions for the discrete wave equation which act like an infinite region of free space in contact with the computational region can be constructed using projection operators. Propagating and evanescent waves coming from within the computational region generate no reflected waves as they cross the boundary. At the same time arbitrary waves may be launched into the computational region. Well known projection operators for one-dimensional waves may be used for this purpose in one dimension. Extensions of these operators to higher dimensions along with numerically efficient approximations to them are described for higher-dimensional problems. The separation of waves into ingoing and outgoing waves inherent in these boundary conditions greatly facilitates diagnostics

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

International Nuclear Information System (INIS)

Luz, H. L. F. da; Gammal, A.; Abdullaev, F. Kh.; Salerno, M.; Tomio, Lauro

2010-01-01

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

Science.gov (United States)

da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro

2010-10-01

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Gauss Seidel-type methods for energy states of a multi-component Bose Einstein condensate

Science.gov (United States)

Chang, Shu-Ming; Lin, Wen-Wei; Shieh, Shih-Feng

2005-01-01

In this paper, we propose two iterative methods, a Jacobi-type iteration (JI) and a Gauss-Seidel-type iteration (GSI), for the computation of energy states of the time-independent vector Gross-Pitaevskii equation (VGPE) which describes a multi-component Bose-Einstein condensate (BEC). A discretization of the VGPE leads to a nonlinear algebraic eigenvalue problem (NAEP). We prove that the GSI method converges locally and linearly to a solution of the NAEP if and only if the associated minimized energy functional problem has a strictly local minimum. The GSI method can thus be used to compute ground states and positive bound states, as well as the corresponding energies of a multi-component BEC. Numerical experience shows that the GSI converges much faster than JI and converges globally within 10-20 steps.

Equation for disentangling time-ordered exponentials with arbitrary quadratic generators

International Nuclear Information System (INIS)

Budanov, V.G.

1987-01-01

In many quantum-mechanical constructions, it is necessary to disentangle an operator-valued time-ordered exponential with time-dependent generators quadratic in the creation and annihilation operators. By disentangling, one understands the finding of the matrix elements of the time-ordered exponential or, in a more general formulation. The solution of the problem can also be reduced to calculation of a matrix time-ordered exponential that solves the corresponding classical problem. However, in either case the evolution equations in their usual form do not enable one to take into account explicitly the symmetry of the system. In this paper the methods of Weyl analysis are used to find an ordinary differential equation on a matrix Lie algebra that is invariant with respect to the adjoint action of the dynamical symmetry group of a quadratic Hamiltonian and replaces the operator evolution equation for the Green's function

First passage time problems in time-dependent fields

International Nuclear Information System (INIS)

Fletcher, J.E.; Havlin, S.; Weiss, G.H.

1988-01-01

This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency omega* for which the mean residence time on the line segment in a minimum. It is shown that for a random walk on a line segment of length L the mean residence time goes like L 2 for large L when omega omega*, but when omega = omega* the dependence is proportional to L. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation

Time-dependent tumour repopulation factors in linear-quadratic equations

International Nuclear Information System (INIS)

Dale, R.G.

1989-01-01

Tumour proliferation effects can be tentatively quantified in the linear-quadratic (LQ) method by the incorporation of a time-dependent factor, the magnitude of which is related both to the value of α in the tumour α/β ratio, and to the tumour doubling time. The method, the principle of which has been suggested by a numbre of other workers for use in fractionated therapy, is here applied to both fractionated and protracted radiotherapy treatments, and examples of its uses are given. By assuming that repopulation of late-responding tissues is significant during normal treatment strategies in terms of the behaviour of the Extrapolated Response Dose (ERD). Although the numerical credibility of the analysis used here depends on the reliability of the LQ model, and on the assumption that the rate of repopulation is constant throughout treatment, the predictions are consistent with other lines of reasoning which point to the advantages of accelerated hyperfractionation. In particular, it is demonstrated that accelerated fractionation represents a relatively 'foregiving' treatment which enables tumours of a variety of sensitivities and clonogenic growth rates to be treated moderately successfully, even though the critical cellular parameters may not be known in individual cases. The analysis also suggests that tumours which combine low intrinsic sensitivity with a very short doubling time might be bettter controlled by low dose-rate continuous therapy than by almost any form of accelerated hyperfractionation. (author). 24 refs.; 5 figs

Spectroscopy of dark soliton states in Bose-Einstein condensates

International Nuclear Information System (INIS)

Bongs, K; Burger, S; Hellweg, D; Kottke, M; Dettmer, S; Rinkleff, T; Cacciapuoti, L; Arlt, J; Sengstock, K; Ertmer, W

2003-01-01

Experimental and numerical studies of the velocity field of dark solitons in Bose-Einstein condensates are presented. The formation process after phase imprinting as well as the propagation of the emerging soliton are investigated using spatially resolved Bragg spectroscopy of soliton states in Bose-Einstein condensates of 87 Rb. A comparison of experimental data to results from numerical simulations of the Gross-Pitaevskii equation clearly identifies the flux underlying a dark soliton propagating in a Bose-Einstein condensate. The results allow further optimization of the phase imprinting method for creating collective excitations of Bose-Einstein condensates

Stability and decay rates of nonisotropic attractive Bose-Einstein condensates

International Nuclear Information System (INIS)

Huepe, C.; Tuckerman, L. S.; Metens, S.; Brachet, M. E.

2003-01-01

Nonisotropic attractive Bose-Einstein condensates are investigated numerically with Newton and inverse Arnoldi methods. The stationary solutions of the Gross-Pitaevskii equation and their linear stability are computed. Bifurcation diagrams are calculated and used to find the condensate decay rates corresponding to macroscopic quantum tunneling, two-three-body inelastic collisions, and thermally induced collapse. Isotropic and nonisotropic condensates are compared. The effect of anisotropy on the bifurcation diagram and the decay rates is discussed. Spontaneous isotropization of the condensates is found to occur. The influence of isotropization on the decay rates is characterized near the critical point

Stripes and honeycomb lattice of quantized vortices in rotating two-component Bose-Einstein condensates

Science.gov (United States)

Kasamatsu, Kenichi; Sakashita, Kouhei

2018-05-01

We study numerically the structure of a vortex lattice in rotating two-component Bose-Einstein condensates with equal atomic masses and equal intra- and intercomponent coupling strengths. The numerical simulations of the Gross-Pitaevskii equation show that the quantized vortices in this situation form lattice configuration accompanying vortex stripes, honeycomb lattices, and their complexes. This is a result of the degeneracy of the system for the SU(2) symmetric operation, which causes a continuous transformation between the above structures. In terms of the pseudospin representation, the complex lattice structures are identified as a hexagonal lattice of doubly winding half skyrmions.

Bose-Einstein condensation and symmetry breaking of a complex charged scalar field

International Nuclear Information System (INIS)

Matos, Tonatiuh; Castellanos, Elias; Suarez, Abril

2017-01-01

In this work the Klein-Gordon equation for a complex scalar field with U(1) symmetry endowed in a mexican-hat scalar field potential with thermal and electromagnetic contributions is written as a Gross-Pitaevskii (GP)-like equation. This equation is interpreted as a charged generalization of the GP equation at finite temperatures found in previous works. Its hydrodynamical representation is obtained and the corresponding thermodynamical properties are derived and related to measurable quantities. The condensation temperature in the non-relativistic regime associated with the aforementioned system within the semiclassical approximation is calculated. Also, a generalized equation for the conservation of energy for a charged bosonic gas is found when electromagnetic fields are introduced, and it is studied how under certain circumstances its breaking of symmetry can give some insight on the phase transition of the system not just into the condensed phase but also on other related systems. (orig.)

Bose-Einstein condensation and symmetry breaking of a complex charged scalar field

Energy Technology Data Exchange (ETDEWEB)

Matos, Tonatiuh [Centro de Investigacion y de Estudios Avanzados del IPN, Departamento de Fisica, Mexico, DF (Mexico); Castellanos, Elias [Centro de Investigacion y de Estudios Avanzados del IPN, Departamento de Fisica, Mexico, DF (Mexico); Universidad Autonoma de Chiapas, Mesoamerican Centre for Theoretical Physics, Tuxtla Gutierrez, Chiapas (Mexico); Suarez, Abril [Centro de Investigacion y de Estudios Avanzados del IPN, Departamento de Fisica, Mexico, DF (Mexico); Universidad Politecnica Metropolitana de Hidalgo, Departamento de Aeronautica, Tolcayuca, Hidalgo (Mexico)

2017-08-15

In this work the Klein-Gordon equation for a complex scalar field with U(1) symmetry endowed in a mexican-hat scalar field potential with thermal and electromagnetic contributions is written as a Gross-Pitaevskii (GP)-like equation. This equation is interpreted as a charged generalization of the GP equation at finite temperatures found in previous works. Its hydrodynamical representation is obtained and the corresponding thermodynamical properties are derived and related to measurable quantities. The condensation temperature in the non-relativistic regime associated with the aforementioned system within the semiclassical approximation is calculated. Also, a generalized equation for the conservation of energy for a charged bosonic gas is found when electromagnetic fields are introduced, and it is studied how under certain circumstances its breaking of symmetry can give some insight on the phase transition of the system not just into the condensed phase but also on other related systems. (orig.)

An explicit marching on-in-time solver for the time domain volume magnetic field integral equation

KAUST Repository

Sayed, Sadeed Bin

2014-07-01

Transient scattering from inhomogeneous dielectric objects can be modeled using time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marching on-in-time (MOT) techniques. Classical MOT-TDVIE solvers expand the field induced on the scatterer using local spatio-temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation in space and time yields a system of equations that is solved by time marching. Depending on the type of the basis and testing functions and the time step, the time marching scheme can be implicit (N. T. Gres, et al., Radio Sci., 36(3), 379-386, 2001) or explicit (A. Al-Jarro, et al., IEEE Trans. Antennas Propag., 60(11), 5203-5214, 2012). Implicit MOT schemes are known to be more stable and accurate. However, under low-frequency excitation, i.e., when the time step size is large, they call for inversion of a full matrix system at very time step.

An explicit marching on-in-time solver for the time domain volume magnetic field integral equation

KAUST Repository

Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan

2014-01-01

Transient scattering from inhomogeneous dielectric objects can be modeled using time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marching on-in-time (MOT) techniques. Classical MOT-TDVIE solvers expand the field induced on the scatterer using local spatio-temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation in space and time yields a system of equations that is solved by time marching. Depending on the type of the basis and testing functions and the time step, the time marching scheme can be implicit (N. T. Gres, et al., Radio Sci., 36(3), 379-386, 2001) or explicit (A. Al-Jarro, et al., IEEE Trans. Antennas Propag., 60(11), 5203-5214, 2012). Implicit MOT schemes are known to be more stable and accurate. However, under low-frequency excitation, i.e., when the time step size is large, they call for inversion of a full matrix system at very time step.

Time-dependent fatigue--phenomenology and life prediction

International Nuclear Information System (INIS)

Coffin, L.F.

1979-01-01

The time-dependent fatigue behavior of materials used or considered for use in present and advanced systems for power generation is outlined. A picture is first presented to show how basic mechanisms and phenomenological information relate to the performance of the component under consideration through the so-called local strain approach. By this means life prediction criteria and design rules can be formulated utilizing laboratory test information which is directly translated to predicting the performance of a component. The body of phenomenological information relative to time-dependent fatigue is reviewed. Included are effects of strain range, strain rate and frequency, environment and wave shape, all of which are shown to be important in developing both an understanding and design base for time dependent fatigue. Using this information, some of the current methods being considered for the life prediction of components are reviewed. These include the current ASME code case, frequency-modified fatigue equations, strain range partitioning, the damage function method, frequency separation and damage rate equations. From this review, it is hoped that a better perspective on future directions for basic material science at high temperature can be achieved

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

Science.gov (United States)

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Davydov–Chaban Hamiltonian in presence of time-dependent potential

Energy Technology Data Exchange (ETDEWEB)

Sobhani, Hadi; Hassanabadi, Hassan, E-mail: h.hassanabadi@shahroodut.ac.ir

2016-09-10

In this article, we have investigated collective effects of atomic nuclei in presence of a time-dependent potential in Davydov–Chaban Hamiltonian. Since such potential has an explicit time-dependency, in order to obtain the wave function of considered system, we should face with time-dependent Schrödinger equation. Obtaining the wave function could be possible using Lewis–Riesenfeld dynamical invariant method. Appropriate dynamical invariant has been constructed after determining the wave functions and values, the wave function will obtain.

Time-dependent mean-field games in the superquadratic case

KAUST Repository

Gomes, Diogo A.

2016-04-06

We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as key techniques used in the subquadratic case, which was studied in a previous publication of the authors, do not extend to the superquadratic setting. The main objective of the present paper is to address these difficulties. Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton−Jacobi equation are obtained here through a novel set of techniques. These explore the parabolic nature of the problem through the nonlinear adjoint method. Well-posedness is proven by combining Lipschitz regularity for the Hamilton−Jacobi equation with polynomial estimates for solutions of the Fokker−Planck equation. Existence of classical solutions is then established under conditions depending only on the growth of the Hamiltonian and the dimension. Our results also add to current understanding of superquadratic Hamilton−Jacobi equations.

Time-dependent mean-field games in the superquadratic case

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard; Sá nchez-Morgado, Hé ctor

2016-01-01

We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as key techniques used in the subquadratic case, which was studied in a previous publication of the authors, do not extend to the superquadratic setting. The main objective of the present paper is to address these difficulties. Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton−Jacobi equation are obtained here through a novel set of techniques. These explore the parabolic nature of the problem through the nonlinear adjoint method. Well-posedness is proven by combining Lipschitz regularity for the Hamilton−Jacobi equation with polynomial estimates for solutions of the Fokker−Planck equation. Existence of classical solutions is then established under conditions depending only on the growth of the Hamiltonian and the dimension. Our results also add to current understanding of superquadratic Hamilton−Jacobi equations.

Preliminary Formulation of Finite Element Solution for the 1-D, 1-G Time Dependent Neutron Diffusion Equation without Consideration about Delay Neutron

Energy Technology Data Exchange (ETDEWEB)

Ryu, Eun Hyun; Song, Yong Mann; Park, Joo Hwan [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2013-05-15

If time-dependent equation is solved with the FEM, the limitation of the input geometry will disappear. It has often been pointed out that the numerical methods implemented in the RFSP code are not state-of-the-art. Although an acceleration method such as the Coarse Mesh Finite Difference (CMFD) for Finite Difference Method (FDM) does not exist for the FEM, one should keep in mind that the number of time steps for the transient simulation is not large. The rigorous formulation in this study will richen the theoretical basis of the FEM and lead to an extension of the dynamics code to deal with a more complicated problem. In this study, the formulation for the 1-D, 1-G Time Dependent Neutron Diffusion Equation (TDNDE) without consideration of the delay neutron will first be done. A problem including one multiplying medium will be solved. Also several conclusions from a comparison between the numerical and analytic solutions, a comparison between solutions with various element orders, and a comparison between solutions with different time differencing will be made to be certain about the formulation and FEM solution. By investigating various cases with different values of albedo, theta, and the order of elements, it can be concluded that the finite element solution is agree well with the analytic solution. The higher the element order used, the higher the accuracy improvements are obtained.

Numerical integration of the Teukolsky equation in the time domain

International Nuclear Information System (INIS)

Pazos-Avalos, Enrique; Lousto, Carlos O.

2005-01-01

We present a fourth-order convergent (2+1)-dimensional, numerical formalism to solve the Teukolsky equation in the time domain. Our approach is first to rewrite the Teukolsky equation as a system of first-order differential equations. In this way we get a system that has the form of an advection equation. This is then used in combination with a series expansion of the solution in powers of time. To obtain a fourth-order scheme we kept terms up to fourth derivative in time and use the advectionlike system of differential equations to substitute the temporal derivatives by spatial derivatives. This scheme is applied to evolve gravitational perturbations in the Schwarzschild and Kerr backgrounds. Our numerical method proved to be stable and fourth-order convergent in r* and θ directions. The correct power-law tail, ∼1/t 2l+3 , for general initial data, and ∼1/t 2l+4 , for time-symmetric data, was found in our runs. We noted that it is crucial to resolve accurately the angular dependence of the mode at late times in order to obtain these values of the exponents in the power-law decay. In other cases, when the decay was too fast and round-off error was reached before a tail was developed, then the quasinormal modes frequencies provided a test to determine the validity of our code

Finite-temperature effects in helical quantum turbulence

Science.gov (United States)

Clark Di Leoni, Patricio; Mininni, Pablo D.; Brachet, Marc E.

2018-04-01

We perform a study of the evolution of helical quantum turbulence at different temperatures by solving numerically the Gross-Pitaevskii and the stochastic Ginzburg-Landau equations, using up to 40963 grid points with a pseudospectral method. We show that for temperatures close to the critical one, the fluid described by these equations can act as a classical viscous flow, with the decay of the incompressible kinetic energy and the helicity becoming exponential. The transition from this behavior to the one observed at zero temperature is smooth as a function of temperature. Moreover, the presence of strong thermal effects can inhibit the development of a proper turbulent cascade. We provide Ansätze for the effective viscosity and friction as a function of the temperature.

Particle-Hole Asymmetry and Brightening of Solitons in a Strongly Repulsive Bose-Einstein Condensate

International Nuclear Information System (INIS)

Balakrishnan, Radha; Satija, Indubala I.; Clark, Charles W.

2009-01-01

We study solitary wave propagation in the condensate of a system of hard-core bosons with nearest-neighbor interactions. For this strongly repulsive system, the evolution equation for the condensate order parameter of the system, obtained using spin-coherent state averages, is different from the usual Gross-Pitaevskii equation (GPE). The system is found to support two kinds of solitons when there is a particle-hole imbalance: a dark soliton that dies out as the velocity approaches the sound velocity and a new type of soliton which brightens and persists all the way up to the sound velocity, transforming into a periodic wave train at supersonic speed. Analogous to the GPE soliton, the energy-momentum dispersion for both solitons is characterized by Lieb II modes.

Analysis of the dual phase lag bio-heat transfer equation with constant and time-dependent heat flux conditions on skin surface

Directory of Open Access Journals (Sweden)

Ziaei Poor Hamed

2016-01-01

Full Text Available This article focuses on temperature response of skin tissue due to time-dependent surface heat fluxes. Analytical solution is constructed for DPL bio-heat transfer equation with constant, periodic and pulse train heat flux conditions on skin surface. Separation of variables and Duhamel’s theorem for a skin tissue as a finite domain are employed. The transient temperature responses for constant and time-dependent boundary conditions are obtained and discussed. The results show that there is major discrepancy between the predicted temperature of parabolic (Pennes bio-heat transfer, hyperbolic (thermal wave and DPL bio-heat transfer models when high heat flux accidents on the skin surface with a short duration or propagation speed of thermal wave is finite. The results illustrate that the DPL model reduces to the hyperbolic model when τT approaches zero and the classic Fourier model when both thermal relaxations approach zero. However for τq = τT the DPL model anticipates different temperature distribution with that predicted by the Pennes model. Such discrepancy is due to the blood perfusion term in energy equation. It is in contrast to results from the literature for pure conduction material, where the DPL model approaches the Fourier heat conduction model when τq = τT . The burn injury is also investigated.

Simulation of time-dependent free-surface Navier-Stokes flows

International Nuclear Information System (INIS)

Muldowney, G.P.

1989-01-01

Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N 3 ) operations per timestep despite the presence of deforming geometry. The first approach is a domain-integral formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a particular-solution formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops

Gross xenon stability

International Nuclear Information System (INIS)

Lewins, J.D.; Wilson, P.P.H.

1997-01-01

The effect of xenon in thermal reactors on steady operation is generally destabilizing. Illustrating this involves the study of appropriate transfer functions, which may be conveniently displayed in three ways: as Bode, Nyquist, and root-locus diagrams. The three forms allow different aspects to be highlighted. These are illustrated for the effect of xenon with allowance not only for the stabilizing effect of the direct yield in fission but also to show the consequences of neglecting the time dependence due to the thermal capacity of the reactor. With careful interpretation, all these forms give an interpretation of stability that is consistent with direct evaluation and promote the understanding of the onset of gross oscillations in power

Effect of the time spent by the photon in the absorbed state on the time-dependent transfer of radiation

International Nuclear Information System (INIS)

Rao, D.M.; Rangarajan, K.E.; Peraiah, A.

1990-01-01

The time-dependent transfer equation is derived for a two-level atomic model which takes both bound-bound and bound-free transitions into account. A numerical scheme is proposed for solving the monochromatic time-dependent transfer equation when the time spent by the photon in the absorbed state is significant. The method can be easily extended to solve the problem of time-dependent line formation of the bound-free continuum. It is used here to study three types of boundary conditions of the incident radiation incident on a scattering atmosphere. The quantitative results show that the relaxation of the radiation field depends on the optical depth of the medium and on the ray's angle of emergence. 21 refs

The recovery of a time-dependent point source in a linear transport equation: application to surface water pollution

International Nuclear Information System (INIS)

Hamdi, Adel

2009-01-01

The aim of this paper is to localize the position of a point source and recover the history of its time-dependent intensity function that is both unknown and constitutes the right-hand side of a 1D linear transport equation. Assuming that the source intensity function vanishes before reaching the final control time, we prove that recording the state with respect to the time at two observation points framing the source region leads to the identification of the source position and the recovery of its intensity function in a unique manner. Note that at least one of the two observation points should be strategic. We establish an identification method that determines quasi-explicitly the source position and transforms the task of recovering its intensity function into solving directly a well-conditioned linear system. Some numerical experiments done on a variant of the water pollution BOD model are presented

almaBTE : A solver of the space-time dependent Boltzmann transport equation for phonons in structured materials

Science.gov (United States)

Carrete, Jesús; Vermeersch, Bjorn; Katre, Ankita; van Roekeghem, Ambroise; Wang, Tao; Madsen, Georg K. H.; Mingo, Natalio

2017-11-01

almaBTE is a software package that solves the space- and time-dependent Boltzmann transport equation for phonons, using only ab-initio calculated quantities as inputs. The program can predictively tackle phonon transport in bulk crystals and alloys, thin films, superlattices, and multiscale structures with size features in the nm- μm range. Among many other quantities, the program can output thermal conductances and effective thermal conductivities, space-resolved average temperature profiles, and heat-current distributions resolved in frequency and space. Its first-principles character makes almaBTE especially well suited to investigate novel materials and structures. This article gives an overview of the program structure and presents illustrative examples for some of its uses. PROGRAM SUMMARY Program Title:almaBTE Program Files doi:http://dx.doi.org/10.17632/8tfzwgtp73.1 Licensing provisions: Apache License, version 2.0 Programming language: C++ External routines/libraries: BOOST, MPI, Eigen, HDF5, spglib Nature of problem: Calculation of temperature profiles, thermal flux distributions and effective thermal conductivities in structured systems where heat is carried by phonons Solution method: Solution of linearized phonon Boltzmann transport equation, Variance-reduced Monte Carlo

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

Science.gov (United States)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

A Method Validation for Determination of Gross Alpha and Gross Beta in Water Sample Using Low Background Gross Alpha/ Beta Counting System

International Nuclear Information System (INIS)

Zal Uyun Wan Mahmood; Norfaizal Mohamed; Nita Salina Abu Bakar

2016-01-01

Method validation (MV) for the measurement of gross alpha and gross beta activity in water (drinking, mineral and environmental) samples using Low Background Gross Alpha/ Beta Counting System was performed to characterize precision, accuracy and reliable results. The main objective of this assignment is to ensure that both the instrument and method always good performed and resulting accuracy and reliable results. Generally, almost the results of estimated RSD, z-score and U_s_c_o_r_e were reliable which are recorded as ≤30 %, less than 2 and less than 1.5, respectively. Minimum Detected Activity (MDA) was estimated based on the counting time of 100 minutes and present background counting value of gross alpha (0.01 - 0.35 cpm) and gross beta (0.50 - 2.18 cpm). Estimated Detection Limit (DL) was 0.1 Bq/ L for gross alpha and 0.2 Bq/ L for gross beta and expended uncertainty was relatively small of 9.77 % for gross alpha and 10.57 % for gross beta. Align with that, background counting for gross alpha and gross beta was ranged of 0.01 - 0.35 cpm and 0.50 - 2.18 cpm, respectively. While, sample volume was set at minimum of 500 mL and maximum of 2000 mL. These proven the accuracy and precision result that are generated from developed method/ technique is satisfactory and method is recommended to be used. Therefore, it can be concluded that the MV found no doubtful on the ability of the developed method. The test result showed the method is suitable for all types of water samples which are contained several radionuclides and elements as well as any impurities that interfere the measurement analysis of gross alpha and gross beta. (author)

Gross alpha/beta analyses in water by liquid scintillation counting

International Nuclear Information System (INIS)

Wong, C.T.; Lawrence Livermore National Laboratory, CA; Soliman, V.M.; Perera, S.K.

2005-01-01

The standard procedure for analyzing gross alpha and gross beta in water is evaporation of the sample and radioactivity determination of the resultant solids by proportional counting. This technique lacks precision, and lacks sensitivity for samples with high total dissolved solids. Additionally, the analytical results are dependent on the choice of radionuclide calibration standard and the sample matrix. Direct analysis by liquid scintillation counting has the advantages of high counting efficiencies and minimal sample preparation time. However, due to the small sample aliquants used for analysis, long count times are necessary to reach required detection limits. The procedure proposed consists of evaporating a sample aliquant to dryness, dissolving the resultant solids in a small volume of dilute acid, followed by liquid scintillation counting to determine radioactivity. This procedure can handle sample aliquants containing up to 500 mg of dissolved solids. Various acids, scintillation cocktail mixtures, instrument discriminator settings, and regions of interest (ROI) were evaluated to determine optimum counting conditions. Precision is improved and matrix effects are reduced as compared to proportional counting. Tests indicate that this is a viable alternative to proportional counting for gross alpha and gross beta analyses of water samples. (author)

TIMEX: a time-dependent explicit discrete ordinates program for the solution of multigroup transport equations with delayed neutrons

International Nuclear Information System (INIS)

Hill, T.R.; Reed, W.H.

1976-01-01

TIMEX solves the time-dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time steps can be taken. Because no iteration is performed the method is exceptionally fast in terms of computing time per time step. Two acceleration methods, exponential extrapolation and rebalance, are utilized to improve the accuracy of the time differencing scheme. Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. The running time for TIMEX is highly problem-dependent, but varies almost linearly with the total number of unknowns and time steps. Provision is made for creation of standard interface output files for angular fluxes and angle-integrated fluxes. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage. 13 tables, 9 figures

A maximum principle for time dependent transport in systems with voids

International Nuclear Information System (INIS)

Schofield, S.L.; Ackroyd, R.T.

1996-01-01

A maximum principle is developed for the first-order time dependent Boltzmann equation. The maximum principle is a generalization of Schofield's κ(θ) principle for the first-order steady state Boltzmann equation, and provides a treatment of time dependent transport in systems with void regions. The formulation comprises a direct least-squares minimization allied with a suitable choice of bilinear functional, and gives rise to a maximum principle whose functional is free of terms that have previously led to difficulties in treating void regions. (Author)

Exact time-dependent exchange-correlation potentials for strong-field electron dynamics

International Nuclear Information System (INIS)

Lein, Manfred; Kuemmel, Stephan

2005-01-01

By solving the time-dependent Schroedinger equation and inverting the time-dependent Kohn-Sham scheme we obtain the exact time-dependent exchange-correlation potential of density-functional theory for the strong-field dynamics of a correlated system. We demonstrate that essential features of the exact exchange-correlation potential can be related to derivative discontinuities in stationary density-functional theory. Incorporating the discontinuity in a time-dependent density-functional calculation greatly improves the description of the ionization process

The time dependent Hartree-Fock-theory for collective nuclear motions

International Nuclear Information System (INIS)

Goeke, K.

1976-11-01

The time-dependent Hartree-Fock theory (TDHF) approximately solves the Schroedinger equation by a variational method in the space of the time-dependent Slater determinants. As the TDHF wave function, similar to the exact solution has the property of being determined completely for all times by the nucleon-nucleon interaction and by assuming initial conditions. TDHF is expected to describe collective motion of nuclei with large amplitudes, too. The subject of this paper is to formulate the TDHF theory and its adiabatic limiting case (ATDHF) suited for setting up a collective Schroedinger equation, to investigate the relations with other theories, and to show the applicability for solving practical problems. (orig./WL) [de

FAST: a three-dimensional time-dependent FEL simulation code

International Nuclear Information System (INIS)

Saldin, E.L.; Schneidmiller, E.A.; Yurkov, M.V.

1999-01-01

In this report we briefly describe the three-dimensional, time-dependent FEL simulation code FAST. The equations of motion of the particles and Maxwell's equations are solved simultaneously taking into account the slippage effect. Radiation fields are calculated using an integral solution of Maxwell's equations. A special technique has been developed for fast calculations of the radiation field, drastically reducing the required CPU time. As a result, the developed code allows one to use a personal computer for time-dependent simulations. The code allows one to simulate the radiation from the electron bunch of any transverse and longitudinal bunch shape; to simulate simultaneously an external seed with superimposed noise in the electron beam; to take into account energy spread in the electron beam and the space charge fields; and to simulate a high-gain, high-efficiency FEL amplifier with a tapered undulator. It is important to note that there are no significant memory limitations in the developed code and an electron bunch of any length can be simulated

QUIPS: Time-dependent properties of quasi-invariant self-gravitating polytropes

International Nuclear Information System (INIS)

Munier, A.; Feix, M.R.

1983-01-01

Quasi-invariance, a method based on group tranformations, is used to obtain time-dependent solutions for the expansion and/or contraction of a self-gravitating sphere of perfect gas with polytopic index n. Quasi-invariance transforms the equations of hydrodynamics into ''dual equations'' exhibiting extra terms such as a friction, a mass source or sink term, and a centripetal/centrifugal force. The search for stationary solutions in this ''dual space'' leads to a new class of time-dependent solutions, the QUIP (for Quasi-invariant polytrope), which generalizes Emden's static model and introduces a characteristic frequency a related to Jean's frequency. The second order differential equation describing the solution is integrated numerically. A critical point is seen always to exist for nnot =3. Solutions corresponding in the ''dual space'' to a time-dependent generalization of Eddington's standard model (n = 3) are discussed. These solutions conserve both the total mass and the energy. A transition between closed and open structures is seen to take place at a particular frequency a/sub c/. For n = 3, no critical point arises in the ''dual space'' due to the self-similar motion of the fluid. A new time-dependent mass-radius relation and a generalized Betti-Ritter relation are obtained. Conclusions about the existence of a minimum Q-factor are presented

Non-autonomous bright–dark solitons and Rabi oscillations in multi-component Bose–Einstein condensates

International Nuclear Information System (INIS)

Kanna, T; Mareeswaran, R Babu; Tsitoura, F; Nistazakis, H E; Frantzeskakis, D J

2013-01-01

We study the dynamics of non-autonomous bright–dark matter-wave solitons in two- and three-component Bose–Einstein condensates. Our setting includes a time-dependent parabolic potential and scattering length, as well as Rabi coupling of the separate hyperfine states. By means of a similarity transformation, we transform the non-autonomous coupled Gross–Pitaevskii equations into the completely integrable Manakov model with defocusing nonlinearity, and construct the explicit form of the non-autonomous soliton solutions. The propagation characteristics for the one-soliton state, and collision scenarios for multiple soliton states are discussed in detail for two types of time-dependent nonlinearities: a kink-like one and a periodically modulated one, with appropriate time-dependence of the trapping potential. We find that in the two-component condensates the nature of soliton propagation is determined predominantly by the nature of the nonlinearity, as well as the temporal modulation of the harmonic potential; switching in this setting is essentially due to Rabi coupling. We also perform direct numerical simulation of the non-autonomous two-component coupled Gross–Pitaevskii equations to corroborate our analytical predictions. More interestingly, in the case of the three-component condensates, we find that the solitons can lead to collision-induced energy switching (energy sharing collision), that can be profitably used to control Rabi switching or vice versa. An interesting possibility of reversal of the nature of the constituent soliton, i.e., bright (dark) into dark (bright) due to Rabi coupling is demonstrated in the three-component setting. (paper)

Exact solutions of Feinberg–Horodecki equation for time-dependent ...

Indian Academy of Sciences (India)

proposed to find the exact solutions of the Feinberg–Horodecki equation for the .... is a polynomial of degree n and satisfies the Rodrigues relation [24] ... The discriminant of expression (15) under the square root has to be zero, so that the.

Numerical studies of time-independent and time-dependent scattering by several elliptical cylinders

Science.gov (United States)

Nigsch, Martin

2007-07-01

A numerical solution to the problem of time-dependent scattering by an array of elliptical cylinders with parallel axes is presented. The solution is an exact one, based on the separation-of-variables technique in the elliptical coordinate system, the addition theorem for Mathieu functions, and numerical integration. Time-independent solutions are described by a system of linear equations of infinite order which are truncated for numerical computations. Time-dependent solutions are obtained by numerical integration involving a large number of these solutions. First results of a software package generating these solutions are presented: wave propagation around three impenetrable elliptical scatterers. As far as we know, this method described has never been used for time-dependent multiple scattering.

Sensitivity and uncertainty analysis for functionals of the time-dependent nuclide density field

International Nuclear Information System (INIS)

Williams, M.L.; Weisbin, C.R.

1978-04-01

An approach to extend the present ORNL sensitivity program to include functionals of the time-dependent nuclide density field is developed. An adjoint equation for the nuclide field was derived previously by using generalized perturbation theory; the present derivation makes use of a variational principle and results in the same equation. The physical significance of this equation is discussed and compared to that of the time-dependent neutron adjoint equation. Computational requirements for determining sensitivity profiles and uncertainties for functionals of the time-dependent nuclide density vector are developed within the framework of the existing FORSS system; in this way the current capability is significantly extended. The development, testing, and use of an adjoint version of the ORIGEN isotope generation and depletion code are documented. Finally, a sample calculation is given which estimates the uncertainty in the plutonium inventory at shutdown of a PWR due to assumed uncertainties in uranium and plutonium cross sections. 8 figures, 4 tables

Approach and separation of quantum vortices with balanced cores

Science.gov (United States)

Kerr, Robert M.; Rorai, C.; Skipper, J.; Sreenivasan, K. R.

2014-11-01

Using two innovations, smooth but different, scaling laws for the reconnection of pairs of initially orthogonal and anti-parallel quantum vortices are obtained using the three-dimensional Gross-Pitaevskii equations. For the anti-parallel case, the scaling laws just before and after reconnection obey the dimensional δ ~ | t - tr| 1 / 2 prediction with temporal symmetry about the reconnection time tr and physical space symmetry about xr, the mid-point between the vortices, with extensions forming the edges of an equilateral pyramid. For all of the orthogonal cases, before reconnection δin ~(t -tr) 1 / 3 and after reconnection δout ~(tr - t) 2 / 3 , which are respectively slower and faster than the dimensional prediction. In these cases, the reconnection takes place in a plane defined by the directions of the curvature and vorticity. Robert.Kerr@warwick.ac.uk.

Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method

International Nuclear Information System (INIS)

Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.

2010-01-01

The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

Science.gov (United States)

Yuzbashyan, Emil A.

2018-05-01

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

Surface harmonics method for two-dimensional time-dependent neutron transport problems of square-lattice nuclear reactors

Energy Technology Data Exchange (ETDEWEB)

Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A. [National Research Centre Kurchatov Institute, Kurchatov Sq. 1, Moscow (Russian Federation)

2013-07-01

Time-dependent equations of the Surface Harmonics Method (SHM) have been derived from the time-dependent neutron transport equation with explicit representation of delayed neutrons for solving the two-dimensional time-dependent problems. These equations have been realized in the SUHAM-TD code. The TWIGL benchmark problem has been used for verification of the SUHAM-TD code. The results of the study showed that computational costs required to achieve necessary accuracy of the solution can be an order of magnitude less than with the use of the conventional finite difference method (FDM). (authors)

Finite-difference solution of the space-angle-lethargy-dependent slowing-down transport equation

Energy Technology Data Exchange (ETDEWEB)

Matausek, M V [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1972-07-01

A procedure has been developed for solving the slowing-down transport equation for a cylindrically symmetric reactor system. The anisotropy of the resonance neutron flux is treated by the spherical harmonics formalism, which reduces the space-angle-Iethargy-dependent transport equation to a matrix integro-differential equation in space and lethargy. Replacing further the lethargy transfer integral by a finite-difference form, a set of matrix ordinary differential equations is obtained, with lethargy-and space dependent coefficients. If the lethargy pivotal points are chosen dense enough so that the difference correction term can be ignored, this set assumes a lower block triangular form and can be solved directly by forward block substitution. As in each step of the finite-difference procedure a boundary value problem has to be solved for a non-homogeneous system of ordinary differential equations with space-dependent coefficients, application of any standard numerical procedure, for example, the finite-difference method or the method of adjoint equations, is too cumbersome and would make the whole procedure practically inapplicable. A simple and efficient approximation is proposed here, allowing analytical solution for the space dependence of the spherical-harmonics flux moments, and hence the derivation of the recurrence relations between the flux moments at successive lethargy pivotal points. According to the procedure indicated above a computer code has been developed for the CDC -3600 computer, which uses the KEDAK nuclear data file. The space and lethargy distribution of the resonance neutrons can be computed in such a detailed fashion as the neutron cross-sections are known for the reactor materials considered. The computing time is relatively short so that the code can be efficiently used, either autonomously, or as part of some complex modular scheme. Typical results will be presented and discussed in order to prove and illustrate the applicability of the

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations. [with applications to Burger equation and stream function-vorticity problem

Science.gov (United States)

Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.

1978-01-01

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

The roles of time and displacement in velocity-dependent volumetric strain of fault zones

Science.gov (United States)

Beeler, N.M.; Tullis, T.E.

1997-01-01

The relationship between measured friction??A and volumetric strain during frictional sliding was determined using a rate and state variable dependent friction constitutive equation, a common work balance relating friction and volume change, and two types of experimental faults: initially bare surfaces of Westerly granite and rock surfaces separated by a 1 mm layer of derivative of fault normal displacement with respect shear displacement, d??n ld??s. An implication of this relationship is that the rate dependence of d??n ld??s contributes to the rate dependence of ??A. Experiments show changes in sliding velocity lead to changes in both fault strength and volume. Analysis of data with the rate and state equations combined with the work balance relationship preclude the conventional interpretation of the direct effect in the rate and state variable constitutive equations. Consideration of a model bare surface fault consisting of an undeformable indentor sliding on a deformable surface reveals a serious flaw in the work balance relationship if volume change is time-dependent. For the model, at zero slip rate indentation creep under the normal load leads to time-dependent strengthening of the fault surface but, according to the work balance relationship, no work is done because compaction or dilatancy can only be induced by shearing. Additional tests on initially bare surfaces and gouges show that fault normal strain in experiments is time-dependent, consistent with the model. This time-dependent fault normal strain, which is not accounted for in the work balance relationship, explains the inconsistency between the constitutive equations and the work balance. For initially bare surface faults, all rate dependence of volume change is due to time dependence. Similar results are found for gouge. We conclude that ??A reflects the frictional resistance that results in shear heating, and no correction needs to be made for the volume changes. The result that time-dependent

Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

International Nuclear Information System (INIS)

Sherrill, M.E.; Abdallah, J. Jr.; Csanak, G.; Kilcrease, D.P.; Dodd, E.S.; Fukuda, Y.; Akahane, Y.; Aoyama, M.; Inoue, N.; Ueda, H.; Yamakawa, K.; Faenov, A.Ya.; Magunov, A.I.; Pikuz, T.A.; Skobelev, I.Yu.

2006-01-01

In this work, we present a model that solves self-consistently the electron and atomic kinetics to characterize highly non-equilibrium plasmas, in particular for those systems where both the electron distribution function is far from Maxwellian and the evolution of the ion level populations are dominated by time-dependent atomic kinetics. In this model, level populations are obtained from a detailed collisional-radiative model where collision rates are computed from a time varying electron distribution function obtained from the solution of the zero-dimensional Boltzmann equation. The Boltzmann collision term includes the effects of electron-electron collisions, electron collisional ionization, excitation and de-excitation. An application for He α spectra from a short pulse laser irradiated argon cluster target will be shown to illustrate the results of our model

Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

Energy Technology Data Exchange (ETDEWEB)

Sherrill, M.E. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States)]. E-mail: manolo@t4.lanl.gov; Abdallah, J. Jr. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Csanak, G. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Kilcrease, D.P. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Dodd, E.S. [Los Alamos National Laboratory, X-1, Los Alamos, NM 87545 (United States); Fukuda, Y. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Akahane, Y. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Aoyama, M. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Inoue, N. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Ueda, H. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Yamakawa, K. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Faenov, A.Ya. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Magunov, A.I. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Pikuz, T.A. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Skobelev, I.Yu. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation)

2006-05-15

In this work, we present a model that solves self-consistently the electron and atomic kinetics to characterize highly non-equilibrium plasmas, in particular for those systems where both the electron distribution function is far from Maxwellian and the evolution of the ion level populations are dominated by time-dependent atomic kinetics. In this model, level populations are obtained from a detailed collisional-radiative model where collision rates are computed from a time varying electron distribution function obtained from the solution of the zero-dimensional Boltzmann equation. The Boltzmann collision term includes the effects of electron-electron collisions, electron collisional ionization, excitation and de-excitation. An application for He{sub {alpha}} spectra from a short pulse laser irradiated argon cluster target will be shown to illustrate the results of our model.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-01-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Energy Technology Data Exchange (ETDEWEB)

Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory; Morel, Jim E [TEXAS A& M UNIV

2008-01-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Science.gov (United States)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Dynamics of bright-bright solitons in Bose-Einstein condensate with Raman-induced one-dimensional spin-orbit coupling

Science.gov (United States)

Wen, Lin; Zhang, Xiao-Fei; Hu, Ai-Yuan; Zhou, Jing; Yu, Peng; Xia, Lei; Sun, Qing; Ji, An-Chun

2018-03-01

We investigate the dynamics of bright-bright solitons in one-dimensional two-component Bose-Einstein condensates with Raman-induced spin-orbit coupling, via the variational approximation and the numerical simulation of Gross-Pitaevskii equations. For the uniform system without trapping potential, we obtain two population balanced stationary solitons. By performing the linear stability analysis, we find a Goldstone eigenmode and an oscillation eigenmode around these stationary solitons. Moreover, we derive a general dynamical solution to describe the center-of-mass motion and spin evolution of the solitons under the action of spin-orbit coupling. The effects of a harmonic trap have also been discussed.

Nonlinear dynamics in a trapped atomic Bose-Einstein condensate induced by an oscillating Gaussian potential

International Nuclear Information System (INIS)

Fujimoto, Kazuya; Tsubota, Makoto

2011-01-01

We consider a trapped atomic Bose-Einstein condensate penetrated by a repulsive Gaussian potential and theoretically investigate the dynamics induced by oscillating the Gaussian potential. Our study is based on the numerical calculation of the two-dimensional Gross-Pitaevskii equation. Our calculation reveals the dependence of the characteristic behavior of the condensate on the amplitude and frequency of the oscillating potential. These dynamics are deeply related to the nucleation and dynamics of quantized vortices and solitons. When the potential oscillates with a large amplitude, it nucleates many vortex pairs that move away from the potential. When the amplitude of the oscillation is small, it nucleates solitons through an annihilation of vortex pairs. We discuss three issues concerning the nucleation of vortices. The first is the phase diagram for the nucleation of vortices and solitons near the oscillating potential. The second is the mechanism and critical velocity of the nucleation. The critical velocity of the nucleation is an important issue in quantum fluids, and we propose an expression for the velocity containing both the coherence length and the size of the potential. The third is the divergence of the nucleation time, which is the time it takes for the potential to nucleate vortices, near the critical parameters for vortex nucleation.

Stability of time-dependent particle-like solutions of some wave equations

International Nuclear Information System (INIS)

Voronov, N.A.

1978-01-01

The proof of the nonstability of the one-dimensional periodical localized solutions of the equation with a spontaneously broken symmetry is given. The stability of the one-dimensional oscillating solutions of the sine-Gordon equation was also considered with regard to such perturbations. As it was expected these solutions proved to be stable

Time-independent integral equation for Maxwell's system. Application of radar cross section computation

International Nuclear Information System (INIS)

Pujols, Agnes

1991-01-01

We prove that the scattering operator for the wave equation in the exterior of an non-homogeneous obstacle exists. Its distribution kernel is represented by a time-dependent boundary integral equation. A space-time integral variational formulation is developed for determining the current induced by the scattering of an electromagnetic wave by an homogeneous object. The discrete approximation of the variational problem using a finite element method in both space and time leads to stable convergent schemes, giving a numerical code for perfectly conducting cylinders. (author) [fr

Determination of gross gamma and gross beta activities in liquid effluent samples. Phase I

International Nuclear Information System (INIS)

Curtis, K.E.; Sood, S.P.

1985-08-01

Several inadequacies in the presently used procedures for gross gamma and gross beta measurements in aqueous wastes have been identified. Both the presence of suspended particulate activity and the use of cesium-137 as a calibration standard can cause gross gamma measurements to overestimate the actual activity in the sample. At the same time, sample preparation for the determination of gross beta activities causes large losses of radioiodine before the measurement step and the presence of solid material can cause a serious decrease in the beta counting efficiency. A combination of these errors could result in large discrepancies between the results obtained by the two measurement methods. Improved procedures are required to overcome these problems

A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media

KAUST Repository

Duru, Kenneth

2014-01-01

A mathematical analysis of the perfectly matched layer (PML) for the time-dependent wave equation in heterogeneous and layered media is presented. We prove the stability of the PML for discontinuous media with piecewise constant coefficients, and derive energy estimates for discontinuous media with piecewise smooth coefficients. We consider a computational setup consisting of smaller structured subdomains that are discretized using high order accurate finite difference operators for approximating spatial derivatives. The subdomains are then patched together into a global domain by a weak enforcement of interface conditions using penalties. In order to ensure the stability of the discrete PML, it is necessary to transform the interface conditions to include the auxiliary variables. In the discrete setting, the transformed interface conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates, thus proving stability and convergence of the numerical method. Finally, we present numerical experiments demonstrating the stability of the PML in a layered medium and high order accuracy of the proposed interface conditions. © 2013 Elsevier Inc.

A Langevin simulation of the Gross-Neveu spectrum

International Nuclear Information System (INIS)

Lacaze, R.; Morel, A.; Petersson, B.

1989-01-01

We study the order parameter of Chiral symmetry, and fermion and boson masses in the Gross-Neveu model as a function of the flavour number N and of the Langevin time step ε in the scaling region. The 1/N dependence of the ε=0 value of the order parameter is in excellent agreement with an analytical calculation up to second order. Care is taken of the important two fermion contribution in the bosonic correlation functions. Mass ratios are found to be ε dependent, but their ε=0 extrapolation is compatible with the analytic expectation

Exponential integrators in time-dependent density-functional calculations

Science.gov (United States)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

Solving Algebraic Riccati Equation Real Time for Integrated Vehicle Dynamics Control

NARCIS (Netherlands)

Kunnappillil Madhusudhanan, A; Corno, M.; Bonsen, B.; Holweg, E.

2012-01-01

In this paper we present a comparison study of different computational methods to implement State Dependent Riccati Equation (SDRE) based control in real time for a vehicle dynamics control application. Vehicles are mechatronic systems with nonlinear dynamics. One of the promising nonlinear control

Time-dependent weak values and their intrinsic phases of evolution

International Nuclear Information System (INIS)

Parks, A D

2008-01-01

The equation of motion for a time-dependent weak value of a quantum-mechanical observable is known to contain a complex valued energy factor (the weak energy of evolution) that is defined by the dynamics of the pre-selected and post-selected states which specify the observable's weak value. In this paper, the mechanism responsible for the creation of this energy is identified and it is shown that the cumulative effect over time of this energy is manifested as dynamical phases and pure geometric phases (the intrinsic phases of evolution) which govern the evolution of the weak value during its measurement process. These phases are simply related to a Pancharatnam phase and Fubini-Study metric distance defined by the Hilbert space evolution of the associated pre-selected and post-selected states. A characterization of time-dependent weak value evolution as Pancharatnam phase angle rotations and Fubini-Study distance scalings of a vector in the Argand plane is discussed as an application of this relationship. The theory of weak values is also reviewed and simple 'gedanken experiments' are used to illustrate both the time-independent and the time-dependent versions of the theory. It is noted that the direct experimental observation of the weak energy of evolution would strongly support the time-symmetric paradigm of quantum mechanics and it is suggested that weak value equations of motion represent a new category of nonlocal equations of motion

Computational Diffusion Magnetic Resonance Imaging Based on Time-Dependent Bloch NMR Flow Equation and Bessel Functions.

Science.gov (United States)

Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I

2016-04-01

Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it

Comparison of gross anatomy test scores using traditional specimens vs. QuickTime Virtual Reality animated specimens

Science.gov (United States)

Maza, Paul Sadiri

In recent years, technological advances such as computers have been employed in teaching gross anatomy at all levels of education, even in professional schools such as medical and veterinary medical colleges. Benefits of computer based instructional tools for gross anatomy include the convenience of not having to physically view or dissect a cadaver. Anatomy educators debate over the advantages versus the disadvantages of computer based resources for gross anatomy instruction. Many studies, case reports, and editorials argue for the increased use of computer based anatomy educational tools, while others discuss the necessity of dissection for various reasons important in learning anatomy, such as a three-dimensional physical view of the specimen, physical handling of tissues, interactions with fellow students during dissection, and differences between specific specimens. While many articles deal with gross anatomy education using computers, there seems to be a lack of studies investigating the use of computer based resources as an assessment tool for gross anatomy, specifically using the Apple application QuickTime Virtual Reality (QTVR). This study investigated the use of QTVR movie modules to assess if using computer based QTVR movie module assessments were equal in quality to actual physical specimen examinations. A gross anatomy course in the College of Veterinary Medicine at Cornell University was used as a source of anatomy students and gross anatomy examinations. Two groups were compared, one group taking gross anatomy examinations in a traditional manner, by viewing actual physical specimens and answering questions based on those specimens. The other group took the same examinations using the same specimens, but the specimens were viewed as simulated three-dimensional objects in a QTVR movie module. Sample group means for the assessments were compared. A survey was also administered asking students' perceptions of quality and user-friendliness of the QTVR

Extended rate equations

International Nuclear Information System (INIS)

Shore, B.W.

1981-01-01

The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

Effectiveness of Gross Model-Based Emotion Regulation Strategies Training on Anger Reduction in Drug-Dependent Individuals and its Sustainability in Follow-up.

Science.gov (United States)

Massah, Omid; Sohrabi, Faramarz; A'azami, Yousef; Doostian, Younes; Farhoudian, Ali; Daneshmand, Reza

2016-03-01

Emotion plays an important role in adapting to life changes and stressful events. Difficulty regulating emotions is one of the problems drug abusers often face, and teaching these individuals to express and manage their emotions can be effective on improving their difficult circumstances. The present study aimed to determine the effectiveness of the Gross model-based emotion regulation strategies training on anger reduction in drug-dependent individuals. The present study had a quasi-experimental design wherein pretest-posttest evaluations were applied using a control group. The population under study included addicts attending Marivan's methadone maintenance therapy centers in 2012 - 2013. Convenience sampling was used to select 30 substance-dependent individuals undergoing maintenance treatment who were then randomly assigned to the experiment and control groups. The experiment group received its training in eight two-hour sessions. Data were analyzed using analysis of co-variance and paired t-test. There was significant reduction in anger symptoms of drug-dependent individuals after gross model based emotion regulation training (ERT) (P emotion regulation strategies training. Based on the results of this study, we may conclude that the gross model based emotion regulation strategies training can be applied alongside other therapies to treat drug abusers undergoing rehabilitation.

Semiclassical approximation to time-dependent Hartree--Fock theory

International Nuclear Information System (INIS)

Dworzecka, M.; Poggioli, R.

1976-01-01

Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form

Stochastic-hydrodynamic model of halo formation in charged particle beams

Directory of Open Access Journals (Sweden)

Nicola Cufaro Petroni

2003-03-01

Full Text Available The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastic-hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schrödinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equations define a collective dynamics of self-interacting systems much in the same spirit as in the Gross-Pitaevskii and Landau-Ginzburg theories of the collective dynamics for interacting quantum many-body systems. Self-consistent solutions of the dynamical equations lead to quasistationary beam configurations with enhanced transverse dispersion and transverse emittance growth. In the limit of a frozen space-charge core it is then possible to determine and study the properties of stationary, stable core-plus-halo beam distributions. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution.

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

International Nuclear Information System (INIS)

Zhang Hong; Li Guo-Hua

2016-01-01

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier–Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. (paper)

FEM for time-fractional diffusion equations, novel optimal error analyses

OpenAIRE

Mustapha, Kassem

2016-01-01

A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with respect to both the convergence order of the approximate solution and the regularity of the initial data. By using novel energy arguments, for each fixed time $t$, optimal error bounds in the spatial $L^2$- and $H^1$-norms are derived for both cases: smooth...

The development of the time dependence of the nuclear EMP electric field

International Nuclear Information System (INIS)

Eng, C.

2009-01-01

The nuclear electromagnetic pulse (EMP) electric field calculated with the legacy code CHAP is compared with the field given by an integral solution of Maxwell's equations, also known as the Jefimenko equation, to aid our current understanding on the factors that affect the time dependence of the EMP. For a fair comparison the CHAP current density is used as a source in the Jefimenko equation. At first, the comparison is simplified by neglecting the conduction current and replacing the standard atmosphere with a constant density air slab. The simplicity of the resultant current density aids in determining the factors that affect the rise, peak and tail of the EMP electric field versus time. The three dimensional nature of the radiating source, i.e. sources off the line-of-sight, and the time dependence of the derivative of the current density with respect to time are found to play significant roles in shaping the EMP electric field time dependence. These results are found to hold even when the conduction current and the standard atmosphere are properly accounted for. Comparison of the CHAP electric field with the Jefimenko electric field offers a direct validation of the high-frequency/outgoing wave approximation.

Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier–Stokes equations with vacuum

Science.gov (United States)

Lü, Boqiang; Shi, Xiaoding; Zhong, Xin

2018-06-01

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier–Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D Cauchy problem of the density-dependent Navier–Stokes equations on the whole space admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Furthermore, we also obtain the large time decay rates of the spatial gradients of the velocity and the pressure, which are the same as those of the homogeneous case.

Continuous-time random walk as a guide to fractional Schroedinger equation

International Nuclear Information System (INIS)

Lenzi, E. K.; Ribeiro, H. V.; Mukai, H.; Mendes, R. S.

2010-01-01

We argue that the continuous-time random walk approach may be a useful guide to extend the Schroedinger equation in order to incorporate nonlocal effects, avoiding the inconsistencies raised by Jeng et al. [J. Math. Phys. 51, 062102 (2010)]. As an application, we work out a free particle in a half space, obtaining the time dependent solution by considering an arbitrary initial condition.

Simulation of Near-Edge X-ray Absorption Fine Structure with Time-Dependent Equation-of-Motion Coupled-Cluster Theory.

Science.gov (United States)

Nascimento, Daniel R; DePrince, A Eugene

2017-07-06

An explicitly time-dependent (TD) approach to equation-of-motion (EOM) coupled-cluster theory with single and double excitations (CCSD) is implemented for simulating near-edge X-ray absorption fine structure in molecular systems. The TD-EOM-CCSD absorption line shape function is given by the Fourier transform of the CCSD dipole autocorrelation function. We represent this transform by its Padé approximant, which provides converged spectra in much shorter simulation times than are required by the Fourier form. The result is a powerful framework for the blackbox simulation of broadband absorption spectra. K-edge X-ray absorption spectra for carbon, nitrogen, and oxygen in several small molecules are obtained from the real part of the absorption line shape function and are compared with experiment. The computed and experimentally obtained spectra are in good agreement; the mean unsigned error in the predicted peak positions is only 1.2 eV. We also explore the spectral signatures of protonation in these molecules.

From interatomic interaction potentials via Einstein field equation techniques to time dependent contact mechanics

International Nuclear Information System (INIS)

Schwarzer, N

2014-01-01

In order to understand the principle differences between rheological or simple stress tests like the uniaxial tensile test to contact mechanical tests and the differences between quasistatic contact experiments and oscillatory ones, this study resorts to effective first principles. This study will show how relatively simple models simulating bond interactions in solids using effective potentials like Lennard-Jones and Morse can be used to investigate the effect of time dependent stress-induced softening or stiffening of these solids. The usefulness of the current study is in the possibility of deriving relatively simple dependences of the bulk-modulus B on time, shear and pressure P with time t. In cases where it is possible to describe, or at least partially describe a material by Lennard-Jones potential approaches, the above- mentioned dependences are even completely free of microscopic material parameters. Instead of bond energies and length, only specific integral parameters like Young’s modulus and Poisson’s ratio are required. However, in the case of time dependent (viscose) material behavior the parameters are not constants anymore. They themselves depend on time and the actual stress field, especially the shear field. A body completely consisting of so called standard linear solid interacting particles will then phenomenologically show a completely different and usually much more complicated mechanical behavior. The influence of the time dependent pressure-shear-induced Young’s modulus change is discussed with respect to mechanical contact experiments and their analysis in the case of viscose materials. (papers)

Dissipative time-dependent quantum transport theory.

Science.gov (United States)

Zhang, Yu; Yam, Chi Yung; Chen, GuanHua

2013-04-28

A dissipative time-dependent quantum transport theory is developed to treat the transient current through molecular or nanoscopic devices in presence of electron-phonon interaction. The dissipation via phonon is taken into account by introducing a self-energy for the electron-phonon coupling in addition to the self-energy caused by the electrodes. Based on this, a numerical method is proposed. For practical implementation, the lowest order expansion is employed for the weak electron-phonon coupling case and the wide-band limit approximation is adopted for device and electrodes coupling. The corresponding hierarchical equation of motion is derived, which leads to an efficient and accurate time-dependent treatment of inelastic effect on transport for the weak electron-phonon interaction. The resulting method is applied to a one-level model system and a gold wire described by tight-binding model to demonstrate its validity and the importance of electron-phonon interaction for the quantum transport. As it is based on the effective single-electron model, the method can be readily extended to time-dependent density functional theory.

Monoenergetic time-dependent neutron transport in an infinite medium with time-varying cross sections

International Nuclear Information System (INIS)

Ganapol, B.D.

1987-01-01

For almost 20 yr, the main thrust of the author's research has been the generation of as many benchmark solutions to the time-dependent monoenergetic neutron transport equation as possible. The major motivation behind this effort has been to provide code developers with highly accurate numerical solutions to serve as standards in the assessment of numerical transport algorithms. In addition, these solutions provide excellent educational tools since the important physical features of neutron transport are still present even though the problems solved are idealized. A secondary motivation, though of equal importance, is the intellectual stimulation and understanding provided by the combination of the analytical, numerical, and computational techniques required to obtain these solutions. Therefore, to further the benchmark development, the added complication of time-dependent cross sections in the one-group transport equation is considered here

Nonlinear time-dependent simulation of helix traveling wave tubes

International Nuclear Information System (INIS)

Peng Wei-Feng; Yang Zhong-Hai; Hu Yu-Lu; Li Jian-Qing; Lu Qi-Ru; Li Bin

2011-01-01

A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory. (interdisciplinary physics and related areas of science and technology)

Applications of alternating direction methods to the solution of the time-dependent heat conduction equation with source and in transients stage

International Nuclear Information System (INIS)

Gebrin, A.N.

1981-10-01

Various types and also some variants of alternating direction methods, (A.D.M.), were applied to the solution of the time-dependent heat conduction equation, with source, in region with axial symetry. The results shown that some of the variants perform consistently better than the Classical Cranck-Nicolson method. Having in mind a combination of accuracy, ability to support larg time steps and computational efficiency, the 'alternating direction explicit', (A.D.E.) method appears as the best choice, being the 'alternating direction checkerboard', (A.D.C), method the second best. Additional operations like the exponential transformation or the truncation pos-correction don't seem to be worth, excect for some special cases. (Author) [pt

Solvable Model of a Generic Trapped Mixture of Interacting Bosons: Many-Body and Mean-Field Properties

Science.gov (United States)

Klaiman, S.; Streltsov, A. I.; Alon, O. E.

2018-04-01

A solvable model of a generic trapped bosonic mixture, N 1 bosons of mass m 1 and N 2 bosons of mass m 2 trapped in an harmonic potential of frequency ω and interacting by harmonic inter-particle interactions of strengths λ 1, λ 2, and λ 12, is discussed. It has recently been shown for the ground state [J. Phys. A 50, 295002 (2017)] that in the infinite-particle limit, when the interaction parameters λ 1(N 1 ‑ 1), λ 2(N 2 ‑ 1), λ 12 N 1, λ 12 N 2 are held fixed, each of the species is 100% condensed and its density per particle as well as the total energy per particle are given by the solution of the coupled Gross-Pitaevskii equations of the mixture. In the present work we investigate properties of the trapped generic mixture at the infinite-particle limit, and find differences between the many-body and mean-field descriptions of the mixture, despite each species being 100%. We compute analytically and analyze, both for the mixture and for each species, the center-of-mass position and momentum variances, their uncertainty product, the angular-momentum variance, as well as the overlap of the exact and Gross-Pitaevskii wavefunctions of the mixture. The results obtained in this work can be considered as a step forward in characterizing how important are many-body effects in a fully condensed trapped bosonic mixture at the infinite-particle limit.

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

Science.gov (United States)

Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

2017-08-01

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

Time evolution of the wave equation using rapid expansion method

KAUST Repository

Pestana, Reynam C.; Stoffa, Paul L.

2010-01-01

Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.

Time evolution of the wave equation using rapid expansion method

KAUST Repository

Pestana, Reynam C.

2010-07-01

Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.

Ordinary differential equation for local accumulation time.

Science.gov (United States)

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

Time-dependent non-equilibrium dielectric response in QM/continuum approaches

Energy Technology Data Exchange (ETDEWEB)

Ding, Feizhi; Lingerfelt, David B.; Li, Xiaosong, E-mail: benedetta.mennucci@unipi.it, E-mail: li@chem.washington.edu [Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States); Mennucci, Benedetta, E-mail: benedetta.mennucci@unipi.it, E-mail: li@chem.washington.edu [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa (Italy)

2015-01-21

The Polarizable Continuum Models (PCMs) are some of the most inexpensive yet successful methods for including the effects of solvation in quantum-mechanical calculations of molecular systems. However, when applied to the electronic excitation process, these methods are restricted to dichotomously assuming either that the solvent has completely equilibrated with the excited solute charge density (infinite-time limit), or that it retains the configuration that was in equilibrium with the solute prior to excitation (zero-time limit). This renders the traditional PCMs inappropriate for resolving time-dependent solvent effects on non-equilibrium solute electron dynamics like those implicated in the instants following photoexcitation of a solvated molecular species. To extend the existing methods to this non-equilibrium regime, we herein derive and apply a new formalism for a general time-dependent continuum embedding method designed to be propagated alongside the solute’s electronic degrees of freedom in the time domain. Given the frequency-dependent dielectric constant of the solvent, an equation of motion for the dielectric polarization is derived within the PCM framework and numerically integrated simultaneously with the time-dependent Hartree fock/density functional theory equations. Results for small molecular systems show the anticipated dipole quenching and electronic state dephasing/relaxation resulting from out-of-phase charge fluctuations in the dielectric and embedded quantum system.

Excitonic effects in solids : time-dependent density functional theory versus the Bethe-Salpeter equation

International Nuclear Information System (INIS)

Sagmeister, S.

2009-01-01

The aim of this work is to compare two state-of-the-art methods for the investigation of excitonic effects in solids, namely Time-Dependent Density Functional Theory (TDDFT) and Many-Body Perturbation Theory (MBPT), for selected simple gap systems as well as semiconducting polymers. Within TDDFT, the linear response framework is used and the Dyson equation for the density-density response function is solved, whereas within MBPT, the Bethe-Salpeter equation (BSE) for the electron-hole correlation function is solved. The dielectric function is obtained as a last step. Both techniques take into account the excitonic effects caused by the interaction of electron-hole pairs. In the former these effects are included in the exchange-correlation (xc) kernel, whereas in the latter they are located in the interaction kernel of the BSE. Kohn-Sham single-particle wave functions obtained from Density Functional Theory within the linearized augmented planewave (LAPW) method are used to calculate all relevant quantities of the formalism. For the simple systems GaAs, Si and LiF are chosen. The role of several approximations to the xc kernel is studied and it is found that for GaAs and Si simple semi-empirical models provide a dielectric function in accordance with the BSE. For the case of LiF, being a system with a weak screening and a strongly bound exciton, only an xc kernel derived from MBPT yields reasonable results but still a slight discrepancy to the BSE is observed. Finally, the semiconducting polymers poly-acetylene and poly(phenylene-vinylene) (PPV) are studied. For both materials the concept of semi-empirical approximations to the xc kernel turns out to be ambiguous due to their low-dimensional character. In the case of poly-acetylene, the xc kernel derived from MBPT yields a dielectric function which is in close but not exact agreement with the one obtained from the BSE. (author) [de

An application of transverse momentum dependent evolution equations in QCD

International Nuclear Information System (INIS)

Ceccopieri, Federico A.; Trentadue, Luca

2008-01-01

The properties and behaviour of the solutions of the recently obtained k t -dependent QCD evolution equations are investigated. When used to reproduce transverse momentum spectra of hadrons in Semi-Inclusive DIS, an encouraging agreement with data is found. The present analysis also supports at the phenomenological level the factorization properties of the Semi-Inclusive DIS cross-sections in terms of k t -dependent distributions. Further improvements and possible developments of the proposed evolution equations are envisaged

Induced voltage due to time-dependent magnetisation textures

International Nuclear Information System (INIS)

Kudtarkar, Santosh Kumar; Dhadwal, Renu

2010-01-01

We determine the induced voltage generated by spatial and temporal magnetisation textures (inhomogeneities) in metallic ferromagnets due to the spin diffusion of non-equilibrium electrons. Using time dependent semi-classical theory as formulated in Zhang and Li and the drift-diffusion model of transport it is shown that the voltage generated depends critically on the difference in the diffusion constants of up and down spins. Including spin relaxation results in a crucial contribution to the induced voltage. We also show that the presence of magnetisation textures results in the modification of the conductivity of the system. As an illustration, we calculate the voltage generated due to a time dependent field driven helimagnet by solving the Landau-Lifshitz equation with Gilbert damping and explicitly calculate the dependence on the relaxation and damping parameters.

Existence results for impulsive evolution differential equations with state-dependent delay

OpenAIRE

Eduardo Hernandez M.; Rathinasamy Sakthivel; Sueli Tanaka Aki

2008-01-01

We study the existence of mild solution for impulsive evolution abstract differential equations with state-dependent delay. A concrete application to partial delayed differential equations is considered.

Modeling Inflation Using a Non-Equilibrium Equation of Exchange

Science.gov (United States)

Chamberlain, Robert G.

2013-01-01

Inflation is a change in the prices of goods that takes place without changes in the actual values of those goods. The Equation of Exchange, formulated clearly in a seminal paper by Irving Fisher in 1911, establishes an equilibrium relationship between the price index P (also known as "inflation"), the economy's aggregate output Q (also known as "the real gross domestic product"), the amount of money available for spending M (also known as "the money supply"), and the rate at which money is reused V (also known as "the velocity of circulation of money"). This paper offers first a qualitative discussion of what can cause these factors to change and how those causes might be controlled, then develops a quantitative model of inflation based on a non-equilibrium version of the Equation of Exchange. Causal relationships are different from equations in that the effects of changes in the causal variables take time to play out-often significant amounts of time. In the model described here, wages track prices, but only after a distributed lag. Prices change whenever the money supply, aggregate output, or the velocity of circulation of money change, but only after a distributed lag. Similarly, the money supply depends on the supplies of domestic and foreign money, which depend on the monetary base and a variety of foreign transactions, respectively. The spreading of delays mitigates the shocks of sudden changes to important inputs, but the most important aspect of this model is that delays, which often have dramatic consequences in dynamic systems, are explicitly incorporated.macroeconomics, inflation, equation of exchange, non-equilibrium, Athena Project

Watching excitons move: the time-dependent transition density matrix

Science.gov (United States)

Ullrich, Carsten

2012-02-01

Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.

Vortices in trapped Bose-Einstein condensates

International Nuclear Information System (INIS)

Jackson, B.

2000-09-01

In this thesis we solve the Gross-Pitaevskii equation numerically in order to model the response of trapped Bose-Einstein condensed gases to perturbations by electromagnetic fields. First, we simulate output coupling of pulses from the condensate and compare our results to experiments. The excitation and separation of eigenmodes on flow through a constriction is also studied. We then move on to the main theme of this thesis: the important subject of quantised vortices in Bose condensates, and the relation between Bose-Einstein condensation and superfluidity. We propose methods of producing vortex pairs and rings by controlled motion of objects. Full three-dimensional simulations under realistic experimental conditions are performed in order to test the validity of these ideas. We link vortex formation to drag forces on the object, which in turn is connected with energy transfer to the condensate. We therefore argue that vortex formation by moving objects is intimately related to the onset of dissipation in superfluids. We discuss this idea in the context of a recent experiment, using simulations to provide evidence of vortex formation in the experimental scenario. Superfluidity is also manifest in the property of persistent currents, which is linked to vortex stability and dynamics. We simulate vortex line and ring motion, and find in both cases precessional motion and thermodynamic instability to dissipation. Strictly speaking, the Gross-Pitaevskii equation is valid only for temperatures far below the BEC transition. We end the thesis by describing a simple finite-temperature model to describe mean-field coupling between condensed and non-condensed components of the gas. We show that our hybrid Monte-Carlo/FFT technique can describe damping of the lowest energy excitations of the system. Extensions to this model and future research directions are discussed in the conclusion. (author)

Long-time behavior for suspension bridge equations with time delay

Science.gov (United States)

Park, Sun-Hye

2018-04-01

In this paper, we consider suspension bridge equations with time delay of the form u_{tt}(x,t) + Δ ^2 u (x,t) + k u^+ (x,t) + a_0 u_t (x,t) + a_1 u_t (x, t- τ ) + f(u(x,t)) = g(x). Many researchers have studied well-posedness, decay rates of energy, and existence of attractors for suspension bridge equations without delay effects. But, as far as we know, there is no work about suspension equations with time delay. In addition, there are not many studies on attractors for other delayed systems. Thus we first provide well-posedness for suspension equations with time delay. And then show the existence of global attractors and the finite dimensionality of the attractors by establishing energy functionals which are related to the norm of the phase space to our problem.

SYNTH-C, Steady-State and Time-Dependent 3-D Neutron Diffusion with Thermohydraulic Feedback

Energy Technology Data Exchange (ETDEWEB)

Brega, E [ENEL-CRTN, Bastioni di Porta Volta 10, Milan (Italy); Salina, E [A.R.S. Spa, Viale Maino 35, Milan (Italy)

1980-04-01

1 - Description of problem or function: SYNTH-C-STEADY and SYNTH-C- TRANS solve respectively the steady-state and time-dependent few- group neutron diffusion equations in three dimensions x,y,z in the presence of fuel temperature and thermal-hydraulic feedback. The neutron diffusion and delayed precursor equations are approximated by a space-time (z,t) synthesis method with axially discontinuous trial functions. Three thermal-hydraulic and fuel heat transfer models are available viz. COBRA-3C/MIT model, lumped parameter (WIGL) model and adiabatic fuel heat-up model. 2 - Method of solution: The steady-state and time-dependent synthesis equations are solved respectively by the Wielandt's power method and by the theta-difference method (in time), both coupled with a block factorization technique and double precision arithmetic. The thermal-hydraulic model equations are solved by fully implicit finite differences (WIGL) or explicit-implicit difference techniques with iterations (COBRA-EC/MIT). 3 - Restrictions on the complexity of the problem: Except for the few- group limitation, the programs have no other fixed limitation so the ability to run a problem depends only on the available computer storage.

Simulating time-dependent energy transfer between crossed laser beams in an expanding plasma

International Nuclear Information System (INIS)

Hittinger, J.A.F.; Dorr, M.R.; Berger, R.L.; Williams, E.A.

2005-01-01

A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width refracting in a prescribed transverse plasma flow with spatial and temporal gradients in velocity and density. The resulting paraxial light equations are discretized spatially with a Crank-Nicholson-type scheme, and these algebraic constraints are nonlinearly coupled with ordinary differential equations in time that describe the ion acoustic response. The entire nonlinear differential-algebraic system is solved using an adaptive, backward-differencing method coupled with Newton's method. A numerical study is conducted in two dimensions that compares the intensity gain of the fully time-dependent coupled mode system with the gain computed under the further assumption of a strongly damped ion acoustic response. The results demonstrate a time-dependent gain suppression when the beam diameter is commensurate with the velocity gradient scale length. The gain suppression is shown to depend on time-dependent beam refraction and is interpreted as a time-dependent frequency shift

Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case

KAUST Repository

Hajaiej, Hichem

2014-03-01

In [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.

Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems

International Nuclear Information System (INIS)

Deumens, E.; Diz, A.; Longo, R.; Oehrn, Y.

1994-01-01

An overview is presented of methods for time-dependent treatments of molecules as systems of electrons and nuclei. The theoretical details of these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Electron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the necessity of constructing potential-energy surfaces. Because of its general formulation, it encompasses many aspects found in other formulations and can serve as a didactic device for clarifying many of the principles and approximations relevant in time-dependent treatments of molecular systems. The END equations are derived from the time-dependent variational principle applied to a chosen family of efficiently parametrized approximate state vectors. A detailed analysis of the END equations is given for the case of a single-determinantal state for the electrons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with the ab initio Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible for the study of small molecular systems. Implementation of the Austin Model 1 semiempirical Hamiltonian is discussed as a route to large molecular systems. The linearized END equations at this level of theory are shown to lead to the random-phase approximation for the coupled system of electrons and nuclei. The qualitative features of the general nonlinear solution are analyzed using the results of the linearized equations as a first approximation. Some specific applications of END are presented, and the comparison with experiment and other theoretical approaches is discussed

Bound State Eigenvalues of the Schroedinger Eq. in two Spatial Variables.

Science.gov (United States)

Rawitscher, George H.; Koltracht, Israel

2002-08-01

An efficient spectral integral equation method (SIEM) has recently been developed for obtaining the scattering solution of a one-dimensional Schroedinger equation.(R.A. Gonzales, S.-Y. Kang, I. Koltracht and G. Rawitscher, J. of Comput. Phys. 153, 160 (1999).) The purpose of the present study is to extend this method to the case of bound-states in more than one dimension. Even though other methods have already been developed for this case, such as finite element methods, the application we have in mind is to solve the non-linear Bose-Einstein condensate case in the presence of an optical lattice. In the presence of a trapping potential alone, a B-E condensate solution has been obtained by a new iterative spectral method which solves the differential equation.(Y.-S. Choi, J. Javanainen, I. Koltracht, M. Koš)trun, P.J. McKenna and N. Savytska "A Fast Algorithm for the Solution of the Time-Independent Gross-Pitaevskii Equation," Submitted to Computational Physics. But this method becomes inadequate for the case that several potential barriers are also present. The reason that the SIEM is expected to be better suited is that it distributes the collocation points much more efficiently into partitions of variable size.

Ansatz from nonlinear optics applied to trapped Bose-Einstein condensates

International Nuclear Information System (INIS)

Keceli, Murat; Ilday, F. Oe.; Oktel, M. Oe.

2007-01-01

A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser (a laser with self-similar propagation of ultrashort pulses), is used as a variational wave function to solve the Gross-Pitaevskii equation for a wide range of interaction parameters. The variational form interpolates between the noninteracting density profile and the strongly interacting Thomas-Fermi profile smoothly. The simple form of the ansatz is modified for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground-state density profile and energy are in very good agreement with both the analytical solutions in the limiting cases of interaction and the numerical solutions in the intermediate regime

Mixed-symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices

International Nuclear Information System (INIS)

Cruz, H. A.; Brazhnyi, V. A.; Konotop, V. V.; Alfimov, G. L.; Salerno, M.

2007-01-01

We study localized modes in binary mixtures of Bose-Einstein condensates embedded in one-dimensional optical lattices. We report a diversity of asymmetric modes and investigate their dynamics. We concentrate on the cases where one of the components is dominant, i.e., has a much larger number of atoms than the other one, and where both components have the numbers of atoms of the same order but different symmetries. In the first case we propose a method of systematically obtaining the modes, considering the ''small'' component as bifurcating from the continuum spectrum. A generalization of this approach combined with the use of the symmetry of the coupled Gross-Pitaevskii equations allows for obtaining breather modes, which are also presented

Superfluid Boundary Layer.

Science.gov (United States)

Stagg, G W; Parker, N G; Barenghi, C F

2017-03-31

We model the superfluid flow of liquid helium over the rough surface of a wire (used to experimentally generate turbulence) profiled by atomic force microscopy. Numerical simulations of the Gross-Pitaevskii equation reveal that the sharpest features in the surface induce vortex nucleation both intrinsically (due to the raised local fluid velocity) and extrinsically (providing pinning sites to vortex lines aligned with the flow). Vortex interactions and reconnections contribute to form a dense turbulent layer of vortices with a nonclassical average velocity profile which continually sheds small vortex rings into the bulk. We characterize this layer for various imposed flows. As boundary layers conventionally arise from viscous forces, this result opens up new insight into the nature of superflows.

Communication: Time-dependent optimized coupled-cluster method for multielectron dynamics

Science.gov (United States)

Sato, Takeshi; Pathak, Himadri; Orimo, Yuki; Ishikawa, Kenichi L.

2018-02-01

Time-dependent coupled-cluster method with time-varying orbital functions, called time-dependent optimized coupled-cluster (TD-OCC) method, is formulated for multielectron dynamics in an intense laser field. We have successfully derived the equations of motion for CC amplitudes and orthonormal orbital functions based on the real action functional, and implemented the method including double excitations (TD-OCCD) and double and triple excitations (TD-OCCDT) within the optimized active orbitals. The present method is size extensive and gauge invariant, a polynomial cost-scaling alternative to the time-dependent multiconfiguration self-consistent-field method. The first application of the TD-OCC method of intense-laser driven correlated electron dynamics in Ar atom is reported.

Similarity transformed coupled cluster response (ST-CCR) theory--a time-dependent similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach.

Science.gov (United States)

Landau, Arie

2013-07-07

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.

Transforming parts of a differential equations system to difference equations as a method for run-time savings in NONMEM.

Science.gov (United States)

Petersson, K J F; Friberg, L E; Karlsson, M O

2010-10-01

Computer models of biological systems grow more complex as computing power increase. Often these models are defined as differential equations and no analytical solutions exist. Numerical integration is used to approximate the solution; this can be computationally intensive, time consuming and be a large proportion of the total computer runtime. The performance of different integration methods depend on the mathematical properties of the differential equations system at hand. In this paper we investigate the possibility of runtime gains by calculating parts of or the whole differential equations system at given time intervals, outside of the differential equations solver. This approach was tested on nine models defined as differential equations with the goal to reduce runtime while maintaining model fit, based on the objective function value. The software used was NONMEM. In four models the computational runtime was successfully reduced (by 59-96%). The differences in parameter estimates, compared to using only the differential equations solver were less than 12% for all fixed effects parameters. For the variance parameters, estimates were within 10% for the majority of the parameters. Population and individual predictions were similar and the differences in OFV were between 1 and -14 units. When computational runtime seriously affects the usefulness of a model we suggest evaluating this approach for repetitive elements of model building and evaluation such as covariate inclusions or bootstraps.

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

Science.gov (United States)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of

Some aspects of the description of relativistic particles in external fields. [Time dependent and time independent potentials

Energy Technology Data Exchange (ETDEWEB)

Labonte, G

1973-01-01

We study the time description of the motion of relativistic particles in both the dependent and time independent potentials. The differential equations of motion considered are the standard linear spin zero and one half equations. They are always meaningful in the sense that, at all times, unique well defined operator valued distributions in the three space variables are determined. We discuss the problem of determining which set of creation and annihilation operators is relevant in a given problem. We examine the implementation of certain simple requirements which seem to be necessary in order for the mathematical formalism to be able to describe a physical system. We show that whenever the equation of motion is homogeneous, the study of all physical requirements reduces to studying Bogoliubov transformations between creation and annihilation operators. We study such transformations where we obtain some new important results concerning their general properties. We examine in detail a quantized field in presence of an external source, electrons and positrons acted upon by a plane electromagnetic wave, Dirac fields acted upon by potentials of the form A(x) delta (t) and A(x) THETA (t-t/sub 0/). We study Dirac fields in presence of potentials which have time dependences which can be represented by sequences of step functions. We then discuss the limiting case where the time dependence is continuous. We prove that the requirements that there exists a unitary evolution operator or that physical particles can be described are exactly equivalent. (auth)

Approximate solution of space and time fractional higher order phase field equation

Science.gov (United States)

Shamseldeen, S.

2018-03-01

This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

Construction of time-dependent dynamical invariants: A new approach

International Nuclear Information System (INIS)

Bertin, M. C.; Pimentel, B. M.; Ramirez, J. A.

2012-01-01

We propose a new way to obtain polynomial dynamical invariants of the classical and quantum time-dependent harmonic oscillator from the equations of motion. We also establish relations between linear and quadratic invariants, and discuss how the quadratic invariant can be related to the Ermakov invariant.

Time-dependent crashworthiness of polyurethane foam

Science.gov (United States)

Basit, Munshi Mahbubul; Cheon, Seong Sik

2018-05-01

Time-dependent stress-strain relationship as well as crashworthiness of polyurethane foam was investigated under constant impact energy with different velocities, considering inertia and strain-rate effects simultaneously during the impact testing. Even though the impact energies were same, the percentage in increase in densification strain due to higher impact velocities was found, which yielded the wider plateau region, i.e. growth in crashworthiness. This phenomenon is analyzed by the microstructure of polyurethane foam obtained from scanning electron microscopy. The equations, coupled with the Sherwood-Frost model and the impulse-momentum theory, were employed to build the constitutive equation of the polyurethane foam and calculate energy absorption capacity of the foam. The nominal stress-strain curves obtained from the constitutive equation were compared with results from impact tests and were found to be in good agreement. This study is dedicated to guiding designer use polyurethane foam in crashworthiness structures such as an automotive bumper system by providing crashworthiness data, determining the crush mode, and addressing a mathematical model of the crashworthiness.

Analog computing for a new nuclear reactor dynamic model based on a time-dependent second order form of the neutron transport equation

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal; Suh, Kune Y.

2011-01-01

This paper considers the concept of analog computing based on a cellular neural network (CNN) paradigm to simulate nuclear reactor dynamics using a time-dependent second order form of the neutron transport equation. Instead of solving nuclear reactor dynamic equations numerically, which is time-consuming and suffers from such weaknesses as vulnerability to transient phenomena, accumulation of round-off errors and floating-point overflows, use is made of a new method based on a cellular neural network. The state-of-the-art shows the CNN as being an alternative solution to the conventional numerical computation method. Indeed CNN is an analog computing paradigm that performs ultra-fast calculations and provides accurate results. In this study use is made of the CNN model to simulate the space-time response of scalar flux distribution in steady state and transient conditions. The CNN model also is used to simulate step perturbation in the core. The accuracy and capability of the CNN model are examined in 2D Cartesian geometry for two fixed source problems, a mini-BWR assembly, and a TWIGL Seed/Blanket problem. We also use the CNN model concurrently for a typical small PWR assembly to simulate the effect of temperature feedback, poisons, and control rods on the scalar flux distribution

Innovative procedure for the determination of gross-alpha/gross-beta activities in drinking water

International Nuclear Information System (INIS)

Wisser, S.; Frenzel, E.; Dittmer, M.

2006-01-01

An alternative sample preparation method for the determination of gross-alpha/beta activity concentrations in drinking water is introduced in this paper. After the freeze-drying of tap water samples, determination by liquid scintillation counting can be applied utilizing alpha/beta separation. It has been shown that there is no adsorption or loss of solid radionuclides during the freeze-drying procedure. However, the samples have to be measured quickly after the preparation since the ingrowth of daughter isotopes negatively effects the measurement. The limits of detection for gross-alpha and gross-beta activity are in the range 25-210 mBq/l, respectively, for a measurement time of only 8-9 h

Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

Directory of Open Access Journals (Sweden)

Te-Wen Tu

2015-01-01

Full Text Available An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.

A time-dependent dusty gas dynamic model of axisymmetric cometary jets

International Nuclear Information System (INIS)

Korosmezey, A.; Gombosi, T.I.

1990-01-01

The present time-dependent, axisymmetric dusty gas dynamical model of inner cometary atmospheres solves the coupled and time-dependent equations of continuity, momentum, and energy for a gas-dust mixture between the surface of the nucleus and 100 km, using an axisymmetric 40 x 40 grid structure. A novel numerical method employing a second-order accurate Godunov-type scheme with dimensional splitting is used to solve the time-dependent pde system. It is established that a subsolar dust spike not predicted by previous calculations is generated by narrow axisymmetric jets, together with a jet cone whose opening angle depends on the jet length. 28 refs

Bose-Einstein condensation in magnetic traps. Introduction to the theory

International Nuclear Information System (INIS)

Pitaevskii, Lev P

1998-01-01

The recent realization of Bose-Einstein condensation in atomic gases opens new possibilities for the observation of macroscopic quantum phenomena. There are two important features of these systems - weak interaction and significant spatial inhomogeneity. Because of this a non-trivial 'zeroth-order' theory exists, compared to the 'first-order' Bogolubov theory. The zeroth-order theory is based on the mean-field Gross-Pitaevskii equation for the condensate ψ-function. The equation is classical in its essence but contains the constant ℎ explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. Elementary excitations define the thermodynamic behavior of the system and result in a Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in quantum collapse-revival of the collective oscillations. (special issue)

Time-dependent angularly averaged inverse transport

International Nuclear Information System (INIS)

Bal, Guillaume; Jollivet, Alexandre

2009-01-01

This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. Such measurement settings find applications in medical and geophysical imaging. We show that the absorption coefficient and the spatial component of the scattering coefficient are uniquely determined by such measurements. We obtain stability results on the reconstruction of the absorption and scattering parameters with respect to the measured albedo operator. The stability results are obtained by a precise decomposition of the measurements into components with different singular behavior in the time domain

Time-dependent quantum fluid density functional theory of hydrogen ...

Indian Academy of Sciences (India)

A time-dependent generalized non-linear Schrödinger equation (GNLSE) of motion was earlier derived in our laboratory by combining density functional theory and quantum fluid dynamics in threedimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on ...

Time-dependent dilatancy for brittle rocks

Directory of Open Access Journals (Sweden)

Jie Li

2017-12-01

Full Text Available This paper presents a theoretical study on time-dependent dilatancy behaviors for brittle rocks. The theory employs a well-accepted postulation that macroscopically observed dilatancy originates from the expansion of microcracks. The mechanism and dynamic process that microcracks initiate from local stress concentration and grow due to localized tensile stress are analyzed. Then, by generalizing the results from the analysis of single cracks, a parameter and associated equations for its evolution are developed to describe the behaviors of the microcracks. In this circumstance, the relationship between microcracking and dilatancy can be established, and the theoretical equations for characterizing the process of rock dilatancy behaviors are derived. Triaxial compression and creep tests are conducted to validate the developed theory. With properly chosen model parameters, the theory yields a satisfactory accuracy in comparison with the experimental results.

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

International Nuclear Information System (INIS)

Blau, Matthias; O'Loughlin, Martin; Meessen, Patrick

2003-01-01

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves. (author)

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

Energy Technology Data Exchange (ETDEWEB)

Blau, Matthias; O' Loughlin, Martin; Meessen, Patrick [SISSA/ISAS, Via Beirut 2-4, 34014 Trieste (Italy)]. E-mail: meessen@sissa.it

2003-09-01

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves. (author)

Determination of the thoron daughter working level by a one gross alpha-count

International Nuclear Information System (INIS)

Bigu, J.; Lau, W.K.

1983-02-01

A study has been done on the determination of the thoron daughter Working Level, WL(Tn), by a one gross α-count. The relationship between the gross α-count rate per unit of volume of air sampled and WL(Tn), denoted the F-factor, has been investigated as a function of sampling time, elapsed time from the end of the sampling period, i.e., waiting time, and the thoron daughter disequilibrium ratio [ThC]/[ThB]. It has been found that F depends on both the waiting time and [ThC]/[ThB]. If α-count measurements are made at least 300 min after the end of sampling, F changes by less than 10 percent over the full range of theoretical values of [ThC]/[ThB], i.e., from 0 to 1. The F-factor is independent of [ThC]/[ThB] at approximately 215 min after the end of sampling. This feature can be used to determine WL(Tn) with higher accuracy and at least 1.5 hr earlier than is commonly done using other one gross α-count methods reported in the literature

Sensitivity analysis of time-dependent laminar flows

International Nuclear Information System (INIS)

Hristova, H.; Etienne, S.; Pelletier, D.; Borggaard, J.

2004-01-01

This paper presents a general sensitivity equation method (SEM) for time dependent incompressible laminar flows. The SEM accounts for complex parameter dependence and is suitable for a wide range of problems. The formulation is verified on a problem with a closed form solution obtained by the method of manufactured solution. Systematic grid convergence studies confirm the theoretical rates of convergence in both space and time. The methodology is then applied to pulsatile flow around a square cylinder. Computations show that the flow starts with symmetrical vortex shedding followed by a transition to the traditional Von Karman street (alternate vortex shedding). Simulations show that the transition phase manifests itself earlier in the sensitivity fields than in the flow field itself. Sensitivities are then demonstrated for fast evaluation of nearby flows and uncertainty analysis. (author)

Time-dependent shock acceleration of energetic electrons including synchrotron losses

International Nuclear Information System (INIS)

Fritz, K.; Webb, G.M.

1990-01-01

The present investigation of the time-dependent particle acceleration problem in strong shocks, including synchrotron radiation losses, solves the transport equation analytically by means of Laplace transforms. The particle distribution thus obtained is then transformed numerically into real space for the cases of continuous and impulsive injections of particles at the shock. While in the continuous case the steady-state spectrum undergoes evolution, impulsive injection is noted to yield such unpredicted features as a pile-up of high-energy particles or a steep power-law with time-dependent spectral index. The time-dependent calculations reveal varying spectral shapes and more complex features for the higher energies which may be useful in the interpretation of outburst spectra. 33 refs

On the algebraic approach to the time-dependent quadratic Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Urdaneta, Ines; Palma, Alejandro [Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico); Sandoval, Lourdes, E-mail: urdaneta@sirio.ifuap.buap.m [Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico)

2010-09-24

The unitary operator V(t) that diagonalizes the time-dependent quadratic Hamiltonian (TDQH) into a time-dependent harmonic oscillator (TDHO) is obtained using a Lie algebra. The method involves a factorization of the TDQH into a TDHO through a unitary Bogoliubov transformation in terms of creation and annihilation operators with time-dependent coefficients. It is shown that this operator can be easily achieved by means of the factorization, together with the commonly known Wei-Norman theorem. We discuss the conditions under which this unitary operator converges to the evolution operator U(t) of the Schroedinger equation for the TDQH, giving then a straightforward calculation of the evolution operator with respect to the procedures published in the literature.

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Directory of Open Access Journals (Sweden)

Emrullah Yaşar

Full Text Available In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI equation with Riemann–Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi–Kober sense. Furthermore, adapting the Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method. Keywords: Fractional Sawada–Kotera–Ito equation, Lie symmetry, Riemann–Liouville fractional derivative, Conservation laws, Exact solutions

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Science.gov (United States)

Zhang, Hong; Li, Guo-Hua

2016-11-01

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).

Fundamentals of time-dependent density functional theory

International Nuclear Information System (INIS)

Marques, Miguel A.L.; Rubio, Angel

2012-01-01

There have been many significant advances in time-dependent density functional theory over recent years, both in enlightening the fundamental theoretical basis of the theory, as well as in computational algorithms and applications. This book, as successor to the highly successful volume Time-Dependent Density Functional Theory (Lect. Notes Phys. 706, 2006) brings together for the first time all recent developments in a systematic and coherent way. First, a thorough pedagogical presentation of the fundamental theory is given, clarifying aspects of the original proofs and theorems, as well as presenting fresh developments that extend the theory into new realms such as alternative proofs of the original Runge-Gross theorem, open quantum systems, and dispersion forces to name but a few. Next, all of the basic concepts are introduced sequentially and building in complexity, eventually reaching the level of open problems of interest. Contemporary applications of the theory are discussed, from real-time coupled-electron-ion dynamics, to excited-state dynamics and molecular transport. Last but not least, the authors introduce and review recent advances in computational implementation, including massively parallel architectures and graphical processing units. Special care has been taken in editing this volume as a multi-author textbook, following a coherent line of thought, and making all the relevant connections between chapters and concepts consistent throughout. As such it will prove to be the text of reference in this field, both for beginners as well as expert researchers and lecturers teaching advanced quantum mechanical methods to model complex physical systems, from molecules to nanostructures, from biocomplexes to surfaces, solids and liquids. (orig.)

Time-Dependent Mean-Field Games with Logarithmic Nonlinearities

KAUST Repository

Gomes, Diogo A.

2015-10-06

In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.

Time-Dependent Mean-Field Games with Logarithmic Nonlinearities

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard

2015-01-01

In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.

Images of a Bose-Einstein condensates: diagonal dynamical Bogoliubov vacuum

International Nuclear Information System (INIS)

Dziarmaga, J.; Sacha, K.; Karkuszewski, Z.

2005-01-01

Evolution of a Bose-Einstein condensate subject to a time-dependent external perturbation can be described by a time-dependent Bogoliubov theory: a condensate initially in its ground state evolves into a time-dependent excited state which can be formally written as a time-dependent Bogoliubov vacuum annihilated by time-dependent quasiparticle annihilation operators. We prove that any Bogoliubov vacuum can be brought to a diagonal form in a time-dependent orthonormal basis. This diagonal form is taylored for simulations of quantum measurements on excited condensates. As an example we work out a model of atomic interferometer where a trap potential is split in two parts by a potential barrier, and then atoms are released by opening the double-well trap potential. In the Gross-Pitaevskii approximation the released atoms give a high contrast interference pattern with repeatable position of interference fringes. In the two-mode tight-binding approximation the effect of phase diffusion makes the position of fringes fluctuate from experiment to experiment but every single realisation of experiment gives a high quality interference pattern. The time-dependent Bogoliubov theory is a more realistic description of the experiment which goes beyond both approximations. Using the diagonal time-dependent Bogoliubov vacuum we show that in addition to position fluctuations the interference pattern is also loosing its high quality contrast. (author)

Singular Hopf bifurcation in a differential equation with large state-dependent delay.

Science.gov (United States)

Kozyreff, G; Erneux, T

2014-02-08

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol's equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.

Estimation of inhalation doses from airborne releases using gross monitors

International Nuclear Information System (INIS)

Goldstein, N.P.

1978-01-01

Monitoring programs at most nuclear facilities involve continuous gross measurements supplemented by periodic isotopic analyses of release samples. The isotopic measurements are required to accurately assess the potential dose from the various effluent streams, but in between these measurements, one depends on the gross monitors to provide approximate indications of the dose. The effluent streams release a variety of nuclides, each with its own dose factor. This means that the relationship between the counting rate in a gross monitor and the potential dose of the effluent being monitored will depend on the isotopic composition of this release. If this composition changes, then the dose indicated by the gross monitor (calibrated for the original group of isotopes) may be significantly in error. The problem of indicating inhalation doses from gross monitoring of airborne releases is considered. In order for this type of monitor to accurately indicate dose, regardless of the isotopic makeup of a release, the analysis shows that its response to each isotope should be proportional to the dose factor of that isotope. These ideas are applied to the monitoring of air particulates using gross beta and gross gamma monitors. The study shows that the former more closely satisfies this condition and as a result, satisfactorily indicates the actual dose from reactor effluents, as determined from detailed isotopic data published in the literature. On the other hand, the gross gamma monitor, with its poorer fit to the condition, provided less than satisfactory accuracy in its dose estimates. In addition, a variety of other mathematical response functions were considered but their dose estimation capabilities were not much better than the straight beta response. The study shows that reasonably accurate dose estimates can be made using properly selected gross monitors, but that significant errors can result with improper ones. (author)

Analytical representation for solution of the neutron point kinetics equation with time-dependent reactivity and free of the stiffness character

International Nuclear Information System (INIS)

Silva, Milena Wollmann da

2013-01-01

In this work, we report a genuine analytical representation for the solution of the neutron point kinetics equation free of the stiffness character, assuming that the reactivity is a continuous and sectionally continuous function of time. To this end, we initially cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix as a sum of a diagonal matrix with a matrix, whose components contain the off-diagonal elements. Next, expanding the neutron density and the delayed neutron precursors concentrations in a truncated series, and replacing these expansions in the matrix equation, we come out with an equation, which allows to construct a recursive system, a first order matrix differential equation with source. The fundamental characteristic of this system relies on the fact that the corresponding matrix is diagonal, meanwhile the source term is written in terms of the matrix with the off-diagonal components. Further, the first equation of the recursive system has no source and satisfies the initial conditions. On the other hand, the remaining equations satisfy the null initial condition. Due to the diagonal feature of the matrix, we attain analytical solutions for these recursive equations. We also mention that we evaluate the results for any time value, without the analytical continuity because the purposed solution is free on the stiffness character. Finally, we present numerical simulations and comparisons against literature results, considering specific the applications for the following reactivity functions: constant, step, ramp, and sine. (author)

Inverse engineering for fast transport and spin control of spin-orbit-coupled Bose-Einstein condensates in moving harmonic traps

Science.gov (United States)

Chen, Xi; Jiang, Ruan-Lei; Li, Jing; Ban, Yue; Sherman, E. Ya.

2018-01-01

We investigate fast transport and spin manipulation of tunable spin-orbit-coupled Bose-Einstein condensates in a moving harmonic trap. Motivated by the concept of shortcuts to adiabaticity, we design inversely the time-dependent trap position and spin-orbit-coupling strength. By choosing appropriate boundary conditions we obtain fast transport and spin flip simultaneously. The nonadiabatic transport and relevant spin dynamics are illustrated with numerical examples and compared with the adiabatic transport with constant spin-orbit-coupling strength and velocity. Moreover, the influence of nonlinearity induced by interatomic interaction is discussed in terms of the Gross-Pitaevskii approach, showing the robustness of the proposed protocols. With the state-of-the-art experiments, such an inverse engineering technique paves the way for coherent control of spin-orbit-coupled Bose-Einstein condensates in harmonic traps.

THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR

KAUST Repository

ARNOLD, ANTON

2012-11-01

We consider the linear WignerFokkerPlanck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for FokkerPlanck type operators in certain weighted L 2-spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge towards the steady state with an exponential rate. © 2012 World Scientific Publishing Company.

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

Science.gov (United States)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Implicit time-dependent finite different algorithm for quench simulation

International Nuclear Information System (INIS)

Koizumi, Norikiyo; Takahashi, Yoshikazu; Tsuji, Hiroshi

1994-12-01

A magnet in a fusion machine has many difficulties in its application because of requirement of a large operating current, high operating field and high breakdown voltage. A cable-in-conduit (CIC) conductor is the best candidate to overcome these difficulties. However, there remained uncertainty in a quench event in the cable-in-conduit conductor because of a difficulty to analyze a fluid dynamics equation. Several scientists, then, developed the numerical code for the quench simulation. However, most of them were based on an explicit time-dependent finite difference scheme. In this scheme, a discrete time increment is strictly restricted by CFL (Courant-Friedrichs-Lewy) condition. Therefore, long CPU time was consumed for the quench simulation. Authors, then, developed a new quench simulation code, POCHI1, which is based on an implicit time dependent scheme. In POCHI1, the fluid dynamics equation is linearlized according to a procedure applied by Beam and Warming and then, a tridiagonal system can be offered. Therefore, no iteration is necessary to solve the fluid dynamics equation. This leads great reduction of the CPU time. Also, POCHI1 can cope with non-linear boundary condition. In this study, comparison with experimental results was carried out. The normal zone propagation behavior was investigated in two samples of CIC conductors which had different hydraulic diameters. The measured and simulated normal zone propagation length showed relatively good agreement. However, the behavior of the normal voltage shows a little disagreement. These results indicate necessity to improve the treatment of the heat transfer coefficient in the turbulent flow region and the electric resistivity of the copper stabilizer in high temperature and high field region. (author)

A numerical study of time-dependent Schrödinger equation for ...

Indian Academy of Sciences (India)

Unknown

Theoretical Chemistry Group, Department of Chemistry, Panjab University,. Chandigarh 160 ... probability, potential energy curve and dipole moment. ... quantum Monte Carlo (DQMC)-type equation.23 The system is then evolved in imaginary.

Coherent states for the time dependent harmonic oscillator: the step function

International Nuclear Information System (INIS)

Moya-Cessa, Hector; Fernandez Guasti, Manuel

2003-01-01

We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for a continuous treatment that differs from former studies that involve the matching of two time independent solutions at the time when the step occurs

Application of the nodal method RTN-0 for the solution of the neutron diffusion equation dependent of time in hexagonal-Z geometry

International Nuclear Information System (INIS)

Esquivel E, J.; Alonso V, G.; Del Valle G, E.

2015-09-01

The solution of the neutron diffusion equation either for reactors in steady state or time dependent, is obtained through approximations generated by implementing of nodal methods such as RTN-0 (Raviart-Thomas-Nedelec of zero index), which is used in this study. Since the nodal methods are applied in quadrangular geometries, in this paper a technique in which the hexagonal geometry through the transfinite interpolation of Gordon-Hall becomes the appropriate geometry to make use of the nodal method RTN-0 is presented. As a result, a computer program was developed, whereby is possible to obtain among other results the neutron multiplication effective factor (k eff ), and the distribution of radial and/or axial power. To verify the operation of the code, was applied to three benchmark problems: in the first two reactors VVER and FBR, results k eff and power distribution are obtained, considering the steady state case of reactor; while the third problem a type VVER is analyzed, in its case dependent of time, which qualitative results are presented on the behavior of the reactor power. (Author)

Time-dependent quantum many-body systems. Linear response, electronic transport, and reduced density matrices

International Nuclear Information System (INIS)

Appel, H.

2007-05-01

In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent density functional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f xc from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the propagation

Time-dependent quantum many-body systems. Linear response, electronic transport, and reduced density matrices

Energy Technology Data Exchange (ETDEWEB)

Appel, H.

2007-05-15

In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent density functional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f{sub xc} from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the

A Sequential, Implicit, Wavelet-Based Solver for Multi-Scale Time-Dependent Partial Differential Equations

Directory of Open Access Journals (Sweden)

Donald A. McLaren

2013-04-01

Full Text Available This paper describes and tests a wavelet-based implicit numerical method for solving partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time-discretization into multiple smaller systems that can be solved sequentially. Included is a test on a basic non-linear problem, with both the results of the test, and the time required to calculate them, compared with control results based on a single system with fine resolution. The method is then tested on a non-trivial problem, its computational time and accuracy checked against control results. In both tests, it was found that the method requires less computational expense than the control. Furthermore, the method showed convergence towards the fine resolution control results.