Inverse Problem for Two-Dimensional Discrete Schr`dinger Equation
Serdyukova, S I
2000-01-01
For two-dimensional discrete Schroedinger equation the boundary-value problem in rectangle M times N with zero boundary conditions is solved. It's stated in this work, that inverse problem reduces to reconstruction of C symmetric five-diagonal matrix with given spectrum and given first k(M,N), 1<-k
Introduction to numerical methods for time dependent differential equations
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
Wave Functions for Time-Dependent Dirac Equation under GUP
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 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)
Relativistic Photoionization Computations with the Time Dependent Dirac Equation
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
Optimal moving grids for time-dependent partial differential equations
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.
Spectral methods for time dependent partial differential equations
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.
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
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 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.
Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation
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.
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.).
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 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
Quantum trajectories for time-dependent adiabatic master equations
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.
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)
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
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
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)
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
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.
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.
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...
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.
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
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.
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.
The large discretization step method for time-dependent partial differential equations
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.
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
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.
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.
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)
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.)
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
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
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.
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
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.
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.
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
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
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.
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.)
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
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
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
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.)
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
Boundary-integral equation formulation for time-dependent inelastic deformation in metals
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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 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)
Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
Muruganandam, P.; Adhikari, S. K.
2009-10-01
Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data
Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations
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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.
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
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)
Angular distribution of scission neutrons studied with time-dependent Schrödinger equation
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
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
Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing
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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.
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
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.
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.
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.
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.)
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
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.
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)
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.
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.
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
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)
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.
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
A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media
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.
Directory of Open Access Journals (Sweden)
Regnier D.
2017-01-01
Full Text Available Accurate knowledge of fission fragment yields is an essential ingredient of numerous applications ranging from the formation of elements in the r-process to fuel cycle optimization in nuclear energy. The need for a predictive theory applicable where no data is available, together with the variety of potential applications, is an incentive to develop a fully microscopic approach to fission dynamics. One of the most promising theoretical frameworks is the time dependent generator coordinate method (TDGCM applied under the Gaussian overlap approximation (GOA. However, the computational cost of this method makes it difficult to perform calculations with more than two collective degree of freedom. Meanwhile, it is well-known from both semi-phenomenological and fully microscopic approaches that at least four or five dimensions may play a role in the dynamics of fission. To overcome this limitation, we develop the code FELIX aiming to solve the TDGCM+GOA equation for an arbitrary number of collective variables. In this talk, we report the recent progress toward this enriched description of fission dynamics. We will briefly present the numerical methods adopted as well as the status of the latest version of FELIX. Finally, we will discuss fragments yields obtained within this approach for the low energy fission of major actinides.
Regnier, D.; Dubray, N.; Schunck, N.; Verrière, M.
2017-09-01
Accurate knowledge of fission fragment yields is an essential ingredient of numerous applications ranging from the formation of elements in the r-process to fuel cycle optimization in nuclear energy. The need for a predictive theory applicable where no data is available, together with the variety of potential applications, is an incentive to develop a fully microscopic approach to fission dynamics. One of the most promising theoretical frameworks is the time dependent generator coordinate method (TDGCM) applied under the Gaussian overlap approximation (GOA). However, the computational cost of this method makes it difficult to perform calculations with more than two collective degree of freedom. Meanwhile, it is well-known from both semi-phenomenological and fully microscopic approaches that at least four or five dimensions may play a role in the dynamics of fission. To overcome this limitation, we develop the code FELIX aiming to solve the TDGCM+GOA equation for an arbitrary number of collective variables. In this talk, we report the recent progress toward this enriched description of fission dynamics. We will briefly present the numerical methods adopted as well as the status of the latest version of FELIX. Finally, we will discuss fragments yields obtained within this approach for the low energy fission of major actinides.
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
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
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
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.
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).
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.
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.
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.
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.)
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)
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
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.
Energy Technology Data Exchange (ETDEWEB)
Campos, F.F. [Universidade Federal de Minas Gerais, Belo Horizonte (Brazil); Birkett, N.R.C. [Oxford Univ. Computing Lab. (United Kingdom)
1996-12-31
The Controlled Cholesky factorisation has been shown to be a robust preconditioner for the Conjugate Gradient method. In this scheme the amount of fill-in is defined in terms of a parameter {eta}, the number of extra elements allowed per column. It is demonstrated how an optimum value of {eta} can be automatically determined when solving time dependent p.d.e.`s using an implicit time step method. A comparison between CCCG({eta}) and the standard ICCG solving parabolic problems on general grids shows CCCG({eta}) to be an efficient general purpose solver.
Isostable reduction with applications to time-dependent partial differential equations.
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.
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.
A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers
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.
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)
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)
Introducing time-dependent molecular fields: a new derivation of the wave equations
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.
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.
Solution of the Lyapunov matrix equation for a system with a time-dependent stiffness matrix
DEFF Research Database (Denmark)
Pommer, Christian; Kliem, Wolfhard
2004-01-01
The stability of the linearized model of a rotor system with non-symmetric strain and axial loads is investigated. Since we are using a fixed reference system, the differential equations have the advantage to be free of Coriolis and centrifugal forces. A disadvantage is nevertheless the occurrence...
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
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
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
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.
International Nuclear Information System (INIS)
Skoczen, A.; Machowski, W.; Kaprzyk, S.
1990-07-01
Computer program aiming at application in quantum mechanics didactics has been proposed. This program can generate the moving pictures of one-dimensional quantum mechanics scattering phenomena. Constructions of this program provide two options. In the first option the wave packet is generated in infinite one-dimensional well which has walls on the borders of graphic window. In the second option the square potential barrier is located in this well and transmission and reflection of wave packet are shown. We have selected a Gaussian wave packet to represent the initial state of the particle. The wave equation is solved numerically by a method discussed in detail. Solutions for the succesive time moments are graphically presented on the monitor screen. In this way observer can watch whole time-development of physical system. Graphically presented results are physically realistic when program parameters satisfy conditions discussed in this paper. (author)
''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
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
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.
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
Energy Technology Data Exchange (ETDEWEB)
Mohamadou, Alidou [Condensed Matter Laboratory, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala (Cameroon); Abdus Salam International Centre for Theoretical Physics, P.O. Box 538, Strada Costiera 11, I-34014 Trieste (Italy); Wamba, Etienne; Kofane, Timoleon C. [Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); Doka, Serge Y. [Higher Teacher Training College, University of Maroua, P.O. Box 55, Maroua (Cameroon); Ekogo, Thierry B. [Departement de Physique, Universite des Sciences et Techniques de Masuku, B.P. 943, Franceville (Gabonese Republic)
2011-08-15
We examine the generation of bright matter-wave solitons in the Gross-Pitaevskii equation describing Bose-Einstein condensates with a time-dependent complex potential, which is composed of a repulsive parabolic background potential and a gravitational field. By performing a modified lens-type transformation, an explicit expression for the growth rate of a purely growing modulational instability is presented and analyzed. We point out the effects of the gravitational field, as well as of the parameter related to the feeding or loss of atoms in the condensate, on the instability growth rate. It is evident from numerical simulations that the feeding with atoms and the magnetic trap have opposite effects on the dynamics of the system. It is shown that the feeding or loss parameter can be well used to control the instability domain. Our study shows that the gravitational field changes the condensate trail of the soliton trains during the propagation. We also perform a numerical analysis to solve the Gross-Pitaevskii equation with a time-dependent complicated potential. The numerical results on the effect of both the gravitational field and the parameter of feeding or loss of atoms in the condensate agree well with predictions of the linear stability analysis. Another result of the present work is the modification of the background wave function in the Thomas-Fermi approximation during the numerical simulations.
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
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
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.
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
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.
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)
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
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)
International Nuclear Information System (INIS)
Strinati, G.C.; Pieri, P.
2004-01-01
The linear response to a space- and time-dependent external disturbance of a system of dilute condensed composite bosons at zero temperature, as obtained from the linearized version of the time-dependent Gross-Pitaevskii equation, is shown to result also from the strong-coupling limit of the time-dependent BCS (or broken-symmetry random-phase) approximation for the constituent fermions subject to the same external disturbance. In this way, it is possible to connect excited-state properties of the bosonic and fermionic systems by placing the Gross-Pitaevskii equation in perspective with the corresponding fermionic approximations
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
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.
A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain
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.
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.
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
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)
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.
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
OpenMP GNU and Intel Fortran programs for solving the time-dependent Gross-Pitaevskii equation
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
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
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
Energy Technology Data Exchange (ETDEWEB)
Davidenko, V. D., E-mail: Davidenko-VD@nrcki.ru; Zinchenko, A. S., E-mail: zin-sn@mail.ru; Harchenko, I. K. [National Research Centre Kurchatov Institute (Russian Federation)
2016-12-15
Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.
International Nuclear Information System (INIS)
Veerasingam, R.
1990-01-01
In fusion plasmas impurities such as carbon, oxygen or nickel can contaminate the plasma and cause degradation of the performance of a fusion device through radiation. However, impurities can also be used as diagnostics to obtain information about a plasma through spectroscopic experiments which can then be used in plasma modeling and simulations. In the past, serial algorithms have been described for either the time dependent or steady state problem. In this paper, we describe a parallel procedure adopted to solve the time-dependent problem. It can be shown that for the steady state problem a parallel procedure would not be a useful application of parallelization because a few seconds of the Central Processing Unit time on a CRAY-XMP or IBM 3090/600S would suffice to obtain the solution, while this is not the case for the time-dependent problem. In order to study the effects of low Z and high Z impurities on the final state of a plasma, time-dependent solutions are necessary. For purposes of diagnostics and comparisons with experiments, a fast turn around time of the simulations would be advantageous. We have implemented a parallel algorithm on and IBM 3090/600S and tested its performance for a typical set of fusion plasma parameters. 4 refs., 1 tab
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).
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...
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Xin, H.; Neytcheva, M.
2015-01-01
Roč. 20, č. 2 (2015), s. 232-260 ISSN 1392-6292 Institutional support: RVO:68145535 Keywords : variable density * phase-field model * Navier-Stokes equations * preconditioning * variable viscosity Subject RIV: BA - General Mathematics Impact factor: 0.468, year: 2015 http://www.tandfonline.com/doi/abs/10.3846/13926292.2015.1021395
Tian, Heng; Chen, GuanHua
2013-10-01
Going beyond the limitations of our earlier works [X. Zheng, F. Wang, C.Y. Yam, Y. Mo, G.H. Chen, Phys. Rev. B 75, 195127 (2007); X. Zheng, G.H. Chen, Y. Mo, S.K. Koo, H. Tian, C.Y. Yam, Y.J. Yan, J. Chem. Phys. 133, 114101 (2010)], we propose, in this manuscript, a new alternative approach to simulate time-dependent quantum transport phenomenon from first-principles. This new practical approach, still retaining the formal exactness of HEOM framework, does not rely on any intractable parametrization scheme and the pole structure of Fermi distribution function, thus, can seamlessly incorporated into first-principles simulation and treat transient response of an open electronic systems to an external bias voltage at both zero and finite temperatures on the equal footing. The salient feature of this approach is surveyed, and its time complexity is analysed. As a proof-of-principle of this approach, simulation of the transient current of one dimensional tight-binding chain, driven by some direct external voltages, is demonstrated.
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.
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.
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2009-12-14
We present a novel theory which enables us to explore the mechanism of reaction selectivity and robust functions in complex systems persisting under thermal fluctuation. The theory constructs a nonlinear coordinate transformation so that the equation of motion for the new reaction coordinate is independent of the other nonreactive coordinates in the presence of thermal fluctuation. In this article we suppose that reacting systems subject to thermal noise are described by a multidimensional Langevin equation without a priori assumption for the form of potential. The reaction coordinate is composed not only of all the coordinates and velocities associated with the system (solute) but also of the random force exerted by the environment (solvent) with friction constants. The sign of the reaction coordinate at any instantaneous moment in the region of a saddle determines the fate of the reaction, i.e., whether the reaction will proceed through to the products or go back to the reactants. By assuming the statistical properties of the random force, one can know a priori a well-defined boundary of the reaction which separates the full position-velocity space in the saddle region into mainly reactive and mainly nonreactive regions even under thermal fluctuation. The analytical expression of the reaction coordinate provides the firm foundation on the mechanism of how and why reaction proceeds in thermal fluctuating environments.
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.
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)
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.
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.
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.
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.)
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
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
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.
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.
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
Silaev, A. A.; Romanov, A. A.; Vvedenskii, N. V.
2018-03-01
In the numerical solution of the time-dependent Schrödinger equation by grid methods, an important problem is the reflection and wrap-around of the wave packets at the grid boundaries. Non-optimal absorption of the wave function leads to possible large artifacts in the results of numerical simulations. We propose a new method for the construction of the complex absorbing potentials for wave suppression at the grid boundaries. The method is based on the use of the multi-hump imaginary potential which contains a sequence of smooth and symmetric humps whose widths and amplitudes are optimized for wave absorption in different spectral intervals. We show that this can ensure a high efficiency of absorption in a wide range of de Broglie wavelengths, which includes wavelengths comparable to the width of the absorbing layer. Therefore, this method can be used for high-precision simulations of various phenomena where strong spreading of the wave function takes place, including the phenomena accompanying the interaction of strong fields with atoms and molecules. The efficiency of the proposed method is demonstrated in the calculation of the spectrum of high-order harmonics generated during the interaction of hydrogen atoms with an intense infrared laser pulse.
Kishi, Ryohei; Nakano, Masayoshi
2011-04-21
A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.
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.
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.
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)
Time Dependent Quantum Mechanics
Morrison, Peter G.
2012-01-01
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic ...
Energy Technology Data Exchange (ETDEWEB)
Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico
2014-12-15
In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.
Chun, Sehun
2017-07-01
Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine-Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell's equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated.
International Nuclear Information System (INIS)
Zagrebaev, V.I.; ); Samarin, V.V.
2006-01-01
Fusion of heavy nuclei was analyzed on the basis of the numerical solution of the Schroedinger three-body and three-dimensional nonstationary equations. One revealed the increase of fuss ion probability in 66 He + 2O Pb reaction caused by transfer and collectivization of valent neutrons [ru
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
Sirenko, Kostyantyn
2013-01-01
A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing transient electromagnetic wave interactions on two-dimensional waveguides. Numerical results demonstrate the proposed method\\'s superiority over the TD-DG-FEM that employs approximate boundary conditions and perfectly matched layers. Additionally, it is shown that the proposed method can produce the solution with ten-eleven digit accuracy when high-order spatial basis functions are used to discretize the Maxwell equations as well as the EACs. © 1963-2012 IEEE.
Energy Technology Data Exchange (ETDEWEB)
Wilcox, T. P.
1973-09-20
The code ANISN-L solves the one-dimensional, multigroup, time-independent Boltzmann transport equation by the method of discrete ordinates. In problems involving a fissionable system, it can calculate the system multiplication or alpha. In such cases, it is also capable of determining isotopic concentrations, radii, zone widths, or buckling in order to achieve a given multiplication or alpha. The code may also calculate fluxes caused by a specified fixed source. Neutron, gamma, and coupled neutron--gamma problems may be solved in either the forward or adjoint (backward) modes. Cross sections describing upscatter, as well as the usual downscatter, may be employed. This report describes the use of ANISN-L; this is a revised version of ANISN which handles both large and small problems efficiently on CDC-7600 computers. (RWR)
International Nuclear Information System (INIS)
Majumdar, A.; Makowitz, H.
1987-10-01
With the development of modern vector/parallel supercomputers and their lower performance clones it has become possible to increase computational performance by several orders of magnitude when comparing to the previous generation of scalar computers. These performance gains are not observed when production versions of current thermal-hydraulic codes are implemented on modern supercomputers. It is our belief that this is due in part to the inappropriateness of using old thermal-hydraulic algorithms with these new computer architectures. We believe that a new generation of algorithms needs to be developed for thermal-hydraulics simulation that is optimized for vector/parallel architectures, and not the scalar computers of the previous generation. We have begun a study that will investigate several approaches for designing such optimal algorithms. These approaches are based on the following concepts: minimize recursion; utilize predictor-corrector iterative methods; maximize the convergence rate of iterative methods used; use physical approximations as well as numerical means to accelerate convergence; utilize explicit methods (i.e., marching) where stability will permit. We call this approach the ''EPIC'' methodology (i.e., Explicit Predictor Iterative Corrector methods). Utilizing the above ideas, we have begun our work by investigating the one-dimensional transient heat conduction equation. We have developed several algorithms based on variations of the Hopscotch concept, which we discuss in the body of this report. 14 refs
Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.
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.
Chyczewski, Thomas Stanley, Jr.
A national interest in High Speed Civil Transports (HSCT) coupled with strict airport noise regulations has prompted the scientific community to investigate new and improved noise prediction strategies. Meeting these airport regulations is considered to be a major design challenge for the HSCT. In light of this effort, a direct simulation strategy for predicting supersonic jet noise is developed in this thesis. Direct simulations are quickly becoming the method of choice due to their generality and ever decreasing expense associated with the development of parallel processors. Supersonic jet noise is known to be dominated by the growth and decay of large scale turbulent structures. The direct simulation approach used here consists of solving the full Navier Stokes equations using high order finite difference techniques to simulate the evolution of these structures and the noise they radiate to the acoustic near field. This near field solution is then extrapolated to the far field using a Kirchhoff method. The numerical algorithm uses a fourth order Runge -Kutta method for the time integration. The spatial derivatives are approximated by a sixth order central scheme. A sixth order filter is used at each interior mesh point to damp frequencies that cannot be resolved by the spatial scheme. Second order filtering is provided only where required for stability. It is found to be confined to specific locations in the jet core and should have no effect on the acoustic solution. Characteristic based nonreflecting conditions are used to minimize reflections at the far field boundaries and have proven to be effective. Additional boundary conditions are required in the form of it model for the nozzle exit flow. The characteristics of the nozzle exit flow can have a significant impact on the noise radiation. This dependence is unfortunate since comprehensive experimental data is not available in this region of the jet. A model is developed here that addresses a variety of
International Nuclear Information System (INIS)
Coskun, E.
1995-09-01
Time-dependent Ginzburg-Landau (TDGL) equations are considered for modeling a thin-film finite size superconductor placed under magnetic field. The problem then leads to the use of so-called natural boundary conditions. Computational domain is partitioned into subdomains and bond variables are used in obtaining the corresponding discrete system of equations. An efficient time-differencing method based on the Forward Euler method is developed. Finally, a variable strength magnetic field resulting in a vortex motion in Type II High T c superconducting films is introduced. The authors tackled the problem using two different state-of-the-art parallel computing tools: BlockComm/Chameleon and PCN. They had access to two high-performance distributed memory supercomputers: the Intel iPSC/860 and IBM SP1. They also tested the codes using, as a parallel computing environment, a cluster of Sun Sparc workstations
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.)
Ziegler, Tom; Krykunov, Mykhaylo; Autschbach, Jochen
2014-09-09
The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.
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 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)
Energy Technology Data Exchange (ETDEWEB)
Cargo, P.; Samba, G
2007-07-01
We consider the P{sub n} model to approximate the transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it gives the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by L. Gosse to solve the P{sub 1} model without absorption term. Moreover, it has the well-balanced property: it preserves the steady solutions of the system. (authors)
Time-dependent problems and difference methods
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 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)
Integrable Time-Dependent Quantum Hamiltonians
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.
International Nuclear Information System (INIS)
Shore, B.W.; Eberly, J.H.
1983-01-01
The definition of a time-dependent spectrum registered by an idealized spectrometer responding to a time-varying electromagnetic field as proposed by Eberly and Wodkiewicz and subsequently applied to the spectrum of laser-induced fluorescence by Eberly, Kunasz, and Wodkiewicz is here extended to allow a stochastically fluctuating (interruption model) environment: we provide an algorithm for numerical determination of the time-dependent fluorescence spectrum of an atom subject to excitation by an intense noisy laser and interruptive relaxation
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.”
Czech Academy of Sciences Publication Activity Database
Zhukov, V.P.; Bulgakova, Nadezhda M.; Fedoruk, M.P.
2017-01-01
Roč. 84, č. 7 (2017), s. 439-446 ISSN 1070-9762 R&D Projects: GA MŠk LO1602; GA ČR GA16-12960S Institutional support: RVO:68378271 Keywords : glass * femtosecond laser pulses * Maxwell's and Schrdinger equations Subject RIV: BH - Optics, Masers, Lasers OBOR OECD: Optics (including laser optics and quantum optics) Impact factor: 0.299, year: 2016
Calvi, Marta
2011-01-01
This review reports preliminary results of time-dependent measurements of decays of $B^0$ mesons and $B^0_s$ mesons coming from the analysis of about 36 pb$^{-1}$ of data collected by the LHCb experiment during the 2010 run of the Large Hadron Collider at $\\sqrt{s}$ = 7 TeV.
Calvi, Marta; Collaboration, for the LHCb
2011-01-01
This review reports preliminary results of time-dependent measurements of decays of B^0 mesons and B^0_s mesons coming from the analysis of about 36 pb^-1 of data collected by the LHCb experiment during the 2010 run of the Large Hadron Collider at sqrt(s)=7 TeV.
Time dependent view factor methods
International Nuclear Information System (INIS)
Kirkpatrick, R.C.
1998-03-01
View factors have been used for treating radiation transport between opaque surfaces bounding a transparent medium for several decades. However, in recent years they have been applied to problems involving intense bursts of radiation in enclosed volumes such as in the laser fusion hohlraums. In these problems, several aspects require treatment of time dependence
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.
Reconstructing time-dependent dynamics
Clemson, Philip; Lancaster, Gemma; Stefanovska, Aneta
2016-01-01
The usefulness of the information extracted from biomedical data relies heavily on the underlying theory of the methods used in its extraction. The assumptions of stationarity and autonomicity traditionally applied to dynamical systems break down when considering living systems, due to their inherent time-variability. Living systems are thermodynamically open, and thus constantly interacting with their environment. This results in highly nonlinear, time-dependent dynamics. The aim of signal a...
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
International Nuclear Information System (INIS)
Senthilvelan, M; Torrisi, M; Valenti, A
2006-01-01
By using Lie's invariance infinitesimal criterion, we obtain the continuous equivalence transformations of a class of nonlinear Schroedinger equations with variable coefficients. We construct the differential invariants of order 1 starting from a special equivalence subalgebra E χ o . We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schr?dinger equations which can be mapped, by means of an equivalence transformation of E χ o , to the well-known cubic Schroedinger equation. We also provide the explicit form of the transformation
Dissipative time-dependent quantum transport theory.
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.
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
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.
Selfsimilar time dependent shock structures
International Nuclear Information System (INIS)
Beck, R.; Drury, L.O.
1985-01-01
Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The same argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions
Selfsimilar time dependent shock structures
Beck, R.; Drury, L. O.
1985-01-01
Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The ame argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions.
Energy Technology Data Exchange (ETDEWEB)
Silva, Milena Wollmann da
2013-08-01
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)
Betweenness in time dependent networks
International Nuclear Information System (INIS)
Alsayed, Ahmad; Higham, Desmond J.
2015-01-01
The concept of betweenness has given rise to a very useful class of network centrality measures. Loosely, betweenness quantifies the level of importance of a node in terms of its propensity to act as an intermediary when messages are passed around the network. In this work we generalize a walk-based betweenness measure to the case of time-dependent networks, such as those arising in telecommunications and on-line social media. We also introduce a new kind of betweenness measure, temporal betweenness, which quantifies the importance of a time-point. We illustrate the effectiveness of these new measures on synthetic examples, and also give results on real data sets involving voice call, email and Twitter
Exact solution of a quantum forced time-dependent harmonic oscillator
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Time dependent mean-field games
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.
Time-dependent crashworthiness of polyurethane foam
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.
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)
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.
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
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
Time-dependent seismic tomography
Julian, B.R.; Foulger, G.R.
2010-01-01
Of methods for measuring temporal changes in seismic-wave speeds in the Earth, seismic tomography is among those that offer the highest spatial resolution. 3-D tomographic methods are commonly applied in this context by inverting seismic wave arrival time data sets from different epochs independently and assuming that differences in the derived structures represent real temporal variations. This assumption is dangerous because the results of independent inversions would differ even if the structure in the Earth did not change, due to observational errors and differences in the seismic ray distributions. The latter effect may be especially severe when data sets include earthquake swarms or aftershock sequences, and may produce the appearance of correlation between structural changes and seismicity when the wave speeds are actually temporally invariant. A better approach, which makes it possible to assess what changes are truly required by the data, is to invert multiple data sets simultaneously, minimizing the difference between models for different epochs as well as the rms arrival-time residuals. This problem leads, in the case of two epochs, to a system of normal equations whose order is twice as great as for a single epoch. The direct solution of this system would require twice as much memory and four times as much computational effort as would independent inversions. We present an algorithm, tomo4d, that takes advantage of the structure and sparseness of the system to obtain the solution with essentially no more effort than independent inversions require. No claim to original US government works Journal compilation ?? 2010 RAS.
Cosmologies with a time dependent vacuum
International Nuclear Information System (INIS)
Sola, Joan
2011-01-01
The idea that the cosmological term Λ should be a time dependent quantity in cosmology is a most natural one. It is difficult to conceive an expanding universe with a strictly constant vacuum energy density, ρ Λ = Λ/(8π G), namely one that has remained immutable since the origin of time. A smoothly evolving vacuum energy density ρ Λ = ρ Λ (ξ(t)) that inherits its time-dependence from cosmological functions ξ = ξ(t), such as the Hubble rate H(t) or the scale factor a(t), is not only a qualitatively more plausible and intuitive idea, but is also suggested by fundamental physics, in particular by quantum field theory (QFT) in curved space-time. To implement this notion, is not strictly necessary to resort to ad hoc scalar fields, as usually done in the literature (e.g. in quintessence formulations and the like). A 'running' Λ term can be expected on very similar grounds as one expects (and observes) the running of couplings and masses with a physical energy scale in QFT. Furthermore, the experimental evidence that the equation of state (EOS) of the dark energy (DE) could be evolving with time/redshift (including the possibility that it might currently behave phantom-like) suggests that a time-variable Λ = Λ(t) term (possibly accompanied by a variable Newton's gravitational coupling too, G = G(t)) could account in a natural way for all these features. Remarkably enough, a class of these models (the 'new cosmon') could even be the clue for solving the old cosmological constant problem, including the coincidence problem.
Time-dependent Autler-Townes spectroscopy
International Nuclear Information System (INIS)
Qamar, Sajid; Zhu, S.-Y.; Zubairy, M Suhail
2003-01-01
Autler-Townes spontaneous emission spectroscopy is revisited for a time-dependent case. We report the results of spontaneous emission spectra for nonstationary scattered light signals using the definition of the time-dependent physical spectrum. This is a rare example of problems where time-dependent spectra can be calculated exactly
Time-dependent Autler-Townes spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Qamar, Sajid [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States); Zhu, S.-Y. [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States); Zubairy, M Suhail [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States)
2003-04-01
Autler-Townes spontaneous emission spectroscopy is revisited for a time-dependent case. We report the results of spontaneous emission spectra for nonstationary scattered light signals using the definition of the time-dependent physical spectrum. This is a rare example of problems where time-dependent spectra can be calculated exactly.
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
Holographic complexity for time-dependent backgrounds
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood, E-mail: davoodmomeni78@gmail.com [Eurasian International Center for Theoretical Physics and Department of General Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Faizal, Mir, E-mail: mirfaizalmir@googlemail.com [Irving K. Barber School of Arts and Sciences, University of British Columbia, Okanagan, 3333 University Way, Kelowna, British Columbia V1V 1V7 (Canada); Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4 (Canada); Bahamonde, Sebastian, E-mail: sebastian.beltran.14@ucl.ac.uk [Department of Mathematics, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Myrzakulov, Ratbay [Eurasian International Center for Theoretical Physics and Department of General Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan)
2016-11-10
In this paper, we will analyze the holographic complexity for time-dependent asymptotically AdS geometries. We will first use a covariant zero mean curvature slicing of the time-dependent bulk geometries, and then use this co-dimension one spacelike slice of the bulk spacetime to define a co-dimension two minimal surface. The time-dependent holographic complexity will be defined using the volume enclosed by this minimal surface. This time-dependent holographic complexity will reduce to the usual holographic complexity for static geometries. We will analyze the time-dependence as a perturbation of the asymptotically AdS geometries. Thus, we will obtain time-dependent asymptotically AdS geometries, and we will calculate the holographic complexity for such time-dependent geometries.
Gholibeigian, Hassan; Gholibeigian, Kazem
2016-03-01
In Sadra's theory, the relative time for an atom (body) which is varying continuously becomes momentums of its involved fundamental particles (strings), (time's relativity) [Gholibeigian, APS March Meeting 2015, abstract #V1.023]. Einstein's theory of special relativity might be special form of Sadra's theory. ``The nature has two magnitudes and two elongations, the one is gradual being (wavy-like motion) which belongs to the time and dividable to the former and the next times in mind, and the other is jerky-like motion which belongs to the space and dividable to the former and the next places'' [Asfar, Mulla Sadra, (1571/2-1640)]. Sadra separated the nature of time from nature of space. Therefore we can match these two natures on wave-particle duality. It means that the nature of time might be wavy-like and the nature of space might be jerky-like. So, there are two independent variable sources for particle(s)' flow with respect of its two natures such as potential of flow and relative time which vary with respect of both space and time. Consequently we propose two additional parts to Schrodinger's equation: H⌢ Ψ +tp ∇t' = ih/2 π ∂/∂t Ψ +tp∂/∂t t' , where tp is Planck's time and t' is relative time: t' = f (m , v , t) = t +/- Δt , in which t is time, m is mass and vis speed of particle . AmirKabir University of Technology, Tehran, Iran.
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 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 Variations of Accretion Disk
Directory of Open Access Journals (Sweden)
Hye-Weon Na
1987-06-01
Full Text Available In dward nova we assume the primary star as a white dwarf and the secondary as the late type star which filled Roche lobe. Mass flow from the secondary star leads to the formation of thin accretion disk around the white dwarf. We use the α parameter as viscosity to maintain the disk form and propose that the outburst in dwarf nova cause the steep increase of source term. With these assumptions we solve the basic equations of stellar structure using Newton-Raphson method. We show the physical parameters like temperature, density, pressure, opacity, surface density, height and flux to the radius of disk. Changing the value of α, we compare several parameters when mass flow rate is constant with those of when luminosity of disk is brightest. At the same time, we obtain time-dependent variations of luminosity and mass of disk. We propose the suitable range of α is 0.15-0.18 to the difference of luminosity. We compare several parameters of disk with those of the normal late type stars which have the same molecular weight of disk is lower. Maybe the outburst in dwarf nova is due to the variation of the α value instead of increment of mass flow from the secondary star.
Time-dependent behavior of concrete
International Nuclear Information System (INIS)
Pfeiffer, P.A.; Tanabe, Tada-aki
1992-01-01
This paper is a condensed version of the material presented at the International Workshop on Finite Element Analysis of Reinforced Concrete, Session 4 -- Time Dependent Behavior, held at Columbia University, New York on June 3--6, 1991. Dr. P.A. Pfeiffer presented recent developments in time-dependent behavior of concrete and Professor T. Tanabe presented a review of research in Japan on time-dependent behavior of concrete. The paper discusses the recent research of time-dependent behavior of concrete in the past few years. 6 refs
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
Exponential integrators in time-dependent density-functional calculations
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.
Energy Technology Data Exchange (ETDEWEB)
Arvieu, R.; Carbonell, J.; Gignoux, C.; Mangin-Brinet, M. [Inst. des Sciences Nucleaires, Grenoble-1 Univ., 38 (France); Rozmej, P. [Uniwersytet Marii Curie-Sklodowskiej, Lublin (Poland)
1997-12-31
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) 3 refs.
Finite element solution of two dimensional time dependent heat equation
International Nuclear Information System (INIS)
Maaz
1999-01-01
A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)
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
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
Competing risks and time-dependent covariates
DEFF Research Database (Denmark)
Cortese, Giuliana; Andersen, Per K
2010-01-01
Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates......, as classified by Kalbfleisch and Prentice [The Statistical Analysis of Failure Time Data, Wiley, New York, 2002] with the intent of clarifying their role and emphasizing the limitations in standard survival models and in the competing risks setting. If random (internal) time-dependent covariates...
Watching excitons move: the time-dependent transition density matrix
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.
Topic 5: Time-Dependent Behavior
International Nuclear Information System (INIS)
Pfeiffer, P.A.; Tanabe, Tada-aki
1991-01-01
This chapter is a report of the material presented at the International Workshop on Finite Element Analysis of Reinforced Concrete, Session 4 -- Time Dependent Behavior, held at Columbia University, New York on June 3--6, 1991. Dr. P.A. Pfeiffer presented recent developments in time-dependent behavior of concrete and Professor T. Tanabe presented a review of research in Japan on time-dependent behavior of concrete. The chapter discusses the recent research of time-dependent behavior of concrete in the past few years in both the USA-European and Japanese communities. The author appreciates the valuable information provided by Zdenek P. Bazant in preparing the USA-European Research section
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)
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
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.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
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.
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
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
Fermions in interaction with time dependent fields
International Nuclear Information System (INIS)
Falkensteiner, P.; Grosse, H.
1988-01-01
We solve a two dimensional model describing the interaction of fermions with time dependent external fields. We work out the second quantized formulation and obtain conditions for equivalence of representations at different times. This implies the existence of sectors which describe charged states. We obtain the time dependence of charges and observe that charge differences become integer for unitary equivalent states. For scattering we require the equivalence of in- and out-representations; nevertheless charged sectors may be reached by suitable interactions and ionization is possible. 20 refs. (Author)
Investigations of Low Temperature Time Dependent Cracking
Energy Technology Data Exchange (ETDEWEB)
Van der Sluys, W A; Robitz, E S; Young, B A; Bloom, J
2002-09-30
The objective of this project was to investigate metallurgical and mechanical phenomena associated with time dependent cracking of cold bent carbon steel piping at temperatures between 327 C and 360 C. Boiler piping failures have demonstrated that understanding the fundamental metallurgical and mechanical parameters controlling these failures is insufficient to eliminate it from the field. The results of the project consisted of the development of a testing methodology to reproduce low temperature time dependent cracking in laboratory specimens. This methodology was used to evaluate the cracking resistance of candidate heats in order to identify the factors that enhance cracking sensitivity. The resultant data was integrated into current available life prediction tools.
Quadratic time dependent Hamiltonians and separation of variables
International Nuclear Information System (INIS)
Anzaldo-Meneses, A.
2017-01-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.
Time-dependent Dyson orbital theory
Gritsenko, O.V.; Baerends, E.J.
2016-01-01
Although time-dependent density functional theory (TDDFT) has become the tool of choice for real-time propagation of the electron density ρN(t) of N-electron systems, it also encounters problems in this application. The first problem is the neglect of memory effects stemming from the, in TDDFT
Biological repair with time-dependent irradiation
International Nuclear Information System (INIS)
Broyles, A.A.; Shapiro, C.S.
1985-01-01
Recent experiments have provided new data that explore the effectiveness of biological repair in assessing damage due to exposures from ionizing radiation. These data are mainly from experiments conducted at constant dose rates, to study the effectiveness per unit dose of different dose rates. Here, we develop new formulae to estimate the effectiveness of an arbitrary time-dependent dose rate exposure
Scheduling with time-dependent execution times
Woeginger, G.J.
1995-01-01
We consider systems of tasks where the task execution times are time-dependent and where all tasks have some common deadline. We describe how to compute in polynomial time a schedule that minimizes the number of late tasks. This answers a question raised in a recent paper by Ho, Leung and Wei.
Hartree--Fock time-dependent problem
Energy Technology Data Exchange (ETDEWEB)
Bove, A; Fano, G [Bologna Univ. (Italy). Istituto di Fisica; Istituto Nazionale di Fisica Nucleare, Bologna (Italy)); Da Prato, G [Rome Univ. (Italy). Istituto di Matematica
1976-06-01
A previous result is generalized. An existence and uniqueness theorem is proved for the Hartree--Fock time-dependent problem in the case of a finite Fermi system interacting via a two body potential which is supposed to be dominated by the kinetic energy part of the one-particle Hamiltonian.
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
Two-dimensional time dependent Riemann solvers for neutron transport
International Nuclear Information System (INIS)
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
Parametric Resonance in a Time-Dependent Harmonic Oscillator
Directory of Open Access Journals (Sweden)
P. N. Nesterov
2013-01-01
Full Text Available In this paper, we study the phenomenon of appearance of new resonances in a timedependent harmonic oscillator under an oscillatory decreasing force. The studied equation belongs to the class of adiabatic oscillators and arises in connection with the spectral problem for the one-dimensional Schr¨odinger equation with Wigner–von Neumann type potential. We use a specially developed method for asymptotic integration of linear systems of differential equations with oscillatory decreasing coefficients. This method uses the ideas of the averaging method to simplify the initial system. Then we apply Levinson’s fundamental theorem to get the asymptotics for its solutions. Finally, we analyze the features of a parametric resonance phenomenon. The resonant frequencies of perturbation are found and the pointwise type of the parametric resonance phenomenon is established. In conclusion, we construct an example of a time-dependent harmonic oscillator (adiabatic oscillator in which the parametric resonances, mentioned in the paper, may occur.
Theoretical information measurement in nonrelativistic time-dependent approach
Najafizade, S. A.; Hassanabadi, H.; Zarrinkamar, S.
2018-02-01
The information-theoretic measures of time-dependent Schrödinger equation are investigated via the Shannon information entropy, variance and local Fisher quantities. In our calculations, we consider the two first states n = 0,1 and obtain the position Sx (t) and momentum Sp (t) Shannon entropies as well as Fisher information Ix (t) in position and momentum Ip (t) spaces. Using the Fourier transformed wave function, we obtain the results in momentum space. Some interesting features of the information entropy densities ρs (x,t) and γs (p,t), as well as the probability densities ρ (x,t) and γ (p,t) for time-dependent states are demonstrated. We establish a general relation between variance and Fisher's information. The Bialynicki-Birula-Mycielski inequality is tested and verified for the states n = 0,1.
Time-dependent generalized Gibbs ensembles in open quantum systems
Lange, Florian; Lenarčič, Zala; Rosch, Achim
2018-04-01
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.
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.
Time-dependent coupled harmonic oscillators: classical and quantum solutions
International Nuclear Information System (INIS)
Macedo, D.X.; Guedes, I.
2014-01-01
In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m 1 = m 2 = m 0 e γt , ω 1 = ω 01 e -γt/2 , ω 2 = ω 02 e -γt/2 and k = k 0 . (author)
Time dependent non-extinction probability for prompt critical systems
International Nuclear Information System (INIS)
Gregson, M. W.; Prinja, A. K.
2009-01-01
The time dependent non-extinction probability equation is presented for slab geometry. Numerical solutions are provided for a nested inner/outer iteration routine where the fission terms (both linear and non-linear) are updated and then held fixed over the inner scattering iteration. Time dependent results are presented highlighting the importance of the injection position and angle. The iteration behavior is also described as the steady state probability of initiation is approached for both small and large time steps. Theoretical analysis of the nested iteration scheme is shown and highlights poor numerical convergence for marginally prompt critical systems. An acceleration scheme for the outer iterations is presented to improve convergence of such systems. Theoretical analysis of the acceleration scheme is also provided and the associated decrease in computational run time addressed. (authors)
Time-dependent scattering in resonance lines
International Nuclear Information System (INIS)
Kunasz, P.B.
1983-01-01
A numerical finite-difference method is presented for the problem of time-dependent line transfer in a finite slab in which material density is sufficiently low that the time of flight between scatterings greatly exceeds the relaxation time of the upper state of the scattering transition. The medium is assumed to scatter photons isotropically, with complete frequency redistribution. Numerical solutions are presented for a homogeneous, time-independent slab illuminated by an externally imposed radiation field which enters the slab at t = 0. Graphical results illustrate relaxation to steady state of trapped internal radiation, emergent energy, and emergent profiles. A review of the literature is also given in which the time-dependent line transfer problem is discussed in the context of recent analytical work
Time dependent policy-based access control
DEFF Research Database (Denmark)
Vasilikos, Panagiotis; Nielson, Flemming; Nielson, Hanne Riis
2017-01-01
also on other attributes of the environment such as the time. In this paper, we use systems of Timed Automata to model distributed systems and we present a logic in which one can express time-dependent policies for access control. We show how a fragment of our logic can be reduced to a logic......Access control policies are essential to determine who is allowed to access data in a system without compromising the data's security. However, applications inside a distributed environment may require those policies to be dependent on the actual content of the data, the flow of information, while...... that current model checkers for Timed Automata such as UPPAAL can handle and we present a translator that performs this reduction. We then use our translator and UPPAAL to enforce time-dependent policy-based access control on an example application from the aerospace industry....
MINARET: Towards a time-dependent neutron transport parallel solver
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.; Maday, Y.; Mula, O.
2013-01-01
We present the newly developed time-dependent 3D multigroup discrete ordinates neutron transport solver that has recently been implemented in the MINARET code. The solver is the support for a study about computing acceleration techniques that involve parallel architectures. In this work, we will focus on the parallelization of two of the variables involved in our equation: the angular directions and the time. This last variable has been parallelized by a (time) domain decomposition method called the para-real in time algorithm. (authors)
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
Algebraic time-dependent variational approach to dynamical calculations
International Nuclear Information System (INIS)
Shi, S.; Rabitz, H.
1988-01-01
A set of time-dependent basis states is obtained with a group of unitary transformations generated by a Lie algebra. Applying the time-dependent variational principle to the trial function subspace constructed from the linear combination of the time-dependent basis states gives rise to a set of ''classical'' equations of motion for the group parameters and the expansion coefficients from which the time evolution of the system state can be determined. The formulation is developed for a general Lie algebra as well as for the commonly encountered algebra containing homogeneous polynominal products of the coordinate Q and momentum P operators (or equivalently the boson creation a/sup dagger/ and annihilation a operators) of order 0, 1, and 2. Explicit expressions for the transition amplitudes are derived by virtue of the cannonical transformation properties of the unitary transformation. The applicability of the present formalism in a variety of problems is implied by two illustrative examples: (a) a parametric amplifier; (b) the collinear collision of an atom with a Morse oscillator
Constitutive model with time-dependent deformations
DEFF Research Database (Denmark)
Krogsbøll, Anette
1998-01-01
are common in time as well as size. This problem is adressed by means of a new constitutive model for soils. It is able to describe the behavior of soils at different deformation rates. The model defines time-dependent and stress-related deformations separately. They are related to each other and they occur...... was the difference in time scale between the geological process of deposition (millions of years) and the laboratory measurements of mechanical properties (minutes or hours). In addition, the time scale relevant to the production history of the oil field was interesting (days or years)....
Time dependent black holes and thermal equilibration
International Nuclear Information System (INIS)
Bak, Dongsu; Gutperle, Michael; Karch, Andreas
2007-01-01
We study aspects of a recently proposed exact time dependent black hole solution of IIB string theory using the AdS/CFT correspondence. The dual field theory is a thermal system in which initially a vacuum density for a non-conserved operator is turned on. We can see that in agreement with general thermal field theory expectation the system equilibrates: the expectation value of the non-conserved operator goes to zero exponentially and the entropy increases. In the field theory the process can be described quantitatively in terms of a thermofield state and exact agreement with the gravity answers is found
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)
Time-dependent patterns in quasivertical cylindrical binary convection
Alonso, Arantxa; Mercader, Isabel; Batiste, Oriol
2018-02-01
This paper reports on numerical investigations of the effect of a slight inclination α on pattern formation in a shallow vertical cylindrical cell heated from below for binary mixtures with a positive value of the Soret coefficient. By using direct numerical simulation of the three-dimensional Boussinesq equations with Soret effect in cylindrical geometry, we show that a slight inclination of the cell in the range α ≈0.036 rad =2∘ strongly influences pattern selection. The large-scale shear flow (LSSF) induced by the small tilt of gravity overcomes the squarelike arrangements observed in noninclined cylinders in the Soret regime, stratifies the fluid along the direction of inclination, and produces an enhanced separation of the two components of the mixture. The competition between shear effects and horizontal and vertical buoyancy alters significantly the dynamics observed in noninclined convection. Additional unexpected time-dependent patterns coexist with the basic LSSF. We focus on an unsual periodic state recently discovered in an experiment, the so-called superhighway convection state (SHC), in which ascending and descending regions of fluid move in opposite directions. We provide numerical confirmation that Boussinesq Navier-Stokes equations with standard boundary conditions contain the essential ingredients that allow for the existence of such a state. Also, we obtain a persistent heteroclinic structure where regular oscillations between a SHC pattern and a state of nearly stationary longitudinal rolls take place. We characterize numerically these time-dependent patterns and investigate the dynamics around the threshold of convection.
Time dependent fracture and cohesive zones
Knauss, W. G.
1993-01-01
This presentation is concerned with the fracture response of materials which develop cohesive or bridging zones at crack tips. Of special interest are concerns regarding crack stability as a function of the law which governs the interrelation between the displacement(s) or strain across these zones and the corresponding holding tractions. It is found that for some materials unstable crack growth can occur, even before the crack tip has experienced a critical COD or strain across the crack, while for others a critical COD will guarantee the onset of fracture. Also shown are results for a rate dependent nonlinear material model for the region inside of a craze for exploring time dependent crack propagation of rate sensitive materials.
Time-dependent Cooling in Photoionized Plasma
Energy Technology Data Exchange (ETDEWEB)
Gnat, Orly, E-mail: orlyg@phys.huji.ac.il [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)
2017-02-01
I explore the thermal evolution and ionization states in gas cooling from an initially hot state in the presence of external photoionizing radiation. I compute the equilibrium and nonequilibrium cooling efficiencies, heating rates, and ion fractions for low-density gas cooling while exposed to the ionizing metagalactic background radiation at various redshifts ( z = 0 − 3), for a range of temperatures (10{sup 8}–10{sup 4} K), densities (10{sup −7}–10{sup 3} cm{sup −3}), and metallicities (10{sup −3}–2 times solar). The results indicate the existence of a threshold ionization parameter, above which the cooling efficiencies are very close to those in photoionization equilibrium (so that departures from equilibrium may be neglected), and below which the cooling efficiencies resemble those in collisional time-dependent gas cooling with no external radiation (and are thus independent of density).
Time dependent mean-field games
Gomes, Diogo A.; Pimentel, Edgard; Sá nchez-Morgado, Hé ctor
2014-01-01
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.
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)
Exact results on diffusion in a piecewise linear potential with a time-dependent sink
Energy Technology Data Exchange (ETDEWEB)
Diwaker, E-mail: diwakerphysics@gmail.com [Central University of Himachal Pradesh, School of Physical and Astronomical Sciences (India); Chakraborty, Aniruddha [Indian Institute of Technology Mandi (India)
2016-02-15
The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.
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
Time-dependent EQPET analysis of TSC
International Nuclear Information System (INIS)
Takahashi, Akito
2006-01-01
Time-dependent fusion rates for 2D and 4D reactions are calculated for squeezing of tetrahedral symmetric condensate (TSC) from about 100 pm size to its minimum size (about 10 fm), within about 75 fs squeezing motion. Life time of the minimum TSC state is yet to be studied. Time-averaged fusion rates are given by assuming the life time of minimum TSC state is negligible. Time-averaged 2D fusion rate was given as 2.9x10 -25 f/s/pair, and time-averaged 4D fusion rate was 5.5x10 -8 f/s/cl. These values are compared with 1.0x10 -20 f/s/pair for 2D and 1.0x10 -9 f/s/cl for 4D, respectively, of previously estimated values by electronic quasi-particle expansion theory/TSC models. Effective fusion time by the TSC squeezing motion was estimated as 0.014 fs: namely fusions may happen in very short time interval. (author)
Deformation aspects of time dependent fracture
International Nuclear Information System (INIS)
Li, C.Y.; Turner, A.P.L.; Diercks, D.R.; Laird, C.; Langdon, T.G.; Nix, W.D.; Swindeman, R.; Wolfer, W.G.; Woodford, D.A.
1979-01-01
For all metallic materials, particularly at elevated temperatures, deformation plays an important role in fracture. On the macro-continuum level, the inelastic deformation behavior of the material determines how stress is distributed in the body and thus determines the driving force for fracture. At the micro-continuum level, inelastic deformation alters the elastic stress singularity at the crack tip and so determines the local environment in which crack advance takes place. At the microscopic and mechanistic level, there are many possibilities for the mechanisms of deformation to be related to those for crack initiation and growth. At elevated temperatures, inelastic deformation in metallic systems is time dependent so that the distribution of stress in a body will vary with time, affecting conditions for crack initiation and propagation. Creep deformation can reduce the tendency for fracture by relaxing the stresses at geometric stress concentrations. It can also, under suitable constraints, cause a concentration of stresses at specific loading points as a result of relaxation elsewhere in the body. A combination of deformation and unequal heating, as in welding, can generate large residual stress which cannot be predicted from the external loads on the body. Acceleration of deformation by raising the temperature can be an effective way to relieve such residual stresses
System reliability time-dependent models
International Nuclear Information System (INIS)
Debernardo, H.D.
1991-06-01
A probabilistic methodology for safety system technical specification evaluation was developed. The method for Surveillance Test Interval (S.T.I.) evaluation basically means an optimization of S.T.I. of most important system's periodically tested components. For Allowed Outage Time (A.O.T.) calculations, the method uses system reliability time-dependent models (A computer code called FRANTIC III). A new approximation, which was called Independent Minimal Cut Sets (A.C.I.), to compute system unavailability was also developed. This approximation is better than Rare Event Approximation (A.E.R.) and the extra computing cost is neglectible. A.C.I. was joined to FRANTIC III to replace A.E.R. on future applications. The case study evaluations verified that this methodology provides a useful probabilistic assessment of surveillance test intervals and allowed outage times for many plant components. The studied system is a typical configuration of nuclear power plant safety systems (two of three logic). Because of the good results, these procedures will be used by the Argentine nuclear regulatory authorities in evaluation of technical specification of Atucha I and Embalse nuclear power plant safety systems. (Author) [es
Time-dependent correlations in electricity markets
International Nuclear Information System (INIS)
Alvarez-Ramirez, Jose; Escarela-Perez, Rafael
2010-01-01
In the last years, many electricity markets were subjected to deregulated operation where prices are set by the action of market participants. In this form, producers and consumers rely on demand and price forecasts to decide their bidding strategies, allocate assets, negotiate bilateral contracts, hedge risks, and plan facility investments. A basic feature of efficient market hypothesis is the absence of correlations between price increments over any time scale leading to random walk-type behavior of prices, so arbitrage is not possible. However, recent studies have suggested that this is not the case and correlations are present in the behavior of diverse electricity markets. In this paper, a temporal quantification of electricity market correlations is made by means of detrended fluctuation and Allan analyses. The approach is applied to two Canadian electricity markets, Ontario and Alberta. The results show the existence of correlations in both demand and prices, exhibiting complex time-dependent behavior with lower correlations in winter while higher in summer. Relatively steady annual cycles in demand but unstable cycles in prices are detected. On the other hand, the more significant nonlinear effects (measured in terms of a multifractality index) are found for winter months, while the converse behavior is displayed during the summer period. In terms of forecasting models, our results suggest that nonlinear recursive models (e.g., feedback NNs) should be used for accurate day-ahead price estimation. In contrast, linear models can suffice for demand forecasting purposes. (author)
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
Time-dependent behavior of rough discontinuities under shearing conditions
Wang, Zhen; Shen, Mingrong; Ding, Wenqi; Jang, Boan; Zhang, Qingzhao
2018-02-01
The mechanical properties of rocks are generally controlled by their discontinuities. In this study, the time-dependent behavior of rough artificial joints under shearing conditions was investigated. Based on Barton’s standard profile lines, samples with artificial joint surfaces were prepared and used to conduct the shear and creep tests. The test results showed that the shear strength of discontinuity was linearly related to roughness, and subsequently an empirical equation was established. The long-term strength of discontinuity can be identified using the inflection point of the isocreep-rate curve, and it was linearly related to roughness. Furthermore, the ratio of long-term and instantaneous strength decreased with the increase of roughness. The shear-stiffness coefficient increased with the increase of shear rate, and the influence of shear rate on the shear stiffness coefficient decreased with the decrease of roughness. Further study of the mechanism revealed that these results could be attributed to the different time-dependent behavior of intact and joint rocks.
FRANTIC: a computer code for time dependent unavailability analysis
International Nuclear Information System (INIS)
Vesely, W.E.; Goldberg, F.F.
1977-03-01
The FRANTIC computer code evaluates the time dependent and average unavailability for any general system model. The code is written in FORTRAN IV for the IBM 370 computer. Non-repairable components, monitored components, and periodically tested components are handled. One unique feature of FRANTIC is the detailed, time dependent modeling of periodic testing which includes the effects of test downtimes, test overrides, detection inefficiencies, and test-caused failures. The exponential distribution is used for the component failure times and periodic equations are developed for the testing and repair contributions. Human errors and common mode failures can be included by assigning an appropriate constant probability for the contributors. The output from FRANTIC consists of tables and plots of the system unavailability along with a breakdown of the unavailability contributions. Sensitivity studies can be simply performed and a wide range of tables and plots can be obtained for reporting purposes. The FRANTIC code represents a first step in the development of an approach that can be of direct value in future system evaluations. Modifications resulting from use of the code, along with the development of reliability data based on operating reactor experience, can be expected to provide increased confidence in its use and potential application to the licensing process
Time-dependent simulation of organic light-emitting diodes
International Nuclear Information System (INIS)
Sharifi, M J
2009-01-01
Several methods to simulate the behavior of organic light-emitting diodes (OLEDs) have been proposed in the past. In this paper, we develop a previous method, based on the master equation, in order to allow the simulation of time-dependent behavior and transient states. The calculation algorithm of the program that we have written is described. The time-dependent behaviors of two simple monolayer devices and of a more complicated three-layer device were simulated by means of this program, and the results are discussed. The results show that the turn-off speed of an OLED might be very slow, especially in the case of a multilayer device. This behavior is related to the low mobility of the organic material in weak electric fields. An interesting feature of the time behavior is pointed out, whereby the recombination rate may become considerably larger after the falling edge of an applied voltage pulse. Moreover, the validity of the transient electro-luminescent method for measuring carrier mobility in organic material has been examined by means of simulation. The results show that there is some inconsistency especially in high electric fields
Time-dependent radioactivity distribution in MAFF
International Nuclear Information System (INIS)
Nebel, F.; Zech, E.; Faestermann, T.; Kruecken, R.; Maier-Komor, P.; Assmann, W.; Szerypo, J.; Gross, M.; Kester, O.; Thirolf, P.G.; Groetzschel, R.
2006-01-01
The Munich Accelerator for Fission Fragments is planned to be installed at the FRM II in Garching. It will operate a uranium-carbide-loaded graphite matrix as a target for neutron-induced fission. The radioactive reaction fragments leave the ion source as both, atoms and ions. For radiation safety it is imperative to have a basic understanding of the fragment distribution within the beam line. Atoms leaving the graphite matrix will spread like a gas and stick to surfaces depending on their species. A probabilistic Monte-Carlo approach is used to predict the surface coating of internal surfaces of the beam line for all fission nuclides. To decrease calculation time, the problem is reduced to two dimensions with the surface areas being a measure for the probability, that they are hit by a particle. The program is completely time dependent to implement radioactive decay. Ions leaving the fission ion source are transported by electrostatic means towards the mass pre-separator, a low-resolution dipole magnet with a complex slit system in the focal plane. All unwanted ions are stopped at the slits, resulting in a high level of radioactive contamination. While it is advantageous for shielding purposes to have the majority of the contamination in one point, precautions must be taken to ensure that it stays that way. Material corrosion caused by sputtering will release previously implanted radionuclides. To reduce this effect, different methods are under investigation, one of which is changing the slit geometry. The considered designs will be described and experimental results will be shown
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
Time-dependent Hartree-Fock dynamics and phase transition in Lipkin-Meshkov-Glick model
International Nuclear Information System (INIS)
Kan, K.; Lichtner, P.C.; Dworzecka, M.; Griffin, J.J.
1980-01-01
The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For two-body interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the ''librations'' and ''rotations'' in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method
Light pressure of time-dependent fields in plasmas
International Nuclear Information System (INIS)
Zeidler, A.; Schnabl, H.; Mulser, P.
1985-01-01
An expression of the light pressure Pi is derived for the case of a nearly monochromatic electromagnetic wave with arbitrarily time-dependent amplitude. Thereby Pi is defined as the time-averaged force density exerted on a plasma by the wave. The resulting equations are valid for both transverse and longitudinal waves. The light pressure turns out to consist of two components: the well-known gradient-type term and a new nonstationary solenoidal term. This is true for warm as well as cold plasmas. The importance of the new term for the generation of static magnetic fields is shown, and a model in which shear forces may result is given. Formulas for the nonstationary light pressure developed previously are discussed
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)
Benchmarking time-dependent neutron problems with Monte Carlo codes
International Nuclear Information System (INIS)
Couet, B.; Loomis, W.A.
1990-01-01
Many nuclear logging tools measure the time dependence of a neutron flux in a geological formation to infer important properties of the formation. The complex geometry of the tool and the borehole within the formation does not permit an exact deterministic modelling of the neutron flux behaviour. While this exact simulation is possible with Monte Carlo methods the computation time does not facilitate quick turnaround of results useful for design and diagnostic purposes. Nonetheless a simple model based on the diffusion-decay equation for the flux of neutrons of a single energy group can be useful in this situation. A combination approach where a Monte Carlo calculation benchmarks a deterministic model in terms of the diffusion constants of the neutrons propagating in the media and their flux depletion rates thus offers the possibility of quick calculation with assurance as to accuracy. We exemplify this approach with the Monte Carlo benchmarking of a logging tool problem, showing standoff and bedding response. (author)
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
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)
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.
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)
Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems
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.
Time-dependent onshore tsunami response
Apotsos, Alex; Gelfenbaum, Guy R.; Jaffe, Bruce E.
2012-01-01
While bulk measures of the onshore impact of a tsunami, including the maximum run-up elevation and inundation distance, are important for hazard planning, the temporal evolution of the onshore flow dynamics likely controls the extent of the onshore destruction and the erosion and deposition of sediment that occurs. However, the time-varying dynamics of actual tsunamis are even more difficult to measure in situ than the bulk parameters. Here, a numerical model based on the non-linear shallow water equations is used to examine the effects variations in the wave characteristics, bed slope, and bottom roughness have on the temporal evolution of the onshore flow. Model results indicate that the onshore flow dynamics vary significantly over the parameter space examined. For example, the flow dynamics over steep, smooth morphologies tend to be temporally symmetric, with similar magnitude velocities generated during the run-up and run-down phases of inundation. Conversely, on shallow, rough onshore topographies the flow dynamics tend to be temporally skewed toward the run-down phase of inundation, with the magnitude of the flow velocities during run-up and run-down being significantly different. Furthermore, for near-breaking tsunami waves inundating over steep topography, the flow velocity tends to accelerate almost instantaneously to a maximum and then decrease monotonically. Conversely, when very long waves inundate over shallow topography, the flow accelerates more slowly and can remain steady for a period of time before beginning to decelerate. These results indicate that a single set of assumptions concerning the onshore flow dynamics cannot be applied to all tsunamis, and site specific analyses may be required.
Time-Dependent Mean-Field Games in the Subquadratic Case
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
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.
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)
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)
The Electromagnetic Field of Elementary Time-Dependent Toroidal Sources
International Nuclear Information System (INIS)
Afanas'ev, G.N.; Stepanovskij, Yu.P.
1994-01-01
The radiation field of toroidal-like time-dependent current configurations is investigated. Time-dependent charge-current sources are found outside which the electromagnetic strengths disappear but the potentials survive. This can be used to carry out time-dependent Aharonov-Bohm-like experiments and the information transfer. Using the Neumann-Helmholtz parametrization of the current density we present the time-dependent electromagnetic field in a form convenient for applications. 17 refs
RAPTOR. I. Time-dependent radiative transfer in arbitrary spacetimes
Bronzwaer, T.; Davelaar, J.; Younsi, Z.; Mościbrodzka, M.; Falcke, H.; Kramer, M.; Rezzolla, L.
2018-05-01
Context. Observational efforts to image the immediate environment of a black hole at the scale of the event horizon benefit from the development of efficient imaging codes that are capable of producing synthetic data, which may be compared with observational data. Aims: We aim to present RAPTOR, a new public code that produces accurate images, animations, and spectra of relativistic plasmas in strong gravity by numerically integrating the equations of motion of light rays and performing time-dependent radiative transfer calculations along the rays. The code is compatible with any analytical or numerical spacetime. It is hardware-agnostic and may be compiled and run both on GPUs and CPUs. Methods: We describe the algorithms used in RAPTOR and test the code's performance. We have performed a detailed comparison of RAPTOR output with that of other radiative-transfer codes and demonstrate convergence of the results. We then applied RAPTOR to study accretion models of supermassive black holes, performing time-dependent radiative transfer through general relativistic magneto-hydrodynamical (GRMHD) simulations and investigating the expected observational differences between the so-called fast-light and slow-light paradigms. Results: Using RAPTOR to produce synthetic images and light curves of a GRMHD model of an accreting black hole, we find that the relative difference between fast-light and slow-light light curves is less than 5%. Using two distinct radiative-transfer codes to process the same data, we find integrated flux densities with a relative difference less than 0.01%. Conclusions: For two-dimensional GRMHD models, such as those examined in this paper, the fast-light approximation suffices as long as errors of a few percent are acceptable. The convergence of the results of two different codes demonstrates that they are, at a minimum, consistent. The public version of RAPTOR is available at the following URL: http://https://github.com/tbronzwaer/raptor
Time-dependent problems in quantum-mechanical state reconstruction
International Nuclear Information System (INIS)
Leonhardt, U.; Bardroff, P. J.
1997-01-01
We study the state reconstruction of wave packets that travel in time-dependent potentials. We solve the problem for explicitly time-dependent potentials. We solve the problem for explicitly time-dependent harmonic oscillators and sketch a general adaptive technique for finding the wave function that matches and observed evolution. (authors)
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
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).
Time-Dependent Damage Investigation of Rock Mass in an In Situ Experimental Tunnel
Jiang, Quan; Cui, Jie; Chen, Jing
2012-01-01
In underground tunnels or caverns, time-dependent deformation or failure of rock mass, such as extending cracks, gradual rock falls, etc., are a costly irritant and a major safety concern if the time-dependent damage of surrounding rock is serious. To understand the damage evolution of rock mass in underground engineering, an in situ experimental testing was carried out in a large belowground tunnel with a scale of 28.5 m in width, 21 m in height and 352 m in length. The time-dependent damage of rock mass was detected in succession by an ultrasonic wave test after excavation. The testing results showed that the time-dependent damage of rock mass could last a long time, i.e., nearly 30 days. Regression analysis of damage factors defined by wave velocity, resulted in the time-dependent evolutional damage equation of rock mass, which corresponded with logarithmic format. A damage viscoelastic-plastic model was developed to describe the exposed time-dependent deterioration of rock mass by field test, such as convergence of time-dependent damage, deterioration of elastic modules and logarithmic format of damage factor. Furthermore, the remedial measures for damaged surrounding rock were discussed based on the measured results and the conception of damage compensation, which provides new clues for underground engineering design.
Photodissociation of NaH using time-dependent Fourier grid method
Indian Academy of Sciences (India)
We have solved the time dependent Schrödinger equation by using the Chebyshev polynomial scheme and Fourier grid Hamiltonian method to calculate the dissociation cross section of NaH molecule by 1-photon absorption from the 1+ state to the 1 state. We have found that the results differ signiﬁcantly from an ...
DEFF Research Database (Denmark)
Rotvig, J.; Smith, H.; Jauho, Antti-Pekka
1996-01-01
We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion for the density matrix is obtained for a two-band model...
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.
Electronic structure and time-dependent description of rotational predissociation of LiH
DEFF Research Database (Denmark)
Jasik, P.; Sienkiewicz, J. E.; Domsta, J.
2017-01-01
parameters and the experimental ones. The dynamics of the rotational predissociation process of the 11Π state were studied by solving the time-dependent Schrödinger equation. The classical experiment of Velasco [Can. J. Phys., 1957, 35, 1204] on dissociation in the 11Π state is explained for the first time...
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
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.
International Nuclear Information System (INIS)
Frank, T.D.
2006-01-01
First-order approximations of time-dependent solutions are determined for stochastic systems perturbed by time-delayed feedback forces. To this end, the theory of delay Fokker-Planck equations is applied in combination with Bayes' theorem. Applications to a time-delayed Ornstein-Uhlenbeck process and the geometric Brownian walk of financial physics are discussed
Nonlinear diffusion in the presence of a time-dependent external electric field
International Nuclear Information System (INIS)
Lima e Silva, T. de; Galvao, R.M.O.
1987-09-01
The influence of a time-dependent external electric field on the nonlinear diffusion process of weakly ionized plasmas is investigated. A new solution of the diffusion equation is obtained for the case when electron-ion collisions can be neglected. (author) [pt
Concept of frequency separation in life prediction for time-dependent fatigue
International Nuclear Information System (INIS)
Coffin, L.F.
1976-01-01
Two methods are described to improve the predictive capability of the frequency-modified fatigue equations for time-dependent fatigue. These built-on the earlier approach and are applicable to severely unbalanced hysteresis loops. Comparisons made with various wave-shape investigations show favorable results. A new form of hysteresis loop is introduced utilizing frequency separation concepts. 4 tables, 11 fig
The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates
Directory of Open Access Journals (Sweden)
Yilun Shang
2013-01-01
Full Text Available We investigate a variant of the stochastic logistic model that allows individual variation and time-dependent infection and recovery rates. The model is described as a heterogeneous density dependent Markov chain. We show that the process can be approximated by a deterministic process defined by an integral equation as the population size grows.
Chaos in Time-Dependent Space-Charge Potentials
Betzel, Gregory T; Sideris, Ioannis V
2005-01-01
We consider a spherically symmetric, homologously breathing, space-charge-dominated beam bunch in the spirit of the particle-core model. The question we ask is: How does the time dependence influence the population of chaotic orbits? The static beam has zero chaotic orbits; the equation of particle motion is integrable up to quadrature. This is generally not true once the bunch is set into oscillation. We quantify the population of chaotic orbits as a function of space charge and oscillation amplitude (mismatch). We also apply a newly developed measure of chaos, one that distinguishes between regular, sticky, and wildly chaotic orbits, to characterize the phase space in detail. We then introduce colored noise into the system and show how its presence modifies the dynamics. One finding is that, despite the presence of a sizeable population of chaotic orbits, halo formation in the homologously breathing beam is much less prevalent than in an envelope-matched counterpart wherein an internal collective mode is ex...
Recovery of time-dependent volatility in option pricing model
Deng, Zui-Cha; Hon, Y. C.; Isakov, V.
2016-11-01
In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).
Time-dependent simulations of disk-embedded planetary atmospheres
Stökl, A.; Dorfi, E. A.
2014-03-01
At the early stages of evolution of planetary systems, young Earth-like planets still embedded in the protoplanetary disk accumulate disk gas gravitationally into planetary atmospheres. The established way to study such atmospheres are hydrostatic models, even though in many cases the assumption of stationarity is unlikely to be fulfilled. Furthermore, such models rely on the specification of a planetary luminosity, attributed to a continuous, highly uncertain accretion of planetesimals onto the surface of the solid core. We present for the first time time-dependent, dynamic simulations of the accretion of nebula gas into an atmosphere around a proto-planet and the evolution of such embedded atmospheres while integrating the thermal energy budget of the solid core. The spherical symmetric models computed with the TAPIR-Code (short for The adaptive, implicit RHD-Code) range from the surface of the rocky core up to the Hill radius where the surrounding protoplanetary disk provides the boundary conditions. The TAPIR-Code includes the hydrodynamics equations, gray radiative transport and convective energy transport. The results indicate that diskembedded planetary atmospheres evolve along comparatively simple outlines and in particular settle, dependent on the mass of the solid core, at characteristic surface temperatures and planetary luminosities, quite independent on numerical parameters and initial conditions. For sufficiently massive cores, this evolution ultimately also leads to runaway accretion and the formation of a gas planet.
Residual distribution for general time-dependent conservation laws
International Nuclear Information System (INIS)
Ricchiuto, Mario; Csik, Arpad; Deconinck, Herman
2005-01-01
We consider the second-order accurate numerical solution of general time-dependent hyperbolic conservation laws over unstructured grids in the framework of the Residual Distribution method. In order to achieve full conservation of the linear, monotone and first-order space-time schemes of (Csik et al., 2003) and (Abgrall et al., 2000), we extend the conservative residual distribution (CRD) formulation of (Csik et al., 2002) to prismatic space-time elements. We then study the design of second-order accurate and monotone schemes via the nonlinear mapping of the local residuals of linear monotone schemes. We derive sufficient and necessary conditions for the well-posedness of the mapping. We prove that the schemes obtained with the CRD formulation satisfy these conditions by construction. Thus the nonlinear schemes proposed in this paper are always well defined. The performance of the linear and nonlinear schemes are evaluated on a series of test problems involving the solution of the Euler equations and of a two-phase flow model. We consider the resolution of strong shocks and complex interacting flow structures. The results demonstrate the robustness, accuracy and non-oscillatory character of the proposed schemes. d schemes
Transient fluctuation relations for time-dependent particle transport
Altland, Alexander; de Martino, Alessandro; Egger, Reinhold; Narozhny, Boris
2010-09-01
We consider particle transport under the influence of time-varying driving forces, where fluctuation relations connect the statistics of pairs of time-reversed evolutions of physical observables. In many “mesoscopic” transport processes, the effective many-particle dynamics is dominantly classical while the microscopic rates governing particle motion are of quantum-mechanical origin. We here employ the stochastic path-integral approach as an optimal tool to probe the fluctuation statistics in such applications. Describing the classical limit of the Keldysh quantum nonequilibrium field theory, the stochastic path integral encapsulates the quantum origin of microscopic particle exchange rates. Dynamically, it is equivalent to a transport master equation which is a formalism general enough to describe many applications of practical interest. We apply the stochastic path integral to derive general functional fluctuation relations for current flow induced by time-varying forces. We show that the successive measurement processes implied by this setup do not put the derivation of quantum fluctuation relations in jeopardy. While in many cases the fluctuation relation for a full time-dependent current profile may contain excessive information, we formulate a number of reduced relations, and demonstrate their application to mesoscopic transport. Examples include the distribution of transmitted charge, where we show that the derivation of a fluctuation relation requires the combined monitoring of the statistics of charge and work.
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
Prospects for time-dependent asymmetries at LHCb
INSPIRE-00260500
2012-01-01
LHCb is already providing leading measurements of time-dependent CP asymmetries with 1 fb$^{-1}$ of data. With the LHCb detector, and further one with the LHCb upgrade, very high-precision time-dependent CP measurements are expected to stringently test the CKM paradigm and to the search for possible small NP effects. A review of the current precision and the prospects for these time-dependent quantities with the LHCb and LHCb upgraded detectors are summarised in this paper.
A Generalized Time-Dependent Harmonic Oscillator at Finite Temperature
International Nuclear Information System (INIS)
Majima, H.; Suzuki, A.
2006-01-01
We show how a generalized time-dependent harmonic oscillator (GTHO) is extended to a finite temperature case by using thermo field dynamics (TFD). We derive the general time-dependent annihilation and creation operators for the system, and obtain the time-dependent quasiparticle annihilation and creation operators for the GTHO by using the temperature-dependent Bogoliubov transformation of TFD. We also obtain the thermal state as a two-mode squeezed vacuum state in the time-dependent case as well as in the time-independent case. The general formula is derived to calculate the thermal expectation value of operators
Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets
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.
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
On time-dependent diffusion coefficients arising from stochastic processes with memory
Carpio-Bernido, M. Victoria; Barredo, Wilson I.; Bernido, Christopher C.
2017-08-01
Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes.
Time-dependent approach to collisional ionization using exterior complex scaling
International Nuclear Information System (INIS)
McCurdy, C. William; Horner, Daniel A.; Rescigno, Thomas N.
2002-01-01
We present a time-dependent formulation of the exterior complex scaling method that has previously been used to treat electron-impact ionization of the hydrogen atom accurately at low energies. The time-dependent approach solves a driven Schroedinger equation, and scales more favorably with the number of electrons than the original formulation. The method is demonstrated in calculations for breakup processes in two dimensions (2D) and three dimensions for systems involving short-range potentials and in 2D for electron-impact ionization in the Temkin-Poet model for electron-hydrogen atom collisions
Coherent states for certain time-dependent systems
International Nuclear Information System (INIS)
Pedrosa, I.A.
1989-01-01
Hartley and Ray have constructed and studied coherent states for the time-dependent oscillator. Here we show how to construct states for more general time-dependent systems. We also show that these states are equivalent to the well-known squeezed states. (author) [pt
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.
International Nuclear Information System (INIS)
Yuece, Cem
2003-01-01
In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained
Numerical studies of time-independent and time-dependent scattering by several elliptical cylinders
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.
An analytical nodal method for time-dependent one-dimensional discrete ordinates problems
International Nuclear Information System (INIS)
Barros, R.C. de
1992-01-01
In recent years, relatively little work has been done in developing time-dependent discrete ordinates (S N ) computer codes. Therefore, the topic of time integration methods certainly deserves further attention. In this paper, we describe a new coarse-mesh method for time-dependent monoenergetic S N transport problesm in slab geometry. This numerical method preserves the analytic solution of the transverse-integrated S N nodal equations by constants, so we call our method the analytical constant nodal (ACN) method. For time-independent S N problems in finite slab geometry and for time-dependent infinite-medium S N problems, the ACN method generates numerical solutions that are completely free of truncation errors. Bsed on this positive feature, we expect the ACN method to be more accurate than conventional numerical methods for S N transport calculations on coarse space-time grids
Time dependent plasma viscosity and relation between neoclassical transport and turbulent transport
International Nuclear Information System (INIS)
Shaing, K.C.
2005-01-01
Time dependent plasma viscosities for asymmetric toroidal plasmas in various collisionality regimes are calculated. It is known that in the symmetric limit the time dependent plasma viscosities accurately describe plasma flow damping rate. Thus, time dependent plasma viscosities are important in modeling the radial electric field of the zonal flow. From the momentum balance equation, it is shown that, at the steady state, the balance of the viscosity force and the momentum source determines the radial electric field of the zonal flow. Thus, for a fixed source, the smaller the viscous force is, the larger the value of the radial electric field is, which in turn suppresses the turbulence fluctuations more and improves turbulence transport. However, the smaller the viscous force also implies the smaller the neoclassical transport fluxes based on the neoclassical flux-force relationship. We thus show that when neoclassical transport fluxes are improved so are the turbulent fluxes in toroidal plasmas. (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
Communication: Time-dependent optimized coupled-cluster method for multielectron dynamics
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.
Time-dependent anisotropic external sources in transient 3-D transport code TORT-TD
International Nuclear Information System (INIS)
Seubert, A.; Pautz, A.; Becker, M.; Dagan, R.
2009-01-01
This paper describes the implementation of a time-dependent distributed external source in TORT-TD by explicitly considering the external source in the ''fixed-source'' term of the implicitly time-discretised 3-D discrete ordinates transport equation. Anisotropy of the external source is represented by a spherical harmonics series expansion similar to the angular fluxes. The YALINA-Thermal subcritical assembly serves as a test case. The configuration with 280 fuel rods has been analysed with TORT-TD using cross sections in 18 energy groups and P1 scattering order generated by the KAPROS code system. Good agreement is achieved concerning the multiplication factor. The response of the system to an artificial time-dependent source consisting of two square-wave pulses demonstrates the time-dependent external source capability of TORT-TD. The result is physically plausible as judged from validation calculations. (orig.)
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.
Time-dependent reliability sensitivity analysis of motion mechanisms
International Nuclear Information System (INIS)
Wei, Pengfei; Song, Jingwen; Lu, Zhenzhou; Yue, Zhufeng
2016-01-01
Reliability sensitivity analysis aims at identifying the source of structure/mechanism failure, and quantifying the effects of each random source or their distribution parameters on failure probability or reliability. In this paper, the time-dependent parametric reliability sensitivity (PRS) analysis as well as the global reliability sensitivity (GRS) analysis is introduced for the motion mechanisms. The PRS indices are defined as the partial derivatives of the time-dependent reliability w.r.t. the distribution parameters of each random input variable, and they quantify the effect of the small change of each distribution parameter on the time-dependent reliability. The GRS indices are defined for quantifying the individual, interaction and total contributions of the uncertainty in each random input variable to the time-dependent reliability. The envelope function method combined with the first order approximation of the motion error function is introduced for efficiently estimating the time-dependent PRS and GRS indices. Both the time-dependent PRS and GRS analysis techniques can be especially useful for reliability-based design. This significance of the proposed methods as well as the effectiveness of the envelope function method for estimating the time-dependent PRS and GRS indices are demonstrated with a four-bar mechanism and a car rack-and-pinion steering linkage. - Highlights: • Time-dependent parametric reliability sensitivity analysis is presented. • Time-dependent global reliability sensitivity analysis is presented for mechanisms. • The proposed method is especially useful for enhancing the kinematic reliability. • An envelope method is introduced for efficiently implementing the proposed methods. • The proposed method is demonstrated by two real planar mechanisms.
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.
Van Meer, R.; Gritsenko, O. V.; Baerends, E. J.
2017-01-01
Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In
Time-dependent friction and solvation time correlation function
International Nuclear Information System (INIS)
Samanta, Alok; Ali, Sk Musharaf; Ghosh, Swapan K
2005-01-01
We have derived a new relation between the time-dependent friction and solvation time correlation function (STCF) for non-polar fluids. The friction values calculated using this relation and simulation results on STCF for a Lennard-Jones fluid are shown to have excellent agreement with the same obtained through mode-coupling theory. Also derived is a relation between the time-dependent dielectric friction and STCF for polar fluids. Routes are thus provided to obtain the time-dependent friction (non-polar as well as dielectric) from an experimentally measured quantity like STCF, even if the interparticle interaction potential is not known
Simulation of time-dependent Heisenberg models in one dimension
DEFF Research Database (Denmark)
Volosniev, A. G.; Hammer, H. -W.; Zinner, N. T.
2016-01-01
In this Letter, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling...... constants can be manipulated by time-dependent driving of the shape of the external confinement. As illustrative examples, we consider a harmonic trapping potential with a variable frequency and an infinite square well potential with a time-dependent barrier in the middle....
Time-dependent behavior of positrons in noble gases
International Nuclear Information System (INIS)
Wadehra, J.M.
1990-01-01
Both equilibrium and nonequilibrium behaviors of positrons in several noble gases are reviewed. Our novel procedure for obtaining the time-dependent behavior of various swarm parameters -- such as the positron drift velocity, average positron energy, positron annihilation rate (or equivalently Z eff ) etc. -- for positrons in pure ambient gases subjected to external electrostatic fields is described. Summaries of time-dependent as well as electric field-dependent results for positron swarms in various noble gases are presented. New time-dependent results for positron swarms in neon are also described in detail. 36 refs., 4 figs., 3 tabs
Evaluation of Time-Dependent Behavior of Soils
DEFF Research Database (Denmark)
Augustesen, Anders; Liingaard, Morten; Lade, Poul V.
2004-01-01
The time-dependent behavior of soils has been investigated extensively through one-dimensional and triaxial test conditions. Most of the observations in literature have focused on the determination of the time-dependent behavior of clayey soils, whereas the reported experimental studies of granular...... situation for soils. That is whether the time-dependent behavior can be characterized as isotach or nonisotach. It seems that the isotach behavior is adequate for describing the time effects in clays in most situations. But for sand, the isotach description is inadequate. Further, the phenomenon...
International Nuclear Information System (INIS)
Mahmoud, K.S.; Szatmary, Z.
2005-01-01
An iterative method was developed for the numerical solution of the coupled two-dimensional time dependent multigroup diffusion equation and delayed precursor equations. Both forward (Explicit) and backward (Implicit) schemes were used. The second scheme was found to be numerically stable, while the first scheme requires that Δt -10 sec. for stability. An example is given for the second method. (authors)
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
Energy Technology Data Exchange (ETDEWEB)
Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.
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
K shortest paths in stochastic time-dependent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Pretolani, Daniele; Andersen, Kim Allan
2004-01-01
A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...
Skinner-Rusk approach to time-dependent mechanics
Cortés, Jorge; Martínez, Sonia; Cantrijn, Frans
2002-01-01
The geometric approach to autonomous classical mechanical systems in terms of a canonical first-order system on the Whitney sum of the tangent and cotangent bundle, developed by Skinner and Rusk, is extended to the time-dependent framework.
Ambiguities in the Lagrangians formalism: the time-dependent case
International Nuclear Information System (INIS)
Moreira, D.T.
1986-01-01
An intrinsic formulation of the equivalence problem for time-dependent Lagrangians is given. A new demostration of a theorem derived by Henneaux (1982) is obtained. The relationship to transformation groups is discussed. (Author) [pt
Time-dependent pseudo-reciprocity relations in neutronics
International Nuclear Information System (INIS)
Modak, R.S.; Sahni, D.C.
2002-01-01
Earlier, certain reciprocity-like relations have been shown to hold in some restricted steady state cases in neutron diffusion and transport theories. Here, the possibility of existence of similar relations in time-dependent situations is investigated
Geometry and dynamics with time-dependent constraints
Evans, Jonathan M.; Jonathan M Evans; Philip A Tuckey
1995-01-01
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.
Stationary solution of a time dependent density matrix formalism
International Nuclear Information System (INIS)
Tohyama, Mitsuru
1994-01-01
A stationary solution of a time-dependent density-matrix formalism, which is an extension of the time-dependent Hartree-Fock theory to include the effects of two-body correlations, is obtained for the Lipkin model hamiltonian, using an adiabatic treatment of the two-body interaction. It is found that the obtained result is a reasonable approximation for the exact solution of the model. (author)
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
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
Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case
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.
Zheng, Xiao; Yam, ChiYung; Wang, Fan; Chen, GuanHua
2011-08-28
We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.
Pomarning-eddington approximation for time-dependent radiation transfer in finite slab media
International Nuclear Information System (INIS)
El-Wakil, S.A.; Degheidy, A.R.; Sallah, M.
2005-01-01
The time-dependent monoenergetic radiation transfer equation with linear anisotropic scattering is proposed. Pomraning-Eddington approximation is used to calculate the radiation intensity in finite plane-parallel media. Numerical results are done for the isotropic media. Shielding calculations are shown for reflectivity and transmissivity at different times. The medium is assumed to have specular-reflecting boundaries. Two different weight functions are introduced to force the boundary conditions to be fulfilled
Similarity solutions of time-dependent relativistic radiation-hydrodynamical plane-parallel flows
Fukue, Jun
2018-04-01
Similarity solutions are examined for the frequency-integrated relativistic radiation-hydrodynamical flows, which are described by the comoving quantities. The flows are vertical plane-parallel time-dependent ones with a gray opacity coefficient. For adequate boundary conditions, the flows are accelerated in a somewhat homologous manner, but terminate at some singular locus, which originates from the pathological behavior in relativistic radiation moment equations truncated in finite orders.
Finite element approximation for time-dependent diffusion with measure-valued source
Czech Academy of Sciences Publication Activity Database
Seidman, T.; Gobbert, M.; Trott, D.; Kružík, Martin
2012-01-01
Roč. 122, č. 4 (2012), s. 709-723 ISSN 0029-599X R&D Projects: GA AV ČR IAA100750802 Institutional support: RVO:67985556 Keywords : measure-valued source * diffusion equation Subject RIV: BA - General Mathematics Impact factor: 1.329, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/kruzik-finite element approximation for time - dependent diffusion with measure-valued source.pdf
Lie Symmetry of the Diffusive Lotka–Volterra System with Time-Dependent Coefficients
Directory of Open Access Journals (Sweden)
Vasyl’ Davydovych
2018-02-01
Full Text Available Lie symmetry classification of the diffusive Lotka–Volterra system with time-dependent coefficients in the case of a single space variable is studied. A set of such symmetries in an explicit form is constructed. A nontrivial ansatz reducing the Lotka–Volterra system with correctly-specified coefficients to the system of ordinary differential equations (ODEs and an example of the exact solution with a biological interpretation are found.
Construction of exact invariants of time-dependent linear nonholonomic dynamical systems
International Nuclear Information System (INIS)
Fu Jingli; Jimenez, Salvador; Tang Yifa; Vazquez, Luis
2008-01-01
In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out
Construction of exact invariants of time-dependent linear nonholonomic dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Fu Jingli [Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)], E-mail: sqfujingli@163.com; Jimenez, Salvador [Departamento de Matematica Aplicada TTII, E.T.S.I. Telecomunicacion, Universidad Politecnica de Madrid, 28040 Madrid (Spain); Tang Yifa [State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Vazquez, Luis [Departamento de Matematica Aplicada Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de Astrobiologia (CSIC-INTA), Torrejon de Ardoz, 28850 Madrid (Spain)
2008-03-03
In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out.
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.
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
Time-dependent resonant tunnelling for parallel-coupled double quantum dots
International Nuclear Information System (INIS)
Dong Bing; Djuric, Ivana; Cui, H L; Lei, X L
2004-01-01
We derive the quantum rate equations for an Aharonov-Bohm interferometer with two vertically coupled quantum dots embedded in each of two arms by means of the nonequilibrium Green function in the sequential tunnelling regime. Based on these equations, we investigate time-dependent resonant tunnelling under a small amplitude irradiation and find that the resonant photon-assisted tunnelling peaks in photocurrent demonstrate a combination behaviour of Fano and Lorentzian resonances due to the interference effect between the two pathways in this parallel configuration, which is controllable by threading the magnetic flux inside this device
Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator
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.
International Nuclear Information System (INIS)
Guan Xiaoxu; Bartschat, Klaus; Schneider, Barry I
2012-01-01
We present theoretical predictions for one-photon double-ionization of H 2 by an xuv laser pulse. The results were obtained by solving the time-dependent Schrödinger equation in prolate spheroidal coordinates. Good agreement is obtained with predictions from other time-dependent and time-independent calculations, except for the recent 'exterior complex scaling' treatment by Tao et al. (Phys. Rev. A 82 023423).
TEMPS, 1-Group Time-Dependent Pulsed Source Neutron Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
1988-01-01
1 - Description of program or function: TEMPS numerically determines the scalar flux as given by the one-group neutron transport equation with a pulsed source in an infinite medium. Standard plane, point, and line sources are considered as well as a volume source in the negative half-space in plane geometry. The angular distribution of emitted neutrons can either be isotropic or mono-directional (beam) in plane geometry and isotropic in spherical and cylindrical geometry. A general anisotropic scattering Kernel represented in terms of Legendre polynomials can be accommodated with a time- dependent number of secondaries given by c(t)=c 0 (t/t 0 ) β , where β is greater than -1 and less than infinity. TEMPS is designed to provide the flux to a high degree of accuracy (4-5 digits) for use as a benchmark to which results from other numerical solutions or approximations can be compared. 2 - Method of solution: A semi-analytic Method of solution is followed. The main feature of this approach is that no discretization of the transport or scattering operators is employed. The numerical solution involves the evaluation of an analytical representation of the solution by standard numerical techniques. The transport equation is first reformulated in terms of multiple collisions with the flux represented by an infinite series of collisional components. Each component is then represented by an orthogonal Legendre series expansion in the variable x/t where the distance x and time t are measured in terms of mean free path and mean free time, respectively. The moments in the Legendre reconstruction are found from an algebraic recursion relation obtained from Legendre expansion in the direction variable mu. The multiple collision series is evaluated first to a prescribed relative error determined by the number of digits desired in the scalar flux. If the Legendre series fails to converge in the plane or point source case, an accelerative transformation, based on removing the
Time-dependent mean-field games in the superquadratic case
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
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.
Time-dependent reliability analysis of flood defences
International Nuclear Information System (INIS)
Buijs, F.A.; Hall, J.W.; Sayers, P.B.; Gelder, P.H.A.J.M. van
2009-01-01
This paper describes the underlying theory and a practical process for establishing time-dependent reliability models for components in a realistic and complex flood defence system. Though time-dependent reliability models have been applied frequently in, for example, the offshore, structural safety and nuclear industry, application in the safety-critical field of flood defence has to date been limited. The modelling methodology involves identifying relevant variables and processes, characterisation of those processes in appropriate mathematical terms, numerical implementation, parameter estimation and prediction. A combination of stochastic, hierarchical and parametric processes is employed. The approach is demonstrated for selected deterioration mechanisms in the context of a flood defence system. The paper demonstrates that this structured methodology enables the definition of credible statistical models for time-dependence of flood defences in data scarce situations. In the application of those models one of the main findings is that the time variability in the deterioration process tends to be governed the time-dependence of one or a small number of critical attributes. It is demonstrated how the need for further data collection depends upon the relevance of the time-dependence in the performance of the flood defence system.
Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics
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
Time dependent convection electric fields and plasma injection
International Nuclear Information System (INIS)
Kaye, S.M.; Kivelson, M.G.
1979-01-01
Large-scale electric fields associated with storms or substorms are responsible for inward convection and energization of plasma sheet plasma. Calculations based on steady state convection theory show that the response to such electric fields qualitatively accounts for many features of the injected particle distribution, but quantitative agreement with the theory has not yet been obtained. It is known that the predictions can be improved by introducing the concept of convection in response to a time dependent electric field. On the other hand, time dependent calculations are sensitive to the choice of initial conditions, and most models have failed to incorporate these conditions in a realistic and self-consistent manner. In this paper we present a more complete model consisting of realisic initial conditions and time dependent convection to explain a typical substorm-associated electron injection event. We find very good agreement between the observed electron flux changes and those predicted by our model
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
Computational complexity of time-dependent density functional theory
International Nuclear Information System (INIS)
Whitfield, J D; Yung, M-H; Tempel, D G; Aspuru-Guzik, A; Boixo, S
2014-01-01
Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn–Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn–Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn-Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn–Sham potential with controllable error bounds. (paper)
Time-dependent Bragg diffraction by multilayer gratings
International Nuclear Information System (INIS)
André, Jean-Michel; Jonnard, Philippe
2016-01-01
Time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional photonic crystals (André J-M and Jonnard P 2015 J. Opt. 17 085609) and also by extending the Takagi–Taupin approach of the dynamical theory of diffraction. The indicial response is calculated. It presents a time delay with a transient time that is a function of the extinction length for reflection geometry and of the extinction length combined with the thickness of the grating for transmission geometry. (paper)
Vacuum radiation induced by time dependent electric field
Directory of Open Access Journals (Sweden)
Bo Zhang
2017-04-01
Full Text Available Many predictions of new phenomena given by strong field quantum electrodynamics (SFQED will be tested on next generation multi-petawatt laser facilities in the near future. These new phenomena are basis to understand physics in extremely strong electromagnetic fields therefore have attracted wide research interest. Here we discuss a new SFQED phenomenon that is named as vacuum radiation. In vacuum radiation, a virtual electron loop obtain energy from time dependent external electric field and radiate an entangled photon pair. Features of vacuum radiation in a locally time dependent electric field including spectrum, characteristic temperature, production rate and power are given.
Characterization of Models for Time-Dependent Behavior of Soils
DEFF Research Database (Denmark)
Liingaard, Morten; Augustesen, Anders; Lade, Poul V.
2004-01-01
Different classes of constitutive models have been developed to capture the time-dependent viscous phenomena ~ creep, stress relaxation, and rate effects ! observed in soils. Models based on empirical, rheological, and general stress-strain-time concepts have been studied. The first part....... Special attention is paid to elastoviscoplastic models that combine inviscid elastic and time-dependent plastic behavior. Various general elastoviscoplastic models can roughly be divided into two categories: Models based on the concept of overstress and models based on nonstationary flow surface theory...
Vacuum radiation induced by time dependent electric field
Energy Technology Data Exchange (ETDEWEB)
Zhang, Bo, E-mail: zhangbolfrc@caep.cn [Department of High Energy Density Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Laboratory of Science and Technology on Plasma Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Zhang, Zhi-meng; Hong, Wei; He, Shu-Kai; Teng, Jian [Department of High Energy Density Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Laboratory of Science and Technology on Plasma Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Gu, Yu-qiu, E-mail: yqgu@caep.cn [Department of High Energy Density Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Laboratory of Science and Technology on Plasma Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China)
2017-04-10
Many predictions of new phenomena given by strong field quantum electrodynamics (SFQED) will be tested on next generation multi-petawatt laser facilities in the near future. These new phenomena are basis to understand physics in extremely strong electromagnetic fields therefore have attracted wide research interest. Here we discuss a new SFQED phenomenon that is named as vacuum radiation. In vacuum radiation, a virtual electron loop obtain energy from time dependent external electric field and radiate an entangled photon pair. Features of vacuum radiation in a locally time dependent electric field including spectrum, characteristic temperature, production rate and power are given.
Time dependent density matrix theory and effective interaction
Energy Technology Data Exchange (ETDEWEB)
Tohyama, Mitsuru [Kyorin Univ., Mitaka, Tokyo (Japan). School of Medicine
1998-07-01
A correlated ground state of {sup 16}O and an E2 giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix theory (TDDM). The Skyrme force is used in the calculation of both a mean field and two-body correlations. It is found that TDDM gives reasonable ground-state correlations and a large spreading width of the E2 giant resonance when single-particle states in the continuum are treated appropriately. (author)
Kinetic study of time-dependent fixation of U{sup VI} on biochar
Energy Technology Data Exchange (ETDEWEB)
Ashry, A. [Division of Agricultural and Environmental Sciences, School of Biosciences, University of Nottingham, Sutton Bonington, Leicestershire LE12 5RD (United Kingdom); Radiation Protection Department, Nuclear Research Centre, Egyptian Atomic Energy Authority, Cairo (Egypt); Bailey, E.H., E-mail: liz.bailey@nottingham.ac.uk [Division of Agricultural and Environmental Sciences, School of Biosciences, University of Nottingham, Sutton Bonington, Leicestershire LE12 5RD (United Kingdom); Chenery, S.R.N. [British Geological Survey, Nicker Hill, Keyworth, Nottingham NG12 5GG (United Kingdom); Young, S.D. [Division of Agricultural and Environmental Sciences, School of Biosciences, University of Nottingham, Sutton Bonington, Leicestershire LE12 5RD (United Kingdom)
2016-12-15
Biochar, a by-product from the production of biofuel and syngas by gasification, was tested as a material for adsorption and fixation of U{sup VI} from aqueous solutions. A batch experiment was conducted to study the factors that influence the adsorption and time-dependent fixation on biochar at 20 °C, including pH, initial concentration of U{sup VI} and contact time. Uranium (U{sup VI}) adsorption was highly dependent on pH but adsorption on biochar was high over a wide range of pH values, from 4.5 to 9.0, and adsorption strength was time-dependent over several days. The experimental data for pH > 7 were most effectively modelled using a Freundlich adsorption isotherm coupled to a reversible first order kinetic equation to describe the time-dependent fixation of U{sup VI} within the biochar structure. Desorption experiments showed that U{sup VI} was only sparingly desorbable from the biochar with time and isotopic dilution with {sup 233}U{sup VI} confirmed the low, or time-dependent, lability of adsorbed {sup 238}U{sup VI}. Below pH 7 the adsorption isotherm trend suggested precipitation, rather than true adsorption, may occur. However, across all pH values (4.5-9) measured saturation indices suggested precipitation was possible: autunite below pH 6.5 and either swartzite, liebigite or bayleyite above pH 6.5.
Time-Dependent Close-Coupling Methods for Electron-Atom/Molecule Scattering
International Nuclear Information System (INIS)
Colgan, James
2014-01-01
The time-dependent close-coupling (TDCC) method centers on an accurate representation of the interaction between two outgoing electrons moving in the presence of a Coulomb field. It has been extensively applied to many problems of electrons, photons, and ions scattering from light atomic targets. Theoretical Description: The TDCC method centers on a solution of the time-dependent Schrödinger equation for two interacting electrons. The advantages of a time-dependent approach are two-fold; one treats the electron-electron interaction essentially in an exact manner (within numerical accuracy) and a time-dependent approach avoids the difficult boundary condition encountered when two free electrons move in a Coulomb field (the classic three-body Coulomb problem). The TDCC method has been applied to many fundamental atomic collision processes, including photon-, electron- and ion-impact ionization of light atoms. For application to electron-impact ionization of atomic systems, one decomposes the two-electron wavefunction in a partial wave expansion and represents the subsequent two-electron radial wavefunctions on a numerical lattice. The number of partial waves required to converge the ionization process depends on the energy of the incoming electron wavepacket and on the ionization threshold of the target atom or ion.
Institute of Scientific and Technical Information of China (English)
Xie Wen-Xian; Xu Wei; Cai Li
2007-01-01
This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.
Reyes, Jonathan; Shadwick, B. A.
2016-10-01
Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.
Student Understanding of Time Dependence in Quantum Mechanics
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-01-01
The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…
Vehicle routing with stochastic time-dependent travel times
Lecluyse, C.; Woensel, van T.; Peremans, H.
2009-01-01
Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator ...
Ranking paths in stochastic time-dependent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele D.
2014-01-01
In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in...
Review of time-dependent fatigue behaviour of structural alloys
International Nuclear Information System (INIS)
Greenstreet, W.L.
1978-01-01
A review and assessment of time-dependent fatigue was needed to provide an understanding of time-dependent fatigue processes, to define the limits of our present knowledge, and to establish bases for the development of verified design methods for structural components and systems for operation at elevated temperatures. This report reviews the present state of understanding of that phenomena, commonly called 'creep fatigue', and separates it into crack-initiation and crack propagation processes. Criteria for describing material behavior for each of these processes are discussed and described within the extent of present knowledge, which is limited largely to experience with one-dimensional loading. Behaviors of types 304 and 316 stainless steel are emphasized. Much of the treatment of time-dependent failure present here is new and of a developing nature; areas of agreement and areas requiring further resolution are enumerated'. These words are from the abstract of the report on a comprehensive study of time-dependent fatigue. This paper briefly reviews some of the contents and discusses important conclusions reached, especially in terms of current status and needs for additional work. (Auth.)
Quantifying Time Dependent Moisture Storage and Transport Properties
DEFF Research Database (Denmark)
Peuhkuri, Ruut H
2003-01-01
This paper describes an experimental and numerical approach to quantify the time dependence of sorption mechanisms for some hygroscopic building - mostly insulation - materials. Some investigations of retarded sorption and non-Fickian phenomena, mostly on wood, have given inspiration to the present...
Simulation of compressible viscous flow in time-dependent domains
Czech Academy of Sciences Publication Activity Database
Česenek, J.; Feistauer, M.; Horáček, Jaromír; Kučera, V.; Prokopova, J.
2013-01-01
Roč. 219, č. 13 (2013), s. 7139-7150 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional support: RVO:61388998 Keywords : time dependent domain * ALE method * semi-implicit time discretization * shock indicator Subject RIV: BI - Acoustics Impact factor: 1.600, year: 2013
Cumulative Beam Breakup with Time-Dependent Parameters
Delayen, J R
2004-01-01
A general analytical formalism developed recently for cumulative beam breakup (BBU) in linear accelerators with arbitrary beam current profile and misalignments [1] is extended to include time-dependent parameters such as energy chirp or rf focusing in order to reduce BBU-induced instabilities and emittance growth. Analytical results are presented and applied to practical accelerator configurations.
Unit-time scheduling problems with time dependent resources
Tautenhahn, T.; Woeginger, G.
1997-01-01
We investigate the computational complexity of scheduling problems, where the operations consume certain amounts of renewable resources which are available in time-dependent quantities. In particular, we consider unit-time open shop problems and unit-time scheduling problems with identical parallel
Investment horizons : A time-dependent measure of asset performance
Ingve Simonsen; Anders Johansen; Mogens H. Jensen
2005-01-01
We review a resent {\\em time-dependent} performance measure for economical time series -- the (optimal) investment horizon approach. For stock indices, the approach shows a pronounced gain-loss asymmetry that is {\\em not} observed for the individual stocks that comprise the index. This difference may hint towards an synchronize of the draw downs of the stocks.
Multicomponent density-functional theory for time-dependent systems
Butriy, O.; Ebadi, H.; de Boeij, P. L.; van Leeuwen, R.; Gross, E. K. U.
2007-01-01
We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried
Propagator of a time-dependent unbound quadratic Hamiltonian system
International Nuclear Information System (INIS)
Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.
1996-01-01
The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct
Measuring time-dependent deformations in metallic MEMS
Bergers, L.I.J.C.; Hoefnagels, J.P.M.; Delhey, N.K.R.; Geers, M.G.D.
2011-01-01
The reliability of metallic microelectromechanical systems (MEMS) depends on time-dependent deformation such as creep. Key to this process is the interaction between microstructural length scales and dimensional length scales, so-called size-effects. As a first critical step towards studying these
Distributional curvature of time-dependent cosmic strings
Wilson, J P
1997-01-01
Colombeau's theory of generalised functions is used to calculate the contributions, at the rotation axis, to the distributional curvature for a time-dependent radiating cosmic string, and hence the mass per unit length of the string source. This mass per unit length is compared with the mass at null infinity, giving evidence for a global energy conservation law.
Introduction to quantum mechanics a time-dependent perspective
Tannor, David J
2007-01-01
"Introduction to Quantum Mechanics" covers quantum mechanics from a time-dependent perspective in a unified way from beginning to end. Intended for upper-level undergraduate and graduate courses this text will change the way people think about and teach quantum mechanics in chemistry and physics departments.
The evolution of streams in a time-dependent potential
Buist, Hans J. T.; Helmi, Amina
2015-01-01
We study the evolution of streams in a time-dependent spherical gravitational potential. Our goal is to establish what are the imprints of this time evolution on the properties of streams as well as their observability. To this end, we have performed a suite of test-particle experiments for a host
The Feynman integral for time-dependent anharmonic oscillators
International Nuclear Information System (INIS)
Grothaus, M.; Khandekar, D.C.; da Silva, J.L.; Streit, L.
1997-01-01
We review some basic notions and results of white noise analysis that are used in the construction of the Feynman integrand as a generalized white noise functional. We show that the Feynman integrand for the time-dependent harmonic oscillator in an external potential is a Hida distribution. copyright 1997 American Institute of Physics
Path integral solution for some time-dependent potential
International Nuclear Information System (INIS)
Storchak, S.N.
1989-12-01
The quantum-mechanical problem with a time-dependent potential is solved by the path integral method. The solution is obtained by the application of the previously derived general formula for rheonomic homogeneous point transformation and reparametrization in the path integral. (author). 4 refs
Inhibitory Synaptic Plasticity - Spike timing dependence and putative network function.
Directory of Open Access Journals (Sweden)
Tim P Vogels
2013-07-01
Full Text Available While the plasticity of excitatory synaptic connections in the brain has been widely studied, the plasticity of inhibitory connections is much less understood. Here, we present recent experimental and theoretical □ndings concerning the rules of spike timing-dependent inhibitory plasticity and their putative network function. This is a summary of a workshop at the COSYNE conference 2012.
Asymptotic time dependent neutron transport in multidimensional systems
International Nuclear Information System (INIS)
Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.
1983-01-01
A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated
Time-Dependent Natural Convection Couette Flow of Heat ...
African Journals Online (AJOL)
Time-Dependent Natural Convection Couette Flow of Heat Generating/Absorbing Fluid between Vertical Parallel Plates Filled With Porous Material. ... The numerical simulation conducted for some saturated liquids reveled that at t ≥ Pr the steady and unsteady state velocities (as well as the temperature of the fluid) ...
Vehicle routing with stochastic time-dependent travel times
Lecluyse, C.; Woensel, van T.; Peremans, H.
2007-01-01
Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the
Coherent states of general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Abstract. By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both in x- and p-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger than Η/2 and is equal to the minimum of the ...
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
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
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.
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.
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.
Examining the time dependence of DAMA's modulation amplitude
Kelso, Chris; Savage, Christopher; Sandick, Pearl; Freese, Katherine; Gondolo, Paolo
2018-03-01
If dark matter is composed of weakly interacting particles, Earth's orbital motion may induce a small annual variation in the rate at which these particles interact in a terrestrial detector. The DAMA collaboration has identified at a 9.3σ confidence level such an annual modulation in their event rate over two detector iterations, DAMA/NaI and DAMA/LIBRA, each with ˜ 7 years of observations. This data is well fit by a constant modulation amplitude for the two iterations of the experiment. We statistically examine the time dependence of the modulation amplitudes, which "by eye" appear to be decreasing with time in certain energy ranges. We perform a chi-squared goodness of fit test of the average modulation amplitudes measured by the two detector iterations which rejects the hypothesis of a consistent modulation amplitude at greater than 80, 96, and 99.6% for the 2-4, 2-5 and 2-6 keVee energy ranges, respectively. We also find that among the 14 annual cycles there are three ≳ 3σ departures from the average in our estimated data in the 5-6 keVee energy range. In addition, we examined several phenomenological models for the time dependence of the modulation amplitude. Using a maximum likelihood test, we find that descriptions of the modulation amplitude as decreasing with time are preferred over a constant modulation amplitude at anywhere between 1σ and 3σ , depending on the phenomenological model for the time dependence and the signal energy range considered. A time dependent modulation amplitude is not expected for a dark matter signal, at least for dark matter halo morphologies consistent with the DAMA signal. New data from DAMA/LIBRA-phase2 will certainly aid in determining whether any apparent time dependence is a real effect or a statistical fluctuation.
General exact solution for homogeneous time-dependent self-gravitating perfect fluids
International Nuclear Information System (INIS)
Gaete, P.; Hojman, R.
1988-01-01
A procedure to obtain the general exact solution of Einstein equations for a self-gravitating spherically-symmetric static perfect fluid obeying an arbitrary equation of state, is applied to time-dependent Kantowsky-Sachs line elements (with spherical, planar and hyperbolic symmetry). As in the static case, the solution is generated by an arbitrary function of the independent variable and its first derivative. To illustrate the results, the whole family of (plane-symmetric) solutions with a ''gamma-law'' equation of state is explicity obtained in terms of simple known functions. It is also shown that, while in the static plane-symmtric line elements, every metric is in one to one correspondence with a ''partner-metric'' (both originated from the same generatrix function), in this case every generatrix function univocally determines one metric. (author) [pt
DEFF Research Database (Denmark)
Gillet, N.; Jault, D.; Finlay, Chris
2015-01-01
between the magnetic field and subdecadal nonzonal motions within the fluid outer core. Both the zonal and the more energetic nonzonal interannual motions were particularly intense close to the equator (below 10∘ latitude) between 1995 and 2010. We revise down the amplitude of the decade fluctuations......We report a calculation of time-dependent quasi-geostrophic core flows for 1940–2010. Inverting recursively for an ensemble of solutions, we evaluate the main source of uncertainties, namely, the model errors arising from interactions between unresolved core surface motions and magnetic fields....... Temporal correlations of these uncertainties are accounted for. The covariance matrix for the flow coefficients is also obtained recursively from the dispersion of an ensemble of solutions. Maps of the flow at the core surface show, upon a planetary-scale gyre, time-dependent large-scale eddies...
Dynamics of the sub-Ohmic spin-boson model: A time-dependent variational study
International Nuclear Information System (INIS)
Wu Ning; Duan Liwei; Zhao Yang; Li Xin
2013-01-01
The Dirac-Frenkel time-dependent variation is employed to probe the dynamics of the zero temperature sub-Ohmic spin-boson model with strong friction utilizing the Davydov D 1 ansatz. It is shown that initial conditions of the phonon bath have considerable influence on the dynamics. Counterintuitively, even in the very strong coupling regime, quantum coherence features still manage to survive under the polarized bath initial condition, while such features are absent under the factorized bath initial condition. In addition, a coherent-incoherent transition is found at a critical coupling strength α≈ 0.1 for s= 0.25 under the factorized bath initial condition. We quantify how faithfully our ansatz follows the Schrödinger equation, finding that the time-dependent variational approach is robust for strong dissipation and deep sub-Ohmic baths (s≪ 1).
Comparison of deterministic and stochastic methods for time-dependent Wigner simulations
Energy Technology Data Exchange (ETDEWEB)
Shao, Sihong, E-mail: sihong@math.pku.edu.cn [LMAM and School of Mathematical Sciences, Peking University, Beijing 100871 (China); Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria)
2015-11-01
Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed. While it has been thoroughly validated against physical benchmarks, no technical study about its numerical accuracy has been performed. To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method. An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions. Several different numerical tests involving the time-dependent evolution of a quantum wave-packet are performed and discussed in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy.
Reactive scattering theory for molecular transitions in time-dependent fields
International Nuclear Information System (INIS)
Peskin, U.; Miller, W.H.
1995-01-01
A new approach is introduced for computing probabilities of molecular transitions in time-dependent fields. The method is based on the stationary (t,t') representation of the Schroedinger equation and is shown to be equivalent to infinite order time-dependent perturbation theory. Bound-to-bound (i.e., photoexcitation) and bound-to-continuum (i.e., photoreaction) transitions are regarded as reactive collisions with the ''time coordinate'' as the reaction coordinate in an extended Hilbert space. A numerical method based on imposing absorbing boundary conditions for the time coordinate in a discrete variable representation framework is introduced. A single operation of the Green's operator provides all the state-specific transition probabilities as well as partial state-resolved (inclusive) reaction probabilities. Illustrative numerical applications are given for model systems
Time-dependent theoretical model of the polar wind: Preliminary results
International Nuclear Information System (INIS)
Gombosi, T.I.; Cravens, T.E.; Nagy, A.F.
1985-01-01
The coupled time dependent continuity, momentum and energy equations of a two ion (O + and H + ) quasineutral plasma were solved in order to extend our understanding of polar wind behavior. This numerical code allows studies of the time dependent behavior of polar wind-type flows into and out of the ionosphere. Initial studies indicate that the typical time constants for electron and ion temperature changes are of the order of minutes and tens of minutes, respectively. The response time of the minor high altitude ion O + is less than an hour, whereas that of the major ion, H + , is many hours. The initial test runs also demonstrate the fact that temporary supersonic flows of both O + and H + are possible, especially in the presence of significant ion heating
Dey, Sudip; Karmakar, Amit
2014-02-01
This paper presents the time dependent response of multiple delaminated angle-ply composite pretwisted conical shells subjected to low velocity normal impact. The finite element formulation is based on Mindlin's theory incorporating rotary inertia and effects of transverse shear deformation. An eight-noded isoparametric plate bending element is employed to satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. A multipoint constraint algorithm is incorporated which leads to asymmetric stiffness matrices. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the contact force, and the time dependent equations are solved by Newmark's time integration algorithm. Parametric studies are conducted with respect to triggering parameters like laminate configuration, location of delamination, angle of twist, velocity of impactor, and impactor's displacement for centrally impacted shells.
Effects of time-dependent diffusion behaviors on the rumor spreading in social networks
International Nuclear Information System (INIS)
Qiu, Xiaoyan; Zhao, Laijun; Wang, Jiajia; Wang, Xiaoli; Wang, Qin
2016-01-01
When considering roles of realistic external forces (e.g. authorities) and internal forces (e.g. the forgetting nature of human), diffusion behaviors like spreading, stifling and forgetting behaviors are time-dependent. They were incorporated in an SIR-like rumor spreading model to investigate the effects to rumor spreading dynamics. Mean-field equations were derived, and the steady state analysis was conducted. Simulations were carried out on different complex networks. We demonstrated that the combination of the three variable diffusion behaviors provides a faster and larger spreading expansion capacity. Network structure matters considerably in rumor spreading dynamics. - Highlights: • We incorporate time-dependent diffusion behaviors into a SIR-like rumor spreading model. • The combination of the three variable diffusion behaviors provides a faster and larger spreading expansion capacity. • Network structure matters considerably in rumor spreading dynamics.
Effects of time-dependent diffusion behaviors on the rumor spreading in social networks
Energy Technology Data Exchange (ETDEWEB)
Qiu, Xiaoyan [School of Management, Shanghai University, Shanghai 200444 (China); Zhao, Laijun, E-mail: ljzhao70@sjtu.edu.cn [Sino–US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai 200030 (China); Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052 (China); Wang, Jiajia [Sino–US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai 200030 (China); Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052 (China); Wang, Xiaoli [School of Management, Shanghai University of Engineering Science, Shanghai 201620 (China); Wang, Qin [College of Transport & Communications, Shanghai Maritime University, Shanghai 201306 (China)
2016-05-27
When considering roles of realistic external forces (e.g. authorities) and internal forces (e.g. the forgetting nature of human), diffusion behaviors like spreading, stifling and forgetting behaviors are time-dependent. They were incorporated in an SIR-like rumor spreading model to investigate the effects to rumor spreading dynamics. Mean-field equations were derived, and the steady state analysis was conducted. Simulations were carried out on different complex networks. We demonstrated that the combination of the three variable diffusion behaviors provides a faster and larger spreading expansion capacity. Network structure matters considerably in rumor spreading dynamics. - Highlights: • We incorporate time-dependent diffusion behaviors into a SIR-like rumor spreading model. • The combination of the three variable diffusion behaviors provides a faster and larger spreading expansion capacity. • Network structure matters considerably in rumor spreading dynamics.
Rotating Hele-Shaw cell with a time-dependent angular velocity
Anjos, Pedro H. A.; Alvarez, Victor M. M.; Dias, Eduardo O.; Miranda, José A.
2017-12-01
Despite the large number of existing studies of viscous flows in rotating Hele-Shaw cells, most investigations analyze rotational motion with a constant angular velocity, under vanishing Reynolds number conditions in which inertial effects can be neglected. In this work, we examine the linear and weakly nonlinear dynamics of the interface between two immiscible fluids in a rotating Hele-Shaw cell, considering the action of a time-dependent angular velocity, and taking into account the contribution of inertia. By using a generalized Darcy's law, we derive a second-order mode-coupling equation which describes the time evolution of the interfacial perturbation amplitudes. For arbitrary values of viscosity and density ratios, and for a range of values of a rotational Reynolds number, we investigate how the time-dependent angular velocity and inertia affect the important finger competition events that traditionally arise in rotating Hele-Shaw flows.
Time-dependent density functional theory for many-electron systems interacting with cavity photons.
Tokatly, I V
2013-06-07
Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows us to calculate the above basic variables by solving self-consistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems. In particular we show that it naturally leads to time-dependent density functional theory for systems coupled to the Caldeira-Leggett bath.
Time-dependent local-to-normal mode transition in triatomic molecules
Cruz, Hans; Bermúdez-Montaña, Marisol; Lemus, Renato
2018-01-01
Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from temporal perspective through time-dependent frequencies of the oscillators. The LNT is established as a polyad-breaking phenomenon from the local standpoint for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation and a local time-dependent polyad is obtained as a tool to identify the LNT. Applications of this formalism to H2O, CO2, O3 and NO2 molecules in the adiabatic, sudden and linear regime are considered.
Unitary relation for the time-dependent SU(1,1) systems
International Nuclear Information System (INIS)
Song, Dae-Yup
2003-01-01
The system whose Hamiltonian is a linear combination of the generators of SU(1,1) group with time-dependent coefficients is studied. It is shown that there is a unitary relation between the system and a system whose Hamiltonian is simply proportional to the generator of the compact subgroup of SU(1,1). The unitary relation is described by the classical solutions of a time-dependent (harmonic) oscillator. Making use of the relation, the wave functions satisfying the Schroedinger equation are given, for a general unitary representation, in terms of the matrix elements of a finite group transformation (Bargmann function). The wave functions of the harmonic oscillator with an inverse-square potential is studied in detail, and it is shown that through an integral, the model provides a way of deriving the Bargmann function for the representation of positive discrete series of SU(1,1)
Energy Technology Data Exchange (ETDEWEB)
Javeri, V. [Gesellschaft fuer Anlagen- und Reaktorsicherheit (GRS) mbH, Koeln (Germany)
1995-03-01
After implementation of TOUGH2 at GRS in summer 91, it was first used to analyse the gas transport in a repository for the nuclear waste with negligible heat generation and to verify the results obtained with ECLIPSE/JAV 92/. Since the original version of TOUGH2 does not directly simulate the decay of radionuclide and the time dependent boundary conditions, it is not a appropriate tool to study the nuclide transport in a porous medium/PRU 87, PRU 91/. Hence, in this paper some modifications are proposed to study the nuclide transport under combined influence of natural convection diffusion, dispersion and time dependent boundary condition. Here, a single phase fluid with two liquid components is considered as in equation of state model for water and brine/PRU 91A/.
Adiabatic theorem for the time-dependent wave operator
International Nuclear Information System (INIS)
Viennot, David; Jolicard, Georges; Killingbeck, John P.; Perrin, Marie-Yvonne
2005-01-01
The application of time-dependent wave operator theory to the development of a quantum adiabatic perturbation theory is treated both theoretically and numerically, with emphasis on the description of field-matter interactions which involve short laser pulses. It is first shown that the adiabatic limit of the time-dependent wave operator corresponds to a succession of instantaneous static Bloch wave operators. Wave operator theory is then shown to be compatible with the two-time Floquet theory of light-matter interaction, thus allowing the application of Floquet theory to cases which require the use of a degenerate active space. A numerical study of some problems shows that the perturbation strength associated with nonadiabatic processes can be reduced by using multidimensional active spaces and illustrates the capacity of the wave operator approach to produce a quasiadiabatic treatment of a nominally nonadiabatic Floquet dynamical system
Considerations on assessment of different time depending models adequacy
International Nuclear Information System (INIS)
Constantinescu, C.
2015-01-01
The operating period of nuclear power plants can be prolonged if it can be shown that their safety has remained on a high level, and for this, it is necessary to estimate how the aged systems, structures and components (SSCs) influence the NPP reliability and safety. To emphasize the ageing aspects the case study presented in this paper will assess different time depending models for rate of occurrence of failures with the goal to obtain the best fitting model. A sensitivity analysis for the impact of burn-in failures was performed to improve the result of the goodness of fit test. Based on the analysis results, a conclusion about the existence or the absence of an ageing trend could be developed. A sensitivity analysis regarding of the reliability parameters was performed, and the results were used to observe the impact over the time-dependent rate of occurrence of failures. (authors)
Non-Perturbative Formulation of Time-Dependent String Solutions
Alexandre, J; Mavromatos, Nikolaos E; Alexandre, Jean; Ellis, John; Mavromatos, Nikolaos E.
2006-01-01
We formulate here a new world-sheet renormalization-group technique for the bosonic string, which is non-perturbative in the Regge slope alpha' and based on a functional method for controlling the quantum fluctuations, whose magnitudes are scaled by the value of alpha'. Using this technique we exhibit, in addition to the well-known linear-dilaton cosmology, a new, non-perturbative time-dependent background solution. Using the reparametrization invariance of the string S-matrix, we demonstrate that this solution is conformally invariant to alpha', and we give a heuristic inductive argument that conformal invariance can be maintained to all orders in alpha'. This new time-dependent string solution may be applicable to primordial cosmology or to the exit from linear-dilaton cosmology at large times.
Time-dependent nonlinear cosmic ray shocks confirming abstract
International Nuclear Information System (INIS)
Dorfi, E.A.
1985-01-01
Numerical studies of time dependent cosmic ray shock structures in planar geometry are interesting because analytical time-independent solutions are available which include the non-linear reactions on the plasma flow. A feature of these time asymptotic solutions is that for higher Mach numbers (M approximately 5) and for a low cosmic ray upstream pressure the solution is not uniquely determined by the usual conservation laws of mass, momentum and energy. These numerical solutions clearly indicate that much work needs to be done before we understand shock acceleration as a time dependent process. The slowness of the process is possibly due to the fact that there is a diffusive flux into the downstream region in addition to the usual advective losses. Analytic investigations of this phenomenon are required
Tokamak power reactor ignition and time dependent fractional power operation
International Nuclear Information System (INIS)
Vold, E.L.; Mau, T.K.; Conn, R.W.
1986-06-01
A flexible time-dependent and zero-dimensional plasma burn code with radial profiles was developed and employed to study the fractional power operation and the thermal burn control options for an INTOR-sized tokamak reactor. The code includes alpha thermalization and a time-dependent transport loss which can be represented by any one of several currently popular scaling laws for energy confinement time. Ignition parameters were found to vary widely in density-temperature (n-T) space for the range of scaling laws examined. Critical ignition issues were found to include the extent of confinement time degradation by alpha heating, the ratio of ion to electron transport power loss, and effect of auxiliary heating on confinement. Feedback control of the auxiliary power and ion fuel sources are shown to provide thermal stability near the ignition curve
The Time-Dependent Structure of the Electron Reconnection Layer
Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha; Klimas, Alex
2009-01-01
Collisionless magnetic reconnection is often associated with time-dependent behavior. Specifically, current layers in the diffusion region can become unstable to tearing-type instabilities on one hand, or to instabilities with current-aligned wave vectors on the other. In the former case, the growth of tearing instabilities typically leads to the production of magnetic islands, which potentially provide feedback on the reconnection process itself, as well as on the rate of reconnection. The second class of instabilities tend to modulate the current layer along the direction of the current flow, for instance generating kink-type perturbations, or smaller-scale turbulence with the potential to broaden the current layer. All of these processes contribute to rendering magnetic reconnection time-dependent. In this presentation, we will provide a summary of these effects, and a discussion of how much they contribute to the overall magnetic reconnection rate.
Transcriptional dynamics with time-dependent reaction rates
Nandi, Shubhendu; Ghosh, Anandamohan
2015-02-01
Transcription is the first step in the process of gene regulation that controls cell response to varying environmental conditions. Transcription is a stochastic process, involving synthesis and degradation of mRNAs, that can be modeled as a birth-death process. We consider a generic stochastic model, where the fluctuating environment is encoded in the time-dependent reaction rates. We obtain an exact analytical expression for the mRNA probability distribution and are able to analyze the response for arbitrary time-dependent protocols. Our analytical results and stochastic simulations confirm that the transcriptional machinery primarily act as a low-pass filter. We also show that depending on the system parameters, the mRNA levels in a cell population can show synchronous/asynchronous fluctuations and can deviate from Poisson statistics.
Transcriptional dynamics with time-dependent reaction rates
International Nuclear Information System (INIS)
Nandi, Shubhendu; Ghosh, Anandamohan
2015-01-01
Transcription is the first step in the process of gene regulation that controls cell response to varying environmental conditions. Transcription is a stochastic process, involving synthesis and degradation of mRNAs, that can be modeled as a birth–death process. We consider a generic stochastic model, where the fluctuating environment is encoded in the time-dependent reaction rates. We obtain an exact analytical expression for the mRNA probability distribution and are able to analyze the response for arbitrary time-dependent protocols. Our analytical results and stochastic simulations confirm that the transcriptional machinery primarily act as a low-pass filter. We also show that depending on the system parameters, the mRNA levels in a cell population can show synchronous/asynchronous fluctuations and can deviate from Poisson statistics. (paper)
Student understanding of time dependence in quantum mechanics
Directory of Open Access Journals (Sweden)
Paul J. Emigh
2015-09-01
Full Text Available [This paper is part of the Focused Collection on Upper Division Physics Courses.] The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing the key role of the energy eigenbasis in determining the time dependence of wave functions. Through analysis of student responses to a set of four interrelated tasks, we categorize some of the difficulties that underlie common errors. The conceptual and reasoning difficulties that have been identified are illustrated through student responses to four sets of questions administered at different points in a junior-level course on quantum mechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.
Time-dependent delayed signatures from energetic photon interrogations
International Nuclear Information System (INIS)
Norman, Daren R.; Jones, James L.; Blackburn, Brandon W.; Haskell, Kevin J.; Johnson, James T.; Watson, Scott M.; Hunt, Alan W.; Spaulding, Randy; Harmon, Frank
2007-01-01
Pulsed photonuclear interrogation environments generated by 8-24 MeV electron linac are rich with time-dependent, material-specific, radiation signatures. Nitrogen-based explosives and nuclear materials can be detected by exploiting these signatures in different delayed-time regions. Numerical and experimental results presented in this paper show the unique time and energy dependence of these signatures. It is shown that appropriate delayed-time windows are essential to acquire material-specific signatures in pulsed photonuclear assessment environments. These developments demonstrate that pulsed, high-energy, photon-inspection environments can be exploited for time-dependent, material-specific signatures through the proper operation of specialized detectors and detection methods
Time-dependent phase error correction using digital waveform synthesis
Doerry, Armin W.; Buskirk, Stephen
2017-10-10
The various technologies presented herein relate to correcting a time-dependent phase error generated as part of the formation of a radar waveform. A waveform can be pre-distorted to facilitate correction of an error induced into the waveform by a downstream operation/component in a radar system. For example, amplifier power droop effect can engender a time-dependent phase error in a waveform as part of a radar signal generating operation. The error can be quantified and an according complimentary distortion can be applied to the waveform to facilitate negation of the error during the subsequent processing of the waveform. A time domain correction can be applied by a phase error correction look up table incorporated into a waveform phase generator.
Time-dependent crack growth and fracture in concrete
International Nuclear Information System (INIS)
Zhou Fan Ping.
1992-02-01
The objectives of this thesis are to study time-dependent fracture behaviour in concrete. The thesis consists of an experimental study, costitutive modelling and numerical analysis. The experimental study was undertaken to investigate the influences of time on material properties for the fracture process zone and on crack growth and fracture in plain concrete structures. The experiments include tensile relaxation tests, bending tests on notched beams to determine fracture energy at varying deflection rates, and sustained bending and compact tensile tests. From the tensile relaxation tests, the envelope of the σ-w relation does not seem to be influenced by holding periods, though some local detrimental effect does occur. Fracture energy seems to decrease as rates become slower. In the sustained loading tests, deformation (deflection or CMOD) growth curves display three stages, as usually observed in a creep rupture test. The secondary stage dominates the whole failure lifetime, and the secondary deformation rate appears to have good correlation with the failure lifetime. A crack model for time-dependent fracture is proposed, by applying the idea of the Fictitious Crack Model. In this model, a modified Maxwell model is introduced for the fracture process zone incorporated with the static σ-w curve as a failure criterion, based on the observation of the tensile relaxation tests. The time-dependent σ-w curve is expressed in an incremental law. The proposed model has been implemented in a finite element program and applied to simulating sustained flexural and compact tensile tests. Numerical analysis includes simulations of crack growth, load-CMOD curves, stress-failure lifetime curves, size effects on failure life etc. The numerical results indicate that the model seems to be able to properly predict the main features of time-dependent fracture behaviour in concrete, as compared with the experimental results. 97 refs
Time-dependent histamine release from stored human blood products
DEFF Research Database (Denmark)
Nielsen, Hans Jørgen; Edvardsen, L; Vangsgaard, K
1996-01-01
.0 (range 176.0-910.0) nmol/l in whole blood and 475.0 (range 360.0-1560.0) nmol/l in plasma-reduced whole blood, while it was undetectable in SAGM blood. Spontaneous histamine release increased in a time-dependent manner from a median of 6.7 (range 2.2-17.4) nmol/l at the time of storage to 175.0 (range 33...
Distributed Scheduling in Time Dependent Environments: Algorithms and Analysis
Shmuel, Ori; Cohen, Asaf; Gurewitz, Omer
2017-01-01
Consider the problem of a multiple access channel in a time dependent environment with a large number of users. In such a system, mostly due to practical constraints (e.g., decoding complexity), not all users can be scheduled together, and usually only one user may transmit at any given time. Assuming a distributed, opportunistic scheduling algorithm, we analyse the system's properties, such as delay, QoS and capacity scaling laws. Specifically, we start with analyzing the performance while \\...
Time dependent response of equatorial ionospheric electric fieldsto magnetospheric disturbances
Fejer, Bela G.; Scherliess, L.
1995-01-01
We use extensive radar measurements of F region vertical plasma drifts and auroral electrojet indices to determine the storm time dependence of equatorial zonal electric fields. These disturbance drifts result from the prompt penetration of high latitude electric fields and from the dynamo action of storm time winds which produce largest perturbations a few hours after the onset of magnetic activity. The signatures of the equatorial disturbance electric fields change significantly depending o...
Relating Time-Dependent Acceleration and Height Using an Elevator
Kinser, Jason M.
2015-01-01
A simple experiment in relating a time-dependent linear acceleration function to height is explored through the use of a smartphone and an elevator. Given acceleration as a function of time, a(t), the velocity function and position functions are determined through integration as in v(t)=? a(t) dt (1) and x(t)=? v(t) dt. Mobile devices such as…
Time dependence of the pH of rain
John A. Kadlecek; Volkar A. Mohnen
1976-01-01
Standard procedures for determining the pH of rain samples usually involve substantial delays from the time of rainfall to the time of analysis. This assumes that no change in pH occurs during the storage period. We have found that this is not always true. We have determined that individual rain water samples possess a time dependent pH which can be correlated with the...
Analysis of multimedian problems on time dependent networks
Salman, F Sibel
1994-01-01
Ankara : The Department of Industrial Engineering and the Institute of Enginering and Science of Bilkent Univ., 1994. Thesis (Master's) -- Bilkent University, 1994. Includes bibliographical references leaves 81-85. Time dependency arises in transportation and computer-communication networks due to factors such as time varying demand, traffic intensity, and road conditions. This necessitates a locational decision to be based on an analysis involving a time horizon. In this st...
Time-dependent effects of cardiovascular exercise on memory
DEFF Research Database (Denmark)
Roig, Marc; Thomas, Richard; Mang, Cameron S
2016-01-01
We present new evidence supporting the hypothesis that the effects of cardiovascular exercise on memory can be regulated in a time-dependent manner. When the exercise stimulus is temporally coupled with specific phases of the memory formation process, a single bout of cardiovascular exercise may...... be sufficient to improve memory. SUMMARY: The timing of exercise in relation to the information to be remembered is critical to maximize the effects of acute cardiovascular exercise on memory....
Time dependent temperature distribution in pulsed Ti:sapphire lasers
Buoncristiani, A. Martin; Byvik, Charles E.; Farrukh, Usamah O.
1988-01-01
An expression is derived for the time dependent temperature distribution in a finite solid state laser rod for an end-pumped beam of arbitrary shape. The specific case of end pumping by circular (constant) or Gaussian beam is described. The temperature profile for a single pump pulse and for repetitive pulse operation is discussed. The particular case of the temperature distribution in a pulsed titanium:sapphire rod is considered.
Time-dependent diffusive acceleration of test particles at shocks
Energy Technology Data Exchange (ETDEWEB)
Drury, L.O' C. (Dublin Inst. for Advanced Studies (Ireland))
1991-07-15
The acceleration of test particles at a steady plane non-relativistic shock is considered. Analytic expressions are found for the mean and the variance of the acceleration time distribution in the case where the diffusion coefficient has an arbitrary dependence on position and momentum. These expressions are used as the basis for an approximation scheme which is shown, by comparison with numerical solutions, to give an excellent representation of the time-dependent spectrum. (author).
Time-dependent diffusive acceleration of test particles at shocks
International Nuclear Information System (INIS)
Drury, L.O'C.
1991-01-01
The acceleration of test particles at a steady plane non-relativistic shock is considered. Analytic expressions are found for the mean and the variance of the acceleration time distribution in the case where the diffusion coefficient has an arbitrary dependence on position and momentum. These expressions are used as the basis for an approximation scheme which is shown, by comparison with numerical solutions, to give an excellent representation of the time-dependent spectrum. (author)
General time-dependent formulation of quantum scattering theory
International Nuclear Information System (INIS)
Althorpe, Stuart C.
2004-01-01
We derive and explain the key ideas behind a time-dependent formulation of quantum scattering theory, applicable generally to systems with a finite-range scattering potential. The scattering is initiated and probed by plane wave packets, which are localized just outside the range of the potential. The asymptotic limits of conventional scattering theory (initiation in the remote past; detection in the remote future) are not taken. Instead, the differential cross section (DCS) is obtained by projecting the scattered wave packet onto the probe plane wave packets. The projection also yields a time-dependent version of the DCS. Cuts through the wave packet, just as it exits the scattering potential, yield time-dependent and time-independent angular distributions that give a close-up picture of the scattering which complements the DCS. We have previously applied the theory to interpret experimental cross sections of chemical reactions [e.g., S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper gives the derivation of the theory, and explains its relation to conventional scattering theory. For clarity, the derivation is restricted to spherical-particle scattering, though it may readily be extended to general multichannel systems. We illustrate the theory using a simple application to hard-sphere scattering
Neutrino flavor instabilities in a time-dependent supernova model
Directory of Open Access Journals (Sweden)
Sajad Abbar
2015-12-01
Full Text Available A dense neutrino medium such as that inside a core-collapse supernova can experience collective flavor conversion or oscillations because of the neutral-current weak interaction among the neutrinos. This phenomenon has been studied in a restricted, stationary supernova model which possesses the (spatial spherical symmetry about the center of the supernova and the (directional axial symmetry around the radial direction. Recently it has been shown that these spatial and directional symmetries can be broken spontaneously by collective neutrino oscillations. In this letter we analyze the neutrino flavor instabilities in a time-dependent supernova model. Our results show that collective neutrino oscillations start at approximately the same radius in both the stationary and time-dependent supernova models unless there exist very rapid variations in local physical conditions on timescales of a few microseconds or shorter. Our results also suggest that collective neutrino oscillations can vary rapidly with time in the regimes where they do occur which need to be studied in time-dependent supernova models.
Nonequilibrium quantum solvation with a time-dependent Onsager cavity
Kirchberg, H.; Nalbach, P.; Thorwart, M.
2018-04-01
We formulate a theory of nonequilibrium quantum solvation in which parameters of the solvent are explicitly depending on time. We assume in a simplest approach a spherical molecular Onsager cavity with a time-dependent radius. We analyze the relaxation properties of a test molecular point dipole in a dielectric solvent and consider two cases: (i) a shrinking Onsager sphere and (ii) a breathing Onsager sphere. Due to the time-dependent solvent, the frequency-dependent response function of the dipole becomes time-dependent. For a shrinking Onsager sphere, the dipole relaxation is in general enhanced. This is reflected in a temporally increasing linewidth of the absorptive part of the response. Furthermore, the effective frequency-dependent response function shows two peaks in the absorptive part which are symmetrically shifted around the eigenfrequency. By contrast, a breathing sphere reduces damping as compared to the static sphere. Interestingly, we find a non-monotonous dependence of the relaxation rate on the breathing rate and a resonant suppression of damping when both rates are comparable. Moreover, the linewidth of the absorptive part of the response function is strongly reduced for times when the breathing sphere reaches its maximal extension.
Neutrino flavor instabilities in a time-dependent supernova model
Energy Technology Data Exchange (ETDEWEB)
Abbar, Sajad; Duan, Huaiyu, E-mail: duan@unm.edu
2015-12-17
A dense neutrino medium such as that inside a core-collapse supernova can experience collective flavor conversion or oscillations because of the neutral-current weak interaction among the neutrinos. This phenomenon has been studied in a restricted, stationary supernova model which possesses the (spatial) spherical symmetry about the center of the supernova and the (directional) axial symmetry around the radial direction. Recently it has been shown that these spatial and directional symmetries can be broken spontaneously by collective neutrino oscillations. In this letter we analyze the neutrino flavor instabilities in a time-dependent supernova model. Our results show that collective neutrino oscillations start at approximately the same radius in both the stationary and time-dependent supernova models unless there exist very rapid variations in local physical conditions on timescales of a few microseconds or shorter. Our results also suggest that collective neutrino oscillations can vary rapidly with time in the regimes where they do occur which need to be studied in time-dependent supernova models.
Time-Dependent-Asymmetric-Linear-Parsimonious Ancestral State Reconstruction.
Didier, Gilles
2017-10-01
The time-dependent-asymmetric-linear parsimony is an ancestral state reconstruction method which extends the standard linear parsimony (a.k.a. Wagner parsimony) approach by taking into account both branch lengths and asymmetric evolutionary costs for reconstructing quantitative characters (asymmetric costs amount to assuming an evolutionary trend toward the direction with the lowest cost). A formal study of the influence of the asymmetry parameter shows that the time-dependent-asymmetric-linear parsimony infers states which are all taken among the known states, except for some degenerate cases corresponding to special values of the asymmetry parameter. This remarkable property holds in particular for the Wagner parsimony. This study leads to a polynomial algorithm which determines, and provides a compact representation of, the parametric reconstruction of a phylogenetic tree, that is for all the unknown nodes, the set of all the possible reconstructed states associated with the asymmetry parameters leading to them. The time-dependent-asymmetric-linear parsimony is finally illustrated with the parametric reconstruction of the body size of cetaceans.
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
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
Time-dependent density functional theory of open quantum systems in the linear-response regime.
Tempel, David G; Watson, Mark A; Olivares-Amaya, Roberto; Aspuru-Guzik, Alán
2011-02-21
Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Görling-Levy perturbation theory is calculated.
Progress Report on Alloy 617 Time Dependent Allowables
Energy Technology Data Exchange (ETDEWEB)
Wright, Julie Knibloe [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-06-01
Time dependent allowable stresses are required in the ASME Boiler and Pressure Vessel Code for design of components in the temperature range where time dependent deformation (i.e., creep) is expected to become significant. There are time dependent allowable stresses in Section IID of the Code for use in the non-nuclear construction codes, however, there are additional criteria that must be considered in developing time dependent allowables for nuclear components. These criteria are specified in Section III NH. St is defined as the lesser of three quantities: 100% of the average stress required to obtain a total (elastic, plastic, primary and secondary creep) strain of 1%; 67% of the minimum stress to cause rupture; and 80% of the minimum stress to cause the initiation of tertiary creep. The values are reported for a range of temperatures and for time increments up to 100,000 hours. These values are determined from uniaxial creep tests, which involve the elevated temperature application of a constant load which is relatively small, resulting in deformation over a long time period prior to rupture. The stress which is the minimum resulting from these criteria is the time dependent allowable stress St. In this report data from a large number of creep and creep-rupture tests on Alloy 617 are analyzed using the ASME Section III NH criteria. Data which are used in the analysis are from the ongoing DOE sponsored high temperature materials program, form Korea Atomic Energy Institute through the Generation IV VHTR Materials Program and historical data from previous HTR research and vendor data generated in developing the alloy. It is found that the tertiary creep criterion determines St at highest temperatures, while the stress to cause 1% total strain controls at low temperatures. The ASME Section III Working Group on Allowable Stress Criteria has recommended that the uncertainties associated with determining the onset of tertiary creep and the lack of significant
International Nuclear Information System (INIS)
Dodonov, V.V.
2009-01-01
Conditions of disappearance of different 'nonclassical' properties (usual and high-order squeezing, sub-Poissonian statistics, negativity of s-parametrized quasidistributions) are derived for a quantum oscillator, whose evolution is governed by the standard master equation of quantum optics with arbitrary time-dependent coefficients.
On semi-inverse solutions for the time-dependent flows of a second-grade fluid
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This paper deals with analytical solutions for the time-dependent equations arising in a second-grade fluid. The solutions have been developed by assuming certain forms of the stream function. Expressions for velocity components are obtained for flows in plane polar, axisymmetric cylindrical, and axisymmetric spherical polar coordinates. The obtained solutions are compared with existing results.
Josephson-like currents in graphene for arbitrary time-dependent potential barriers
Savel'ev, Sergey E.; Hausler, Wolfgang; Hanggi, Peter
2011-01-01
From the exact solution of the Dirac-Weyl equation we find unusual currents j_y running in y-direction parallel to a time-dependent scalar potential barrier W(x,t) placed upon a monolayer of graphene, even for vanishing momentum component p_y. In their sine-like dependence on the phase difference of wave functions, describing left and right moving Dirac fermions, these currents resemble Josephson currents in superconductors, including the occurance of Shapiro steps at certain frequencies of p...
Specific features of time-dependent Psub(N) approximations in spherical geometry
International Nuclear Information System (INIS)
Peltzer, P.; Pucker, N.
1979-01-01
Approximations to the time-dependent linear transport equation can result in more serious distortions in the description of the actual physical situation than in the stationary problem. This is demonstrated in detail for the case of a neutron pulse in spherical geometry, treated within a P 1 approximation. One has to pay special attention to the singularity at r = 0 and to the effect of the boundary conditions. Effects similar to those shown here are also to be expected in connection with Psub(N) approximations of higher order. (Auth.)
Basic and heavy ion scattering in time dependent Hartree-Fock Theory
International Nuclear Information System (INIS)
Weiss, M.S.
1984-01-01
Time Dependent Hartree-Fock theory, TDHF, is the most sophisticated, microscopic approach to nuclear dynamics yet practiced. Although it is far from a description of nature it does allow us to examine multiply interactive many-body systems semi quantum mechanically and to visualize otherwise covert processes. Some of the properties of the TDHF equations are stated leaving the interested reader to one of several excellent review articles for the derivations. Some of the applications to the collision of heavy ions are briefly described
Time-dependent density functional theory for open quantum systems with unitary propagation.
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.
Simulation of three-dimensional, time-dependent, incompressible flows by a finite element method
International Nuclear Information System (INIS)
Chan, S.T.; Gresho, P.M.; Lee, R.L.; Upson, C.D.
1981-01-01
A finite element model has been developed for simulating the dynamics of problems encountered in atmospheric pollution and safety assessment studies. The model is based on solving the set of three-dimensional, time-dependent, conservation equations governing incompressible flows. Spatial discretization is performed via a modified Galerkin finite element method, and time integration is carried out via the forward Euler method (pressure is computed implicitly, however). Several cost-effective techniques (including subcycling, mass lumping, and reduced Gauss-Legendre quadrature) which have been implemented are discussed. Numerical results are presented to demonstrate the applicability of the model
International Nuclear Information System (INIS)
Ganapol, B.D.; Sumini, M.
1990-01-01
The time dependent space second order discrete form of the monokinetic transport equation is given an analytical solution, within the Laplace transform domain. Th A n dynamic model is presented and the general resolution procedure is worked out. The solution in the time domain is then obtained through the application of a numerical transform inversion technique. The justification of the research relies in the need to produce reliable and physically meaningful transport benchmarks for dynamic calculations. The paper is concluded by a few results followed by some physical comments
Time-dependent approach to electron scattering and ionization in the s-wave model
International Nuclear Information System (INIS)
Ihra, W.; Draeger, M.; Handke, G.; Friedrich, H.
1995-01-01
The time-dependent Schroedinger equation is integrated for continuum states of two-electron atoms in the framework of the s-wave model, in which both electrons are restricted to having vanishing individual orbital angular momenta. The method is suitable for studying the time evolution of correlations in the two-electron wave functions and yields probabilities for elastic and inelastic electron scattering and for electron-impact ionization. The spin-averaged probabilities for electron-impact ionization of hydrogen in the s-wave model reproduce the shape of the experimentally observed integrated ionization cross section remarkably well for energies near and above the maximum
Remarks on time-dependent [current]-density functional theory for open quantum systems.
Yuen-Zhou, Joel; Aspuru-Guzik, Alán
2013-08-14
Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems. Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particle-particle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.
International Nuclear Information System (INIS)
Oliveira, J.V.P. de; Cardona, A.V.; Vilhena, M.T.M.B. de
2002-01-01
In this work, we present a new approach to solve the one-dimensional time-dependent discrete ordinates problem (S N problem) in a slab. The main idea is based upon the application of the spectral method to the set of S N time-dependent differential equations and solution of the resulting coupling equations by the LTS N method. We report numerical simulations
A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media
Duru, Kenneth
2014-01-01
, 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
Solution of the time-dependent Schrodinger equation for highly symmetric potentials
Czech Academy of Sciences Publication Activity Database
Schmidt, B.; Kaprálová-Žďánská, Petra Ruth
2000-01-01
Roč. 127, 2-3 (2000), s. 290-308 ISSN 0010-4655 Institutional research plan: CEZ:AV0Z4040901 Keywords : DISCRETE VARIABLE REPRESENTATIONS * FILTER DIAGONALIZATION * MOLECULAR-DYNAMICS Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.090, year: 2000
Time-dependent Ginzburg-Landau equations for rotating and accelerating superconductors
Czech Academy of Sciences Publication Activity Database
Lipavský, P.; Bok, J.; Koláček, Jan
2013-01-01
Roč. 492, Sept (2013), 144-151 ISSN 0921-4534 R&D Projects: GA ČR(CZ) GAP204/11/0015 Institutional support: RVO:68378271 Keywords : superconductivity * Ginzburg-Landau theory * London field Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.110, year: 2013
Numerical time-dependent partial differential equations for scientists and engineers
Brio, Moysey; Zakharian, Aramais R
2010-01-01
It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on bas...
Numerical solver of the time-dependent Schroedinger equation with Coulomb singularities
International Nuclear Information System (INIS)
Gordon, Ariel; Jirauschek, Christian; Kaertner, Franz X.
2006-01-01
This paper addresses a very fundamental and important problem in the numerical analysis of atomic and molecular systems: How to discretize Hamiltonians with divergent potential terms, such as Coulomb singularities. At the point of a Coulomb singularity, the wave function cannot be described by a Taylor series expansion, which results in problems when standard discretization schemes are used. We propose using the known asymptotic form of the wave function near the singularity instead of the (nonexistent) Taylor series. This principle, namely discretization by asymptotic behavior correspondence (ABC), is employed in this paper for obtaining grid-discretizations for the Coulomb potential in Cartesian, cylindrical and spherical coordinate systems. We show that computations with the ABC discretization are faster and more precise than with a naive discretization by orders of magnitude. The ABC discretization is well suited for the standard numerical time propagators, such as the Crank-Nicholson, Peaceman-Rachford, and leapfrog schemes. We use the latter, since it is faster and has the same order of accuracy. The leapfrog scheme is generalized to allow absorbing potentials at the grid boundaries
Characterizing time-dependent mechanics in metallic MEMS
Directory of Open Access Journals (Sweden)
Geers M.G.D.
2010-06-01
Full Text Available Experiments for characterization of time-dependent material properties in free-standing metallic microelectromechanical system (MEMS pose challenges: e.g. fabrication and handling (sub-μm sized specimens, control and measurement of sub-μN loads and sub-μm displacements over long periods and various temperatures [1]. A variety of experimental setups have been reported each having their pros and cons. One example is a micro-tensile tester with an ingenious electro-static specimen gripping system [2] aiding simple specimen design giving good results at μN and sub-μm levels, but without in-situ full-field observations. Other progressive examples assimilate the specimen, MEMS actuators and load cells on a single chip [3,4] yielding significant results at nN and nm levels with in-situ TEM/SEM observability, though not without complications: complex load actuator/sensor calibration per chip, measures to reduce fabrication failure and unfeasible cofabrication on wafers with commercial metallic MEMS. This work aims to overcome these drawbacks by developing experimental methods with high sensitivity, precision and in-situ full-field observation capabilities. Moreover, these should be applicable to simple free-standing metallic MEMS that can be co-fabricated with commercial devices. These methods will then serve in systematic studies into size-effects in time-dependent material properties. First a numeric-experimental method is developed. It characterizes bending deformation of onwafer μm-sized aluminum cantilevers. A specially designed micro-clamp is used to mechanically apply a constant precise deflection of the beam (zres <50 nm for a prolonged period, see fig. 1. After this period, the deflection by the micro-clamp is removed. Full-field height maps with the ensuing deformation are measured over time with confocal optical profilometry (COP. This yields the tip deflection as function of time with ~3 nm precision, see fig.2. To extract material
Time-Dependent Neutron and Photon Dose-Field Analysis
Energy Technology Data Exchange (ETDEWEB)
Wooten, Hasani Omar [Georgia Inst. of Technology, Atlanta, GA (United States)
2005-08-01
A unique tool is developed that allows the user to model physical representations of complicated glovebox facilities in two dimensions and determine neutral-particle flux and ambient dose-equivalent fields throughout that geometry. The Pandemonium code, originally designed to determine flux and dose-rates only, is improved to include realistic glovebox geometries, time-dependent source and detector positions, time-dependent shielding thickness calculations, time-integrated doses, a representative criticality accident scenario based on time-dependent reactor kinetics, and more rigorous photon treatment. A primary benefit of this work has been an extensive analysis and improvement of the photon model that is not limited to the application described in this thesis. The photon model has been extended in energy range to 10 MeV to include photons from fission and new photon buildup factors have been included that account for the effects of photon buildup at slant-path thicknesses as a function of angle, where the mean free path thickness has been preserved. The overall system of codes is user-friendly and it is directly applicable to facilities such as the plutonium facility at Los Alamos National Laboratory, where high-intensity neutron and photon emitters are regularly used. The codes may be used to determine a priori doses for given work scenarios in an effort to supply dose information to process models which will in turn assist decision makers on ensuring as low as reasonably achievable (ALARA) compliance. In addition, coupling the computational results of these tools with the process model visualization tools will help to increase worker safety and radiological safety awareness.
Time-dependent theory of double ionization of helium under XUV radiation
International Nuclear Information System (INIS)
Nikolopoulos, L A A; Lambropoulos, P
2007-01-01
We present non-perturbative time-dependent calculations of single and double ionization of helium, under XUV radiation of photon energy ranging from 40 to 45 eV, through the direct propagation of the time-dependent Schroedinger equation. The time-dependent wavefunction of the atom under the field is expanded in terms of correlated multichannel states normalized with incoming-wave boundary conditions. In addition to presenting a new non-perturbative approach to the three-body problem, in a fully correlated scheme, capable of providing in the same calculation photoelectron energy and angularly resolved spectra, as well as cross sections through the lowest non-vanishing order transition amplitude, we also present a detailed comparison of the values of certain key quantities that have been obtained through a variety of other methods. The degree of agreement we find, while lending credence to the approach and its versatility, also highlights the remaining open questions in this novel context of double ionization
Noether symmetries and integrability in time-dependent Hamiltonian mechanics
Directory of Open Access Journals (Sweden)
Jovanović Božidar
2016-01-01
Full Text Available We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.
Time-dependent asymmetries in Bs decays at LHCb
Blouw, Johan
2007-01-01
The LHCb experiment will search for New Physics in Bs mixing. The Bs mixing phase will be extracted from the measurement of the time-dependent CP asymmetry in exclusive Bs decays governed by the $b \\to c\\bar{c}s$ quark level transition. Large New Physics effects can be discovered or excluded with the data collected during the very first physics run of LHC. Based on Monte Carlo simulations of the LHCb detector, the expected sensitivity with 2 fb$^{-1}$ on the CP-violation parameter $\\phi_s$, is $\\sigma(\\phi_s)$ = 0.022.
Signal restoration for NMR imaging using time-dependent gradients
International Nuclear Information System (INIS)
Frahm, J.; Haenicke, W.
1984-01-01
NMR imaging experiments that employ linear but time-dependent gradients for encoding spatial information in the time-domain signals result in distorted images when treated with conventional image reconstruction techniques. It is shown here that the phase and amplitude distortions can be entirely removed if the timeshape of the gradient is known. The method proposed is of great theoretical and experimental simplicity. It consists of a retransformation of the measured time-domain signal and corresponds to synchronisation of the signal sampling with the time-development of the gradient field strength. The procedure complements other treatments of periodically oscillating gradients in NMR imaging. (author)
Frictional Heating with Time-Dependent Specific Power of Friction
Directory of Open Access Journals (Sweden)
Topczewska Katarzyna
2017-06-01
Full Text Available In this paper analytical solutions of the thermal problems of friction were received. The appropriate boundary-value problems of heat conduction were formulated and solved for a homogeneous semi–space (a brake disc heated on its free surface by frictional heat fluxes with different and time-dependent intensities. Solutions were obtained in dimensionless form using Duhamel's theorem. Based on received solutions, evolution and spatial distribution of the dimensionless temperature were analyzed using numerical methods. The numerical results allowed to determine influence of the time distribution of friction power on the spatio-temporal temperature distribution in brake disc.
Perspective: Fundamental aspects of time-dependent density functional theory
Energy Technology Data Exchange (ETDEWEB)
Maitra, Neepa T. [Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065 (United States)
2016-06-14
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
Time-dependent coolant velocity measurements in an operating BWR
International Nuclear Information System (INIS)
Luebbesmeyer, D.; Crowe, R.D.
1980-01-01
A method to measure time-dependent fluid velocities in BWR-bundle elements by noise analysis of the incore-neutron-detector signals is shown. Two application examples of the new method are given. The time behaviour of the fluid velocity in the bundle element during a scheduled power excursion of the plant. The change of power was performed by changing the coolant flow through the core The apparent change of the fluid velocity due to thermal elongation of the helix-drive of the TIP-system. A simplified mathematical model was derived for this elongation to use as a reference to check the validity of the new method. (author)
Scattering theory for explicitely time-dependent interactions
International Nuclear Information System (INIS)
Perusch, M.
1982-01-01
Multiple ionization of hydrogen atoms has got increased attention in recent years in connection with high-power lasers. Due to the strong external electromagnetic fields, perturbation theory is no longer valid. The expression for the multiple ionization probability contains the projections of the time-dependent Hamilton operators and the Moeller operators. The main point of the present work is a proof of existence and completeness of the Moeller operators. The proof of existence and completeness is given. The final chapter contains a physical interpretation and discussion of the multiple ionization probability. (G.Q.)
Shapes and dynamics from the time-dependent mean field
International Nuclear Information System (INIS)
Stevenson, P.D.; Goddard, P.M.; Rios, A.
2015-01-01
Explaining observed properties in terms of underlying shape degrees of freedom is a well-established prism with which to understand atomic nuclei. Self-consistent mean-field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time-dependent extension of the mean-field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of 28 Si in the first case, and 240 Pu in the latter case
Time-dependent density-functional theory concepts and applications
Ullrich, Carsten A
2011-01-01
Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s
On particle creation by a time-dependent scalar field
International Nuclear Information System (INIS)
Dolgov, A.D.; Kirilova, D.P.
1989-01-01
The probability of particles creation by a homogeneous scalar field Χ (t) is calculated. Explicit analytical expressions are obtained in two limiting cases in the quasiclassical approximation and in the framework of perturbation theory. In the case when the mass of the created particles is defined by the time-dependent field Χ (t) according to the expression g Χ (t) Ψ-barΨ, where Χ (t) =Χ 0 cos (ωt), it is shown that the creation probability is suppresed not exponentially, but as ω 1/2 . Some cosmological consequences of the results are discussed. 13 refs
Filter frequency response of time dependent signal using Laplace transform
Energy Technology Data Exchange (ETDEWEB)
Shestakov, Aleksei I. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2018-01-16
We analyze the effect a filter has on a time dependent signal x(t). If X(s) is the Laplace transform of x and H (s) is the filter Transfer function, the response in frequency space is X (s) H (s). Consequently, in real space, the response is the convolution (x*h) (t), where hi is the Laplace inverse of H. Effects are analyzed and analytically for functions such as (t/t_{c})^{2} e^{-t/t$_c$}, where t_{c} = const. We consider lowpass, highpass and bandpass filters.
Evaluation of design safety factors for time-dependent buckling
International Nuclear Information System (INIS)
Stone, C.M.; Nickell, R.E.
1977-02-01
The ASME Boiler and Pressure Vessel Code rules concerning time-dependent (creep) buckling for Class 1 nuclear components have recently been changed. Previous requirements for a factor of ten on service life have been replaced with a factor of safety of 1.5 on loading for load-controlled buckling. This report examines the supposed equivalence of the two rules from the standpoint of materials behavior--specifically, the secondary creep strain rate exponent. The comparison is made using results obtained numerically for an axially-loaded, cylindrical shell with varying secondary creep exponents. A computationally efficient scheme for analyzing creep buckling problems is also presented
Fitting a function to time-dependent ensemble averaged data
DEFF Research Database (Denmark)
Fogelmark, Karl; Lomholt, Michael A.; Irbäck, Anders
2018-01-01
Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion...... method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software....
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 time-dependent prize-collecting arc routing problem
DEFF Research Database (Denmark)
Black, Dan; Eglese, Richard; Wøhlk, Sanne
2013-01-01
with the time of day. Two metaheuristic algorithms, one based on Variable Neighborhood Search and one based on Tabu Search, are proposed and tested for a set of benchmark problems, generated from real road networks and travel time information. Both algorithms are capable of finding good solutions, though......A new problem is introduced named the Time-Dependent Prize-Collecting Arc Routing Problem (TD-PARP). It is particularly relevant to situations where a transport manager has to choose between a number of full truck load pick-ups and deliveries on a road network where travel times change...
Radiation effects on time-dependent deformation: Creep and growth
International Nuclear Information System (INIS)
Simonen, E.P.
1989-03-01
Observations of irradiation creep strain as well as irradiation growth strain and related microstructures are reviewed and compared to mechanisms for radiation effects on time-dependent deformation. Composition, microstructure, stress and temperature affect irradiation creep less than thermal creep. Irradiation creep rates can often dominate thermal creep rates, particularly at low temperatures and low stresses. Irradiation creep mechanisms are classified in two general categories: (1) stress-induced preferential absorption and (2) climb-glide. In the former, creep results from dislocation climb, whereas in the latter, creep results from dislocation glide. The effects of irradiation creep on failure modes in nuclear environments are discussed. 53 refs., 18 figs., 1 tab
Time-dependent shell-model theory of dissipative heavy-ion collisions
International Nuclear Information System (INIS)
Ayik, S.; Noerenberg, W.
1982-01-01
A transport theory is formulated within a time-dependent shell-model approach. Time averaging of the equations for macroscopic quantities lead to irreversibility and justifies weak-coupling limit and Markov approximation for the (energy-conserving) one- and two-body collision terms. Two coupled equations for the occupation probabilities of dynamical single-particle states and for the collective variable are derived and explicit formulas for transition rates, dynamical forces, mass parameters and friction coefficients are given. The applicability of the formulation in terms of characteristic quantities of nuclear systems is considered in detail and some peculiarities due to memory effects in the initial equilibration process of heavy-ion collisions are discussed. (orig.)
An adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems
International Nuclear Information System (INIS)
Baranger, M.; Veneroni, M.
1977-11-01
It is shown how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and one starts from the time-dependent Hartree-Fock equation. To this, the adiabatic approximation is added, and the energy in powers of an adiabatic parameter is expanded, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The adiabatic equations of motion are derived in different ways and their analogy with classical mechanics is stressed. The role of the adiabatic hypothesis and its range of validity, are analyzed in detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given and the moment of inertia under rotation is that of Thouless and Valatin
MODICO, 1-D Time-Dependent 1 Group, 2 Group Neutron Diffusion with Delayed Neutron Precursors
International Nuclear Information System (INIS)
Camiciola, P.; Cundari, D.; Montagnini, B.
1992-01-01
1 - Description of program or function: The program solves the 1-D time-dependent one and two group coarse-mesh neutron diffusion equations, coupled with the equations for the delayed-neutron precursor, in plane geometry. 2 - Method of solution: The program is based on a simple coarse-mesh cubic approximation formula for the spatial behaviour of the flux inside each interval. An implicit scheme (the time-integrated method) is used for the advancement of the solution. The resulting (block three-diagonal) matrix is inverted at each time step by Thomas' method. 3 - Restrictions on the complexity of the problem: Number of coarse- mesh intervals LE 80; number of material regions LE 10; number of delayed-neutron precursor groups LE 10. Typical mesh sizes range from 5 cm to 20 cm; typical step length (non-prompt critical transients) ranges from 0.005 to 0.1 seconds
On shallow water waves in a medium with time-dependent
Directory of Open Access Journals (Sweden)
Hamdy I. Abdel-Gawad
2015-07-01
Full Text Available In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE’s.
Entanglement entropy with a time-dependent Hamiltonian
Sivaramakrishnan, Allic
2018-03-01
The time evolution of entanglement tracks how information propagates in interacting quantum systems. We study entanglement entropy in CFT2 with a time-dependent Hamiltonian. We perturb by operators with time-dependent source functions and use the replica trick to calculate higher-order corrections to entanglement entropy. At first order, we compute the correction due to a metric perturbation in AdS3/CFT2 and find agreement on both sides of the duality. Past first order, we find evidence of a universal structure of entanglement propagation to all orders. The central feature is that interactions entangle unentangled excitations. Entanglement propagates according to "entanglement diagrams," proposed structures that are motivated by accessory spacetime diagrams for real-time perturbation theory. To illustrate the mechanisms involved, we compute higher-order corrections to free fermion entanglement entropy. We identify an unentangled operator, one which does not change the entanglement entropy to any order. Then, we introduce an interaction and find it changes entanglement entropy by entangling the unentangled excitations. The entanglement propagates in line with our conjecture. We compute several entanglement diagrams. We provide tools to simplify the computation of loop entanglement diagrams, which probe UV effects in entanglement propagation in CFT and holography.
Time-dependent methodology for fault tree evaluation
International Nuclear Information System (INIS)
Vesely, W.B.
1976-01-01
Any fault tree may be evaluated applying the method called the kinetic theory of fault trees. The basic feature of this method as presented here is in that any information on primary failure, type failure or peak failure is derived from three characteristics: probability of existence, failure intensity and failure density. The determination of the said three characteristics for a given phenomenon yields the remaining probabilistic information on the individual aspects of the failure and on their totality for the whole observed period. The probabilistic characteristics are determined by applying the analysis of phenomenon probability. The total time dependent information on the peak failure is obtained by using the type failures (critical paths) of the fault tree. By applying the said process the total time dependent information is obtained for every primary failure and type failure of the fault tree. In the application of the method of the kinetic theory of fault trees represented by the PREP and KITT programmes, the type failures are first obtained using the deterministic testing method or using the Monte Carlo simulation (PREP programme). The respective characteristics are then determined using the kinetic theory of fault trees (KITT programmes). (Oy)
Rayleigh-Taylor mixing with time-dependent acceleration
Abarzhi, Snezhana
2016-10-01
We extend the momentum model to describe Rayleigh-Taylor (RT) mixing driven by a time-dependent acceleration. The acceleration is a power-law function of time, similarly to astrophysical and plasma fusion applications. In RT flow the dynamics of a fluid parcel is driven by a balance per unit mass of the rates of momentum gain and loss. We find analytical solutions in the cases of balanced and imbalanced gains and losses, and identify their dependence on the acceleration exponent. The existence is shown of two typical regimes of self-similar RT mixing-acceleration-driven Rayleigh-Taylor-type and dissipation-driven Richtymer-Meshkov-type with the latter being in general non-universal. Possible scenarios are proposed for transitions from the balanced dynamics to the imbalanced self-similar dynamics. Scaling and correlations properties of RT mixing are studied on the basis of dimensional analysis. Departures are outlined of RT dynamics with time-dependent acceleration from canonical cases of homogeneous turbulence as well as blast waves with first and second kind self-similarity. The work is supported by the US National Science Foundation.
Interacting particle systems in time-dependent geometries
Ali, A.; Ball, R. C.; Grosskinsky, S.; Somfai, E.
2013-09-01
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be described effectively by space-time trajectories of interacting particles, such as domain boundaries in two-dimensional growth or river networks. We study trajectories embedded in time-dependent geometries, and the main focus is on uniformly expanding or decreasing domains for which we obtain an exact mapping to simple fixed domain systems while preserving the local scale invariance properties. This approach was recently introduced in Ali et al (2013 Phys. Rev. E 87 020102(R)) and here we provide a detailed discussion on its applicability for self-affine Markovian models, and how it can be adapted to self-affine models with memory or explicit time dependence. The mapping corresponds to a nonlinear time transformation which converges to a finite value for a large class of trajectories, enabling an exact analysis of asymptotic properties in expanding domains. We further provide a detailed discussion of different particle interactions and generalized geometries. All our findings are based on exact computations and are illustrated numerically for various examples, including Lévy processes and fractional Brownian motion.
Smooth time-dependent receiver operating characteristic curve estimators.
Martínez-Camblor, Pablo; Pardo-Fernández, Juan Carlos
2018-03-01
The receiver operating characteristic curve is a popular graphical method often used to study the diagnostic capacity of continuous (bio)markers. When the considered outcome is a time-dependent variable, two main extensions have been proposed: the cumulative/dynamic receiver operating characteristic curve and the incident/dynamic receiver operating characteristic curve. In both cases, the main problem for developing appropriate estimators is the estimation of the joint distribution of the variables time-to-event and marker. As usual, different approximations lead to different estimators. In this article, the authors explore the use of a bivariate kernel density estimator which accounts for censored observations in the sample and produces smooth estimators of the time-dependent receiver operating characteristic curves. The performance of the resulting cumulative/dynamic and incident/dynamic receiver operating characteristic curves is studied by means of Monte Carlo simulations. Additionally, the influence of the choice of the required smoothing parameters is explored. Finally, two real-applications are considered. An R package is also provided as a complement to this article.
Some notes on time dependent Thomas Fermi approximation
International Nuclear Information System (INIS)
Holzwarth, G.
1979-01-01
The successful use of effective density-dependent potentials in static Hartree-Fock calculations for nuclear ground-state properties has led to the question whether it is possible to obtain significant further simplification by approximating also the kinetic energy part of the ground state energy by a functional of the local density alone. The great advantage of such an approach is that its complexity is independent of particle number; the size of the system enters only through parameters, Z and N. The simple 'extended Thomas Fermi' functionals are based on the assumption of a spherically symmetric local Fermi surface throughout the nucleus and they represent the 'liquid drop' part of the static total energy. Given this static formalism which is solved directly for the local density without considering individual particles one might ask for a possible dynamical extension in the same sense as TDHF is a dynamical extension of the static HF approach. The aim of such a Time Dependent Thomas Fermi (TDTF) approximation would be to determine directly the time-dependent local single-particle density from given initial conditions and the single-particle current density without following each particle on its individual orbit
Time-dependent crack growth in steam generator tube leakage
International Nuclear Information System (INIS)
Chung, H.D.; Lee, J.H.; Park, Y.W.; Choi, Y.H.
2006-01-01
In general, cracks found in steam generator tubes have semi-elliptical shapes and it is assumed to be rectangular shape for conservatism after crack penetration. Hence, the leak and crack growth behavior has not been clearly understood after the elliptical crack penetrates the tube wall. Several experimental results performed by Argonne Nation Laboratory exhibited time-dependent crack growth behavior of rectangular flaws as well as trapezoidal flaws under constant pressure. The crack growth faster than expected was observed in both cases, which is likely attributed to time-dependent crack growth accompanied by fatigue sources such as the interaction between active jet and crack. The stress intensity factor, K 1 , is necessary for the prediction of the observed fatigue crack growth behavior. However, no K 1 solution is available for a trapezoidal flaw. The objective of this study is to develop the stress intensity factor which can be used for the fatigue analysis of a trapezoidal crack. To simplify the analysis, the crack is assumed to be a symmetric trapezoidal shape. A new K 1 formula for axial trapezoidal through-wall cracks was proposed based on the FEM results. (author)
Time-dependent Models of Magnetospheric Accretion onto Young Stars
Energy Technology Data Exchange (ETDEWEB)
Robinson, C. E.; Espaillat, C. C. [Department of Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215 (United States); Owen, J. E. [Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 (United States); Adams, F. C., E-mail: connorr@bu.edu [Physics Department, University of Michigan, Ann Arbor, MI 48109 (United States)
2017-04-01
Accretion onto Classical T Tauri stars is thought to take place through the action of magnetospheric processes, with gas in the inner disk being channeled onto the star’s surface by the stellar magnetic field lines. Young stars are known to accrete material in a time-variable manner, and the source of this variability remains an open problem, particularly on the shortest (∼day) timescales. Using one-dimensional time-dependent numerical simulations that follow the field line geometry, we find that for plausibly realistic young stars, steady-state transonic accretion occurs naturally in the absence of any other source of variability. However, we show that if the density in the inner disk varies smoothly in time with ∼day-long timescales (e.g., due to turbulence), this complication can lead to the development of shocks in the accretion column. These shocks propagate along the accretion column and ultimately hit the star, leading to rapid, large amplitude changes in the accretion rate. We argue that when these shocks hit the star, the observed time dependence will be a rapid increase in accretion luminosity, followed by a slower decline, and could be an explanation for some of the short-period variability observed in accreting young stars. Our one-dimensional approach bridges previous analytic work to more complicated multi-dimensional simulations and observations.
Time-dependent Models of Magnetospheric Accretion onto Young Stars
International Nuclear Information System (INIS)
Robinson, C. E.; Espaillat, C. C.; Owen, J. E.; Adams, F. C.
2017-01-01
Accretion onto Classical T Tauri stars is thought to take place through the action of magnetospheric processes, with gas in the inner disk being channeled onto the star’s surface by the stellar magnetic field lines. Young stars are known to accrete material in a time-variable manner, and the source of this variability remains an open problem, particularly on the shortest (∼day) timescales. Using one-dimensional time-dependent numerical simulations that follow the field line geometry, we find that for plausibly realistic young stars, steady-state transonic accretion occurs naturally in the absence of any other source of variability. However, we show that if the density in the inner disk varies smoothly in time with ∼day-long timescales (e.g., due to turbulence), this complication can lead to the development of shocks in the accretion column. These shocks propagate along the accretion column and ultimately hit the star, leading to rapid, large amplitude changes in the accretion rate. We argue that when these shocks hit the star, the observed time dependence will be a rapid increase in accretion luminosity, followed by a slower decline, and could be an explanation for some of the short-period variability observed in accreting young stars. Our one-dimensional approach bridges previous analytic work to more complicated multi-dimensional simulations and observations.
On the measurement of time-dependent quantum phases
International Nuclear Information System (INIS)
Barut, A.O.; Bozic, M.; Klarsfeld, S.; Maric, Z.
1991-11-01
We have evaluated the exact (Pancharatnam) phase differences between the final state l ψ(t) > and various initial states for a spin 1/2-particle in a rotating magnetic field B(t). For the initial states l n; B ef (0) >, which are eigenstates of the spin component along the direction of the initial effective field B ef (0), the exact phase has an energy dependent part, and an energy independent part. It is shown that these states l n; B ef (0) > are cyclic and their corresponding Aharonov-Anandan phases are evaluated. In the adiabatic limit we discuss different choices of time-dependent bases and the relationship between the exact phase, the Born-Fock-Schiff phase and Berry's phase. We propose experiments (neutron) to verify separately the exact and the adiabatic evolution laws, as well as to measure the adiabatic phases associated with different choices of time-dependent basis vectors. (author). 37 refs, 5 figs, 1 tab
Time-dependent strains and stresses in a pumpkin balloon
Gerngross, T.; Xu, Y.; Pellegrino, S.
This paper presents a study of pumpkin-shaped superpressure balloons consisting of gores made from a thin polymeric film attached to high stiffness meridional tendons This type of design is being used for the NASA ULDB balloons The gore film shows considerable time-dependent stress relaxation whereas the behaviour of the tendons is essentially time-independent Upon inflation and pressurization the instantaneous i e linear-elastic strain and stress distributions in the film show significantly higher values in the meridional direction However over time and due to the biaxial visco-elastic stress relaxation of the the gore material the em hoop strains increase and the em meridional stresses decrease whereas the em remaining strain and stress components remain substantially unchanged These results are important for a correct assessment of the structural integrity of a pumpkin balloon in a long-duration mission both in terms of the material performance and the overall stability of the shape of the balloon An experimental investigation of the time dependence of the biaxial strain distribution in the film of a 4 m diameter 48 gore pumpkin balloon is presented The inflated shape of selected gores has been measured using photogrammetry and the time variation in strain components at some particular points of these gores has been measured under constant pressure and temperature The results show good correlation with a numerical study using the ABAQUS finite-element package that includes a widely used model of
Kinetic study of time-dependent fixation of U"V"I on biochar
International Nuclear Information System (INIS)
Ashry, A.; Bailey, E.H.; Chenery, S.R.N.; Young, S.D.
2016-01-01
Biochar, a by-product from the production of biofuel and syngas by gasification, was tested as a material for adsorption and fixation of U"V"I from aqueous solutions. A batch experiment was conducted to study the factors that influence the adsorption and time-dependent fixation on biochar at 20 °C, including pH, initial concentration of U"V"I and contact time. Uranium (U"V"I) adsorption was highly dependent on pH but adsorption on biochar was high over a wide range of pH values, from 4.5 to 9.0, and adsorption strength was time-dependent over several days. The experimental data for pH > 7 were most effectively modelled using a Freundlich adsorption isotherm coupled to a reversible first order kinetic equation to describe the time-dependent fixation of U"V"I within the biochar structure. Desorption experiments showed that U"V"I was only sparingly desorbable from the biochar with time and isotopic dilution with "2"3"3U"V"I confirmed the low, or time-dependent, lability of adsorbed "2"3"8U"V"I. Below pH 7 the adsorption isotherm trend suggested precipitation, rather than true adsorption, may occur. However, across all pH values (4.5-9) measured saturation indices suggested precipitation was possible: autunite below pH 6.5 and either swartzite, liebigite or bayleyite above pH 6.5.
International Nuclear Information System (INIS)
Judson, R.S.; McGarrah, D.B.; Sharafeddin, O.A.; Kouri, D.J.; Hoffman, D.K.
1991-01-01
We compare three time-dependent wave packet methods for performing elastic scattering calculations from screened Coulomb potentials. The three methods are the time-dependent amplitude density method (TDADM), what we term a Cayley-transform method (CTM), and the Chebyshev propagation method of Tal-Ezer and Kosloff. Both the TDADM and the CTM are based on a time-dependent integral equation for the wave function. In the first, we propagate the time-dependent amplitude density, |ζ(t)right-angle=U|ψ(t)right-angle, where U is the interaction potential and |ψ(t)right-angle is the usual time-dependent wave function. In the other two, the wave function is propagated. As a numerical example, we calculate phase shifts and cross sections using a screened Coulomb, Yukawa type potential over the range 200--1000 eV. One of the major advantages of time-dependent methods such as these is that we get scattering information over this entire range of energies from one propagation. We find that in most cases, all three methods yield comparable accuracy and are about equally efficient computationally. However for l=0, where the Coulomb well is not screened by the centrifugal potential, the TDADM requires smaller grid spacings to maintain accuracy
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
Time-dependent, many-body scattering theory and nuclear reaction applications
International Nuclear Information System (INIS)
Levin, F.S.
1977-01-01
The channel component state form of the channel coupling array theory of many-body scattering is briefly reviewed. These states obey a non-hermitian matrix equation whose exact solution yields the Schroedinger eigenstates, eigenvalues and scattering amplitudes. A time-dependent formulation of the theory is introduced in analogy to the time-dependent Schrodinger equation and several consequences of the development are noted. These include an interaction picture, a single (matrix) S operator, and the usual connection between the t = 0 time-dependent and the time-independent scattering states. Finally, the channel component states (psi/sub j/) are shown to have the useful property that only psi/sub j/ has (two-body) outgoing waves in channel j: psi/sub m/, m not equal to j, is asymptotically zero in two-body channel j. This formalism is then considered as a means for direct nuclear reaction analysis. Typical bound state approximations are introduced and it is shown that a DWBA amplitude occurs in only one channel. The non-time-reversal invariance of the approximate theory is noted. Results of calculations based on a realistic model for two sets of light-ion induced, one-particle transfer reactions are discussed and compared with the coupled reaction channel (CRC) results using the CRC procedure of Cotanch and Vincent. Angular distributions for the two calculational methods are found to be similar in shape and magnitude. Higher ordercorrections are small as are time-reversal non-invariant effects. Post- and prior-type CRC calculations are seen to differ; the latter are closer to the full CRC results
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
TWODEE-2/MOD3, 2-D Time-Dependent Fuel Elements Thermal Analysis after PWR LOCA
International Nuclear Information System (INIS)
Lauben, G. N.
2001-01-01
1 - Description of problem or function: WREM-TOODEE2 is a two- dimensional, time-dependent, fuel-element thermal analysis program. Its primary purpose is to evaluate fuel-element thermal response during post-LOCA refill and reflood in a pressurized water reactor (PWR). 2 - Method of solution: TOODEE2 calculations are carried out in a two-dimensional mesh region defined in slab or cylindrical geometry by orthogonal grid lines. Coordinates which form order pairs are labeled x-y in slab geometry, and those in cylindrical geometry are labeled r-z for the axisymmetric case and r-theta for the polar case. Conduction and radiation are the only heat transfer mechanisms assumed within the boundaries of the mesh region. Convective and boiling heat transfer mechanisms are assumed at the boundaries. The program numerically solves the two-dimensional, time-dependent, heat conduction equation within the mesh region. 3 - Restrictions on the complexity of the problem: WREM-TOODEE2 considers only axisymmetric geometry although the equations for slab and polar geometry are included in the program
A time-dependent neutron transport model and its coupling to thermal-hydraulics
International Nuclear Information System (INIS)
Pautz, A.
2001-01-01
A new neutron transport code for time-dependent analyses of nuclear systems has been developed. The code system is based on the well-known Discrete Ordinates code DORT, which solves the steady-state neutron/photon transport equation in two dimensions for an arbitrary number of energy groups and the most common regular geometries. For the implementation of time-dependence a fully implicit first-order scheme was employed to minimize errors due to temporal discretization. This requires various modifications to the transport equation as well as the extensive use of elaborated acceleration mechanisms. The convergence criteria for fluxes, fission rates etc. had to be strongly tightened to ensure the reliability of results. To perform coupled analyses, an interface to the GRS system code ATHLET has been developed. The nodal power densities from the neutron transport code are passed to ATHLET to calculate thermal-hydraulic system parameters, e.g. fuel and coolant temperatures. These are in turn used to generate appropriate nuclear cross sections by interpolation of pre-calculated data sets for each time step. Finally, to demonstrate the transient capabilities of the coupled code system, the research reactor FRM-II has been analysed. Several design basis accidents were modelled, like the loss of off site power, loss of secondary heat sink and unintended control rod withdrawal. (author)
Existence of a time-dependent heat flux-related ponderomotive effect
International Nuclear Information System (INIS)
Schamel, H.; Sack, C.
1980-01-01
The existence of a new ponderomotive effect associated with high-frequency waves is pointed out. It originates when time-dependency, mean velocities, or divergent heat fluxes are involved and it supplements the two effects known previously, namely, the ponderomotive force and fake heating. Two proofs are presented; the first is obtained by establishing the momentum equations generalized by including radiation effects and the second by solving the quasi-linear-type diffusion equation explicitly. For a time-dependent wave packet the solution exhibits a new contribution in terms of an integral over previous states. Owing to this term, the plasma has a memory which leads to a breaking of the time symmetry of the plasma response. The range, influenced by the localized wave packet, expands during the course of time due to streamers emanating from the wave active region. Perturbations, among which is the heat flux, are carried to remote positions and, consequently, the region accessible to wave heating is increased. The density dip appears to be less pronounced at the center, and its generation and decay are delayed. The analysis includes a self-consistent action of high-frequency waves as well as the case of traveling wave packets. In order to establish the existence of this new effect, the analytical results are compared with recent microwave experiments. The possibility of generating fast particles by this new ponderomotive effect is emphasized
Time dependent variation of carrying capacity of prestressed precast beam
Le, Tuan D.; Konečný, Petr; Matečková, Pavlína
2018-04-01
The article deals with the evaluation of the precast concrete element time dependent carrying capacity. The variation of the resistance is inherited property of laboratory as well as in-situ members. Thus the specification of highest, yet possible, laboratory sample resistance is important with respect to evaluation of laboratory experiments based on the test machine loading capabilities. The ultimate capacity is evaluated through the bending moment resistance of a simply supported prestressed concrete beam. The probabilistic assessment is applied. Scatter of random variables of compressive strength of concrete and effective height of the cross section is considered. Monte Carlo simulation technique is used to investigate the performance of the cross section of the beam with changes of tendons’ positions and compressive strength of concrete.
On the time-dependent radiative transfer in photospheric plasmas
International Nuclear Information System (INIS)
Schultz, A.L.; Schweizer, M.A.
1987-01-01
The paper is the second of a series investigating time-dependent radiative transfer processes of x-rays in photospheric plasmas. A quantitative discussion is presented of analytical results derived earlier along with a comparison with Monte Carlo simulations. The geometry considered is a homogeneous plasma ball with radius R. The source is concentrated on a concentric shell with radius r 0 < R. Point sources at the centre of the ball or semi-infinite geometries are discussed as limiting cases. Diffusion profiles are given for every scattering order and the total profile appears as the sum over these individual profiles. The comparison with Monte Carlo results is used to test the accuracy of the analytical approach and to adjust the time profiles of the first few scattering orders. The analytical theory yields good results over a wide range of situations. (author)
Timing intervals using population synchrony and spike timing dependent plasticity
Directory of Open Access Journals (Sweden)
Wei Xu
2016-12-01
Full Text Available We present a computational model by which ensembles of regularly spiking neurons can encode different time intervals through synchronous firing. We show that a neuron responding to a large population of convergent inputs has the potential to learn to produce an appropriately-timed output via spike-time dependent plasticity. We explain why temporal variability of this population synchrony increases with increasing time intervals. We also show that the scalar property of timing and its violation at short intervals can be explained by the spike-wise accumulation of jitter in the inter-spike intervals of timing neurons. We explore how the challenge of encoding longer time intervals can be overcome and conclude that this may involve a switch to a different population of neurons with lower firing rate, with the added effect of producing an earlier bias in response. Experimental data on human timing performance show features in agreement with the model’s output.
A gauge invariant theory for time dependent heat current
International Nuclear Information System (INIS)
Chen, Jian; ShangGuan, Minhui; Wang, Jian
2015-01-01
In this work, we develop a general gauge-invariant theory for AC heat current through multi-probe systems. Using the non-equilibrium Green’s function, a general expression for time-dependent electrothermal admittance is obtained where we include the internal potential due to the Coulomb interaction explicitly. We show that the gauge-invariant condition is satisfied for heat current if the self-consistent Coulomb interaction is considered. It is known that the Onsager relation holds for dynamic charge conductance. We show in this work that the Onsager relation for electrothermal admittance is violated, except for a special case of a quantum dot system with a single energy level. We apply our theory to a nano capacitor where the Coulomb interaction plays an essential role. We find that, to the first order in frequency, the heat current is related to the electrochemical capacitance as well as the phase accumulated in the scattering event. (paper)
Histogram bin width selection for time-dependent Poisson processes
International Nuclear Information System (INIS)
Koyama, Shinsuke; Shinomoto, Shigeru
2004-01-01
In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method
Histogram bin width selection for time-dependent Poisson processes
Energy Technology Data Exchange (ETDEWEB)
Koyama, Shinsuke; Shinomoto, Shigeru [Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502 (Japan)
2004-07-23
In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.
The time-dependent Aharonov–Casher effect
Energy Technology Data Exchange (ETDEWEB)
Singleton, Douglas, E-mail: dougs@csufresno.edu [Department of Physics, California State University Fresno, Fresno, CA 93740-8031 (United States); ICTP South American Institute for Fundamental Research, UNESP – Univ. Estadual Paulista, Rua Dr. Bento T. Ferraz 271, 01140-070, São Paulo, SP (Brazil); Ulbricht, Jaryd, E-mail: julbrich@ucsc.edu [Physics Department, University of California Santa Cruz, Santa Cruz, CA 95064 (United States); Department of Physics, California State University Fresno, Fresno, CA 93740-8031 (United States)
2016-02-10
In this paper we give a covariant expression for Aharonov–Casher phase. This expression is a combination of the canonical electric field, Aharonov–Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov–Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the time dependent electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic fields lead to non-zero phases, and we look at the interplay between these electric and magnetic phases.