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Gradient Stability of Numerical Algorithms in Local Nonequilibrium Problems of Critical Dynamics

Galenko, Peter and Lebedev, Vladimir and Sysoeva, A. (2011) Gradient Stability of Numerical Algorithms in Local Nonequilibrium Problems of Critical Dynamics. Computational Mathematics and Mathematical Physics, 51 (6), pp. 1074-1090.

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Abstract

The critical dynamics of a spatially inhomogeneous system are analyzed with allowance for local nonequilibrium, which leads to a singular perturbation in the equations due to the appearance of a second time derivative. An extension is derived for the Eyre theorem, which holds for classical critical dynamics described by first-order equations in time and based on the local equilibrium hypothesis. It is shown that gradient-stable numerical algorithms can also be constructed for second-order equations in time by applying the decomposition of the free energy into expansive and contractive parts, which was suggested by Eyre for classical equations. These gradient-stable algorithms yield a monotonically nondecreasing free energy in simulations with an arbitrary time step. It is shown that the gradient stability conditions for the modified and classical equations of critical dynamics coincide in the case of a certain time approximation of the inertial dynamics relations introduced for describing local nonequilibrium. Model problems illustrating the extended Eyre theorem for critical dynamics problems are considered.

Document Type:Article
Title:Gradient Stability of Numerical Algorithms in Local Nonequilibrium Problems of Critical Dynamics
Authors:
AuthorsInstitution or Email of Authors
Galenko, Peterpeter.galenko@dlr.de
Lebedev, VladimirUdmurt Ste University, Izhevsk
Sysoeva, A.Udmurt State University, Izhevsk
Date:2011
Journal or Publication Title:Computational Mathematics and Mathematical Physics
Refereed publication:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:51
Page Range:pp. 1074-1090
Status:Published
Keywords:Undercooling of Materials
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Research under Space Conditions
DLR - Research area:Raumfahrt
DLR - Program:R FR - Forschung unter Weltraumbedingungen
DLR - Research theme (Project):R - Vorhaben Materialwissenschaftliche Forschung
Location: Köln-Porz
Institutes and Institutions:Institute of Materials Physics in Space
Deposited By: Dieter Herlach
Deposited On:28 Jul 2011 14:57
Last Modified:26 Feb 2013 15:05

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