UNSPECIFIED (2004) Fitting SDE models to nonlinear Kac-Zwanzig heat bath models. PHYSICA D-NONLINEAR PHENOMENA, 199 (3-4). pp. 279-316. doi:10.1016/j.physd.2004.04.011

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Abstract

We study a class of "particle in a heat bath" models, which are a generalization of the well-known Kac-Zwanzig class of models, but where the coupling between the distinguished particle and the it heat bath particles is through nonlinear springs. The heat bath particles have random initial data drawn from an equilibrium Gibbs density. The primary objective is to approximate the forces exerted by the heat bath-which we do not want to resolve-by a stochastic process. By means of the central limit theorem for Gaussian processes, and heuristics based on linear response theory, we demonstrate conditions under which it is natural to expect that the trajectories of the distinguished particle can be weakly approximated, as n --> infinity, by the solution of a Markovian SDE. The quality of this approximation is verified by numerical calculations with parameters chosen according to the linear response theory. Alternatively, the parameters of the effective equation can be chosen using time series analysis. This is done and agreement with linear response theory is shown to be good. (C) 2004 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	PHYSICA D-NONLINEAR PHENOMENA
Publisher:	ELSEVIER SCIENCE BV
ISSN:	0167-2789
Official Date:	15 December 2004
Dates:	Date Event 15 December 2004 UNSPECIFIED
Volume:	199
Number:	3-4
Number of Pages:	38
Page Range:	pp. 279-316
DOI:	10.1016/j.physd.2004.04.011
Publication Status:	Published

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