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Analysis and Experiments for a Computational Model of a Heat Bath

Stuart, A. M. and Warren, J. O. (1999) Analysis and Experiments for a Computational Model of a Heat Bath. Journal of Statistical Physics, 97 (3/4). pp. 687-723. ISSN 0022-4715. doi:10.1023/A:1004667325896.

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A question of some interest in computational statistical mechanics is whether macroscopic quantities can be accurately computed without detailed resolution of the fastest scales in the problem. To address this question a simple model for a distinguished particle immersed in a heat bath is studied (due to Ford and Kac). The model yields a Hamiltonian system of dimension 2N+2 for the distinguished particle and the degrees of freedom describing the bath. It is proven that, in the limit of an infinite number of particles in the heat bath (N→∞), the motion of the distinguished particle is governed by a stochastic differential equation (SDE) of dimension 2. Numerical experiments are then conducted on the Hamiltonian system of dimension 2N+2 (N≫1) to investigate whether the motion of the distinguished particle is accurately computed (i.e., whether it is close to the solution of the SDE) when the time step is small relative to the natural time scale of the distinguished particle, but the product of the fastest frequency in the heat bath and the time step is not small—the underresolved regime in which many computations are performed. It is shown that certain methods accurately compute the limiting behavior of the distinguished particle, while others do not. Those that do not are shown to compute a different, incorrect, macroscopic limit.

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Additional Information:© 1999 Plenum Publishing Corporation. Received February 23, 1999; final June 9, 1999. The work of A.M.S. was supported by the National Science Foundation under Grant DMS-95-0487 and by the EPSRC, U.K. The work of J.O.W. was supported by a Department of Defense National Defense Science and Engineering Graduate Fellowship Program.
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Subject Keywords:Computational statistical mechanics; molecular dynamics; Hamiltonian systems; stiff oscillatory systems; stochastic differential equations; Langevin equation; symplectic methods; energy-conserving methods
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ44
Issue or Number:3/4
Record Number:CaltechAUTHORS:20170609-161129844
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Official Citation:Stuart, A.M. & Warren, J.O. Journal of Statistical Physics (1999) 97: 687. doi:10.1023/A:1004667325896
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78073
Deposited By: Tony Diaz
Deposited On:09 Jun 2017 23:25
Last Modified:15 Nov 2021 17:36

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