Analysis of the backward‐euler/langevin method for molecular dynamics

Charles S. Peskin

Research output: Contribution to journalArticle

Abstract

This paper develops the theory of a recently introduced computational method for molecular dynamics. The method in question uses the backward‐Euler method to solve the classical Langevin equations of a molecular system. Parameters are chosen to produce a cutoff frequency ωc, which may be set equal to kT/h to simulate quantum‐mechanical effects. In the present paper, an ensemble of identical Hamiltonian systems modeled by the backward‐Euler/Langevin method is considered, an integral equation for the equilibrium phase‐space density is derived, and an asymptotic analysis of that integral equation in the limit Δt → 0 is performed. The result of this asymptotic analysis is a second‐order partial differential equation for the equilibrium phase‐space density expressed as a function of the constants of the motion. This equation is solved in two special cases: a system of coupled harmonic oscillators and a diatomic molecule with a stiff bond.

Original languageEnglish (US)
Pages (from-to)599-645
Number of pages47
JournalCommunications on Pure and Applied Mathematics
Volume43
Issue number5
DOIs
StatePublished - 1990

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Asymptotic analysis
Molecular Dynamics
Integral equations
Molecular dynamics
Asymptotic Analysis
Hamiltonians
Phase Space
Integral Equations
Cutoff frequency
Computational methods
Partial differential equations
Langevin Equation
Coupled Oscillators
Harmonic Oscillator
Computational Methods
Molecules
Hamiltonian Systems
Ensemble
Partial differential equation
Motion

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Analysis of the backward‐euler/langevin method for molecular dynamics. / Peskin, Charles S.

In: Communications on Pure and Applied Mathematics, Vol. 43, No. 5, 1990, p. 599-645.

Research output: Contribution to journalArticle

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