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Analysis of the backward-euler/langevin method for molecular dynamics
- Source :
- Communications on Pure and Applied Mathematics. 43:599-645
- Publication Year :
- 1990
- Publisher :
- Wiley, 1990.
-
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.
Details
- ISSN :
- 10970312 and 00103640
- Volume :
- 43
- Database :
- OpenAIRE
- Journal :
- Communications on Pure and Applied Mathematics
- Accession number :
- edsair.doi...........c68bdb7b25e16c84a4e4981aa697a5c7