TY - JOUR
T1 - Analysis of the backward‐euler/langevin method for molecular dynamics
AU - Peskin, Charles S.
PY - 1990/7
Y1 - 1990/7
N2 - 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.
AB - 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.
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U2 - 10.1002/cpa.3160430503
DO - 10.1002/cpa.3160430503
M3 - Article
AN - SCOPUS:84990619660
SN - 0010-3640
VL - 43
SP - 599
EP - 645
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 5
ER -