A stochastic Hamiltonian formulation applied to dissipative particle dynamics

TL;DR

This paper introduces a stochastic Hamiltonian formulation for dissipative particle dynamics, enabling the development of structure-preserving numerical schemes that improve long-term simulation stability.

Contribution

It extends Hamiltonian dynamics to stochastic dissipative systems and develops new integrators, including modifications of existing methods, for more efficient DPD simulations.

Findings

Schemes preserve structure in deterministic parts of DPD

Numerical analysis shows improved long-term stability

Includes and generalizes existing velocity-Verlet methods

Abstract

In this paper, a stochastic Hamiltonian formulation (SHF) is proposed and applied to dissipative particle dynamics (DPD) simulations. As an extension of Hamiltonian dynamics to stochastic dissipative systems, the SHF provides necessary foundations and great convenience for constructing efficient numerical integrators. As a first attempt, we develop the St\"ormer--Verlet type of schemes based on the SHF, which are structure-preserving for deterministic Hamiltonian systems without external forces, the dissipative forces in DPD. Long-time behaviour of the schemes is shown numerically by studying the damped Kubo oscillator. In particular, the proposed schemes include the conventional Groot-Warren's modified velocity-Verlet method and a modified version of Gibson-Chen-Chynoweth as special cases. The schemes are applied to DPD simulations and analysed numerically.