Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics

TL;DR

This paper introduces pairwise adaptive thermostats for dissipative particle dynamics, enhancing accuracy and stability through a novel Langevin approach and a superconvergent Nosé--Hoover--Langevin variant, validated by numerical experiments.

Contribution

It proposes a pairwise adaptive Langevin thermostat and a superconvergent Nosé--Hoover--Langevin method for DPD, improving accuracy, stability, and efficiency in simulations.

Findings

Enhanced accuracy and stability in DPD simulations.

Superconvergence of the Nosé--Hoover--Langevin method.

Effective numerical validation in equilibrium and nonequilibrium conditions.

Abstract

We examine the formulation and numerical treatment of dissipative particle dynamics (DPD) and momentum-conserving molecular dynamics. We show that it is possible to improve both the accuracy and the stability of DPD by employing a pairwise adaptive Langevin thermostat that precisely matches the dynamical characteristics of DPD simulations (e.g., autocorrelation functions) while automatically correcting thermodynamic averages using a negative feedback loop. In the low friction regime, it is possible to replace DPD by a simpler momentum-conserving variant of the Nos\'{e}--Hoover--Langevin method based on thermostatting only pairwise interactions; we show that this method has an extra order of accuracy for an important class of observables (a superconvergence result), while also allowing larger timesteps than alternatives. All the methods mentioned in the article are easily implemented. Numerical experiments are performed in both equilibrium and nonequilibrium settings; using Lees--Edwards boundary conditions to induce shear flow.