Langevin Trajectories between Fixed Concentrations

TL;DR

This paper introduces a simulation method for modeling Langevin particle trajectories between fixed concentration baths, accurately maintaining steady state fluxes without boundary artifacts.

Contribution

It presents a novel simulation scheme that preserves fixed concentrations and realistic physics at boundaries in Langevin trajectory models.

Findings

Accurately maintains fixed concentrations in simulations.

Replicates steady state fluxes without boundary layers.

Provides a physically consistent simulation approach.

Abstract

We consider the trajectories of particles diffusing between two infinite baths of fixed concentrations connected by a channel, e.g. a protein channel of a biological membrane. The steady state influx and efflux of Langevin trajectories at the boundaries of a finite volume containing the channel and parts of the two baths is replicated by termination of outgoing trajectories and injection according to a residual phase space density. We present a simulation scheme that maintains averaged fixed concentrations without creating spurious boundary layers, consistent with the assumed physics.