Better than counting: Density profiles from force sampling

TL;DR

This paper introduces a force-based sampling method to accurately compute density profiles in simulations, reducing statistical noise and computation time compared to traditional counting methods.

Contribution

The authors propose a novel force sampling approach for density profiles that improves accuracy and efficiency over standard counting techniques in particle simulations.

Findings

Force sampling yields lower statistical uncertainty.

Method reduces computation time in simulations.

Applicable to Monte Carlo, Brownian, and Molecular Dynamics.

Abstract

Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. Here we investigate an alternative method based on a histogram of the local force density. Via an exact sum rule the density profile is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations. We have tested the method in Monte Carlo, Brownian Dynamics and Molecular Dynamics simulations. The results carry a statistical uncertainty smaller than that of the standard, counting, method, reducing therefore the computation time.