Simulating sticky particles: A Monte Carlo method to sample a stratification

TL;DR

This paper introduces a Monte Carlo sampling method for systems with particles that can form and break bonds, modeling complex stratified state spaces in materials science and biology.

Contribution

The paper presents a novel Monte Carlo algorithm capable of sampling distributions on stratifications with dynamic constraints, extending existing methods to more realistic particle interactions.

Findings

Effective sampling of stratified manifolds demonstrated in polymer physics.

Application to colloid self-assembly shows improved modeling accuracy.

Method enables volume calculations in high-dimensional spaces.

Abstract

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample probability distributions subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. More generally, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions.