A Simulation Algorithm for Brownian Dynamics on Complex Curved Surfaces

TL;DR

This paper introduces a novel simulation algorithm for modeling Brownian dynamics of colloidal particles on complex, non-trivially curved surfaces using triangle mesh approximations, enabling studies on diverse geometries.

Contribution

The work develops a new algorithm that simulates particle dynamics on complex surfaces by combining global force calculations with local position updates, applicable to highly intricate geometries.

Findings

Accurately captures diffusion and transport on complex surfaces.

Successfully simulates particles on torus and knot geometries.

Reveals effects of curvature and topology on particle behavior.

Abstract

Brownian dynamics of colloidal particles on complex surfaces has found important applications in diverse physical, chemical and biological processes. However, current Brownian dynamics simulation algorithms mostly work for relatively simple surfaces that can be analytically parameterized. In this work, we develop an algorithm to enable Brownian dynamics simulation on extremely complex surfaces. We approximate complex surfaces with triangle mesh surfaces and employ a novel scheme to perform particle simulation on these triangle mesh surfaces. Our algorithm computes forces and velocities of particles in global coordinates but updates their positions in local coordinates, which benefits from the advantages of simulation schemes in both global and local coordinate alone. We benchmark the proposed algorithm with theory and then simulate Brownian dynamics of both single and multiple particles on torus and knot surfaces. The results show that our method captures well diffusion, transport, and crystallization of colloidal particles on complex surfaces with non-trivial topology. This study offers an efficient strategy for elucidating the impact of curvature, geometry, and topology on particle dynamics and microstructure formation in complex environments.