Stochastic and Coarse-Grained Two-Dimensional Modeling of Directional Particle Movement

TL;DR

This paper develops a stochastic microscopic model for directional particle movement in 2D, derives a macroscopic conservation law system, and validates it through numerical simulations, including second-order corrections.

Contribution

It introduces a new stochastic microscopic model and derives a corresponding analytically-tractable macroscopic system for 2D particle movement.

Findings

Good agreement between microscopic and macroscopic models

Microscopic model exhibits slightly more diffusion

Second-order corrections improve model accuracy

Abstract

We study the evolution of interacting groups of agents in two-dimensional geometries. We introduce a microscopic stochastic model that includes floor fields modeling the global flow of individual groups as well as local interaction rules. From this microscopic model we derive an analytically-tractable system of conservation laws that governs the evolution of the macroscopic densities. Numerical simulations show good agreement between the system of conservation laws and the microscopic model, though the latter is slightly more diffusive. We conclude by deriving second-order corrections to the system of conservation laws.