The mean-field limit for particle systems with uniform full-rank constraints

TL;DR

This paper proves the convergence, well-posedness, and stability of the mean-field limit for a particle system with full-rank constraints, inspired by skeletal muscle tissue behavior, linking microscopic and macroscopic dynamics.

Contribution

It establishes the mean-field limit and stability results for particle systems with uniform full-rank coupling, a novel approach motivated by biological tissue modeling.

Findings

Proved convergence of the particle system to the mean-field PDE.

Established well-posedness of the mean-field PDE.

Provided stability estimates for the system.

Abstract

We consider a particle system with uniform coupling between a macroscopic component and individual particles. The constraint for each particle is of full rank, which implies that each movement of the macroscopic component leads to a movement of all particles and vice versa. Skeletal muscle tissues share a similar property which motivates this work. We prove convergence of the mean-field limit, well-posedness and a stability estimate for the mean-field PDE.