# Modelling pattern formation through differential repulsion

## TL;DR

This paper develops a two-species particle interaction model to understand cell segregation, deriving a macroscopic description from microscopic rules, and analyzing the conditions for segregation with comparisons to simulations and experiments.

## Contribution

It introduces a novel two-species interaction model for cell segregation and derives a macroscopic PDE from microscopic particle dynamics.

## Key findings

- Segregation occurs within specific parameter ranges.
- Macroscopic model aligns well with particle simulations.
- Results suggest potential links to biological experiments.

## Abstract

Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a macroscopic one and we analyze it. In particular, we determine the range of parameters for which segregation is expected. We compare our analytical results and numerical simulations of the macroscopic model to direct simulations of the particles, and comment on possible links with experiments.