Modelling pattern formation through differential repulsion

Julien Barre (1) , Pierre Degond (2) , Diane Peurichard (3) , Ewelina Zatorska (4)

1 IDP - Institut Denis Poisson
2 Department of Mathematics [Imperial College London]
3 MAMBA - Modelling and Analysis for Medical and Biological Applications
4 UCL London - Department of Mathematics

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.

Domaines: Mathématiques [math]

Julien Barre, Pierre Degond, Diane Peurichard, Ewelina Zatorska. Modelling pattern formation through differential repulsion. Networks and Heterogeneous Media, 2020, 15 (3), pp.307-352. ⟨10.3934/nhm.2020021⟩. ⟨hal-02499520⟩