Analysis of macroscopic phenomena in many-particle systems

par Dr Marina Ferreira

mardi 18 avr. 2023, 14:00 → 15:00 Europe/Paris

 

Macroscopic population-level behaviour may be observed in large systems of interacting particles. These phenomena are not encoded in the individual particles, but they emerge when the number of particles is large enough. How do these phenomena emerge? Motivated by concrete applications in physics and biology, this question is discussed in the cases of (1) systems of coalescing particles, and (2) dense hard-particle systems.

Coalescing particle systems are studied at the mesoscopic scale using Smoluchowski coagulation-type equations. Longtime behaviour and emergence of patterns in multicomponent systems are obtained by means of fixed-point arguments and measure theorical tools.

On the other hand, hard-particle systems are studied at the microscopic scale. Algorithms based on non-convex optimization and modelling tools for packed systems, combined with in vivo laboratory experiments, indicate how shape and growth of a pseudostratified epithelial tissue emerge from the dynamics of individual cells.