Séminaire de Probabilités commun ICJ/UMPA

Jamming pair of general run-and-tumble particles: Exact results and universality classesA venir

par Manon Michel (Université Clermont Ferrand)

Europe/Paris
Bâtiment Braconnier, salle Fokko du Cloux (Université Lyon 1)

Bâtiment Braconnier, salle Fokko du Cloux

Université Lyon 1

Description

Run-and-tumble particles (RTP) are a paradigmatic active matter model, typically modelling the evolution of bacteria. I will present how, by directly modelling the system of two RTP on a torus at the continuous-space and -time level thanks to piecewise deterministic Markov processes (PDMP), we can derive the conservation conditions which sets the invariant distribution and explicitly construct two universality classes for the steady state, the detailed-jamming and the global-jamming classes. They respectively identify with the preservation or not of a detailed symmetry at the level of the dynamical internal states between probability flows entering and exiting jamming configurations. I will further discuss how a spectral analysis of the tumble kernel gives explicit expressions for the invariant measure in the general case. Interestingly, the invariant measure follows, away from jamming configurations, a catenary-like constraint, which results from the interplay between probability conservation and the dynamical skewness introduced by the jamming interactions. This work shows the powerful analytical approach PDMP provide for the study of the stationary behaviors of RTP sytems and motivates their future applications to larger systems, with the goal to derive microscopic conditions for motility-induced phase transitions.