Ce jeudi 19 février 2026 à 14h, le Laboratoire de Mathématique Appliqués du Havre (LMAH) accueille Léo Meyer de l’Université de Vienne, pour un exposé intitulé :
Emergent Phase Transitions in Collective Dynamics: Numerical Approximation and Band Formation
Résumé :
I will present the result of a collaboration with Pierre Degind and Sara Merino-Aceituno. We study the emergence of band patterns in the Vicsek model, a minimal agent-based model of alignment dynamics with noise. Agent-based simulations on periodic domains display coexisting ordered (high-density, aligned) bands and disordered (low-density, non-aligned) regions, a phenomenon not explained by classical parameter-driven phase transitions. We review prior kinetic and macroscopic results that identify an Emergent Phase Transition (EPT): depending on the local density ρ relative to a critical threshold ρc, different PDEs govern different spatial regions—Self-Organized Hydrodynamics (SOH) in the ordered regime (ρ > ρc) and a degenerate diffusive correction (at order ε) in the disordered regime (ρ < ρc). Building on this framework, we propose a model that couples the ordered and disordered macroscopic equations to simulate the continuum dynamics, with the goals of reproducing band formation at the macroscopic level, exploring pattern formation, and connecting the linear stability properties of the coupled model with those of SOH.
L’exposé sera retransmis en visioconférence.
Les personnes souhaitant assister à l’exposé à distance pourront se connecter via un lien. Pour l’obtenir, contacter les organisateurs.
