Title
Formation of clusters and coarsening in locally attractive interacting particle systems
Abstract
How do weakly interacting diffusions on the one-dimensional torus behave under finite-range attractive interactions? In this talk, we explore different effects, such as cluster formation, and how multi-cluster states coarsen into single-cluster states. Depending on the parameter regime, this coarsening can occur through two competing mechanisms: 1. Coalescence, where clusters move and merge like coalescing Brownian motions. 2. Mass exchange: Individual particles detach from one cluster and attach to other clusters, enabling mass transfer between clusters. Based on a version of the Eyring-Kramers law, we introduce a joint model to describe these effects and argue that the corresponding deterministic mean-field PDE exhibits dynamical metastability through the mass exchange.
Moreover, we introduce a new variant of the strict Riesz rearrangement to characterize the global minimizers of the free energy, showing that they are either uniform or single-cluster states, i.e., symmetrically decreasing.
Joint work with R. Gvalani, M. Hairer, G. Pavliotis, and A. Schlichting.
Please note that the seminar will take place in person in room 140 of Huxley Building.