Mesoscale Models and Many-Body Systems - IPAM at UCLA

Explore a 27-minute lecture on mesoscale models and many-body systems presented by Robert Batterman from the University of Pittsburgh at IPAM's Mathematics of Collective Intelligence Workshop. Delve into the fascinating world of scale-dependent behaviors in many-body systems, examining how continuum equations like Navier-Stokes effectively model fluid behavior at larger scales while failing at molecular and atomic levels. Investigate the concept of relative autonomy in continuum equations and the crucial role of mesoscale structures in explaining this phenomenon. Discover connections between homogenization theory, renormalization group arguments, and the coding of mesoscale structures in continuum model parameters. Gain insights into the potential applications of mesoscale structures in understanding learning processes in deep neural networks. The lecture covers key topics such as motivation, two approaches, materials, volume averaging, stress-strain relations, two-phase random medium, and non-equilibrium systems.

Motivation
Two approaches
Materials
Volume averaging
Stress strain relations
Twophase random medium
Nonequilibrium systems