One often aims to describe the collective behaviour of an infinite number of particles by the differential equation governing the evolution of their density. The theory of hydrodynamic limits addresses this problem. In this talk, the focus will be on linking the particles with the geometry of the macroscopic evolution. Zero-range processes will be used as guiding example. The geometry of the associated hydrodynamic limit, a nonlinear diffusion equation, will be derived. Large deviations serve as a tool of scale-bridging to describe the many-particle dynamics by partial differential equations (PDEs) revealing the geometry as well. Finally, time permitting we will discuss the near-minimum structure, studying the fluctuations around the minimum state described by the deterministic PDE.
Particles and the geometry/thermodynamics of macroscopic evolution
Johannes Zimmer (Bath)
Tue, 21/03/2017 - 16:00