Box ball systems and hard rods

by Prof. Pablo A. Ferrari (Universidad de Buenos Aires)

Monday 4 Apr 2022, 09:00 → Tuesday 12 Apr 2022, 11:00 Europe/Rome

Abstract

I will discuss two cellular automata. The box ball system is a transport cellular automaton which present soliton behavior. The system of hard rods consists on billiard balls travelling ballistically and interchanging speeds at collisions and some variants. I will discuss invariant measures and generalized hydrodynamics. The course will be based on work in progress and the papers listed below. 

C. Boldrighini, R. L. Dobrushin, and Yu. M. Sukhov,
One-dimensional hard rod caricature of hydrodynamics,
J. Stat. Phys. 31 (1983), no. 3, 577–616.

C. Boldrighini and Yu. M. Suhov,
One-dimensional hard-rod caricature of hydro-dynamics:
“Navier-Stokes correction” for local equilibrium initial states,
Comm. Math. Phys. 189 (1997), no. 2, 577–590.

David A. Croydon and Makiko Sasada,
Generalized hydrodynamic limit for the box-ball system,
Comm. Math. Phys. 383 (2021), no. 1, 427–463.

Pablo A. Ferrari, Chi Nguyen, Leonardo T. Rolla, and Minmin Wang,
Soliton decomposition of the box-ball system,
Forum Math. Sigma 9 (2021), no. e60, 37. 

 

The time schedule of the course may be found at the following webpage.