Sandpile model for a toy-model of fluid flow – Yvan Le Borgne (Université de Bordeaux)
martedì 18 mar 2025 1:30 PM — 2:30 PM Saletta Riunioni Seminars, Seminar on Combinatorics, Lie Theory, and Topology
Sandpile model, also called chip-firing game, is a fully discrete diffusion model of grains between the vertices of a graph. On highly symmetric graphs, like complete or bipartite complete graphs, it has links with quantities in symmetric functions studied for example in Pisa by Michele D'Adderio and Alessandro Iraci. This talk will focus instead on the also well-studied (sub-)grids of the square lattice. We propose and analyse a toy-model for a two-dimensional flow of grains perturbated by an obstacle on a bi-infinite canal. Structures of sandpile model allow precise solutions to classical questions in computational fluid dynamics. In particular we obtain the definition of exact algorithmic boundary conditions on a finite rectangular domain. Moreover in the simplest case, we have a detailed description of the convergence along the simulation from the initial random state to a steady random state.