2022/05/20 by Ferdinando Auricchio, Giuseppe Toscani, Auricchio, Ferdinando +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #FOS: Physical sciences #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2205.09996
openalex publication_date 2022/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper we study a novel Fokker-Planck-type model that is designed to mimic manufacturing processes through the dynamics characterizing a large set of agents. In particular, we describe a many-agent system interacting with a target domain in such a way that each agent/particle is attracted by the center of mass of the target domain with the aim to uniformly cover this zone. To this end, we first introduce a mean-field model with discontinuous flux whose large time behavior is such that the steady state is globally continuous and uniform over a connected portion of the domain. We prove that a diffusion coefficient that guarantees that a given portion of mass enters in the target domain exists and that it is unique. Furthermore, convergence to equilibrium in 1D is provided through a reformulation of the initial problem involving a nonconstant diffusion function. The extension to 2D is explored numerically by means of recently introduced structure preserving methods for Fokker-Planck equations.