Uniform-in-time estimates on the size of chaos for interacting Brownian particles
We analyze the propagation of chaos of a mean-field system of classical Brownian particles interacting via a smooth long-range potential in form of sharp, uniform-in-time estimates on many-particle correlation functions. The kinetic Langevin setting and the overdamped Brownian dynamics are covered.
Jun 2, 2024
Particle method for the numerical simulation of the path-dependent McKean-Vlasov equation
We present the particle method for simulating the solution to the path-dependent McKean-Vlasov equation.
Jun 1, 2024
Asymptotic Behavior of Degenerate Linear Kinetic Equations with Non-Isothermal Boundary Conditions
We study the degenerate linear Boltzmann equation inside a bounded domain with the Maxwell and the Cercignani-Lampis boundary conditions, two generalizations of the diffuse reflection, with variable temperature. We prove for the first time the existence of a steady state and a rate of convergence towards it without assumptions on the temperature variations.
Feb 1, 2024
Homogenization of Active Suspensions and Reduction of Effective Viscosity
We consider a suspension of active rigid particles (swimmers) in a steady Stokes flow, using for simplicity a steady-state model where particles are distributed according to a stationary ergodic random process, and we study its homogenization in the macroscopic limit. An analysis in the dilute regime shows that the activity of the particles can either increase or decrease the effective viscosity (depending on the swimming mechanism), in a way that strongly differs from the well-known effect of passive suspensions.
Mar 1, 2023