Dynamics of Noise-Driven Inelastic Particle Systems

Description

We will investigate the problem of noise-driven particles that experience dissipativecollisions with other particles and boundaries. Even in the absence of noise, such systemscan exhibit extremely rich dynamics including highly degenerate bifurcation structuresand non-uniqueness of solutions. We will formulate a general framework that allows usto study the dynamics in a number of canonical regimes. This will allow us to studysystems in which the particles are attached to springs and experience body forces.Moreover, during collisions with boundaries particles experience energy input that caneither be deterministic or random. For technical reasons explained in the proposal, wewill study these systems by using an ultra-weak formulation involving the dual Fokker-Planck equation. This system presents a number of challenges, because it containscomplicated non-local boundary conditions. Nevertheless, by considering sets of localproblems we will develop methods that can determine a number of theoretical propertiesof the problem. This approach will also allow us to develop a particularly efficientnumerical method for obtaining the solution. Using these ideas we will analyze particlessystems and pay particular attention to determine how noise affects systems with highlydegenerate dynamics.