Scaling limit of particle systems, incompressible Navier-Stokes equation and Boltzmann equation.
Scaling of a random walk on a supercritical contact process
We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the random walk...
Second class particles in the rarefaction fan
Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system
We give a review of results on the initial value problem for the Vlasov--Poisson system, concentrating on the main ingredients in the proof of global existence of classical solutions.
Semiclassical, asymptotics and dispersive effects for Hartree-Fock systems
Shape transition under excess self-intersections for transient random walk
We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.
Simulating Kinetic Processes in Time and Space on a Lattice
We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that...
Some results for poisoning in a catalytic model.
Steady states for a fragmentation equation with size diffusion
The existence of a one-parameter family of stationary solutions to a fragmentation equation with size diffusion is established. The proof combines a fixed point argument and compactness techniques.
Stochastic dynamics macroscopically governed by the porous medium equation for isothermal flow.