Objective
1. Einstein relation for a tracer particle in simple exclusion processes: Einstein relation relates the mobility of a charged particle in the presence of an external field to its self-diffusion coefficient. In my Ph.D. thesis I prove that such a relation is valid for a tracer particle in symmetric simple exclusion processes in 3 or more dimensions. We would like to investigate its validity in dimensions 1 and 2, as well as in mean zero asymmetric simple exclusion processes.
2. The motion of a tracer particle in simple exclusion with reflecting boundary : The diffusively rescaled position of a tracer particle in simple exclusion converges to a Brownian motion. When the translation invariance symmetry is broken the question remains open . It is expected that when we consider a symmetric simple exclusion process on the positive integers with reflecting boundary at zero the position of the particle will converge to a reflected Brownian motion. This is a question we would like to investigate.
3. Asymptotic density in a coalescing driven system: Consider a particle system which consists of particles of two types, say A and B. Particles A (ambient gas molecules) perform simple exclusion and they swap places with particles B (aerosol particles), which also coagulate at a certain rate when they come close. We are interested in the asymptotic behavior in time of the density of particles B.
Topic(s)
Data not availableCall for proposal
Data not availableFunding Scheme
RGI - Research grants (individual fellowships)Coordinator
CB3 0WB CAMBRIDGE
United Kingdom