We consider a kinetic model for a system of two species of particles interacting through a long range repulsive potential and a reservoir at given temperature. The model is described by a set of two coupled Vlasov-Fokker-Plank equations. The important front solution, which represents the phase boundary, is a one-dimensional stationary solution on the real line with given asymptotic values at in...

We consider a kinetic model for a system of two species of particles interacting through a long range repulsive potential and a reservoir at given temperature. The model is described by a set of two coupled Vlasov-Fokker-Plank equations. The important front solution, which represents the phase transition, is a one-dimensional stationary solution on the real line with given asymptotic values at ...

We propose a stochastic model in evolutionary game theory where individuals (or subpopulations) can mutate changing their strategies randomly (but rarely) and explore the external environment. This environment affects the selective pressure by modifying the payoff arising from the interactions between strategies. We derive a Fokker-Plank integro-differential equation and provide Monte-Carlo sim...

We propose an energetic interpretation of stochastic processes described by Langevin equations with non-uniform temperature. In order to avoid Itô-Stratonovich dilemma, we start with a Kramers equation, and derive a Fokker-Plank equation by the renormalization group method. We give a proper definition of heat for the system. Based on our formulations, we analyze two examples, the Thomson effect...

Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker–Plank model, with inhomogeneous diffusion and variable mobility parameters. We develop large time asymptotic analysis such nonstandard models reformulating extending classical entropy method, under assumption periodic boundary condition. In addition, illustrative numerical tests are presented t...

We consider self-propelled particles confined between two parallel plates, moving with a constant velocity while their direction changes by rotational diffusion. The probability distribution of such micro-organisms in environment is singular because accumulate at the boundaries. This leads us to distinguish densities bulk and They satisfy degenerate Fokker–Planck system we propose boundary cond...

A system to heat electrons and possibly drive off-axis field-aligned current is under development on the Madison Symmetric Torus RFP. Staged experiments have reached an input power of 150kW at 3.6GHz and have produced a localized increase in SXR emission during rf injection. This measured emission is consistent with modeling in its location, energy spectrum and dependence on radial diffusion wi...

A systems approach model for prostate cancer in prostate duct, as a sub-system of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled Fokker-Plank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and...