We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavi...

The dynamics of the open or closed state region of an ion channel may be described by a probability density p(x,t) which satisfies a Fokker-Planck equation. The closed state dwell-time distribution fc(t) derived from the Fokker-Planck equation with a nonlinear diffusion coefficient D(x) proportional to exp(-gamma(x)), gamma>0 and a linear ramp potential Uc(x), is in good agreement with experime...

The Fokker–Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by strongly non-Gaussian noises. In particular, they yield strongly non-Gaussian anomalous diffusion which seems to be relevant in different domains of Physics....

The evolution of spherical single-mass star clusters driven by two-body relaxation was followed beyond core collapse by numerically solving the orbit-averaged Fokker-Planck equation in energy–angular momentum space. The heating effect by three-body binaries was incorporated in the Fokker-Planck models. The development of velocity anisotropy after the core collapse is discussed in detail. The an...

In this paper, we develop and analyze numerical methods for high dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a formulation of the equation as system ordinary differential (ODEs) on finite-dimensional parameter space with parameters inherited such normalizing flows. We call ODEs neural parametric equations. The fact that can be vi...