Related papers: Anomalous diffusion and anisotropic nonlinear Fokk…
Active particles (i.e., self-propelled particles or called microswimmers), different from passive Brownian particles, possess more complicated translational and angular dynamics, which can generate a series of anomalous transport phenomena.…
Using exact expressions for the persistence probability and for the leading eigenvalue of the Focker-Planck operator of a random walk in a random environment we establish a fundamental relation between the statistical properties of…
The nonequilibrium Fokker-Planck dynamics with a non-conservative drift field, in dimension $N\geq 2$, can be related with the non-Hermitian quantum mechanics in a real scalar potential $V$ and in a purely imaginary vector potential -$iA$…
The nonlinear coefficients defining the mean electromotive force (i.e., the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, the nonlinear kappa-tensor, etc.) are calculated for an anisotropic turbulence. A…
A theoretical framework is developed for the phenomenon of non-Gaussian normal diffusion that has experimentally been observed in several heterogeneous systems. From the Fokker-Planck equation with the dynamical structure with largely…
Turbulent transport near the X-point of a large tokamak is examined using local, gradient-driven simulations that determine the saturated plasma profiles. The distribution of a representative set of particle tracers evolving within these…
I present a case where there is an exact re-interpretation for the third order derivative term in a Fokker-Planck equation, purely in terms of ordinary drift and diffusion.
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global well-posedness result with instantaneous smoothness effect,…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
We show that anomalous diffusion arises in two different models for the motion of randomly forced and weakly damped particles: one is a generalisation of the Ornstein-Uhlenbeck process with a random force which depends on position as well…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
We consider a Langevin equation with variable drift and diffusion coefficients separable in time and space and its corresponding Fokker-Planck equation in the Stratonovich approach. From this Fokker-Planck equation we obtain a class of…
We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of…
We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic…
The typical transverse momentum $Q_s(t)$ (or "saturation" momentum) acquired by a hard particle propagating through a $\mathcal{N}=4$ SYM plasma increases over time like $t^\gamma$, with an anomalous exponent $\gamma>1/2$ characteristic of…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a unified treatment of the available literature along with some…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the L\'evy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary…