Related papers: Fractional advection-diffusion-asymmetry equation
Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…
We derive backward and forward fractional Schr\"odinger type of equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and…
Anomalous diffusion constitutes a relation between tracer flux and tracer density gradient that is inherently nonlocal in space and/or time. Previous studies emphasize the non-Gaussian character of the tracer distribution that arises from…
Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle number conservation and locality, in systems with sufficient damping. In this paper we consider diffusive processes in the bulk of Weyl semimetals, which are exotic…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
The foundations of the fractional diffusion equation are investigated based on coupled and decoupled continuous time random walks (CTRW). For this aim we find an exact solution of the decoupled CTRW, in terms of an infinite sum of stable…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the…
Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated…
A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with arbitrary-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the…
Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…
This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
We consider the limit of a linear kinetic equation, with reflection-transmission-absorption at an interface, with a degenerate scattering kernel. The equation arise from a microscopic chain of oscillators in contact with a heat bath. In the…
From Liouville's equation, a phase-space multi-scale transport equation is systematically derived. The proposed phase-space multi-scale transport equation based on the first principle indicates that the nonlinear stochastic transport is due…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…
We study anomalous transport arising in disordered one-dimensional spin chains, specifically focusing on the subdiffusive transport typically found in a phase preceding the many-body localization transition. Different types of transport can…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…