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We derive a relativistically covariant (although not manifestly so) equation for the distribution function of particles accelerated at shocks, which applies also to extremely relativistic shocks, and arbitrarily anisotropic particle…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
Fundamental solution of Fokker - Planck equation is built by means of the Fourier transform method. The result is checked by direct calculation. Changes: missed factor in (29), (30), corrected (31), (35), removed former (36), added…
The covariant form of the multivariable diffusion-drift process is described by the covariant Fokker--Planck equation using the standard toolbox of Riemann geometry. The covariant form of the equivalent Langevin stochastic differential…
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker--Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation…
A generalized Fokker-Planck equation is derived to describe particle kinetics in specific situations when the probability transition function (PTF) has a long tail in momentum space. The equation is valid for an arbitrary value of the…
The general covariant Fokker-Planck equations associated with the two different versions of covariant Langevin equation in Part I of this series of work are derived, both lead to the same reduced Fokker-Planck equation for the…
A spectral solution method is proposed to solve a previuously developed non-equilibrium statistical model describing partial thermalization of produced charged hadrons in relativistic heavy-ion collisions, thus improving the accuracy of the…
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…
A relation between Fick-Jacobs and Schr\"{o}dinger equation is shown. When the diffusion coefficient is constant, exact solutions for Fick-Jacobs equation are obtained. Using a change of variable the general case is studied.
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…
We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…
In this work, we propose adaptive deep learning approaches based on normalizing flows for solving fractional Fokker-Planck equations (FPEs). The solution of a FPE is a probability density function (PDF). Traditional mesh-based methods are…
We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the…
We introduce a generalization of Obukhov's model [A.M. Obukhov, Adv. Geophys. 6, 113 (1959)] for the description of the joint position-velocity statistics of a single fluid particle in fully developed turbulence. In the presented model the…
This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has interesting scaling properties, which result in a…
This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper…
We investigate a family of generalized Fokker-Planck equations that contains Richardson and porous media equations as members. Considering a confining drift term that is related to an effective potential, we show that each equation of this…
Employing time-dependent projection formalism, a Fokker-Planck equation with non-Markovian transport coefficients is derived for large amplitude collective motion. Properties of transport coefficients for diffusion processes in a potential…
The equilibrium-dispersive model of the linear GC (gas chromatography) was derived using both assumptions and the method of its derivation different from the known in literature. It was concluded that this model is a specific case of the…