Related papers: Similarity transformations approach for a generali…
The object of this paper is the uniqueness for a $d$-dimensional Fokker-Planck type equation with non-homogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic…
We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain…
We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…
In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
We analyse a generalised Fokker-Planck equation by making essential use of its linearisability through a Cole-Hopf transformation. We determine solutions of travelling wave and multi-kink type by resorting to a geometric construction in the…
The solutions of the radiative transfer equation, known for the energy density, do not satisfy the fundamental transitivity property for Green's functions expressed by Chapman-Kolmogorov's relation. I show that this property is retrieved by…
This work studies exact solvability of a class of fractional reaction-diffusion equation with the Riemann-Liouville fractional derivatives on the half-line in terms of the similarity solutions. We derived the conditions for the equation to…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
I report a study of the nonstationary one-dimensional Fokker-Planck solutions by means of the strictly isospectral method of supesymmetric quantum mechanics. The main conclusion is that this technique can lead to a space-dependent…
We propose a prescription based on the Fokker-Planck equation in the Stratonovich approach, with the diffusion coefficient dependent on temporal and spatial coordinates, for describing heat conduction by phonons in small structures. This…
We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional…
We study the general solution of the Fokker-Planck equation in d dimensions with arbitrary space and time dependent diffusion matrix and drift term. We show how to construct the solution, for arbitrary initial distributions, as an…
We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…
We present a simple and systematic procedure to determine the effective dynamics of a Brownian particle coupled to a rapidly fluctuating correlated medium, modeled as a scalar Gaussian field, under spatial confinement. The method allows us,…
The aim of this paper is to rewrite the Fokker - Planck equation according to transformation of space coordinates. This is nontrivial problem, because transformation of space coordinates induces transformation of velocities. We can use…
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…
We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit…
The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph…
The interaction of charged particles, moving in a uniform magnetic field, with a plane-polarized gravitational wave is considered using the Fokker-Planck- Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact…