We study the behavior of skyrmions in thin films under the action of stochastic torques arising from thermal fluctuations. We find that the Brownian motion of skyrmions is described by a stochastic Thiele’s equation and its corresponding Fokker-Planck equation. The resulting Fokker-Planck equation is recognized as the one for a high-friction Brownian particle which has been studied extensively ...

We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavytailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite variance of the rescaled transition probability de...

We establish a new and intriguing connection between the FokkerPlanck equation with gradient drift term and an associated free energy functional. Namely, we demonstrate that such a Fokker-Planck equation may be interpreted as a gradient flux, or a steepest descent, of a free energy functional with respect to a certain metric. This is accomplished through the construction of a time-discrete iter...

We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The properties of the degree distribution in the stationary state is analysed by use of the Fokker-Planck equation. For a broad range of parameters exponential degree...

Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad theory for open quantum systems. We deduce the density matrix of the damped harmonic oscillator from the solution of the Fokker-Planck equation for the coherent state representation, obtained from the master equation fo...

We extend a recently developed relation between the master equation describing the Parrondo’s games and the formalism of the Fokker–Planck equation to the case in which the games are modified with the introduction of “self–transition probabilities”. This accounts for the possibility that the capital can neither increase nor decrease during a game. Using this exact relation, we obtain expression...

We aim to derive a phenomenological approach link the theories of anomalous transport governed by fractional calculus and stochastic theory with conductivity behavior semi-empirical formalism involving Debye, Cole-Cole, Cole-Davidson, Havriliak-Negami type equations. want determine processes in amorphous semiconductors insulators developing theoretical over some mathematical instruments methods...

A new algorithm for nonconvex optimization by means of a so-called Fokker-Planck Learning Machine is proposed in this paper. This is done by considering the Fokker-Planck (FP) equation related to continuous simulated annealing, which has been proven to convergence to the global optimum under certain conditions. An approximate solution to the FP equation is sought by parametrizing the transition...

In this article we derive Fokker Planck equation for incompressible fluid and investigate its properties

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N -body diffusion processes, in the context of Kac’s propagation-of-chaos limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N → ∞ of a simple linear diffusion equation on 3N − C-dimens...