Stochastic dynamics o f a soliton in a long optical fiber is analysed within the framework of the nonlinear Schr6dinger equation. It is shown that in the case of periodic perturbations describing, e.g. sound propagation along a fiber, adiabatic dynamics of a soliton may be stochastic, and the condition for this stochastic motion is obtained. In the case of random perturbations we obtain the sol...

The focus of this paper is a convergence study of the frequency sensitive competitive learning (FSCL) algorithm. We approximate the final phase of FSCL learning by a diffusion process described by the Fokker-Plank equation. Sufficient and necessary conditions are presented for the convergence of the diffusion process to a local equilibrium. The analysis parallels that by Ritter-Schulten (1988) ...

We present suucient and necessary conditions for the convergence of Frequency Sensitive Competitive Learning (FSCL) algorithm to a local equilibrium. The nal phase of the FSCL convergence is analyzed by describing the process with a Fokker-Plank equation. The analysis parallels that by Ritter and Schulten for the KSFM algorithm. We show that the convergence conditions involve only the learning ...

Abstract The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, dynamics is ubiquitous because thermal fluctuations. Fokker–Plank–Smoluchowski equation models time evolution probability density selected degrees freedom in diffusive regime it is, therefore, a workhorse chemistry. In this paper we report on development implementation variational quan...

During rf heating on minority ions and current drive the velocity distribution is determined by the balance between the wave-particle interaction and the relaxation through Coulomb collision. This is simulated by the Monte Carlo code fido [1–3], which solves the Fokker-Planck equation in the low collisionality banana-transport regime, including finite orbit width and rf induced transport. The f...

A class of nonlinear Fokker–Planck equations with nonlocal interactions may include many important cases, such as porous medium external potentials and aggregation–diffusion models. The trajectory equation the Fokker–Plank can be derived based on an energetic variational approach. structure‐preserving numerical scheme that is mass conservative, energy stable, uniquely solvable, positivity prese...

Viscoelasticity and variable mass are common phenomena in Micro-Electro-Mechanical Systems (MEMS), could be described by a fractional derivative damping stochastic process, respectively. To study the dynamic influence cased viscoelasticity mass, stationary response of kind nonlinear systems with variable-mass derivative, is investigated this paper. Firstly, an approximately equivalent system st...

Barrier crossing calculations in chemical reaction-rate theory typically assume that the barrier is large compared to temperature. When vanishes, however, there a qualitative change behavior. Instead of barrier, particles slide down sloping potential. We formulate renormalization group description this noisy saddle-node transition. derive universal scaling behavior and corrections for mean esca...

Abstract In this review paper, we recall, in a unifying manner, our recent results concerning the Lie symmetries of nonlinear Fokker-Plank equations, associated to (weighted) Tsallis and Kaniadakis entropies. The special values parameters, highlighted by classification these symmetries, clearly indicate algebraic geometric invariants which differentiate algebras involved. We compare with ones p...