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Understanding how the release of stored magnetic energy contributes to the generation of non-thermal high energy particles during solar flares is an important open problem in solar physics. Magnetic reconnection plays a fundamental role in…
A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably…
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For…
When particles are magnetized, a diffusion process is influenced by the ambient magnetic field. While the entropy increases, the constancy of the magnetic moment puts a constraint. Here, we compare the E-cross-B diffusion caused by random…
We study the Fokker-Planck diffusion equation with diffusion coefficient depending periodically on the space variable. Inside a periodic array of inclusions the diffusion coefficient is reduced by a factor called the diffusion magnitude. We…
Scattering rates for a Goldreich-Sridhar (GS) spectrum of anisotropic, incompressible, magnetohydrodynamic turbulence are calculated in the quasilinear approximation. Because the small-scale fluctuations are constrained to have wave vectors…
We calculate the short time and the long time diffusion coefficient of a spherical tracer particle in a polymer solution in the low density limit by solving the Smoluchowski equation for a two-particle system and applying a generalized…
The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to It\^o diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the…
Finite-size scaling arguments naturally lead us to introduce a coordinate-dependent diffusion coefficient in a Fokker-Planck description of the late stage dynamics of unbiased polymer translocation through a membrane pore. The solution for…
In this study, we generalize the Fokker-Planck equation to two-dimensional cases, including potential functions with periodic boundary conditions and piecewise-defined structures, to analyze the probability distribution in multi-field…
Pre-asymptotic transport of a scalar quantity passively advected by a velocity field formed by a large-scale component superimposed to a small-scale fluctuation is investigated both analytically and by means of numerical simulations.…
We investigate the mean electromotive force in the kinematic framework, that is, ignoring the back-reaction of the magnetic field on the fluid velocity, under the assumption of axisymmetric turbulence determined by the presence of either…
For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose…
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an…
A new Fokker-Planck equation is developed for treating resonance line scattering, especially relevant to the treatment of Lyman alpha in the early universe. It is a "corrected" form of the equation of Rybicki & Dell'Antonio that now obeys…
Diffusion in inhomogeneous materials can be described by both the Fick and Fokker--Planck diffusion equations. Here, we study a mixed Fick and Fokker-Planck diffusion problem with coefficients rapidly oscillating both in space and time. We…
We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T.…
We revisit the Fokker-Planck based theory of driven polymer translocation through a narrow nanopore. A bead-spring model of a uniformly charged polyelectrolyte chain translocating through a semi-implicit model of a nanopore embedded in a…
A theoretical analysis of active motion on curved surfaces is presented in terms of a generalization of the Telegrapher's equation. Such generalized equation is explicitly derived as the polar approximation of the hierarchy of equations…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…