Nonergodic subdiffusion from Brownian motion in an inhomogeneous medium.

Scaled Brownian motion as a mean-field model for continuous-time random walks.

We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient D(t)=αD0tα-1 (Batchelor's equation) which, for α<1, is often used for fitting experimental data for subdiffusion of unclear genesis. We show that this process is a close relative of subdiffusive continuous-time random walks and describes the motion of...

Diffusion in Inhomogeneous Systems

Single-particle diffusion, also known as Brownian motion, is the random motion of a particle in space due to collisions with its surrounding medium. The theory of diffusion in a homogeneous medium, one with a constant diffusion coefficient, is well established and recognized. The theoretical basis of diffusion in heterogeneous environments, where the diffusion coefficient varies in space, is fa...

Effects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium

This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...

Fractional Brownian motion in presence of two fixed adsorbing boundaries

Abstract. We study the long-time asymptotics of the probability Pt that the Riemann-Liouville fractional Brownian motion with Hurst index H does not escape from a fixed interval [−L, L] up to time t. We show that for any H ∈]0, 1], for both subdiffusion and superdiffusion regimes, this probability obeys ln(Pt) ∼ −t2H/L2, i.e. may decay slower than exponential (subdiffusion) or faster than expon...

Parameter estimation for nonergodic Ornstein-Uhlenbeck process driven by the weighted fractional Brownian motion