We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes...

Unified model equations hidden in microstructure evolution are discovered in this paper. The governing equations in Lifshitz–Slyozov–Wagner theory, and diffusion screening theory are derived with some approximations from the unified model equations. The governing equations in multiparticle...

In this paper, from the unifying viewpoint we will cover our recent work on the nonequilibrium statistical description of anomalous diffusion and application of this theory to explaining late experiment. We will study the motion of a particle under the influence of a random force modeled as...

We investigate the diffusion motion of a Brownian particle which is acted upon by both a friction force with memory effect and a noise. The noise is expressed as f(X,t) ~ X-0̄F(t), σ 0, where X and t are the displacement and time, respectively, and F(t) has the long-time correlation effect...

A particle diffusing in a disordered medium with a Gaussian distribution of potential well depths is studied. The transition rates are related to the random potentials in the well-known Arrhenius form. A log-normal distribution of transition rates is naturally established. Finally, we show that...