The anisotropic sub-diffusion random walks on multi-dimensional comb structure model have been studied in the continuum approximation. The problem is that in the considered model mean square displacements on different directions have different power temporal dependencies. So this case...

We propose and study an analytic model for growing interfaces in the presence of Brownian diffusion and hopping transport. The model is based on a continuum formulation of mass conservation at the interface, including reactions. The Burgers-KPZ equation for the rate of elevation change emerges...

The fractional Fokker–Planck equation, were used to describe the anomalous diffusion in external fields, is derived using a comb-like structure as a background model. For the force-free case, the distribution function associated with space dependence diffusion coefficient along the backbone of...

Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation–dissipation theorem (FDT). This hierarchy means that ergodicity...

Einstein's theory of Brownian motion is revisited in order to formulate a generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement distribution are relaxed, the fractional derivative naturally...

We analyze an anisotropic fractional diffusion equation that extends some known diffusion equations by considering a diffusion coefficient with spatial and time dependence, the presence of external forces and time fractional derivatives. We obtain new exact classes of solutions for a linear...

Exact time-dependent solutions representing generalized one-dimensional Ornstein–Uhlenbeck processes are derived from nonlinear Fokker–Planck equations and the corresponding diffusion processes are studied. The corresponding systems are related to the Renyi entropy and entropies proposed by...

We present evidence of the existence of a superdiffusive regime in systems with correlated disorder for which localization is suppressed. An expression for anomalous electrical conductivity at low frequencies is found by using a generalized Langevin equation whose memory function accounts for...

This manuscript uses a statistical-mechanical approach to study the effect of the adhesion, caused by the modifier of cell adhesion (MOCA) protein on cell locomotion. The MOCA protein regulates cell–cell adhesion, and we explore its potential role in cell movement. We present a series of...