The motion of two magnetic holes in a rotating magnetic field is studied both experimentally and numerically. The transport in the azimuthal direction is anomalous and is shown to be well modelled by a fractal time random walk for which the probability distribution of waiting times τ follows a...

The Zaller theory of opinion formation is reformulated with one free parameter μ, which measures the largest possible ideological distance which can be made by a citizen in one mental step. Our numerical results show the transient effects: (i) the political awareness, measured by the number of...

Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating...

In the last decade the subordinated processes have become popular and have found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called arithmetic Brownian motion). The first one, so called...

It is well known that Brownian diffusion is characterized by a mean-squared displacement which varies linearly in time, 〈r2〉∼t and that anomalous diffusion, by a mean-square displacement which is nonlinear in time, 〈r2〉∼tα. It is generally accepted that fractional diffusion, which...

We empirically quantify the relation between trading activity—measured by the number of transactions N—and the price change G(t) for a given stock, over a time interval [t,t+Δt]. We relate the time-dependent standard deviation of price changes—volatility—to two microscopic quantities:...

We study the center of mass motion of single endodermal Hydra cells in two kinds of cellular aggregates: endodermal and ectodermal. The mean square displacement displays anomalous super-diffusion with 〈x2〉∼tα where α1. The velocity distribution function is non-Gaussian and fits well the...

Lévy processes have been widely used to model a large variety of stochastic processes under anomalous diffusion. In this note we show that Lévy processes play an important role in the study of the Generalized Langevin Equation (GLE). The solution to the GLE is proposed using stochastic...

Porous materials such as sedimentary rocks often show a fractal character at certain length scales. Deterministic fractal generators, iterated upto several stages and then repeated periodically, provide a realistic model for such systems. On the fractal, diffusion is anomalous, and obeys the law...

We investigate the solutions of a generalized diffusion equation which extends some known equations such as the fractional diffusion equation and the porous medium equation. We start our study by considering the linear case and the nonlinear case afterward. The linear case is analyzed taking...