Small-scale models in the form of random walks, combining Gaussian jumps, advection by mean flow field and possibly very long sorbing durations, correspond to experimental data in many porous media, in the laboratory and in the field. Within this frame-work, solutes are observed in two phases,...

We investigate the influence of a weak uniform bias on chaotic diffusion generated by iterated one-dimensional maps which, in the absence of the bias, lead to subdiffusion.

Many authors have documented that it is challenging to explain exchange rate fluctuations with macroeconomic fundamentals: a random walk forecasts future exchange rates better than existing macroeconomic models. This paper applies newly developed tests for nested model that are robust to the...

We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact renormalization group calculations that there is a dynamical...

Graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications. In addition, exponential growth of real-world graphs such as social networks, biological networks and electrical circuits demands clustering algorithms with...

The relation between diffusion and conductivity is established for a case of diffusing particle moved by means of Levy hops. It is shown that due to an unusual character of the Levy flight a particle velocity depends on electrical field in nonlinear way in arbitrary weak fields. A nonlinear...

We present a variety of models of random walk, discrete in space and time, suitable for simulating random variables whose probability density obeys a space–time fractional diffusion equation.

We report some experimental results for quasi-two-dimensional electrocrystallization of copper under magnetic fields. Such results are theoretically investigated by large scale simulations of a DLA-like model in which random walkers can move along circular vortices enhanced by the Lorentz force....

In the framework of the one-dimensional fractal time random walk (FTRW) relaxation model, we rigorously show that the frequency domain response takes, in both nonbiased and biased walks, the only possible Cole-Cole form. The underlying reason for this is the specific form of the relaxation...

Empirical data for stock and stock-indexes returns that is available for international markets as well as for the Russian stock market is introduced and discussed. Random walk process with a specific law of an elementary independent increment (jump) in some random walk space is proposed for a...