The transport properties of Lévy walks are discussed in the framework of continuous time random walks (CTRW) with coupled memories. This type of walks may lead to anomalous diffusion where the mean squared displacement 〈r2(t)〉∼tα with α≠1. We focus on the enhanced diffusion limit,...

The concept of multifractality is applied in the analysis of molecular spectra. A scaling relationship is established between moments of the spectral intensities and the experimental resolution. The obtained scaling exponents are shown to support a non-random distribution of intensities. Using...

We investigate a model system which consists of a chain of particles that interact with two periodic potentials representing two confining plates, one of which is externally driven. The model leads to a spectrum of rich behaviors in the motion of the top driven plate: stick–slip, intermittent...

We investigate two coupled properties of Lévy stable random motions: the first passage times (FPTs) and the first passage leapovers (FPLs). While, in general, the FPT problem has been studied quite extensively, the FPL problem has hardly attracted any attention. Considering a particle that...

We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker–Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions explicitly. The CTRW curve exhibits aging, i.e., it is...

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.

The basic characteristics of molecular systems under shear are briefly reviewed and methods to control friction are proposed. These control methods allow to eliminate chaotic stick–slip motion, and modify frictional forces. The possibilities to control friction are demonstrated using a model...