Area and perimeter covered by anomalous diffusion processes

Anomalous and Apparently Anomalous Diffusion in the Area of Neurophysiology

1. Introduction In the central nervous system information is transmitted from neuron to neuron due to functional contacts, or synapses, where a chemical intermediary, or neurotransmitter, releases following electrical signals in presynaptic cells; its binding to surface receptors triggers an influx of ions into the postsynaptic cells causing the shift of membrane potential away from the resting...

Anomalous Diffusion, Stable Processes, and Generalised Functions

Anomalous diffusion, stable processes, and generalized functions.

The evolution equations in real space and time corresponding to a class of anomalous diffusion processes are examined. As special cases, evolution equations corresponding to stable processes are derived using the theory of generalized functions, recovering some known results differently interpreted, and an evolution law for stable processes of order unity.

Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes

Andrey G. Cherstvy, Aleksei V. Chechkin, 3 and Ralf Metzler 4 Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany Department of Physics, Tampere Univ...

Hitting probability for anomalous diffusion processes.

We present the universal features of the hitting probability Q(x,L), the probability that a generic stochastic process starting at x and evolving in a box [0, L] hits the upper boundary L before hitting the lower boundary at 0. For a generic self-affine process, we show that Q(x,L)=Q(z=x/L) has a scaling Q(z) approximately z;{phi} as z-->0, where phi=theta/H, H, and theta being the Hurst and pe...