Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

¹ Institute of Radio Astronomy - 4 Chervonopraporna St., 61002 Kharkov, Ukraine
² Institute of Physics, Wrocław University of Technology - Wyb. Wyspiańkiego 27, 50-370 Wrocław, Poland, EU

^a astex@ukr.net

Received: 24 May 2010
Accepted: 5 August 2010

Abstract

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently. Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.