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arXiv · 1111.3014

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

Aleksander Stanislavsky·Karina Weron·Justyna Trzmiel
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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.

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Aleksander Stanislavsky, Karina Weron, Justyna Trzmiel. 2011-11-13. Subordination model of anomalous diffusion leading to the two-power-law relaxation responses. https://doi.org/10.1209/0295-5075%2F91%2F40003

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