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

TL;DR

This paper introduces a subordination model for anomalous diffusion that explains two-power-law relaxation responses, providing explicit functions and equations that extend beyond traditional Havriliak-Negami models.

Contribution

It develops a novel subordination-based framework for modeling nonexponential relaxation with two power-law regimes, applicable to experimentally observed cases beyond existing models.

Findings

Derived explicit relaxation function and kinetic equation

Established a new two-power-law relaxation law

Linked the new model to Havriliak-Negami function

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.