Nearly constant loss - the 2nd universality of AC conductivity by scaling down subsequent random walk steps by 1/t^(1/2)

Abstract

In the frequency domain, the nearly constant loss, is characterized by a slope 1 in log of the real part of the electrical conductivity vs log frequency plots. It can be explained by an anomalous diffusion, defined by a random walk with the mean square displacement proportional to the logarithm of time, rather than being linearly proportional to time, as in normal diffusion. The present work suggests a random walk algorithm that leads to anomalous, logarithmic time dependence. That has been accomplished by scaling down the subsequent random walk displacements by a factor, 1/t^(1/2)