Two-time scale subordination in physical processes with long-term memory

Aleksander Stanislavsky; Karina Weron

doi:10.1016/j.aop.2007.04.011

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arXiv · 1111.3192

Two-time scale subordination in physical processes with long-term memory

Aleksander Stanislavsky·Karina Weron

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Abstract

We use the two-time scale subordination in order to describe dynamical processes in continuous media with a long-term memory. Our consideration touches two physical examples in detail. First we study a temporal evolution of the species concentration for the trapping reaction in which a diffusing reactant is surrounded by a sea of randomly moving traps. The analysis is based on the random-variable formalism of anomalous diffusive processes. We find that the empirical trapping-reaction law, according to which the reactant concentration decreases in time as a product of an exponential and a stretched exponential function, can be explained by the two-time scale subordination of random processes. Another example is connected with a state equation for continuous media with memory. If the pressure and the density of a medium are subordinated in two different random processes, then the ordinary state equation becomes fractional with two time scales. This allows one to arrive at the state equation of Bagley-Torvik type.

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Aleksander Stanislavsky, Karina Weron. 2011-11-14. Two-time scale subordination in physical processes with long-term memory. https://doi.org/10.1016/j.aop.2007.04.011

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