Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-11-14
Annals of Physics 323, 643(2008)
Physics
Condensed Matter
Statistical Mechanics
15 pages
Scientific paper
10.1016/j.aop.2007.04.011
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.
Stanislavsky Aleksander
Weron Karina
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