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

We describe dynamical processes in continuous media with a long-term memory. Our consideration is based on a stochastic subordination idea and concerns two physical examples in detail. First we study a temporal evolution of the species concentration in a trapping reaction in which a diffusing reacta...

Full description

Saved in:
Bibliographic Details
Published in:Annals of physics 2008-03, Vol.323 (3), p.643-653
Main Authors: Stanislavsky, Aleksander, Weron, Karina
Format: Article
Language:English
Subjects:
02.50.Ey
02.50.−r
82.40.−g
Anomalous diffusion
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Continuous medium with memory
DIFFUSION
EQUATIONS
EVOLUTION
FUNCTIONS
Mathematics
Memory
Nonexponential relaxation
Physics
RANDOMNESS
RELAXATION
Stochastic models
STOCHASTIC PROCESSES
Subordination
Time
TRAPPING
Trapping reaction
TRAPS
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We describe dynamical processes in continuous media with a long-term memory. Our consideration is based on a stochastic subordination idea and concerns two physical examples in detail. First we study a temporal evolution of the species concentration in a trapping reaction in which a diffusing reactant is surrounded by a sea of randomly moving traps. The analysis uses 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 a 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 Bagley–Torvik type of state equation.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2007.04.011