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

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.

15 pages

References in corpus (3)

• Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
• Fractional dynamics from the ordinary Langevin equation
• Trapping reactions with subdiffusive traps and particles

Cited by in corpus (6)

• Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes
• Fractional Brownian motion time-changed by gamma and inverse gamma process
• Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations
• Bivariate Tempered Space-Fractional Poisson Process and Shock Models
• Mixtures of Tempered Stable Subordinators
• Time-changed Poisson processes of order $k$