Diffusion and relaxation controlled by tempered alpha-stable processes.
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered alpha-stable processes. The tempering results in the existence of all moments of operational time. The subordination by the inverse tempered alpha-stable process provides diffusion (relaxation) that occupies an intermediate place between subdiffusion (Cole-Cole law) and normal diffusion (exponential law). Here we obtain explicitly the Fokker-Planck equation and the Cole-Davidson relaxation function. This model includes subdiffusion as a particular case.
Stanislavsky
Aleksander
A
Institute of Radio Astronomy, 4 Chervonopraporna Street, 61002 Kharkov, Ukraine. alexstan@ri.kharkov.ua
Weron
Karina
K
Weron
Aleksander
A