Diffusion and Relaxation Controlled by Tempered \alpha-stable Processes

Autor:	Stanislavsky, Aleksander, Weron, Karina, Weron, Aleksander
Rok vydání:	2011
Předmět:	Condensed Matter - Statistical Mechanics Physics - Data Analysis Statistics and Probability
Zdroj:	Phys. Rev. E 78, 051106 (2008)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevE.78.051106
Popis:	We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random operational time \tau. The tempering results in the existence of all moments of \tau. 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, the mean square displacement and the relaxation function. This model includes subdiffusion as a particular case. Comment: 4 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1111.3018 Zobrazit plný text záznamu View this record from Arxiv