Renewal and memory origin of anomalous diffusion: a discussion of their joint action.
The adoption of the formalism of fractional calculus is an elegant way to simulate either subdiffusion or superdiffusion from within a renewal perspective where the occurrence of an event at a given time t does not have any memory of the events occurring at earlier times. We illustrate a physical model to assign infinite memory to renewal anomalous diffusion and we find (i) a condition where the simultaneous action of a renewal and a memory source of subdiffusion generates localization and (ii) a condition where they make subdiffusion weaker and superdiffusion emerge. We argue that our approach may provide important contributions to the current search to distinguish the renewal from the memory source of subdiffusion.
Instituto de Alta Investigación, Universidad de Tarapacá-Casilla 6-D Arica, Chile.
Mauro
M
Bologna
Information Science Directorate, Army Research Office, Research Triangle Park, North Carolina 27709, USA.
Bruce J
BJ
West
Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA.
Paolo
P
Grigolini