Onset of anomalous diffusion from local motion rules

Sarah de Nigris (1, 2, 3) , Timoteo Carletti (4) , Renaud Lambiotte (2, 3)

1 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
2 NaXys - Namur Center for Complex Systems [Namur]
3 UNamur - Université de Namur [Namur]
4 Department of Mathematics

Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are Lévy flights, where the walkers are allowed to perform jumps, the " flights " , that can eventually be very long as their length distribution is asymptotically power-law distributed. In our work, we present a model in which walkers are allowed to perform, on a 1D lattice, " cascades " of n unitary steps instead of one jump of a randomly generated length, as in the Lévy case, where n is drawn from a cascade distribution pn. We show that this local mechanism may give rise to superdiffusion or normal diffusion when pn is distributed as a power law. We also introduce waiting times that are power-law distributed as well and therefore the probability distribution scaling is steered by the two PDF's power-law exponents. As a perspective, our approach may engender a possible generalization of anomalous diffusion in context where distances are difficult to define, as in the case of complex networks, and also provide an interesting model for diffusion in temporal networks.

Mots clés: Lévy flights; Statistical mechanics; Random walks on graph; anomalous diffusion

Domaines: Mécanique statistique [cond-mat.stat-mech]

Sarah de Nigris, Timoteo Carletti, Renaud Lambiotte. Onset of anomalous diffusion from local motion rules. 2016. ⟨hal-01391763⟩