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Résumé
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 Levy flights, where the walkers are allowed to perform jumps, the flights, that can eventually be very long as their length distribution is asymptotically powerlaw 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 Levy case. Instead of imposing a length distribution, we thus define our process by its cascade distribution pn. We first derive the connections between the two distributions and show that this local mechanism may give rise to superdiffusion or normal diffusion when pn is distributed as a power law. We also investigate the interplay of this process with the possibility to be stuck on a node, introducing waiting times that are powerlaw distributed as well. In this case, the competition of the two processes extends the palette of the reachable diffusion regimes and, again, this switch relies on the two PDF's powerlaw 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.
langue originale  Anglais 

Editeur  Namur center for complex systems 
Nombre de pages  11 
Etat de la publication  Publié  1 juin 2016 
Empreinte digitale
Examiner les sujets de recherche de « Onset of anomalous diffusion from local motion rules ». Ensemble, ils forment une empreinte digitale unique.Projets
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PAI n°P7/19  DYSCO: Dynamical systems, control and optimization (DYSCO)
WINKIN, J., Blondel, V., Vandewalle, J., Pintelon, R., Sepulchre, R., Vande Wouwer, A. & Sartenaer, A.
1/04/12 → 30/09/17
Projet: Recherche