Onset of anomalous diffusion from local motion rules

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Résumé

Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation in 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 one-dimensional 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 p_n. We show that this local mechanism may give rise to superdiffusion or normal diffusion when p_n 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 local distributions 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.
langueAnglais
Nombre de pages8
journalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Les DOIs
étatPublié - 13 févr. 2017

Empreinte digitale

Anomalous Diffusion
Power Law
Motion
Cascade
Jump
Model
cascades
flight
Superdiffusion
Lévy Flights
Power-law Distribution
Waiting Time
Complex Networks
Diffusion Process
Navigation
Animals
Probability Distribution
Exponent
Scaling
Generalization

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    title = "Onset of anomalous diffusion from local motion rules",
    abstract = "Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation in animals and also in human mobility. One way to create such regimes are L\{'e}vy 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 areallowed to perform, on a one-dimensional lattice, “cascades” of n unitary steps instead of one jump of a randomly generated length, as in the L\{'e}vy case, where n is drawn from a cascade distribution p_n. We show that this local mechanism may give rise to superdiffusion or normal diffusion when p_n 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 local distributions 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.",
    keywords = "random walks, anomalous diffusion, levy flight, microscopic model",
    author = "{De Nigris}, Sarah and Timoteo Carletti and Renaud Lambiotte",
    year = "2017",
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    AB - Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation in 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 areallowed to perform, on a one-dimensional 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 p_n. We show that this local mechanism may give rise to superdiffusion or normal diffusion when p_n 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 local distributions 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.

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    KW - anomalous diffusion

    KW - levy flight

    KW - microscopic model

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