### 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 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 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 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.

Original language | English |
---|---|

Article number | 022113 |

Number of pages | 8 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 95 |

Issue number | 2 |

DOIs | |

Publication status | Published - 13 Feb 2017 |

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### Keywords

- random walks
- anomalous diffusion
- levy flight
- microscopic model

### Cite this

}

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 95, no. 2, 022113. https://doi.org/10.1103/PhysRevE.95.022113

**Onset of anomalous diffusion from local motion rules.** / De Nigris, Sarah; Carletti, Timoteo; Lambiotte, Renaud.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Onset of anomalous diffusion from local motion rules

AU - De Nigris, Sarah

AU - Carletti, Timoteo

AU - Lambiotte, Renaud

PY - 2017/2/13

Y1 - 2017/2/13

N2 - 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 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 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.

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 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 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 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.

KW - random walks

KW - anomalous diffusion

KW - levy flight

KW - microscopic model

UR - http://www.scopus.com/inward/record.url?scp=85013835166&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.95.022113

DO - 10.1103/PhysRevE.95.022113

M3 - Article

VL - 95

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 2

M1 - 022113

ER -