Onset of anomalous diffusion from local motion rules

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Abstract

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 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 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 power-law 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 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 languageEnglish
PublisherNamur center for complex systems
Number of pages11
Publication statusPublished - 1 Jun 2016

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cascades
flight
navigation
animals
switches
exponents

Keywords

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

Cite this

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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 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 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 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 power-law 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 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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author = "{De Nigris}, Sarah and Timoteo Carletti and Renaud Lambiotte",
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publisher = "Namur center for complex systems",

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

Namur center for complex systems, 2016. 11 p.

Research output: Book/Report/JournalOther report

TY - BOOK

T1 - Onset of anomalous diffusion from local motion rules

AU - De Nigris, Sarah

AU - Carletti, Timoteo

AU - Lambiotte, Renaud

PY - 2016/6/1

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N2 - 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 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 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 power-law 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 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 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 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 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 power-law 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 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 - microscopic model

M3 - Other report

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PB - Namur center for complex systems

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