Onset of anomalous diffusion from local motion rules
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 ca...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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American Physical Society
2017
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| _version_ | 1826267454703140864 |
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| author | de Nigris, S Carletti, T Lambiotte, R |
| author_facet | de Nigris, S Carletti, T Lambiotte, R |
| author_sort | de Nigris, S |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T20:54:28Z |
| format | Journal article |
| id | oxford-uuid:38b65303-873a-40a8-8b15-7ddccdccc279 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:54:28Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:38b65303-873a-40a8-8b15-7ddccdccc2792022-03-26T13:51:43ZOnset of anomalous diffusion from local motion rulesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:38b65303-873a-40a8-8b15-7ddccdccc279EnglishSymplectic Elements at OxfordAmerican Physical Society2017de Nigris, SCarletti, TLambiotte, RAnomalous 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. |
| spellingShingle | de Nigris, S Carletti, T Lambiotte, R Onset of anomalous diffusion from local motion rules |
| title | Onset of anomalous diffusion from local motion rules |
| title_full | Onset of anomalous diffusion from local motion rules |
| title_fullStr | Onset of anomalous diffusion from local motion rules |
| title_full_unstemmed | Onset of anomalous diffusion from local motion rules |
| title_short | Onset of anomalous diffusion from local motion rules |
| title_sort | onset of anomalous diffusion from local motion rules |
| work_keys_str_mv | AT denigriss onsetofanomalousdiffusionfromlocalmotionrules AT carlettit onsetofanomalousdiffusionfromlocalmotionrules AT lambiotter onsetofanomalousdiffusionfromlocalmotionrules |