Anomalous diffusion and the Moses effect in an aging deterministic model
We decompose the anomalous diffusive behavior found in an aging system into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau–Manneville map. The increments can have long-time correlations, fat-tailed distributio...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aaeea2 |
| _version_ | 1797750551349297152 |
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| author | Philipp G Meyer Vidushi Adlakha Holger Kantz Kevin E Bassler |
| author_facet | Philipp G Meyer Vidushi Adlakha Holger Kantz Kevin E Bassler |
| author_sort | Philipp G Meyer |
| collection | DOAJ |
| description | We decompose the anomalous diffusive behavior found in an aging system into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau–Manneville map. The increments can have long-time correlations, fat-tailed distributions and be non-stationary. Each of these properties can cause anomalous diffusion through what is known as the Joseph, Noah and Moses effects, respectively. The model can have either sub- or super-diffusive behavior, which we find is generally due to a combination of the three effects. Scaling exponents quantifying each of the three constitutive effects are calculated using analytic methods and confirmed with numerical simulations. They are then related to the scaling of the distribution of the process through a scaling relation. Finally, the importance of the Moses effect in the anomalous diffusion of experimental systems is discussed. |
| first_indexed | 2024-03-12T16:34:20Z |
| format | Article |
| id | doaj.art-500b3afba81446ab996c816c53cce657 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:34:20Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-500b3afba81446ab996c816c53cce6572023-08-08T14:57:03ZengIOP PublishingNew Journal of Physics1367-26302018-01-01201111303310.1088/1367-2630/aaeea2Anomalous diffusion and the Moses effect in an aging deterministic modelPhilipp G Meyer0https://orcid.org/0000-0002-8341-2419Vidushi Adlakha1Holger Kantz2https://orcid.org/0000-0001-6921-6094Kevin E Bassler3https://orcid.org/0000-0001-7700-2037Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, Dresden D-01187, GermanyDepartment of Physics, University of Houston , Houston, TX 77204, United States of America; Texas Center for Superconductivity, University of Houston , Houston, TX 77204, United States of AmericaMax-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, Dresden D-01187, GermanyDepartment of Physics, University of Houston , Houston, TX 77204, United States of America; Texas Center for Superconductivity, University of Houston , Houston, TX 77204, United States of America; Department of Mathematics, University of Houston , Houston, TX 77204, United States of AmericaWe decompose the anomalous diffusive behavior found in an aging system into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau–Manneville map. The increments can have long-time correlations, fat-tailed distributions and be non-stationary. Each of these properties can cause anomalous diffusion through what is known as the Joseph, Noah and Moses effects, respectively. The model can have either sub- or super-diffusive behavior, which we find is generally due to a combination of the three effects. Scaling exponents quantifying each of the three constitutive effects are calculated using analytic methods and confirmed with numerical simulations. They are then related to the scaling of the distribution of the process through a scaling relation. Finally, the importance of the Moses effect in the anomalous diffusion of experimental systems is discussed.https://doi.org/10.1088/1367-2630/aaeea2anomalous diffusionaginginfinite ergodic theorychaosnonequilibrium statistical mechanics |
| spellingShingle | Philipp G Meyer Vidushi Adlakha Holger Kantz Kevin E Bassler Anomalous diffusion and the Moses effect in an aging deterministic model New Journal of Physics anomalous diffusion aging infinite ergodic theory chaos nonequilibrium statistical mechanics |
| title | Anomalous diffusion and the Moses effect in an aging deterministic model |
| title_full | Anomalous diffusion and the Moses effect in an aging deterministic model |
| title_fullStr | Anomalous diffusion and the Moses effect in an aging deterministic model |
| title_full_unstemmed | Anomalous diffusion and the Moses effect in an aging deterministic model |
| title_short | Anomalous diffusion and the Moses effect in an aging deterministic model |
| title_sort | anomalous diffusion and the moses effect in an aging deterministic model |
| topic | anomalous diffusion aging infinite ergodic theory chaos nonequilibrium statistical mechanics |
| url | https://doi.org/10.1088/1367-2630/aaeea2 |
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