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Langevin equation in complex media and anomalous diffusion
The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many q...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6127165/ https://www.ncbi.nlm.nih.gov/pubmed/30158182 http://dx.doi.org/10.1098/rsif.2018.0282 |
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author | Vitali, Silvia Sposini, Vittoria Sliusarenko, Oleksii Paradisi, Paolo Castellani, Gastone Pagnini, Gianni |
author_facet | Vitali, Silvia Sposini, Vittoria Sliusarenko, Oleksii Paradisi, Paolo Castellani, Gastone Pagnini, Gianni |
author_sort | Vitali, Silvia |
collection | PubMed |
description | The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle's dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations. |
format | Online Article Text |
id | pubmed-6127165 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-61271652018-09-07 Langevin equation in complex media and anomalous diffusion Vitali, Silvia Sposini, Vittoria Sliusarenko, Oleksii Paradisi, Paolo Castellani, Gastone Pagnini, Gianni J R Soc Interface Life Sciences–Physics interface The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle's dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations. The Royal Society 2018-08 2018-08-29 /pmc/articles/PMC6127165/ /pubmed/30158182 http://dx.doi.org/10.1098/rsif.2018.0282 Text en © 2018 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Life Sciences–Physics interface Vitali, Silvia Sposini, Vittoria Sliusarenko, Oleksii Paradisi, Paolo Castellani, Gastone Pagnini, Gianni Langevin equation in complex media and anomalous diffusion |
title | Langevin equation in complex media and anomalous diffusion |
title_full | Langevin equation in complex media and anomalous diffusion |
title_fullStr | Langevin equation in complex media and anomalous diffusion |
title_full_unstemmed | Langevin equation in complex media and anomalous diffusion |
title_short | Langevin equation in complex media and anomalous diffusion |
title_sort | langevin equation in complex media and anomalous diffusion |
topic | Life Sciences–Physics interface |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6127165/ https://www.ncbi.nlm.nih.gov/pubmed/30158182 http://dx.doi.org/10.1098/rsif.2018.0282 |
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