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.

Vitali, S., Sposini, V., Sliusarenko, O., Paradisi, P., Castellani, G., Pagnini, G. (2018). Langevin equation in complex media and anomalous diffusion. JOURNAL OF THE ROYAL SOCIETY INTERFACE, 15(145), 20180282-20180297 [10.1098/rsif.2018.0282].

Langevin equation in complex media and anomalous diffusion

VITALI, SILVIA
Membro del Collaboration Group
;
SPOSINI, VITTORIA
Membro del Collaboration Group
;
PARADISI, PAOLO
Membro del Collaboration Group
;
Castellani, Gastone
Funding Acquisition
;
Pagnini, Gianni
Methodology
2018

Abstract

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.
2018
Vitali, S., Sposini, V., Sliusarenko, O., Paradisi, P., Castellani, G., Pagnini, G. (2018). Langevin equation in complex media and anomalous diffusion. JOURNAL OF THE ROYAL SOCIETY INTERFACE, 15(145), 20180282-20180297 [10.1098/rsif.2018.0282].
Vitali, Silvia; Sposini, Vittoria; Sliusarenko, Oleksii; Paradisi, Paolo; Castellani, Gastone; Pagnini, Gianni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/643577
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