Langevin equation in complex media and anomalous diffusion. Issue 145 (29th August 2018)

• Record Type: Journal Article
• Authors: Vitali, Silvia; Sposini, Vittoria; Sliusarenko, Oleksii; Paradisi, Paolo; Castellani, Gastone; Pagnini, Gianni
• Is Part Of: Journal of the Royal Society interface. Volume 15:Issue 145(2018)
• Publication Date: 2018-08-29
• Subjects: anomalous diffusion -- heterogeneous media -- biological transport -- Gaussian processes -- space–time fractional diffusion equation -- fractional Brownian motion; Physical sciences -- Research -- Periodicals; Life sciences -- Research -- Periodicals; Interdisciplinary research -- Periodicals; 570.5
• DOI: 10.1098/rsif.2018.0282
• Languages: English
• ISSNs: 1742-5689

Abstract

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.