TY  - JOUR
A1  - Vitali, Silvia
A1  - Sposini, Vittoria
A1  - Sliusarenko, Oleksii
A1  - Paradisi, Paolo
A1  - Castellani, Gastone
A1  - Pagnini, Gianni
T1  - Langevin equation in complex media and anomalous diffusion
JF  - Interface : journal of the Royal Society
N2  - 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.
KW  - anomalous diffusion
KW  - heterogeneous media
KW  - biological transport
KW  - Gaussian processes
KW  - space-time fractional diffusion equation
KW  - fractional Brownian motion
Y1  - 2018
U6  - https://doi.org/10.1098/rsif.2018.0282
SN  - 1742-5689
SN  - 1742-5662
VL  - 15
IS  - 145
PB  - Royal Society
CY  - London
ER  -