2018
Journal article  Open Access

Langevin equation in complex media and anomalous diffusion

Vitali S., Sposini V., Sliusarenko O., Paradisi P., Castellani G., Pagnini G.

Bioengineering  44  Biotechnology  Biological transport  Heterogeneous media  Anomalous diffusion  Biochemistry  Statistical Mechanics (cond-mat.stat-mech)  FOS: Physical sciences  Physics - Biological Physics  Life Sciences–Physics interface  space–time fractional diffusion equation  Biomaterials  Biomedical Engineering  Condensed Matter - Statistical Mechanics  Gaussian Process  Biomaterial  30  Research Article  16  Gaussian processe  Space-time fractional diffusion equation  Biophysics  Biophysic  space-time fractional diffusion  1004  Institut für Physik und Astronomie  Biological Physics (physics.bio-ph)  Gaussian processes  Fractional Brownian motion 

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.

Source: Journal of the Royal Society interface (Print) 15 (2018). doi:10.1098/rsif.2018.0282

Publisher: The Royal Society,, London , Regno Unito


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BibTeX entry
@article{oai:it.cnr:prodotti:399836,
	title = {Langevin equation in complex media and anomalous diffusion},
	author = {Vitali S. and Sposini V. and Sliusarenko O. and Paradisi P. and Castellani G. and Pagnini G.},
	publisher = {The Royal Society,, London , Regno Unito},
	doi = {10.1098/rsif.2018.0282 and 10.48550/arxiv.1806.11508},
	journal = {Journal of the Royal Society interface (Print)},
	volume = {15},
	year = {2018}
}