# 30th Marian Smoluchowski Symposium on Statistical Physics

3-8 September 2017
Poland timezone

## Stochastic processes for fractional kinetics with application to anomalous diffusion in living cells

8 Sep 2017, 09:20
15m
56 ()

oral

### Speaker

Gianni Pagnini (BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country - Spain)

### Description

Fractional kinetics is derived from Gaussian processes when the medium where the diffusion takes place is characterized by a population of length-scales [1]. This approach is analogous to the generalized grey Brownian motion [2], and it can be used for modelling anomalous diffusion in complex media. In particular, the resulting stochastic process can show sub-diffusion, ergodicity breaking, p variation, and aging with a behaviour in qualitative agreement with single-particle tracking experiments in living cells. Moreover, for a proper distribution of the length-scales, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking [3].  [1] Pagnini G. and Paradisi P., A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 19, 408–440 (2016) [2] Mura A. and Pagnini G., Characterizations and simulations of a class of stochastic processes to model anomalous diffusion. J. Phys. A: Math. Theor. 41, 285003 (2008) [3] Molina–García D., Pham T. Minh, Paradisi P., Manzo C. and Pagnini G., Fractional kinetics emerging from ergodicity breaking in random media. Phys. Rev. E. 94, 052147 (2016)

### Primary author

Gianni Pagnini (BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country - Spain)

### Co-authors

Carlo Manzo (Universitat de Vic - Universitat Central de Catalunya (UVic-UCC), Vic, Spain) Daniel Molina-García (BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country - Spain) Paolo Paradisi (ISTI - CNR, Pisa, Italy)

### Presentation Materials

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