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

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

56

oral Session 12

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)

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