Yann Lanoiselée (BCAM)

A unifying approach to diffusive transport in annealed heterogeneous media

In this seminar, we will discuss the thermal diffusion in heterogeneous media through the lenses of stochastic processes. Transport as the mesoscopic scale is dominated by thermal fluctuations yielding stochastic motion. While stochastic motion in homogeneous media is understood since Einstein and his derivation of Brownian motion, its extension to heterogeneous media remains to elucidate. Heterogeneity induces induce statistical deviations from Brownian motion as will be discussed in the context of diffusion in living cells. The two main effects are anomalous diffusion where the mean squared displacement displays a power-law scaling and non-Gaussian displacement statistics which may occur at the same time. We will discuss how anomalous and non-Gaussian diffusion articulate. 

To do so, we introduce the concept of Randomly Modulated Gaussian Processes [1] as a unifying framework for modelling, analysing and classifying diffusion in heterogeneous media. This formulation incorporates correlations in the displacements together with correlated fluctuations of their amplitudes. Most known models of anomalous diffusion (including Continuous-Time Random Walk, fractional Brownian motion but also Lévy flights) and random diffusivity can be described and generalized within this framework. Moreover, the unified view identifies the main statistical properties to be probed experimentally for a reliable classification of diffusive dynamics.