Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 60: Anomalous Diffusion (joint session DY/BP)

DY 60.12: Talk

Thursday, March 15, 2018, 13:00–13:15, BH-N 334

Non-Gaussian Brownian and viscoelastic diffusion — •Ralf Metzler — Institute of Physics & Astronomy, U Potsdam, Potsdam

Brownian motion as well as viscoelastic anomalous diffusion are stochastic processes driven by Gaussian noise. A growing number of systems is reported in which the mean squared displacement is linear or anomalous, yet the associated probability densities are non-Gaussian. Examples include Brownian motion with exponential probability density for the motion of colloidal beads along tubular structures or in semiflexible polymer networks. Stretched Gaussian shapes along with Brownian motion are seen for the motion of cells on surfaces. Viscoelastic, anomalous motion is observed for submicron tracers in both bacteria and yeast cells. In many systems, at sufficiently long times a crossover to Gaussian behaviour is observed.

In this presentation I will introduce the various observations of non-Gaussian diffusion. In particular, I will report large scale simulations of lipid bilayer systems: in the dilute case viscoelastic and Gaussian diffusion is observed, while in protein-crowded situations stretched Gaussians are observed. This behaviour can, to a good extent, be explained due to geometric constrictions on the motion. I will then introduce a mathematical model for the description of non-Gaussian motion in terms of a stochastically varying diffusion coefficient. In the short time limit this approach is equivalent to the known approach of superstatistics, while at long times a crossover to Gaussian statistics with an effective diffusivity is found.