Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn


Speaker: Mykyta Chubynsky, University of Ottawa

Title: Diffusing diffusivity: A model of anomalous and 'anomalous Brownian' diffusion * Colloquium on Complex and Biological Systems

Time: Fri, Apr 19, 2013, 11:00am

Place: bldg 28, room 0.108

Wang et al. [Proc. Nat. Acad. Sci. USA 106 (2009) 15160] have found that in several very different systems (the surface of lipid tubes, entangled actin networks, mixtures of colloids of different sizes), the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian displacement distribution (DD), with roughly exponential tails at short times, a situation they termed 'anomalous yet Brownian' diffusion. The diversity of systems in which the phenomenon is observed (the surface of lipid tubes, entangled actin networks, mixtures of colloids of different sizes) calls for a generic model. We point out that lack of 'direction memory' in the particle trajectory (a jump in a particular direction does not change the probability of subsequent jumps in that direction) is sufficient for obtaining a strictly linear MSD (assuming that the system is pre-equilibrated), but if at the same time there is 'diffusivity memory' (a particle diffusing faster than average is likely to keep diffusing faster for some time), the DD will be non-Gaussian at short times. A gradual change in diffusivity can be due to the environment of the particle changing slowly on its own, the particle moving between different environments, or both. In our model, this is represented by the particle diffusivity itself undergoing a (perhaps biased) random walk ('diffusing diffusivity'). The DD is exactly exponential at short times if the distribution of diffusivities is itself exponential, but an exponential remains a good fit to the DD for a variety of diffusivity distributions. Our model can also be modified to produce subdiffusion. I will also point out the similarity of our model to some models of financial market price fluctuations, discuss an alternative model based on continuous-time random walks and consider yet another system with similar properties, proton spins undergoing dephasing as they diffuse among magnetic nanoparticles. This work was carried out with G. W. Slater and H. W. de Haan.

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Udo Schwarz, Zentrum für Dynamik komplexer Systeme,
Universität Potsdam, Campus Golm Karl-Liebknecht-Str. 24, 14476 Potsdam, building 28, room 2.107
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