B1877
Title: Modelling intermittent anomalous diffusion with switching fractional Brownian motion
Authors: Michal Balcerek - Wroclaw University of Science and Technology (Poland) [presenting]
Diego Krapf - Colorado State University (United States)
Ralf Metzler - University of Potsdam (Germany)
Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland)
Krzysztof Burnecki - Wroclaw University of Science and Technology (Poland)
Abstract: The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due to which the motion changes along the trajectories. Such effects manifest themselves as spatiotemporal correlations. Despite the broad occurrence of heterogeneous complex systems in nature, their analysis is still quite poorly understood and tools to model them are largely missing. The contribution to tackling this problem is by employing an integral representation of Mandelbrot's fractional Brownian motion that is compliant with varying motion parameters while maintaining long memory. Two types of switching fractional Brownian motion are presented and analysed, with transitions arising from a Markovian stochastic process and scale-free intermittent processes. Simple formulas are obtained for classical statistics of the processes, namely the mean squared displacement and the power spectral density. Further, a method to identify switching fractional Brownian motion based on the distribution of displacements is described. A validation of the model is given for experimental measurements of the motion of quantum dots in the cytoplasm of live mammalian cells that were obtained by single-particle tracking.
