Brownian motion is one of the most fundamental processes in non-equilibrium statistical physics. High resolution data from single particle tracking and supercomputing across the scales demonstrate deviations from the simple law of Brownian motion. I will introduce the concept of "doubly-stochastic" processes for the modelling of transport in heterogeneous systems, before turning to "anomalous...

Strong symmetries of Fractional Brownian Motion (FBM) make its Hurst index $H$ the unifying number governing both its short (fractal dimension $2-H$) and long time (mean squared displacement $\propto t^{2H}$) properties. This fact restricts some of its applications—crucially it makes it impossible to describe an increasing number of regime switching anomalous diffusion systems in which the...

The study of synchronous dynamics has traditionally focused on the identification of threshold parameter values for the transition to synchronization, and on the nature of such transition. The dynamical process whereby systems of self-sustained oscillators synchronize, however, has been much less studied. While one might reasonably expect such a process to be strongly system-dependent, in Ref....