School of Mathematics

Stefan Grosskinsky

Stefan Grosskinsky abstract

Mathematics Institute, University of Warwick

Effect of non-Markovian dynamics on pattern formation and transport

Most microscopic models of complex (biological) systems are probabilistic, i.e. hidden degrees of freedom are modeled by noise with a postulated distribution. This is often assumed to be uncorrelated in time for simplicity, but in many applications the statistics of the activating noise has non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. We investigate the effect of non-Markovian noise on pattern formation in microbial population growth and collective transport properties of molecular motors. Both are modeled by continuous-time jump processes where we replace the exponential waiting times between growth or jump events of individuals by more regular distributions with a lower variation coefficient. This introduces temporal correlations, that lead to spatial correlations and affect the long-time behaviour of the system. Since correlation lengths are finite, both systems remain in the KPZ universality class, which determines the scaling between temporal and spatial correlations.

This is joint work with Adnan Ali, Rosemary Harris, and Diana Khoromskaia.