Dr Colm Connaughton, Mathematics Institute Warwick Centre for Complexity Science, University of Warwick

Abstract: The Smoluchowski coagulation equation, or variations of it, arise in many applications and models ranging from colloid physics to river networks to growth of networks. The scaling theory of this equation reveals a rich set of behaviours depending on how the coalescence kernel behaves as a funcion of cluster size. In this talk I will concentrate on "pathological" kernels which are believed to exhibit an extreme form of singular behaviour known as "instantaneous gelation" in which the dynamics leads to the formation of infinite clusters in zero time. I will discuss how this behaviour can be understood by considering the behaviour of a regularised Smoluchowski equation as the regularisation is removed.

This approach gives some insight into what, at first sight, is a rather difficult phenomenon to analyse and seems to lead to some novel new phenomena.