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Gelation phenomena in cluster-cluster aggregation

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Consider a large cloud of particles which are moved around in space by a random transport process such as diffusion. If these particles are “sticky” so that they clump together irreversibly upon contact then the resulting distribution of cluster sizes evolves in time since smaller clusters stick to each other to produce larger ones. The statistical dynamics of such sticky particles has applications in surface physics, colloids, granular materials, bio-physics and atmospheric science. It also provides a rich variety of non-equilibrium phenomena for theoretical analysis. One of the most striking of these phenomena is the so-called gelation transition which, roughly speaking, corresponds to the generation of clusters of infinite size in a finite time. In this talk, I will discuss the scaling theory of cluster aggregation at the level of mean field theory and explain the meaning of the gelation transition. At the end I will discuss the somewhat mysterious phenomenon of “instantaneous” gelation and its relation to some problems in cloud physics.

This talk is part of the British Antarctic Survey series.

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