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Lucasian Professorship Inaugural Lecture - Two Theories of Jamming Transitions

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If drivers on a crowded road try to move slowly they will succeed, but if they try to move faster the result is a stationary traffic jam. Related jamming transitions arise in various other contexts and I will describe theories for two such cases. The first concerns a model of self-propelled repulsive particles, which is relevant to swimming microbes and their synthetic analogues, but could also describe dodgems at a funfair. Here, jamming causes phase separation into dense and dilute regions—an outcome that would, without self-propulsion, require attractions between the particles. The second jamming transition arises on shearing a dense suspension of hard spheres: a free-flowing fluid suddenly solidifies when pushed too hard. This is disruptive in industrial contexts, and can be appreciated in the kitchen by adding a little water to corn-starch or custard powder. I will show how a smooth stress dependence of the mean friction at individual particle contacts leads inevitably to a discontinuity in macroscopic behaviour.

This talk is part of the Faculty of Mathematics Lectures series.

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