Title: The mathematics of active matter

Speaker: Tanniamole Liverpool (Univesity of Bristol)

Abstract:

A flock of birds, a shoal of fish, a swarm of robots, a colony of swimming bacteria; these are examples of systems composed of interacting units that consume energy and collectively generate motion and mechanical forces on their environment. They show a rich variety of collective behaviour, much of which remains mysterious. In recent years we have come to call such systems active matter. Clearly, biology (living systems) provides numerous examples of these active matter systems. I will explain why we call them active matter. Essentially, this is because they share some of the properties of the constituents of what we call matter, i.e. solids, liquids, and gases in that they are made of many interacting components. However, they have fundamental differences in that many conservation laws that govern the interactions of normal (passive) matter are not obeyed by their active components. (Equilibrium) statistical mechanics has formed the framework for how we understand the properties of matter. I will argue that ideas developed in statistical mechanics must be augmented by a number of new mathematical structures to describe these systems. Then I will describe some recent theoretical work developing this framework for characterising the behaviour of active matter systems. Finally, I will apply it to describe some recent experimental work studying collections of electrically driven colloidal rollers moving in two dimensions.

Short Bio:

I am in the Applied Mathematics Institute of the School of Mathematics at Bristol. My research primarily involves theoretical descriptions of complex fluids (membranes, polymers, gels, …). I am increasingly interested in the study of “soft biological matter” (DNA, proteins, the cytoskeleton, gene regulation, …), and the organising principles behind this highly interesting active (living) state of matter.

Contact: t.liverpool@bristol.ac.uk

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