3pm - 4pm
Wednesday 2 December 2020

Something from nothing: Investigating the emergence of localised patterns

A seminar in the Taste of Research Undergraduate Seminar Series designed by mathematics PhD students to introduce year 2, 3 and 4 mathematics students to a taste of mathematics doctoral research.

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The event will be held on Zoom.

Speakers

Abstract

Ferrofluids, magnetic fluids consisting of iron nanoparticles, provide a good experimental medium to investigate properties of nonlinear waves. For a vertically-applied magnetic field, there exists a critical field strength at which spikes emerge from the ferrofluid, arranging in geometric patterns. In 2005, isolated spikes were observed experimentally; these 'spot' solutions were seen to drift around the domain and interact with each other, suggesting that were an example of `localised' patterns.

By introducing some theory surrounding ODEs, bifurcations, and multi-scale dynamics, we investigate why these patterns emerge and identify the types of  localised axisymmetric (radial) solutions that may appear in this experiment.