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Title: Spiral pinballs, cardiac tissue and deforming capacitors
Author: Langham, Jacob
ISNI:       0000 0004 6348 9755
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2017
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‘Spiral pinballs’ are resonantly drifting spiral waves in excitable media that reflect from boundaries. Instead of reflecting at an angle equal to the one at which they approach the boundary—like a ray of light reflecting from a mirror—they reflect in a preferred direction. This invites comparison with a number of other complex systems that behave as nonspecular billiards, including bouncing droplets on a vibrated bath, swimming microorganisms and segments of chemical waves. In the first part of this thesis, we study the trajectories of spiral pinball reflections. A catalogue of interesting behaviours is discovered in both the small- and large-core rotation regimes and the long-term billiard dynamics is briefly considered. By using an asymptotic theory, we examine the reflection process in detail and thereby explain many of the observed phenomena. The second part of this thesis concerns itself with modelling spiral wave activity in a deforming medium. Our motivation stems from cardiac tissue, in which spiral waves and mechanical deformation are reciprocally coupled. We describe a simple modelling approach for this system and discuss its implementation. Various different results are presented using this model. Finally we consider a problem from the engineering world. Dielectric elastomers are flexible capacitors that undergo nonlinear elastic deformations in response to forces arising from electric surface charges. We propose a novel modelling approach that decomposes these forces into a compressive stress and a tangential shear. The tangential component corresponds to a fringing effect that is usually considered to be negligible. Via numerical simulations and comparison with experimental data we show that it nonetheless has an important role to play in selecting the deformed shapes that these systems adopt. In some cases, we are able to compute multiple equilibrium configurations and it is shown that doing so is necessary to obtain the most physically relevant states.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics