Drift of scroll waves in thin layers caused by thickness features: asymptotic theory and numerical simulations.
A scroll wave in a very thin layer of excitable medium is similar to a spiral wave, but its behavior is affected by the layer geometry. We identify the effect of sharp variations of the layer thickness, which is separate from filament tension and curvature-induced drifts described earlier. We outline a two-step asymptotic theory describing this effect, including asymptotics in the layer thickness and calculation of the drift of so-perturbed spiral waves using response functions. As specific examples, we consider drift of scrolls along thickness steps, ridges, ditches, and disk-shaped thickness variations. Asymptotic predictions agree with numerical simulations.
Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom.
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Biktasheva
Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium.
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Dierckx
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom.
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Biktashev
D003198:Computer Simulation; D008962:Models, Theoretical; D013016:Sound