Singular perturbation equations for 3-d excitable media
UNSPECIFIED (2001) Singular perturbation equations for 3-d excitable media. In: Annual Scientific Conference of the Society-for-Applied-Mathematics-and-Mechanics (GAMM 2000), UNIV GOTTINGEN, GOTTINGEN, GERMANY, APR 02-07, 2000. Published in: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 81 (Suppl. 1). S81-S84.Full text not available from this repository.
In this paper the idea of Prandtl's boundary layer is exported to a field other than fluid dynamics. Excitable media, such as nerve fibers and heart tissue are typically modelled with a reaction-diffusion equations containing two chemical species that evolve on very different time scales. In three dimensions solutions of these equations take the form of rotating scroll waves (interfaces) ending on filaments. The ratio of the two time scales defines a natural small parameter epsilon. Exploiting the inherent smallness of epsilon, singular perturbation methods are used to derive three-dimensional equations for each of the two boundary layers : interface region (scroll) and filament region (core), and for the associated outer region. For scrolls with uniform twist about straight filaments, this matched asymptotic expansion method is also used to derive free-boundary equations not only at leading order but also at first order. Both orders are validated against full solutions of the reaction-diffusion equations. Using these two orders and with no adjustable parameters, the shape and frequency of waves are correctly predicted for most cases of physical interest.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
|Journal or Publication Title:||ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK|
|Publisher:||WILEY-V C H VERLAG GMBH|
|Number of Pages:||4|
|Title of Event:||Annual Scientific Conference of the Society-for-Applied-Mathematics-and-Mechanics (GAMM 2000)|
|Location of Event:||UNIV GOTTINGEN, GOTTINGEN, GERMANY|
|Date(s) of Event:||APR 02-07, 2000|
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