dorsal/arxiv
View SchemaDiffusive Boundary Layers in the Free-Surface Excitable Medium Spiral
| Authors | David A. Kessler, Herbert Levine |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9701004 |
| URL | https://arxiv.org/abs/patt-sol/9701004 |
| DOI | 10.1103/PhysRevE.55.R3847 |
Abstract
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to one involving the motion of a free surface separating the excited and quiescent phases. In this work, we study the free surface problem in the limit of small diffusivity for the slow field variable. Specifically, we show that a previously found spiral solution in the diffusionless limit can be extended to finite diffusivity, without significant alteration. This extension involves the creation of a variety of boundary layers which cure all the undesirable singularities of the aforementioned solution. The implications of our results for the study of spiral stability are briefly discussed.
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"abstract": "Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a\ngreat variety of excitable systems. In the limit of a large separation in\ntimescale between fast excitation and slow recovery, one can reduce the spiral\nproblem to one involving the motion of a free surface separating the excited\nand quiescent phases. In this work, we study the free surface problem in the\nlimit of small diffusivity for the slow field variable. Specifically, we show\nthat a previously found spiral solution in the diffusionless limit can be\nextended to finite diffusivity, without significant alteration. This extension\ninvolves the creation of a variety of boundary layers which cure all the\nundesirable singularities of the aforementioned solution. The implications of\nour results for the study of spiral stability are briefly discussed.",
"arxiv_id": "patt-sol/9701004",
"authors": [
"David A. Kessler",
"Herbert Levine"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.55.R3847",
"title": "Diffusive Boundary Layers in the Free-Surface Excitable Medium Spiral",
"url": "https://arxiv.org/abs/patt-sol/9701004"
},
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