Spirals in excitable media: The free-boundary limit with diffusion

David A. Kessler; Raz Kupferman

doi:10.1016/0167-2789(96)00135-2

Spirals in excitable media: The free-boundary limit with diffusion

David A. Kessler, Raz Kupferman

Department of Physics - at Bar-Ilan University

Lucent

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We solve numerically for the steady-state spiral in the thin-interface limit, including the effects of diffusion of the slow field. The calculation is performed using a generalization of the hybrid scheme of Keener. In this method, the diffusion equation is solved on a suitable mapped lattice while the eikonal equation relating the field on the interface to the interfacial velocity and curvature is solved independently. We present results for the selected frequency and tip radius as a function of the various parameters. We note that a stability analysis based on these results may be performed.

Original language	English
Pages (from-to)	509-516
Number of pages	8
Journal	Physica D: Nonlinear Phenomena
Volume	97
Issue number	4
DOIs	https://doi.org/10.1016/0167-2789(96)00135-2
State	Published - 1996

Bibliographical note

Funding Information:
DAK acknowledges useful conversations with J. Schiff and H. Levine. He also acknowledges the support of the Raschi Foundation. DAK and RK acknowledge the support of Grant No. 9200051 from the United States - Israel Binational Science Foundation (BSF).

Funding

DAK acknowledges useful conversations with J. Schiff and H. Levine. He also acknowledges the support of the Raschi Foundation. DAK and RK acknowledge the support of Grant No. 9200051 from the United States - Israel Binational Science Foundation (BSF).

Funders	Funder number
Raschi Foundation	9200051
United States - Israel Binational Science Foundation
United States-Israel Binational Science Foundation

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10.1016/0167-2789(96)00135-2

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title = "Spirals in excitable media: The free-boundary limit with diffusion",

abstract = "We solve numerically for the steady-state spiral in the thin-interface limit, including the effects of diffusion of the slow field. The calculation is performed using a generalization of the hybrid scheme of Keener. In this method, the diffusion equation is solved on a suitable mapped lattice while the eikonal equation relating the field on the interface to the interfacial velocity and curvature is solved independently. We present results for the selected frequency and tip radius as a function of the various parameters. We note that a stability analysis based on these results may be performed.",

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note = "Funding Information: DAK acknowledges useful conversations with J. Schiff and H. Levine. He also acknowledges the support of the Raschi Foundation. DAK and RK acknowledge the support of Grant No. 9200051 from the United States - Israel Binational Science Foundation (BSF).",

year = "1996",

doi = "10.1016/0167-2789(96)00135-2",

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AU - Kupferman, Raz

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PY - 1996

Y1 - 1996

N2 - We solve numerically for the steady-state spiral in the thin-interface limit, including the effects of diffusion of the slow field. The calculation is performed using a generalization of the hybrid scheme of Keener. In this method, the diffusion equation is solved on a suitable mapped lattice while the eikonal equation relating the field on the interface to the interfacial velocity and curvature is solved independently. We present results for the selected frequency and tip radius as a function of the various parameters. We note that a stability analysis based on these results may be performed.

AB - We solve numerically for the steady-state spiral in the thin-interface limit, including the effects of diffusion of the slow field. The calculation is performed using a generalization of the hybrid scheme of Keener. In this method, the diffusion equation is solved on a suitable mapped lattice while the eikonal equation relating the field on the interface to the interfacial velocity and curvature is solved independently. We present results for the selected frequency and tip radius as a function of the various parameters. We note that a stability analysis based on these results may be performed.

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Spirals in excitable media: The free-boundary limit with diffusion

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