Abstract
Travelling wave patterns occur frequently in chemically reacting systems; these include planar fronts, target patterns and spiral structures. We review the dispersion relation for planar waves, including the effects of diffusion in the "slow" field for a simplified piecewise-linear model, with a focus on the scaling behavior with respect to the relative rate of the "fast" and "slow" reactions. We discuss the implications of these results for spirals, showing the origins of Fife scaling and deriving a boundary-integral formulation of the spiral equations. We discuss the generalization to more realistic models, in particular, the popular Oregonator model for Belousov-Zhabotinskii reactions.
| Original language | English |
|---|---|
| Pages (from-to) | 1-14 |
| Number of pages | 14 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 39 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Oct 1989 |
| Externally published | Yes |
Bibliographical note
Funding Information:The work of D.A.K. was supported by U.S. Department of Energy, Grant No. DE-FG-02-85ER54189. H.L. was supported in part by a grant from DARPA under the University Research Initiative Grant No. N00014-86-K-0758, and by the Alfred Sloan Foundation.
Funding
The work of D.A.K. was supported by U.S. Department of Energy, Grant No. DE-FG-02-85ER54189. H.L. was supported in part by a grant from DARPA under the University Research Initiative Grant No. N00014-86-K-0758, and by the Alfred Sloan Foundation.
| Funders | Funder number |
|---|---|
| U.S. Department of Energy | DE-FG-02-85ER54189 |
| Defense Advanced Research Projects Agency | N00014-86-K-0758 |
| Alfred P. Sloan Foundation |