Stationary patterns of chemical concentration in the Belousov-Zhabotinskii reaction

Forbes L.K. (1990) Stationary patterns of chemical concentration in the Belousov-Zhabotinskii reaction. Physica D: Nonlinear Phenomena, 43 1: 140-152. doi:10.1016/0167-2789(90)90022-H

Author Forbes L.K.
Title Stationary patterns of chemical concentration in the Belousov-Zhabotinskii reaction
Journal name Physica D: Nonlinear Phenomena   Check publisher's open access policy
ISSN 0167-2789
Publication date 1990
Sub-type Article (original research)
DOI 10.1016/0167-2789(90)90022-H
Volume 43
Issue 1
Start page 140
End page 152
Total pages 13
Subject 2604 Applied Mathematics
3109 Statistical and Nonlinear Physics
Abstract The Belousov-Zhabotinskii (BZ) reaction is a complicated chemical reaction which has the property that, instead of progressing smoothly from reactants to products or perhaps reaching equilibrium, it may instead exhibit periodic oscillations in the concentrations of certain intermediate products. In addition, spatially periodic patterns may occur when diffusion of the chemical species is taken into account. This paper investigates these patterns in the one-dimensional case in which a time-independent stripy pattern would be observed, corresponding to standing waves of chemical concentration being formed across the containing vessel. The Oregonator model of the reaction is assumed, and the resulting differential equations are solved using Fourier-series expansions. Each Fourier coefficient is then further expressed as a high-order perturbation series in an appropriate small parameter. The series are summed using various acceleration techniques, and are also analyzed to provide some insight into the mathematical structure of the solution. Large-amplitude concentration patterns have been generated in this way, and are discussed. The possibility of pattern generation when all three diffusion coefficients are equal is discussed in detail.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
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