Isothermal flame balls: Effect of autocatalyst decay

Éva Jakab, D. Horváth, John H. Merkin, Stephen K. Scott, Péter L. Simon, A. Tóth

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The steady, spherically symmetric solutions to the reaction-diffusion equations based on a simple autocatalytic reaction followed by the decay of the autocatalyst are considered. Three parameters—the orders with respect to the autocatalyst in the autocatalysis p and in the decay q and the rate of decay of the autocatalyst relative to its autocatalytic production [Formula presented]—determine the steady concentration profiles. Numerical integrations for a fixed value of the order of the autocatalyst show that the concentration profiles have different forms depending on whether [Formula presented] or [Formula presented] In the former case, there is a critical decay rate [Formula presented] for solutions to exist, with multiple solutions for [Formula presented] In the latter case, there is a single solution for each value of K. This difference in the nature of the solution is confirmed by an analysis for p large. The temporal stability of the isothermal flame balls is examined, with temporally stable solutions being possible, provided that the ratio of the diffusion coefficient of the autocatalyst to that of the reactant is sufficiently small. The change in stability appears only when there are multiple solutions and is through a subcritical Hopf bifurcation.

Original languageEnglish
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume68
Issue number3
DOIs
Publication statusPublished - Jan 1 2003

Fingerprint

Flame
balls
flames
Ball
Decay
decay
Multiple Solutions
autocatalysis
reaction-diffusion equations
Symmetric Solution
Stable Solution
profiles
Reaction-diffusion Equations
numerical integration
Decay Rate
Hopf Bifurcation
Numerical integration
Diffusion Coefficient
decay rates
diffusion coefficient

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Isothermal flame balls : Effect of autocatalyst decay. / Jakab, Éva; Horváth, D.; Merkin, John H.; Scott, Stephen K.; Simon, Péter L.; Tóth, A.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 68, No. 3, 01.01.2003.

Research output: Contribution to journalArticle

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