publications by David Needham.

Papers Published

1. Needham, D.J. and Leach, J.A. and Merkin, J.H., The effects of a complexation reaction on travelling wave-fronts in a quadratic autocatalytic system, Q. J. Mech. Appl. Math. (UK), vol. 58 (2005), pp. 577 - 99 [hbi022] .
   (last updated on 2007/04/06)

   Abstract:
   A model which describes the effect that a complexation reaction can have on the propagation of reaction fronts in a quadratic autocatalytic system is considered. An initial-value problem is set up, which involves the (dimensionless) parameters K, the equilibrium constant for the complexation reaction, and σ, the initial concentration of the complexing agent. This initial-value problem is analysed, with global existence and uniqueness being established. Numerical integrations indicate the formation of permanent-form travelling waves at large times. The equations that govern the travelling waves in the model are treated in detail. It is determined that there is a minimum propagation speed υ_min lying in the range υ₀≡2/(1+σ)⩽υ_min⩽2, with the value υ₀ corresponding to the minimum speed derived from the linearization of the travelling wave equations. The existence of a curve C is established, which divides the (K,σ) parameter plane into two regions, one where υ_min=υ₀ and one where υ_min> υ₀ with waves propagating faster than their linearized speed in this region. The curve C is determined numerically together with the dependence of υ_min on K and σ

   Keywords:
   initial value problems;integration;reaction kinetics theory;wave equations;wave propagation;