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, Quarterly Journal of Mechanics and Applied Mathematics, vol. 58 no. 4 (2005), pp. 577 - 599 [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 v_min lying in the range v₀ equivalent 2/(1+σ) [less-than or equal to] v_min [less-than or equal to] 2, with the value v₀ 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 v_min = v₀ and one where v_min > v₀ with waves propagating faster than their linearized speed in this region. The curve C is determined numerically together with the dependence of v_min on K and σ. © The Author 2005. Published by Oxford University Press; all rights reserved.

   Keywords:
   Catalysis;Mathematical models;Initial value problems;Integration;Wave equations;Approximation theory;Differential equations;Eigenvalues and eigenfunctions;