par Boon, Jean-Pierre ;Lutsko, James ;Lutsko, Christopher
Référence Central European Journal of Physics, 10, 3, page (631-636)
Publication Publié, 2012-06
Article révisé par les pairs
Résumé : A microscopic theory for reaction-difusion (R-D) processes is developed from Einstein's master equation including a reactive term. The mean field formulation leads to a generalized R-D equation for the n-th order annihilation reaction A + A + A + ... + A → 0, and the steady state solutions exhibit long range power law behavior showing the relative dominance of sub-diffusion over reaction effects in constrained systems, or conversely short range concentration distribution with finite support describing situations where diffusion is slow and extinction is fast. We apply the theory to analyze experimental data for morphogen gradient formation in the wing disc of the Drosophila embryo. © 2012 Versita Warsaw and Springer-Verlag Wien.