Mixing time of A + B -> 0 in 1D

Abstract

A mixing time density of $A + B \to 0$ on a finite one dimensional domain is defined for general initial and boundary conditions in which $A$ and $B$ diffuse at the same rate. The density is a measure of the number of $A$ and $B$ particles that mix through the center of the reaction zone. It also corresponds to the reaction density for the special case in which $A$ and $B$ annihilate upon contact. An exact expression is found for the generating function of the mixing time. The analysis is extended to multiple reaction fronts and finitely ramified fractals. The full method involves using the kernel of the Laplace transform integral operator to map and analyze a moving homogeneous Dirichlet interior point condition.