Effect of an initial fractal distribution of particles in coagulation and annihilation reaction-diffusion models

We consider coagulation (A + A → A) and annihilation (A + A → 0) models on a lattice. The initial distribution of particles has a fractal dimension γ. We find that the fractal spatial distribution is preserved along the course of the reaction and that the particle number decay differs from known results for these models. In one dimension the decay goes as t−γ/2 for 0 < γ < 1, in two dimensions as [t/ln(Bt)]−γ/2 for 0 < γ < 2, where the constant B depends on the lattice type, and in three dimensions as t−γ/3 for 0 < 7 < 3.