Scaling behavior of diffusion limited annihilation reactions on random media

Abstract

We investigate numerically the kinetics of diffusion limited annihilation reactions in disordered binary square lattices where the reacting particles are constrained to diffuse on a concentration p of the lattice sites. We find that the asymptotic decay of the particle concentration in the percolative regime is of the form c(t, p)Ϫc r (p) ϰ t Ϫd s /2 , where c r (p) is the concentration of residual particles. We recover well known results such as d s (pϾ p c )ϭdϭ2 with logarithmic corrections, and d s (p c )ϭ1.34Ϯ0.02. For pϽp c we employ a scaling theory and collapse the data onto a universal form dc/dtϭ Ϫ(d s (p c )/2ϩ1) f (t/), with being a characteristic diffusion time and f (t/) representing the crossover from a power law decay to a stretched exponential one. We relate the present results with the kinetics of the excitation reaction ͑triplet ϩ triplet → singlet͒ on isotopic mixed crystals of naphthalene.

Diffusion-limited coalescence and annihilation in random media

“…For example, if the distribution of reaction-domain sizes is exponential, ψ(V ) = ρe −ρV , we obtain c coal res = c 0 ρ/(c 0 + ρ) and c annil res = c 0 ρ/(2c 0 + ρ). De Albuquerque and Lyra [14] performed a lattice computation for the residual concentration of particles for annihilation in two-dimensional percolation, under the assumption that there is initially one particle per site.…”

“…Diffusion-limited reactions are far less understood than their reaction-limited counterpart. Simple reaction models such as diffusion-limited coalescence, A + A → A, and annihilation, A + A → 0, have attracted much recent attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14], since their kinetics in one-dimensional space may be analyzed exactly, and they shed light on other less tractable reaction schemes. Moreover, coalescence and annihilation serve as models of exciton dynamics in several real systems.…”

Anomalous coalescence from a nonlinear Schroedinger equation with a quintic term: interpretation through Thompson's approach

“…Anomalous di usion conditions are also considered [9,10] by including coalescence. It is important to mention that some other di usion reaction models were already considered before [11][12][13][14].…”

Anomalous coalescence phenomena under stationary regime condition through Thompson's method

“…Albuquerque and Lyra [34] investigated numerically the kinetics of di usion-limited annihilation reactions in disordered binary square lattices where the reacting particles are constrained to di use on a concentration of lattice sites. The di usion-limited annihilation (DLA) models were well explored by many ways.…”