Equilibrium of two-species annihilation with input

Reaction efficiency effects on binary chemical reactions

We study the effect of the variation of reaction efficiency in binary reactions. We use the well-known A + B → 0 model, which has been extensively studied in the past. We perform simulations on this model where we vary the efficiency of reaction, i.e., when two particles meet they do not instantly react, as has been assumed in previous studies, but they react with a probability γ, where γ is in the range 0 < γ < 1. Our results show that at small γ values the system is reaction limited, but as γ increases it crosses over to a diffusion limited behavior. At early times, for small γ values, the particle density falls slower than for larger γ values. This fall-off goes over a crossover point, around the value of γ = 0.50 for high initial densities. Under a variety of conditions simulated, we find that the crossover point was dependent on the initial concentration but not on the lattice size. For intermediate and long times simulations, all γ values (in the depleted reciprocal density versus time plot) converge to the same behavior. These theoretical results are useful in models of epidemic reactions and epidemic spreading, where a contagion from one neighbor to the next is not always successful but proceeds with a certain probability, an analogous effect with the reaction probability examined in the current work.

Catastrophe in diffusion-controlled annihilation dynamics: from formation to universal explosion

We present a systematic theory of formation of the universal annihilation catastrophe which develops in an open system where species A and B diffuse from the bulk of a restricted medium and die on its surface (desorb) by the reaction A+B-->0 . This phenomenon arises in the diffusion-controlled limit as a result of self-organizing explosive growth (drop) of the surface concentrations of, respectively, slow and fast particles (concentration explosion), and manifests itself in the form of an abrupt singular jump of the desorption flux relaxation rate. As striking results we find the dependences of time and amplitude of the catastrophe on the initial particle number, and answer the basic questions of when and how universality is achieved.

Influence of auto-organization and fluctuations on the kinetics of a monomer-monomer catalytic scheme

We study analytically the kinetics of an elementary bimolecular reaction scheme of the Langmuir-Hinshelwood type taking place on a d-dimensional catalytic substrate. We propose a general approach that takes into account explicitly the influence of spatial correlations on the time evolution of the mean particle density. With this approach, we recover some known results concerning the time evolution of the mean particle density and establish others.