Antonio Cadilhe

Exact solutions of anisotropic diffusion-limited reactions with coagulation and annihilation

We report exact results for one-dimensional reaction-diffusion modelsA+A→inert,A+A→A, andA+B→inert, where in the latter case like particles coagulate on encounters and move as clusters. Our study emphasizes anisotropy of hopping rates; no changes in universal properties are found, due to anisotropy, in all three reactions. The method of solution employs mapping onto a model of coagulating positive integer charges. The dynamical rules are synchronous, cellular-automaton type. All the asymptotic large-time results for particle densities are consistent, in the framework of universality, with other model results with different dynamical rules, when available in the literature.

RANDOM SEQUENTIAL ADSORPTION OF MIXTURES OF DIMERS AND MONOMERS ON A PRE-TREATED BETHE LATTICE

We report studies of random sequential adsorption on the pre-patterned Bethe lattice. We consider a partially covered Bethe lattice, on which monomers and dimers deposit competitively. Analytical solutions are obtained and discussed in the context of recent efforts to use pre-patterning as a tool to improve self-assembly in micro- and nano-scale surface structure engineering.

Anisotropic diffusion-limited reactions with coagulation and annihilation.

One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and

EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous dynamics. Asymptotic large-time results for particle densities are derived and discussed in the framework of universality.

Exact Solutions of Low-Dimensional Reaction-Diffusion Systems

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.