Scaling Model of Annihilation-Diffusion Kinetics for Charged Particles with Long-Range Interactions

We present the growth dynamics of an island of particles $A$ injected from a localized $A$-source into the sea of particles $B$ and dying in the course of diffusion-controlled annihilation $A+B\to 0$. We show that in the 1d case the island unlimitedly grows at any source strength $\Lambda$, and the dynamics of its growth {\it does not depend} asymptotically on the diffusivity of $B$ particles. In the 3d case the island grows only at $\Lambda > \Lambda_{c}$, achieving asymptot...

We study reaction zones in three different versions of the A+B->0 system. For a steady state formed by opposing currents of A and B particles we derive scaling behavior via renormalization group analysis. By use of a previously developed analogy, these results are extended to the time-dependent case of an initially segregated system. We also consider an initially mixed system, which forms reaction zones for dimension d<4. In this case an extension of the steady-state analogy ...

We study the two particle annihilation reaction $A+B\rightarrow \emptyset$ on interconnected scale free networks, using different interconnecting strategies. We explore how the mixing of particles and the process evolution are influenced by the number of interconnecting links, by their functional properties, and by the interconnectivity strategies in use. We show that the reaction rates on this system are faster than what was observed in other topologies, due to the better pa...

We present results from computer simulations for diffusion-limited $n$-species annihilation, $A_i+A_j\to0$ $(i,j=1,2,...,n;i\neq j)$, on the line, for lattices of up to $2^{28}$ sites, and where the process proceeds to completion (no further reactions possible), involving up to $10^{15}$ time steps. These enormous simulations are made possible by the renormalized reaction-cell method (RRC). Our results suggest that the concentration decay exponent for $n$ species is $\a(n)=(n...

We derive the multi-fractal scaling of probability distributions of multi-particle configurations for the binary reaction-diffusion system $A+A \to \emptyset$ in $d \leq 2$ and for the ternary system $3A \to \emptyset$ in $d=1$. For the binary reaction we find that the probability $P_{t}(N, \Delta V)$ of finding $N$ particles in a fixed volume element $\Delta V$ at time $t$ decays in the limit of large time as $(\frac{\ln t}{t})^{N}(\ln t)^{-\frac{N(N-1)}{2}}$ for $d=2$ and $...

We derive an improved mean-field approximation for k-body annihilation reactions kA --> inert, for hard-core diffusing particles on a line, annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping and annihilation processes are correlated to mimic chemical reactions. Our new mean-field theory accounts for hard-core particle properties and has a larger region of applicability than the standard chemical rate equation especially for large k values. Criteria...

We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability for a pair-annihilation event decays as a power-law in the distance between particles, with a tunable exponent. Such long-range processes arise naturally in various classical settings, such as chemical reactions involving reagents with long-range electromagnetic interactions. They also i...

We address via numerical simulation the two-dimensional bimolecular annihilation reaction $A + A \to \emptyset$ in the presence of quenched, random impurities. Renormalization group calculations have suggested that this reaction displays anomalous kinetics at long times, $c_{A}(t) \sim at^{\delta -1}$, for certain types of topological or charged reactants and impurities. Both the exponent and the prefactor depend on the strength of disorder. The decay exponents determined fro...

We study the density of clustered immobile reactants in the diffusion-controlled single species annihilation. An initial state in which these impurities occupy a subspace of codimension d' leads to a substantial enhancement of their survival probability. The Smoluchowski rate theory suggests that the codimensionality plays a crucial role in determining the long time behavior. The system undergoes a transition at d'=2. For d'<2, a finite fraction of the impurities survive: ni(...

The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential and scaling limit. Our focus in this paper is on particle systems with long-range interactions. The derivation here is formal, but it provides an interpretation of particle systems as the motion of a particle in a random force field with a ...