Related papers: Comment on ``Critical behavior of a two-species re…
We show that solutions of the chemical reaction-diffusion system associated to $A+B\rightleftharpoons C$ in one spatial dimension can be approximated in $L^2$ on any finite time interval by solutions of a space discretized ODE system which…
We consider a reaction-diffusion model incorporating the reactions A -> 0, A -> 2A and 2A -> 3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order…
We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected…
The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…
It is shown by the method of renormalized field theory that in contrast to a statement based on a mathematically ill-defined invariance transformation and found in most of the recent publications on growth models with surface diffusion, the…
Recent work on exact renormalization group flow equations has pointed out the possibility to study critical phenomena in continuous dimension D of space. In an investigation of the O(N) model the dimension N of the fields may be seen as a…
The influence of long-range interactions decaying in d dimensions as 1/R^{d+\sigma} on the critical behavior of systems with Fisher's correlation-function exponent for short-range interactions \eta_{SR}<0, is re-examined. Such systems,…
We briefly review some common diffusion-limited reactions with emphasis on results for two-species reactions with anisotropic hopping. Our review also covers single-species reactions. The scope is that of providing reference and general…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
We consider diffusion-limited reactions A_i + A_j -> 0 (1 <= i < j <= q) in d space dimensions. For q > 2 and d >= 2 we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is…
The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic…
The critical dynamics of superconductors is studied using renormalization group and duality arguments. We show that in extreme type II superconductors the dynamic critical exponent is given exactly by $z=3/2$. This result does not rely on…
A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…
The phase transitions of the recently introduced 2A -> 3A, 4A -> 0 reaction-diffusion model (G.Odor, PRE 69 036112 (2004)) are explored in two dimensions. This model exhibits site occupation restriction and explicit diffusion of isolated…
In a recent work, Dantas and Stilck studied a model that generalizes the contact process model with diffusion. Our approach, based on the supercritical expansion, showed that for a weak diffusion regime the crossover exponent between the…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type…
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…
We provide finite-size scaling estimates for the dynamical critical exponent of the even parity-conserving universality class of critical behavior through exact numerical diagonalizations of the time evolution operator of an…
With extensive Monte Carlo simulations, we present high-precision estimates of the critical exponents of branching annihilating random walks with two offspring, a prototypical model of the directed Ising universality class in one dimension.…
The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features, called Luttinger liquid behavior. Critical exponents and certain thermodynamic quantities are expected to be related among each…