Theory of Branching and Annihilating Random Walks

A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate equation, which predicts only an active phase, remains qualitatively correct near $d_c = 2$ dimensions; but below $d_c' \approx 4/3$ a nontrivial transition to an inactive phase governed by power law behavior appears. For $m$ odd there is a dynamic phase transition for any $d \leq 2$ which is described by the directed percolation universality class.Comment: 4 pages, revtex, no figures; final version with slight changes, now accepted for publication in Phys. Rev. Let

Does hardcore interaction change absorbing type critical phenomena?

It has been generally believed that hardcore interaction is irrelevant to absorbing type critical phenomena because the particle density is so low near an absorbing phase transition. We study the effect of hardcore interaction on the N species branching annihilating random walks with two offspring and report that hardcore interaction drastically changes the absorbing type critical phenomena in a nontrivial way. Through Langevin equation type approach, we predict analytically the values of the scaling exponents, $\nu_{\perp} = 2, z = 2, \alpha = 1/2, \beta = 2$ in one dimension for all N > 1. Direct numerical simulations confirm our prediction. When the diffusion coefficients for different species are not identical, $\nu_{\perp}$ and $\beta$ vary continuously with the ratios between the coefficients.Comment: 4 pages, 1 figur

Nonequilibrium Critical Dynamics of a Three Species Monomer-Monomer Model

We study a three species monomer-monomer catalytic surface reaction model with a reactive steady state bordered by three equivalent unreactive phases where the surface is saturated with one species. The transition from the reactive to a saturated phase shows directed percolation critical behavior. Each pair of these reactive-saturated phase boundaries join at a bicritical point where the universal behavior is in the even branching annihilating random walk class. We find the crossover exponent from bicritical to critical behavior and a new exponent associated with the bicritical interface dynamics.Comment: 4 pages RevTex. 4 eps figures included with psfig.sty. Uses multicol.sty. Accepted for publication in PR

Criticality of natural absorbing states

We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating random walk with $N\geq 2$ species both with and without hard-core interaction. We show that certain static characteristics of the so-called natural absorbing states develop power law singularities which signal the approach of the critical point. These results are also explained using random walk arguments. In addition to that we show that when dynamics of our model is considered as a minimum finding procedure, it has the best efficiency very close to the critical point.Comment: 6 page

Interacting Monomer-Dimer Model with Infinitely Many Absorbing States

We study a modified version of the interacting monomer-dimer (IMD) model that has infinitely many absorbing (IMA) states. Unlike all other previously studied models with IMA states, the absorbing states can be divided into two equivalent groups which are dynamically separated infinitely far apart. Monte Carlo simulations show that this model belongs to the directed Ising universality class like the ordinary IMD model with two equivalent absorbing states. This model is the first model with IMA states which does not belong to the directed percolation (DP) universality class. The DP universality class can be restored in two ways, i.e., by connecting the two equivalent groups dynamically or by introducing a symmetry-breaking field between the two groups.Comment: 5 pages, 5 figure

Numerical Study of a Field Theory for Directed Percolation

A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened sensitivity to fluctuationsattending multiplicative noise in the vicinity of an absorbing state, a useful method requires discretization of the field variable as well as of space and time. When applied to the field theory for directed percolation in 1+1 dimensions, the method yields critical exponents which compare well against accepted values.Comment: 18 pages, LaTeX, 6 figures available upon request LC-CM-94-00

Mean-Field Analysis and Monte Carlo Study of an Interacting Two-Species Catalytic Surface Reaction Model

We study the phase diagram and critical behavior of an interacting one dimensional two species monomer-monomer catalytic surface reaction model with a reactive phase as well as two equivalent adsorbing phase where one of the species saturates the system. A mean field analysis including correlations up to triplets of sites fails to reproduce the phase diagram found by Monte Carlo simulations. The three phases coexist at a bicritical point whose critical behavior is described by the even branching annihilating random walk universality class. This work confirms the hypothesis that the conservation modulo 2 of the domain walls under the dynamics at the bicritical point is the essential feature in producing critical behavior different from directed percolation. The interfacial fluctuations show the same universal behavior seen at the bicritical point in a three-species model, supporting the conjecture that these fluctuations are a new universal characteristic of the model.Comment: 11 pages using RevTeX, plus 4 Postscript figures. Uses psfig.st

The homeostatic chemokine CCL21 predicts mortality in aortic stenosis patients and modulates left ventricular remodeling

BACKGROUND: CCL21 acting through CCR7, is termed a homeostatic chemokine. Based on its role in concerting immunological responses and its proposed involvement in tissue remodeling, we hypothesized that this chemokine could play a role in myocardial remodeling during left ventricular (LV) pressure overload. METHODS AND RESULTS: Our main findings were: (i) Serum levels of CCL21 were markedly raised in patients with symptomatic aortic stenosis (AS, n = 136) as compared with healthy controls (n = 20). (ii) A CCL21 level in the highest tertile was independently associated with all-cause mortality in these patients. (iii) Immunostaining suggested the presence of CCR7 on macrophages, endothelial cells and fibroblasts within calcified human aortic valves. (iv). Mice exposed to LV pressure overload showed enhanced myocardial expression of CCL21 and CCR7 mRNA, and increased CCL21 protein levels. (v) CCR7-/- mice subjected to three weeks of LV pressure overload had similar heart weights compared to wild type mice, but increased LV dilatation and reduced wall thickness. CONCLUSIONS: Our studies, combining experiments in clinical and experimental LV pressure overload, suggest that CCL21/CCR7 interactions might be involved in the response to pressure overload secondary to AS