Fluctuation and relaxation properties of pulled fronts: a possible scenario for non-Kardar-Parisi-Zhang behavior

We argue that while fluctuating fronts propagating into an unstable state should be in the standard KPZ universality class when they are {\em pushed}, they should not when they are {\em pulled}: The universal $1/t$ velocity relaxation of deterministic pulled fronts makes it unlikely that the KPZ equation is the appropriate effective long-wavelength low-frequency theory in this regime. Simulations in 2$D$ confirm the proposed scenario, and yield exponents $\beta \approx 0.29\pm 0.01$, $\zeta \approx 0.40\pm 0.02$ for fluctuating pulled fronts, instead of the KPZ values $\beta=1/3$, $\zeta = 1/2$. Our value of $\beta$ is consistent with an earlier result of Riordan {\em et al.}Comment: Replaced with revised versio

Two site self consistent method for front propagation in reaction-diffusion system

We study front propagation in the reaction diffusion process $A\leftrightarrow2A$ on one dimensional lattice with hard core interaction between the particles. We propose a two site self consistent method (TSSCM) to make analytic estimates for the front velocity and are in excellent agreement with the simulation results for all parameter regimes. We expect that the simplicity of the method will allow one to use this technique for estimating the front velocity in other reaction diffusion processes as well.Comment: 6 figure

The universality class of fluctuating pulled fronts

It has recently been proposed that fluctuating ``pulled'' fronts propagating into an unstable state should not be in the standard KPZ universality class for rough interface growth. We introduce an effective field equation for this class of problems, and show on the basis of it that noisy pulled fronts in {\em d+1} bulk dimensions should be in the universality class of the {\em (d+1)+1}D KPZ equation rather than of the {\em d+1}D KPZ equation. Our scenario ties together a number of heretofore unexplained observations in the literature, and is supported by previous numerical results.Comment: 4 pages, 2 figure

Steady State and Dynamics of Driven Diffusive Systems with Quenched Disorder

We study the effect of quenched disorder on nonequilibrium systems of interacting particles, specifically, driven diffusive lattice gases with spatially disordered jump rates. The exact steady-state measure is found for a class of models evolving by drop-push dynamics, allowing several physical quantities to be calculated. Dynamical correlations are studied numerically in one dimension. We conjecture that the relevance of quenched disorder depends crucially upon the speed of the kinematic waves in the system. Time-dependent correlation functions, which monitor the dissipation of kinematic waves, behave as in pure system if the wave speed is non-zero. When the wave speed vanishes, e.g. for the disordered exclusion process close to half filling, disorder is strongly relevant and induces separation of phases with different macroscopic densities. In this case the exponent characterizing the dynamical correlation function changes.Comment: 4 pages, RevTeX, 4 eps figures included using 'psfig.sty

Front Propagation and Diffusion in the A <--> A + A Hard-core Reaction on a Chain

We study front propagation and diffusion in the reaction-diffusion system A $\leftrightharpoons$ A + A on a lattice. On each lattice site at most one A particle is allowed at any time. In this paper, we analyze the problem in the full range of parameter space, keeping the discrete nature of the lattice and the particles intact. Our analysis of the stochastic dynamics of the foremost occupied lattice site yields simple expressions for the front speed and the front diffusion coefficient which are in excellent agreement with simulation results.Comment: 5 pages, 5 figures, to appear in Phys. Rev.

Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes

We study the effect of quenched spatial disorder on the steady states of driven systems of interacting particles. Two sorts of models are studied: disordered drop-push processes and their generalizations, and the disordered asymmetric simple exclusion process. We write down the exact steady-state measure, and consequently a number of physical quantities explicitly, for the drop-push dynamics in any dimensions for arbitrary disorder. We find that three qualitatively different regimes of behaviour are possible in 1-$d$ disordered driven systems. In the Vanishing-Current regime, the steady-state current approaches zero in the thermodynamic limit. A system with a non-zero current can either be in the Homogeneous regime, chracterized by a single macroscopic density, or the Segregated-Density regime, with macroscopic regions of different densities. We comment on certain important constraints to be taken care of in any field theory of disordered systems.Comment: RevTex, 17pages, 18 figures included using psfig.st