The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion process in the reference frame moving with the average velocity of the front. Here we address pushed fronts, where the front velocity in the deterministic limit is affected by higher-order reactions and is therefore larger than the linear spread velocity. For a subclass of these fronts -- strongly pushed fronts -- the effective diffusion constant $D_f\sim 1/N$ of the front can be calculated, in the leading order, via a perturbation theory in $1/N \ll 1$, where $N\gg 1$ is the typical number of particles in the transition region. This perturbation theory, however, overestimates the contribution of a few fast particles in the leading edge of the front. We suggest a more consistent calculation by introducing a spatial integration cutoff at a distance beyond which the average number of particles is of order 1. This leads to a non-perturbative correction to $D_f$ which even becomes dominant close to the transition point between the strongly and weakly pushed fronts. At the transition point we obtain a logarithmic correction to the $1/N$ scaling of $D_f$. We also uncover another, and quite surprising, effect of the fast particles in the leading edge of the front. Because of these particles, the position fluctuations of the front can be described as a diffusion process only on very long time intervals with a duration $Δt \gg τ_N$, where $τ_N$ scales as $N$. At intermediate times the position fluctuations of the front are anomalously large and non-diffusive. Our extensive Monte-Carlo simulations of a particular reacting lattice gas model support these conclusions.
Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations
由于反应和扩散的散粒噪声，传播到亚稳态的反应前沿的位置波动。最近的理论[B]。Meerson，P.V. Sasorov，and Y. Kaplan，Phys.Rev.E84，011147（2011）]给出了弱噪声极限中的前扩散系数的封闭解析表达式。在这里，我们测试这个理论在随机模拟涉及反应和扩散粒子在一维晶格。我们还研究了一个小的噪声引起的系统性的前速度的移动相比，从空间连续的确定性反应扩散方程的预测。
