论文标题
随机反应的速度波动前面传播到不稳定状态：强烈推动的前部
Velocity fluctuations of stochastic reaction fronts propagating into an unstable state: strongly pushed fronts
论文作者
论文摘要
反应扩散前线的经验速度，传播到不稳定状态，由于反应和扩散的镜头噪声而波动。在某些条件下，这些波动可以描述为在参考框架移动的平均速度的参考框架中的扩散过程。在这里，我们解决了推动的正面，其中确定性极限中的前速度受高阶反应的影响，因此大于线性扩散速度。对于这些前沿的子类 - 强烈推动的前部 - 可以通过$ 1/n \ ll 1 $的扰动理论以领先顺序计算出前面的有效扩散常数$ d_f \ sim 1/n $，其中$ n \ gg 1 $是$ n \ gg 1 $是过渡区域中的典型粒子。然而，这种扰动理论高估了前缘前缘的一些快速粒子的贡献。我们建议通过在距离的距离处引入空间积分截止截止值，这是一个更加一致的计算，超过了粒子的平均数量为1。这导致非扰动校正至$ d_f $，甚至在强大和弱推向的前部之间的过渡点上占主导地位。在过渡点，我们获得了$ D_F $的$ 1/N $规模的对数校正。我们还揭示了快速粒子在前缘的另一个且令人惊讶的效果。由于这些粒子，前部的位置波动只能将其描述为一个扩散过程，只有很长的时间间隔，持续时间$Δt\ ggggτ_n$，其中$τ_n$ scales scales as scales as $ n $。在中间，前部的位置波动异常大且不扩散。我们对特定反应晶格气体模型的广泛蒙特卡洛模拟支持了这些结论。
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.
