Khain Evgeniy, Meerson Baruch, Sasorov Pavel
Department of Physics, Oakland University, Rochester, Michigan 48309, USA.
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Phys Rev E. 2020 Aug;102(2-1):022137. doi: 10.1103/PhysRevE.102.022137.
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}∼1/N of the front can be calculated, in the leading order, via a perturbation theory in 1/N≪1, where N≫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 nonperturbative 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≫τ_{N}, where τ_{N} scales as N. At intermediate times the position fluctuations of the front are anomalously large and nondiffusive. Our extensive Monte Carlo simulations of a particular reacting lattice gas model support these conclusions.
反应扩散前沿向不稳定状态传播时的经验速度，会因反应和扩散的散粒噪声而波动。在某些条件下，这些波动可以在随前沿平均速度移动的参考系中被描述为一个扩散过程。这里我们讨论被推动的前沿，在确定性极限下前沿速度受高阶反应影响，因此大于线性扩散速度。对于这类前沿的一个子类——强推动前沿——前沿的有效扩散常数(D_f\sim1/N)，在主导阶次下，可以通过(1/N\ll1)的微扰理论来计算，其中(N\gg1)是过渡区域中典型的粒子数。然而，这个微扰理论高估了前沿前沿少数快速粒子的贡献。我们建议通过引入一个空间积分截止来进行更一致的计算，在该截止距离之外粒子的平均数量为(1)量级。这导致对(D_f)的非微扰修正，甚至在强推动前沿和弱推动前沿之间的过渡点附近成为主导。在过渡点，我们得到对(D_f)的(1/N)标度的对数修正。我们还发现了前沿前沿快速粒子的另一个相当令人惊讶的效应。由于这些粒子，前沿的位置波动只有在持续时间(\Delta t\gg\tau_N)（其中(\tau_N)与(N)成比例）的非常长的时间间隔上才能被描述为一个扩散过程。在中间时间，前沿的位置波动异常大且非扩散。我们对一个特定反应晶格气体模型进行的广泛蒙特卡罗模拟支持了这些结论。
