Cohen Elisheva, Kessler David A, Levine Herbert
Department of Physics, Bar-Ilan University, Ramat-Gan, IL52900 Israel.
Phys Rev Lett. 2005 Apr 22;94(15):158302. doi: 10.1103/PhysRevLett.94.158302. Epub 2005 Apr 20.
We introduce and study a new class of fronts in finite particle-number reaction-diffusion systems, corresponding to propagating up a reaction-rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equations. Instead, one can incorporate some aspects of the fluctuations via introducing a density cutoff. Using this method, we derive analytic expressions for the front velocity dependence on bulk particle density and show self-consistently why this cutoff approach can get the correct leading-order physics.
我们引入并研究了有限粒子数反应扩散系统中的一类新前沿，它对应于沿着反应速率梯度向上传播。我们表明，这些系统没有传统的平均场极限，因为随机过程中长时间前沿解的性质与通过求解平均场确定性反应扩散方程得到的解本质上不同。相反，通过引入密度截止，可以纳入涨落的一些方面。利用这种方法，我们推导出前沿速度对体粒子密度的依赖关系的解析表达式，并自洽地说明了为什么这种截止方法能够得到正确的主导阶物理。
