论文标题
Fisher和Kolmogorov，Petrovskii和Piskunov波的随机方法，用于稀释和浓缩溶液中不同扩散性的物种
Stochastic approach to Fisher and Kolmogorov, Petrovskii, and Piskunov wave fronts for species with different diffusivities in dilute and concentrated solutions
论文作者
论文摘要
Fisher和Kolmogorov，Petrovskii和Piskunov类型的波动局部涉及两种具有不同扩散系数的物种A和B，$ d_a $和$ d_b $是使用稀释和浓缩溶液中的主方程方法研究的。物种A和B应该参与自催化反应A+B-> 2a。与确定性描述的结果相反，稀释案例中从主方程中得出的前速敏感地取决于物种B的扩散系数B。对确定性方程的线性分析，在反应术语中截止截止，无法解释$ d_b> d_a> d_a $的前速下降。在集中溶液的情况下，与交叉扩散相关的过渡速率源自相应的扩散通量。在稀释案例中获得的波前的特性仍然有效，但通过交叉扩散来减轻不同扩散系数的影响。
A wave front of Fisher and Kolmogorov, Petrovskii, and Piskunov type involving two species A and B with different diffusion coefficients $D_A$ and $D_B$ is studied using a master equation approach in dilute and concentrated solutions. Species A and B are supposed to be engaged in the autocatalytic reaction A+B -> 2A. Contrary to the results of a deterministic description, the front speed deduced from the master equation in the dilute case sensitively depends on the diffusion coefficient of species B. A linear analysis of the deterministic equations with a cutoff in the reactive term cannot explain the decrease of the front speed observed for $D_B > D_A$. In the case of a concentrated solution, the transition rates associated with cross-diffusion are derived from the corresponding diffusion fluxes. The properties of the wave front obtained in the dilute case remain valid but are mitigated by cross-diffusion which reduces the impact of different diffusion coefficients.
