Institute of Solid State Physics, Chernogolovka, Moscow district, 142432, Russia.
Phys Rev E. 2019 Dec;100(6-1):062121. doi: 10.1103/PhysRevE.100.062121.
We present a systematic analysis of diffusion-controlled interaction and collapse of two identical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ compared to their characteristic initial size and a relatively large initial ratio of island to sea concentrations, the evolution dynamics of the island-sea-island system is determined unambiguously by the dimensionless parameter Λ=N_{0}/N_{Ω}, where N_{0} is the initial particle number in the island and N_{Ω} is the initial number of sea particles in the volume Ω=(2ℓ)^{d}. It is established that (a) there is a d-dependent critical value Λ_{★} above which island coalescence occurs; (b) regardless of d the centers of each of the islands move toward each other along a universal trajectory merging in a united center at the d-dependent critical value Λ_{s}≥Λ_{★}; (c) in one-dimensional systems Λ_{★}=Λ_{s}, therefore, at Λ<Λ_{★} each of the islands dies individually, whereas at Λ>Λ_{★} coalescence is completed by collapse of a single-centered island in the system center; (d) in two- and three-dimensional systems in the range Λ_{★}<Λ<Λ_{s} coalescence is accompanied by subsequent fragmentation of a two-centered island and is completed by individual collapse of each of the islands. We discuss a detailed picture of coalescence, fragmentation, and collapse of islands focusing on evolution of their shape and on behavior of the relative width of the reaction front at the final collapse stage and in the vicinity of starting coalescence and fragmentation points. We demonstrate that in a wide range of parameters, the front remains sharp up to a narrow vicinity of the coalescence, fragmentation, and collapse points.
我们对在相同物种扩散系数下的 sharp 反应前沿 A+B→0 的传播过程中，两个相同的、空间分离的 d 维 A 粒子岛在 B 粒子海中的扩散控制相互作用和坍缩进行了系统分析。我们表明，在岛中心之间的初始距离 2ℓ 足够大于它们的初始特征尺寸，并且岛与海的初始浓度比相对较大的情况下，岛海岛系统的演化动力学明确由无量纲参数 Λ=N_{0}/N_{Ω} 决定，其中 N_{0} 是岛上的初始粒子数，N_{Ω} 是体积 Ω=(2ℓ)^{d} 中海粒子的初始数。结果表明：(a)存在一个依赖于 d 的临界值 Λ_{★}，超过该值后岛就会发生合并；(b)无论 d 如何，每个岛的中心都沿着一个通用轨迹相互靠近，在依赖于 d 的临界值 Λ_{s}≥Λ_{★} 处合并为一个统一的中心；(c)在一维系统中，Λ_{★}=Λ_{s}，因此，在 Λ<Λ_{★} 时，每个岛都会单独死亡，而在 Λ>Λ_{★} 时，合并是通过系统中心单中心岛的坍缩完成的；(d)在二维和三维系统中，在 Λ_{★}<Λ<Λ_{s} 的范围内，合并伴随着双中心岛的后续分裂，并通过每个岛的单独坍缩完成。我们详细讨论了岛的合并、分裂和坍缩的情况，重点关注了它们形状的演化以及在最终坍缩阶段和在起始合并和分裂点附近的反应前沿相对宽度的行为。我们证明，在广泛的参数范围内，前沿在接近合并、分裂和坍缩点的狭窄范围内仍然保持尖锐。
