Farjoun Yossi, Neu John C
G. Millán Institute of Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, Madrid, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051607. doi: 10.1103/PhysRevE.83.051607. Epub 2011 May 20.
A previous paper [Y. Farjoun and J. C. Neu, Phys. Rev. E 78, 051402 (2008)] presents a simple kinetic model of the initial creation transient, starting from pure monomer. During this transient the majority of clusters are created, and the distribution of cluster sizes that emerges from it is predicted to be discontinuous at the largest cluster size. It is well known that the further evolution according to the Lifshitz-Slyozov model of coarsening preserves this discontinuity. The result is at odds with the original proposal of Lifshitz and Slyozov, that the physical late-stage coarsening distribution is the smooth one. The current paper presents an analytic-numerical solution of the Lifshitz-Slyozov equations, starting from the discontinuous creation distribution. Of course, this analysis selects the discontinuous late-stage coarsening distribution, but there is much more. It resolves the intermediate stages between the creation transient and late-state coarsening and provides specific scales of time and cluster size that characterize the onset of coarsening.
之前的一篇论文[Y. 法尔琼和J. C. 诺伊，《物理评论E》78, 051402 (2008)]提出了一个从纯单体开始的初始生成瞬态的简单动力学模型。在这个瞬态过程中，大部分团簇形成，并且预计从该过程中出现的团簇尺寸分布在最大团簇尺寸处是不连续的。众所周知，根据利夫希茨 - 斯廖佐夫粗化模型的进一步演化会保留这种不连续性。这一结果与利夫希茨和斯廖佐夫最初的提议相悖，他们认为物理后期粗化分布是平滑的。本文给出了从不连续的生成分布开始的利夫希茨 - 斯廖佐夫方程的解析 - 数值解。当然，这种分析选择了不连续的后期粗化分布，但还有更多内容。它解决了生成瞬态和后期粗化之间的中间阶段问题，并提供了表征粗化开始的特定时间尺度和团簇尺寸。
