论文标题
在成核和生长过程中的动态缩放和随机分形
Dynamic scaling and stochastic fractal in nucleation and growth processes
论文作者
论文摘要
研究了各种不同生长速度的稳定相（S期）的一类成核和生长模型。结果表明，对于增长速度，$ v \ sim s（t）/t $和$ v \ sim x/τ（x）$，其中$ s（t）$和$τ$是亚稳态相（M相）和平均成核时间的平均域大小和平均成核时间的平均域大小，遵循功率法之后的m频率衰变。此外，在不同时间的快照$ t $用于收集域尺寸$ x $ m期$ x $的分布功能的数据，以遵守动态缩放。使用数据崩溃的想法，我们表明每个快照都是一个自相似的分形。但是，对于$ v = {\ rm const。} $，例如在经典的kolmogorov-johnson-mehl-avrami（kJMA）模型中，对于$ v \ sim 1/t $，m频率的衰减是指数的，并且它们不伴随动态量表。我们发现数值模拟和分析结果之间的完美一致性。
A class of nucleation and growth models of a stable phase (S-phase) is investigated for various different growth velocities. It is shown that for growth velocities $v\sim s(t)/t$ and $v\sim x/τ(x)$, where $s(t)$ and $τ$ are the mean domain size of the metastable phase (M-phase) and the mean nucleation time respectively, the M-phase decays following a power law. Furthermore, snapshots at different time $t$ are taken to collect data for the distribution function $c(x,t)$ of the domain size $x$ of M-phase are found to obey dynamic scaling. Using the idea of data-collapse we show that each snapshot is a self-similar fractal. However, for $v={\rm const.}$ like in the classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) model and for $v\sim 1/t$ the decay of the M-phase are exponential and they are not accompanied by dynamic scaling. We find a perfect agreement between numerical simulation and analytical results.
