全寿命碎裂过程的随机模拟及其碎片分布的动力学标度律
Stochastic modeling on fragmentation process over lifetime and its dynamical scaling law of fragment distribution
摘要：
我们提出了一个随机模型的碎片化过程中，考虑到碎片的寿命作为其大小的函数的Gibrat过程的基础上开发。如果寿命由片段大小的幂函数确定，则数值结果表明，通过按平均片段大小缩放大小，可以将不同时间的大小分布折叠成单个时不变曲线（即，该分布服从动态标度律）。如果寿命由碎片尺寸的对数函数决定，则分布不服从标度律。通过对主方程的标度分析，得到了服从标度律的充要条件。
英文摘要：
We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical results indicate that size distributions at different times can be collapsed into a single time-invariant curve by scaling size by average fragment size (i.e., the distribution obeys the dynamical scaling law). If lifetime is determined by a logarithmic function of fragment size, the distribution does not obey the scaling law. The necessary and sufficient condition that the scaling law is obeyed is obtained by a scaling analysis of the master equation.
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