离散多组分破碎的统计力学
Statistical Mechanics of Discrete Multicomponent Fragmentation
摘要：
我们制定的离散多组分碎裂事件的统计使用的方法借用统计力学。我们生成的合奏的所有可行的分布，可以形成一个单一的整数多组分质量被分解成固定数量的片段，并计算在集合中的所有分布的组合多重性。我们定义了随机碎裂的条件下，分布的概率成正比于它的重数，并获得了配分函数和封闭形式的平均分布。然后，我们引入了一个功能，偏见的概率分布产生系统的方式片段分布，偏离任何任意程度的随机情况。我们证实了理论的结果，通过蒙特卡罗模拟和演示的例子中，在筛分的碎片分布的组分进行优先混合或偏析相对于母体颗粒。
英文摘要：
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
