论文标题
离散多组分碎片的统计力学
Statistical Mechanics of Discrete Multicomponent Fragmentation
论文作者
论文摘要
我们使用从统计力学借用的方法来制定离散多组分碎片事件的统计。我们生成所有可行分布的集合，当单个整数多组分质量分解为固定数量的片段并计算集合中所有分布的组合多样性时，可以形成。我们通过以下条件定义随机碎片，即分布的概率与其多重性成正比，并以封闭形式获得分区函数和平均分布。然后，我们引入了一个功能，该功能偏向于以系统的方式片段分布产生的分布概率，该分布偏离随机情况。我们通过蒙特卡洛模拟证实了该理论的结果，并演示了片段分布的筛分切割中的成分相对于父粒子的优先混合或隔离。
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.
