质量相关的不可逆凝聚的精确解
Exact solutions for mass-dependent irreversible aggregations
摘要：
我们考虑与质量相关的聚集过程（k+1）X -> X，给定初始状态下的单位质量粒子数.一个集群被选择成与其质量成比例，并与一维中的k个邻居合并，或者在混合良好的情况下与随机选择的k个其他集群合并。我们找到了相同的组合精确解的概率找到任何给定的配置的粒子在一个环或线，以及在良好的混合的情况下。单个团簇的质量分布具有标度律，并给出了有限尺寸标度形式。讨论了它与经典的不可逆凝聚核和的关系。
英文摘要：
We consider the mass-dependent aggregation process (k+1)X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one either with k-neighbors in one dimension, or -- in the well-mixed case -- with k other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given configuration of particles on a ring or line, and in the well-mixed case. The mass distribution of a single cluster exhibits scaling laws and the finite size scaling form is given. The relation to the classical sum kernel of irreversible aggregation is discussed.
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。
