炸药渗流的Achlioptas规则的反演
Inverting the Achlioptas rule for explosive percolation
摘要：
在通常的Achlioptas过程中，在每一步中都会选择一些随机选择的最小集群合并在一起。由此产生的聚集过程导致了巨星系团的延迟诞生和所谓的爆炸渗流转变，显示出一系列异常特征。我们探索一个过程与相反的选择规则，其中最大的集群的随机选择的合并在一起。我们开发了一种基于Smoluchowski方程的这种渗流理论，找到了渗流阈值，并描述了这种连续过渡的标度性质，即临界指数和振幅，以及标度函数。我们表明，定性地说，这种转变是类似于普通的渗流之一，虽然发生在连接较少的系统。
英文摘要：
In the usual Achlioptas processes the smallest clusters of a few randomly chosen ones are selected to merge together at each step. The resulting aggregation process leads to the delayed birth of a giant cluster and the so-called explosive percolation transition showing a set of anomalous features. We explore a process with the opposite selection rule, in which the biggest clusters of the randomly chosen ones merge together. We develop a theory of this kind of percolation based on the Smoluchowski equation, find the percolation threshold, and describe the scaling properties of this continuous transition, namely, the critical exponents and amplitudes, and scaling functions. We show that, qualitatively, this transition is similar to the ordinary percolation one, though occurring in less connected systems.
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。
