论文标题
关于破碎，聚集和渗透的最新发展
Recent development on fragmentation, aggregation and percolation
论文作者
论文摘要
在本文中，我概述了像罗伯特·齐夫（Robert Ziff）这样有成就的研究人员如何影响全球的新一代研究人员，例如重力作为一种行动。在80年代，齐夫（Ziff）为碎裂动力学做出了重大贡献，然后是聚集动力学。在这里，我将讨论在碎片和聚集过程中出现的分形和多曲线，其中动态受非平凡的保护定律管辖。然后，我讨论了我最近的作品和渗透率的结果，在该验证中，我广泛使用了Newman-Ziff快速蒙特卡洛算法。为此，我定义了熵，该熵为定义特定的热量铺平了道路，并表明渗透的关键指数遵守Rushbrooke的不平等。此外，我们讨论了熵和顺序参数如何共同帮助我们检查渗透是否伴随着订单级别的过渡。熵的想法还有助于解释为什么鼓励小簇比大簇更快地生长的原因使过渡爆炸性。
In this article, I have outlined how an accomplished researcher like Robert Ziff has influenced a new generation of researchers across the globe like gravity as an action-at-a-distance. In the 80s Ziff made significant contributions to the kinetics of fragmentation followed by the kinetics of aggregation. Here, I will discuss fractal and multifractal that emerges in fragmentation and aggregation processes where the dynamics is governed by non-trivial conservation laws. I have then discussed my recent works and results on percolation where I made extensive use of Newman-Ziff fast Monte Carlo algorithm. To this end, I have defined entropy which paved the way to define specific heat and show that the critical exponents of percolation obey Rushbrooke inequality. Besides, we discuss how entropy and order parameter together can help us to check whether the percolation is accompanied by order-disorder transition or not. The idea of entropy also help to explain why encouraging smaller cluster to grow faster than larger clusters makes the transition explosive.
