Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or disordered? If they are ordered, how are they ordered and what kinds of defects do they possess? Originally introduced to study problems in pure mathematics, Voronoi tessellations have become a powerful and versatile tool for analyzing countless problems in pure and applied physics. In this paper we explain the basics of Voronoi tessellations and the shapes they produce, and describe how they can be used to study many physical systems.
翻译:许多物理系统可以作为空间中嵌入的粒子的集成加以研究,通过确定性进化方程式进行演化。自然问题涉及这些安排的特征如何——它们是定序的还是混乱的?如果定序的,是订购的,是如何定序的,是何种缺陷的?最初是为了研究纯数学方面的问题而引进的,Voronoois的星系变异已成为分析纯物理和应用物理学中无数问题的强大和多功能的工具。在本文中,我们解释了Voronooois的熔化和它们产生的形状的基本原理,并描述了如何利用它们来研究许多物理系统。