多边形平面镶嵌中的E2分布和统计规律性
E2 distribution and statistical regularity in polygonal planar tessellations
摘要：
从太阳能超颗粒到玻利维亚的盐滩，从树叶上的静脉到果蝇翼盘上的细胞，基于太阳能的网络表现出极大的复杂性，但相似性仍然存在，统计分布可以非常一致。基于99多边形镶嵌的各种各样的物理起源的分析，这项工作证明了无处不在的指数分布的平方范数的变形张量，$E^{2}$，这直接导致普遍存在的伽玛分布的多边形纵横比。$E^{2}$分布又作为$χ^{2}$分布出现，并且开发了一个分析框架来计算其统计数据。$E^{2}$与许多能量形式密切相关，其玻尔兹曼特征允许伪温度的定义。再加上其他关键变量（如顶点位移）的正态性，这项工作揭示了所有系统中普遍存在的正态性
英文摘要：
From solar supergranulation to salt flat in Bolivia, from veins on leaves to cells on Drosophila wing discs, polygon-based networks exhibit great complexities, yet similarities persist and statistical distributions can be remarkably consistent. Based on analysis of 99 polygonal tessellations of a wide variety of physical origins, this work demonstrates the ubiquity of an exponential distribution in the squared norm of the deformation tensor, $E^{2}$, which directly leads to the ubiquitous presence of Gamma distributions in polygon aspect ratio. The $E^{2}$ distribution in turn arises as a $χ^{2}$-distribution, and an analytical framework is developed to compute its statistics. $E^{2}$ is closely related to many energy forms, and its Boltzmann-like feature allows the definition of a pseudo-temperature. Together with normality in other key variables such as vertex displacement, this work reveals regularities universally present in all systems alike
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