论文标题
多边形平面镶嵌的E2分布和统计规律性
E2 distribution and statistical regularity in polygonal planar tessellations
论文作者
论文摘要
从太阳能超晶到玻利维亚的盐平坦，从叶子上的静脉到果蝇翼圆盘上的细胞，基于多边形的网络表现出很大的复杂性，但是相似性持续存在，统计分布可以非常一致。基于对多种物理起源的99个多边形细胞的分析，这项工作证明了变形张量的平方规范中指数分布的无处不在，$ e^{2} $直接导致Polygon applations Gamma分布的无处不在。 $ e^{2} $分布又作为$χ^{2} $ - 分布出现，并开发了一个分析框架来计算其统计信息。 $ e^{2} $与许多能量形式密切相关，其类似玻尔兹曼的功能允许定义一个伪型 - 温度。与其他关键变量（例如顶点位移）中的正态性，这项工作揭示了所有系统中普遍存在的规律性
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
