论文标题
硬圆形弧的密集包装
Dense packings of hard circular arcs
论文作者
论文摘要
这项工作调查了一致的坚硬无限量 - 在二维欧几里得空间中的圆形弧。它专注于那些可说的大小的人，其亚倾斜角$θ\ in \ weft（π，2π\右）$。与那些可以称为未成年人的undot $θ\ in \ weft [0，π\ right] $不同的是$ the的$θ\，这是两个硬度无限的圆形的$ the $ the的$ the（\ weft）的$ the（\ eft）。在彼此之间进行了安排，例如，可复制的AD无限，尽管这是无限型颗粒，尽管这些凹陷是无限的，但最密集的包装量是有限的。紧凑型圆形圆形圆形弧形，其中特定的$θ$依赖性的圆形（反）（反）顺时针互动。
This work investigates dense packings of congruent hard infinitesimally--thin circular arcs in the two-dimensional Euclidean space. It focuses on those denotable as major whose subtended angle $θ\in \left ( π, 2π\right ]$. Differently than those denotable as minor whose subtended angle $θ\in \left [0, π\right]$, it is impossible for two hard infinitesimally-thin circular arcs with $θ\in \left ( π, 2π\right ]$ to arbitrarily closely approach once they are arranged in a configuration, e.g. on top of one another, replicable ad infinitum without introducing any overlap. This makes these hard concave particles, in spite of being infinitesimally thin, most densely pack with a finite number density. This raises the question as to what are these densest packings and what is the number density that they achieve. Supported by Monte Carlo numerical simulations, this work shows that one can analytically construct compact closed circular groups of hard major circular arcs in which a specific, $θ$-dependent, number of them (anti-)clockwise intertwine. These compact closed circular groups then arrange on a triangular lattice. These analytically constructed densest-known packings are compared to corresponding results of Monte Carlo numerical simulations to assess whether they can spontaneously turn up.
