二维Voronoi中从对称性破缺到泊松点过程 镶嵌：六边形的一般性质

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

摘要翻译：
我们将平面的正则正方形和蜂窝状Voronoi镶嵌的性质与Poisson-Voronoi情形的性质联系起来，从而在一个共同的框架下分析对称破缺过程和镶嵌生成点的均匀随机分布的方法。我们考虑由规则位置被参数α控制的高斯噪声扰动的点产生的镶嵌的系综模拟。我们研究Voronoi细胞的边数、面积和周长。对于alpha>0，六边形是最常见的一类细胞，2参数伽玛分布很好地描述了几何特征的统计特性。噪声引起的对称性破坏了正方形镶嵌，而蜂窝六边形镶嵌是非常稳定的，对于小而有限的噪声，α<0.1时，所有的Voronoi单元都是六边形。对于中等量的高斯噪声，由于两个受扰动的镶嵌的统计量是不可区分的，因此丢失了对特定的未受扰动镶嵌的记忆。当alpha>2时，结果收敛于Poisson-Voronoi镶嵌的结果。n边胞的性质随着α的变化而变化，直到达到Poisson-Voronoi极限时，α>2。证实了周长的Desch定律不成立，并建立了n的平方根依赖关系。限制在六角形单元内的单元面积和周长的系综平均值与全系综平均值相吻合；这可能意味着边数作为一个热力学状态变量在n=6附近波动；这强化了这样一种观点，即六边形除了其普遍存在的数值突出之外，还可以作为二维Voronoi镶嵌中的一般多边形。
---
英文标题：
《From symmetry break to Poisson point process in 2D Voronoi
  tessellations: the generic nature of hexagons》
---
作者：
Valerio Lucarini
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
--
一级分类：Computer Science        计算机科学
二级分类：Computational Geometry        计算几何
分类描述：Roughly includes material in ACM Subject Classes I.3.5 and F.2.2.
大致包括ACM课程I.3.5和F.2.2中的材料。
--
一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
--
一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
--
一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
--

---
英文摘要：
  We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random distributions of tessellation-generating points. We consider ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise controlled by the parameter alpha. We study the number of sides, the area, and the perimeter of the Voronoi cells. For alpha>0, hexagons are the most common class of cells, and 2-parameter gamma distributions describe well the statistics of the geometrical characteristics. The symmetry break due to noise destroys the square tessellation, whereas the honeycomb hexagonal tessellation is very stable and all Voronoi cells are hexagon for small but finite noise with alpha<0.1. For a moderate amount of Gaussian noise, memory of the specific unperturbed tessellation is lost, because the statistics of the two perturbed tessellations is indistinguishable. When alpha>2, results converge to those of Poisson-Voronoi tessellations. The properties of n-sided cells change with alpha until the Poisson-Voronoi limit is reached for alpha>2. The Desch law for perimeters is confirmed to be not valid and a square root dependence on n is established. The ensemble mean of the cells area and perimeter restricted to the hexagonal cells coincides with the full ensemble mean; this might imply that the number of sides acts as a thermodynamic state variable fluctuating about n=6; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be taken as generic polygons in 2D Voronoi tessellations.
---
PDF链接：
https://arxiv.org/pdf/708.0977

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：NOI 六边形 对称性 点过程 一般性 周长 位置 系综 六边形 噪声