只有加布里埃尔邻居的多面泊松-沃罗诺伊小区

IF 2.2 3区物理与天体物理 Q2 MECHANICS

Journal of Statistical Mechanics: Theory and Experiment Pub Date : 2024-07-02 DOI:10.1088/1742-5468/ad5434

H J Hilhorst

{"title":"只有加布里埃尔邻居的多面泊松-沃罗诺伊小区","authors":"H J Hilhorst","doi":"10.1088/1742-5468/ad5434","DOIUrl":null,"url":null,"abstract":"Let be the probability for a planar Poisson–Voronoi cell to be n-sided and have only Gabriel neighbors. Using an exact coordinate transformation followed by scaling arguments and a mean-field type calculation, we obtain the asymptotic expansion of in the limit of large n. We determine several statistical properties of a many-sided cell obeying this ‘Gabriel condition.’ In particular, the cell perimeter, when parametrized as a function of the polar angle θ, behaves as a Brownian bridge on the interval . We point out similarities and differences with related problems in random geometry.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"49 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Many-sided Poisson–Voronoi cells with only Gabriel neighbors\",\"authors\":\"H J Hilhorst\",\"doi\":\"10.1088/1742-5468/ad5434\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let be the probability for a planar Poisson–Voronoi cell to be n-sided and have only Gabriel neighbors. Using an exact coordinate transformation followed by scaling arguments and a mean-field type calculation, we obtain the asymptotic expansion of in the limit of large n. We determine several statistical properties of a many-sided cell obeying this ‘Gabriel condition.’ In particular, the cell perimeter, when parametrized as a function of the polar angle θ, behaves as a Brownian bridge on the interval . We point out similarities and differences with related problems in random geometry.\",\"PeriodicalId\":17207,\"journal\":{\"name\":\"Journal of Statistical Mechanics: Theory and Experiment\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Mechanics: Theory and Experiment\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1742-5468/ad5434\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Mechanics: Theory and Experiment","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1742-5468/ad5434","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}

引用次数: 0

摘要

设一个平面泊松-沃罗诺伊单元为 n 边且只有加布里埃尔邻域的概率。通过精确的坐标变换、缩放参数和均场型计算，我们得到了大 n 极限的渐近展开。特别是，当细胞周长被参数化为极角 θ 的函数时，其行为就像区间上的布朗桥。我们指出了与随机几何中相关问题的异同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Many-sided Poisson–Voronoi cells with only Gabriel neighbors

Let be the probability for a planar Poisson–Voronoi cell to be n-sided and have only Gabriel neighbors. Using an exact coordinate transformation followed by scaling arguments and a mean-field type calculation, we obtain the asymptotic expansion of in the limit of large n. We determine several statistical properties of a many-sided cell obeying this ‘Gabriel condition.’ In particular, the cell perimeter, when parametrized as a function of the polar angle θ, behaves as a Brownian bridge on the interval . We point out similarities and differences with related problems in random geometry.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Statistical Mechanics: Theory and Experiment 物理-力学

CiteScore

4.50

自引率

12.50%

发文量

210

审稿时长

1.0 months

期刊介绍： JSTAT is targeted to a broad community interested in different aspects of statistical physics, which are roughly defined by the fields represented in the conferences called ''Statistical Physics''. Submissions from experimentalists working on all the topics which have some ''connection to statistical physics are also strongly encouraged. The journal covers different topics which correspond to the following keyword sections. 1. Quantum statistical physics, condensed matter, integrable systems Scientific Directors: Eduardo Fradkin and Giuseppe Mussardo 2. Classical statistical mechanics, equilibrium and non-equilibrium Scientific Directors: David Mukamel, Matteo Marsili and Giuseppe Mussardo 3. Disordered systems, classical and quantum Scientific Directors: Eduardo Fradkin and Riccardo Zecchina 4. Interdisciplinary statistical mechanics Scientific Directors: Matteo Marsili and Riccardo Zecchina 5. Biological modelling and information Scientific Directors: Matteo Marsili, William Bialek and Riccardo Zecchina