非扁平正方形平顶：特征描述

IF 1.2 3区数学 Q1 MATHEMATICS

Milan Journal of Mathematics Pub Date : 2022-01-01 Epub Date: 2022-03-24 DOI:10.1007/s00032-022-00350-5

Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli

{"title":"非扁平正方形平顶：特征描述","authors":"Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli","doi":"10.1007/s00032-022-00350-5","DOIUrl":null,"url":null,"abstract":"Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the nonflatness of the tiles gives rise to nontrivial geometries, with configurations bending, wrinkling, or even rolling up in one direction.","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"90 1","pages":"131-175"},"PeriodicalIF":1.2000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9242529/pdf/","citationCount":"0","resultStr":"{\"title\":\"Tilings with Nonflat Squares: A Characterization.\",\"authors\":\"Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli\",\"doi\":\"10.1007/s00032-022-00350-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the nonflatness of the tiles gives rise to nontrivial geometries, with configurations bending, wrinkling, or even rolling up in one direction.\",\"PeriodicalId\":49811,\"journal\":{\"name\":\"Milan Journal of Mathematics\",\"volume\":\"90 1\",\"pages\":\"131-175\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9242529/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Milan Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00032-022-00350-5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2022/3/24 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Milan Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00032-022-00350-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/3/24 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

受二维材料系统建模的启发，我们对三维中相同的非平面正方形排列进行了描述。我们证明，这种排列的精细几何形状完全可以用方块的相互方向模式来描述，而且这些模式是周期性的、一维的。与平面情况不同的是，瓷砖的非平面性导致了非复杂的几何形状，其构型在一个方向上弯曲、起皱甚至卷起。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Tilings with Nonflat Squares: A Characterization.

查看原文本刊更多论文

Tilings with Nonflat Squares: A Characterization.

Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the nonflatness of the tiles gives rise to nontrivial geometries, with configurations bending, wrinkling, or even rolling up in one direction.

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

Milan Journal of Mathematics 数学-数学

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists. Many of the articles will be "invited contributions" from speakers in the "Seminario Matematico e Fisico di Milano". However, also other authors are welcome to submit articles which are in line with the "Aims and Scope" of the journal.