Abstract
Background
Lewis’s law and Aboav-Weaire’s law are two fundamental laws used to describe the topology of two-dimensional (2D) structures; however, their theoretical bases remain unclear.
Methods
We used R software with the Conicfit package to fit ellipses based on the geometric parameters of polygonal cells of ten different kinds of natural and artificial 2D structures.
Results
Our results indicated that the cells could be classified as an ellipse’s inscribed polygon (EIP) and that they tended to form the ellipse’s maximal inscribed polygon (EMIP). This phenomenon was named as ellipse packing. On the basis of the number of cell edges, cell area, and semi-axes of fitted ellipses, we derived and verified new relations of Lewis’s law and Aboav-Weaire’s law.
Conclusions
Ellipse packing is a short-range order that places restrictions on the cell topology and growth pattern. Lewis’s law and Aboav-Weaire’s law mainly reflect the effect of deformation from circle to ellipse on cell area and the edge number of neighboring cells, respectively. The results of this study could be used to simulate the dynamics of cell topology during growth.
Funder
National Key Research and Development Program of China
Subject
General Agricultural and Biological Sciences,General Biochemistry, Genetics and Molecular Biology,General Medicine,General Neuroscience
Reference37 articles.
1. The arrangement of grains in a polycrystal;Aboav;Metallography,1970
2. The arrangement of cells in a net;Aboav;Metallography,1980
3. The arrangement of cells in a net. II;Aboav;Metallography,1983
4. The arrangement of cells in a net. IV;Aboav;Metallography,1985
5. CaGe—a virtual environment for studying some special classes of plane graphs—an update;Brinkmann;Match Communications in Mathematical and in Computer Chemistry,2010
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献