From 20 hyperbolic forests to 30 Euclidean entangled thickets

被引:46
作者
Hyde, ST [1 ]
Oguey, C
机构
[1] Australian Natl Univ, Res Sch Phys Sci, Canberra, ACT 0200, Australia
[2] Univ Cergy Pontoise, LPTM, F-95031 Cergy Pontoise, France
关键词
D O I
10.1007/PL00011063
中图分类号
O469 [凝聚态物理学];
学科分类号
070205 ;
摘要
A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces: including the P,D, gyroid and H surfaces. Some of these graphs are natural generalisations of bicontinuous topologies to bi-, tri-, quadra- and octa-continuous forms, Interwoven layer graphs and periodic sets of finite clusters also emerge from the algorithm. Many of the graphs are chiral. The generated graphs are compared with some organo-metallic molecular crystals with multiple frameworks and molecular mesophases found in copolymer melts.
引用
收藏
页码:613 / 630
页数:18
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