Periodic entanglement II: weavings from hyperbolic line patterns
Periodic entanglement II: weavings from hyperbolic line patterns
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DOI：
10.1107/s0108767313001682
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发表时间：
2013-05-01
期刊：
影响因子：
--
通讯作者：
Hyde, Stephen T.
中科院分区：
文献类型：
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作者：
Evans, Myfanwy E.;Robins, Vanessa;Hyde, Stephen T.
有序的圆柱体阵列（称为棒填料）现在广泛用于晶体结构的描述。这些被概括为包括具有圆形横截面的长丝的晶体堆积阵列，包括其中心轴是通用螺旋的曲线圆柱体。通过将双曲平面 (H-2) 中的线图案投影到欧几里得空间 (E-3) 中的立方 genus-3 三周期最小曲面（原始曲面、菱形曲面和螺旋曲面）来构造一套最简单的此类通用棒填料。最简单的设计对应于包含传统圆柱形细丝的“经典”棒填料。更复杂的填料包含相互缠绕的细丝的三维阵列，这些细丝可以无限延伸或形成三维编织的有限环。引入了这些编织物的规范“理想”嵌入的概念，该概念是从结嵌入的概念中推广出来的，并通过收紧编织以最小化长丝长度与体积之比来通过算法发现。收紧算法建立在 SONO 算法的基础上，用于寻找理想的结构象。描述了三种不同类别的编织。
Ordered arrays of cylinders, known as rod packings, are now widely used in descriptions of crystalline structures. These are generalized to include crystallographic packed arrays of filaments with circular cross sections, including curvilinear cylinders whose central axes are generic helices. A suite of the simplest such general rod packings is constructed by projecting line patterns in the hyperbolic plane (H-2) onto cubic genus-3 triply periodic minimal surfaces in Euclidean space (E-3): the primitive, diamond and gyroid surfaces. The simplest designs correspond to 'classical' rod packings containing conventional cylindrical filaments. More complex packings contain three-dimensional arrays of mutually entangled filaments that can be infinitely extended or finite loops forming three-dimensional weavings. The concept of a canonical 'ideal' embedding of these weavings is introduced, generalized from that of knot embeddings and found algorithmically by tightening the weaving to minimize the filament length to volume ratio. The tightening algorithm builds on the SONO algorithm for finding ideal conformations of knots. Three distinct classes of weavings are described.