十次拟周期镶嵌的点过程
Point processes for decagonal quasiperiodic tilings
摘要：
提出了十次拟周期镶嵌膨胀定则的一般构造原理。原型被限定为具有单位边的多边形。平铺的膨胀规则是瓦片的扩展和划分的组合，其中扩展的瓦片可以被任意划分，只要保持原瓦片的集合。一种特定的点装饰过程被证明是有用的识别可能的划分规则。该方法是能够产生广泛的十边形平铺，其中许多是手性和具有分形边界的原子表面。提出了两个新的十次镶嵌族，一个是四次的，另一个是三次的。详细研究了具有菱形、五边形和六边形原型的三元镶嵌的性质。
英文摘要：
A general construction principle of inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of an expansion and a division of the tiles, where the expanded tiles can be divided arbitrarily as far as the set of prototiles is maintained. A certain kind of point decoration processes turns out to be useful for the identification of possible division rules. The method is capable of generating a broad range of decagonal tilings, many of which are chiral and have atomic surfaces with fractal boundaries. Two new families of decagonal tilings are presented; one is quarternary and the other ternary. Properties of the ternary tilings with rhombic, pentagonal, and hexagonal prototiles are investigated in detail.
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