生成二十面体三壳层团簇准周期堆积的算法
Algorithm for generating quasiperiodic packings of icosahedral three-shell clusters
摘要：
条带投影法是产生具有预定局部结构的准周期图案的最重要方法。我们已经得到了一个非常有效的算法，这种方法允许使用它在超空间的非常高的维度。在math-ph/0504036中给出了二维簇的算法版本和十次双壳层簇的应用（10维超空间中的条带投影）。在这种情况下使用的FORTRAN 90程序是非常快的（在3分钟内获得700-800点）。我们提出了一个应用程序，我们的算法的三维集群。将三维物理空间嵌入到31维超空间中，利用条带投影方法，生成由正二十面体的12个顶点组成的三壳层二十面体簇的互穿平移副本的准周期堆积第一壳层是正十二面体的20个顶点（第二壳层），第二壳层是二十半十二面体的30个顶点（第三壳层）。在个人计算机奔腾4与Fortran PowerStation版本4.0（微软开发工作室），我们获得400-500分，在10分钟内。更多详细信息、参考书目和样本可以在网站上找到：http://fpcm5.fizica.unibuc.ro/~ncotfas/
英文摘要：
The strip projection method is the most important way to generate quasiperiodic patterns with predefined local structure. We have obtained a very efficient algorithm for this method which allows one to use it in superspaces of very high dimension. A version of this algorithm for two-dimensional clusters and an application to decagonal two-shell clusters (strip projection in a 10-dimensional superspace) has been presented in math-ph/0504036. The program in FORTRAN 90 used in this case is very fast (700-800 points are obtained in 3 minutes). We present an application of our algorithm to three-dimensional clusters. The physical three-dimensional space is embedded into a 31-dimensional superspace and the strip projection method is used in order to generate a quasiperiodic packing of interpenetrating translated copies of a three-shell icosahedral cluster formed by the 12 vertices of a regular icosahedron (the first shell), the 20 vertices of a regular dodecahedron (the second shell) and the 30 vertices of an icosidodecahedron (the third shell). On a personal computer Pentium 4 with Fortran PowerStation version 4.0 (Microsoft Developer Studio) we obtain 400-500 points in 10 minutes. More details, bibliography and samples can be found on the website: http://fpcm5.fizica.unibuc.ro/~ncotfas/
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