利用電腦輔助視覺化研究準晶格圖樣

Abstract

本論文研製之利用電腦輔助研究產生Quasi-crystal圖樣，是利用黎曼和的方式切分貝塞爾函數 所產生出Quasi-crystal圖樣的一般產生方程式，其程式結構與平面波疊加方程式相等。同義可證，利用同樣的方式分切貝塞爾函數 所產生出的Quasi-crystal圖樣產生式，其程式不僅產生出更多不同樣式的圖樣，而且它的特性與平面波疊加的相對相位特性相同；最後利用改變平面波的動量分布來還原古典圓形彈子球台軌跡，產生出不同維度的quasi-crystal圖像，其所產生出來的圖樣是前述的方式的數倍，進而看見更多美麗的Quasi-crystal圖樣。我們希望藉由這些通式去看到更多與自然界或數學界相似的Quasi-crystal美麗的圖樣及利用此通式來產生更多不同類型的Quasi-crystal圖樣以便後續之研究之模擬。

A procedure is computer-aided visualization for investigation of quasi- crystal patterns. The function which has been partitioned by “Riemann sum” divided Bessel function into n subintervals. It has been called a general generation of quasi-crystal patterns and approximated to the function which is a superposition of plane wave. By extension, another function which divided Bessel function has been approximated to the function that is plane wave control by varying relative phase. Finally, the momentum distribution of plane wave reapportioning has been restored to the period orbit of classical circle billiard. It can also product the different quasi-crystal patterns which is more than relative phase module. In the future, we wish the researchers who will find the quasi-crystal patterns in experiment can verify by our function. They also use the function to extend other generation function.