SuperCircle.xlsx

Spreadsheet containing data derived from use of associated Mathematica notebook. <br>Data consists of three tabs:<br>1. SuperCircle - exploration of :<br>i. a=b=1, n=mii a=b=2, n=miii a=1, b=2, n=m<br>as a function of n, and MaxCellMeasure (grid spacing for numerical evaluation)<br>2. SuperEllipse - exploration of:<br>a=b=1, n=2, m<br>as a function of m, and MaxCellMeasure (grid spacing for numerical evaluation)<br>3. Presentation Figures - Contains copies of the data from SuperCircle, including analyses to explore:<br>i Convergence as a function of MaxCellMeasure ii Ground state energy as a function of log(n)iii Convergence of superformula region area and ground state energy compared to the square defined by n = Inf.

本电子表格包含源自配套Mathematica笔记本运行所得的数值数据。
数据集包含三个工作表：
1. 超圆（SuperCircle）：探究a=b=1、n=m；a=b=2、n=m；a=1、b=2、n=m三种场景下，参数n与MaxCellMeasure（数值计算所用网格间距）对结果的影响规律。
2. 超椭圆（SuperEllipse）：探究a=b=1、n=2的场景下，参数m与MaxCellMeasure（数值计算所用网格间距）对结果的影响规律。
3. 演示图形（Presentation Figures）：包含超圆工作表的数据集副本，并附带用于探究以下内容的分析结果：
i. 以MaxCellMeasure为变量的收敛特性；
ii. 以log(n)为变量的基态能量；
iii. 相较于n趋近于无穷时的正方形区域，超公式区域面积与基态能量的收敛特性。