Nodal Surface Approximations to the Zero Equipotential Surfaces for Cubic Lattices
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- 作者：Paul J.F. Gandy and Jacek Klinowski
- 关键词：equipotential surfaces ; nodal surfaces ; triply periodic minimal surfaces ; mean curvature ; Gaussian curvature
- 刊名：Journal of Mathematical Chemistry
- 出版时间：2002
- 出版年：2002
- 期刊代码：44_02599791
- 类别：ch
- 卷：31
- 期：1
- 页码：1-16
- 数据来源：sp
摘要
Models of electrostatic surfaces in atomic crystals rely on equations involving the Jacobi theta functions. Numerical integration of these is prohibitively time consuming, making it difficult to examine the properties of the fields which give rise to the surfaces. We give simple expressions for the key electrostatic surfaces using Fourier expansions in basis sets of nodal surfaces. Any surface may be computed in seconds in a form ammenable to further analysis. The distribution of the mean and Gaussian curvatures over each surface has been visualised by assigning colours so that the range from minimum to maximum value spans blue to red. We similarly explore the mean and Gaussian scalar fields over a range of triply periodic surfaces of the same morphology.