Quasicrystalline Minimal Surfaces

9412561肥皂膜被认为是具有二十面体对称性的最简单的物理系统。 数值构造这样一个表面与恒定的平均曲率，预计将推进我们的准晶态的理解。 这种方法将检验平铺描述在准晶中的普适性。 本文的工作是为了获得一种新的方法来理解没有瓦片的准晶。 这将通过数值构造表面来实现，例如表现出二十面体对称性的肥皂膜。 这项研究将测试平铺描述的通用性。

9412561 A soap film is proposed as the simplest physical system which possesses icosahedral symmetry. Numerical construction of such a surface with constant mean curvature is expected to advance our understanding of the quasicrystalline state. This approach will test the universality of tiling description in quasicrystals. %%% The proposed work is to obtain a new way to to understand the quasicrystals without tiles. This will be achieved by numerically constructing surfaces such as soap films which exhibit icosahedral symmetry. This research will test universality of the tiling description.