Crystal Frameworks, Matrix-valued Functions and Rigidity Operators
Crystal Frameworks, Matrix-valued Functions and Rigidity Operators
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水晶框架、矩阵值函数和刚性运算符
DOI：
10.1007/978-3-0348-0648-0_26
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
S. Power
中科院分区：
文献类型：
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作者：
S. Power
本文介绍和评述了晶体骨架的无穷小动力学，即周期性离散键节结构的无穷小动力学，d = 2，3，…我们讨论了有限杆-关节框架理论的基本对象刚性矩阵、刚性算子、矩阵函数表示和低能声子。这些声子在材料晶体中，如石英和沸石，被称为刚性单元模式，或RUM，并与刚性单元的相对运动有关，如石英的四面体多面体键结模型中的SiO 4四面体。我们还介绍了半无限晶体框架，双晶体框架和相关的多变量Toeplitz算子。
An introduction and survey is given of some recent work on the infinitesimal dynamics of crystal frameworks, that is, of translationally periodic discrete bond-node structures in ℝd, for d = 2,3,... We discuss the rigidity matrix, a fundamental object from finite bar-joint framework theory, rigidity operators, matrix-function representations and low energy phonons. These phonons in material crystals, such as quartz and zeolites, are known as rigid unit modes, or RUMs, and are associated with the relative motions of rigid units, such as SiO4 tetrahedra in the tetrahedral polyhedral bondnode model for quartz. We also introduce semi-infinite crystal frameworks, bi-crystal frameworks and associated multi-variable Toeplitz operators.