A mathematical framework is presented to represent turbostratic disorder in materials like carbon blacks, smectites and twistedn-layer graphene. In particular, the set of all possible disordered layers, including rotated, shifted and curved layers, forms a stochastic sequence governed by a hidden Markov model. The probability distribution over the set of layer types is treated as an element of a Hilbert space and, using the tools of Fourier analysis and functional analysis, expressions are developed for the scattering cross sections of a broad class of disordered materials.

中文翻译：

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用于描述应用于炭黑和石墨烯的乱层无序的隐马尔可夫模型

提出了一个数学框架来表示炭黑、蒙脱石和扭曲等材料中的乱层无序n层石墨烯。特别是，所有可能的无序层的集合，包括旋转、移位和弯曲层，形成由隐马尔可夫模型控制的随机序列。层类型集上的概率分布被视为希尔伯特空间的元素，并使用傅里叶分析和泛函分析工具，为一大类无序材料的散射横截面开发了表达式。