Anitas Eugen Mircea, Slyamov Azat
Joint Institute for Nuclear Research, Dubna, Moscow region, Russian Federation.
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania.
PLoS One. 2017 Jul 13;12(7):e0181385. doi: 10.1371/journal.pone.0181385. eCollection 2017.
Small-angle scattering (SAS) technique is applied to study the nano and microstructural properties of spatial patterns generated from chaos game representation (CGR). Using a simplified version of Debye formula, we calculate and analyze in momentum space, the monodisperse scattering structure factor from a system of randomly oriented and non-interacting 2D Sierpinski gaskets (SG). We show that within CGR approach, the main geometrical and fractal properties, such as the overall size, scaling factor, minimal distance between scattering units, fractal dimension and the number of units composing the SG, can be recovered. We confirm the numerical results, by developing a theoretical model which describes analytically the structure factor of SG. We apply our findings to scattering from single scale mass fractals, and respectively to a multiscale fractal representing DNA sequences, and for which an analytic description of the structure factor is not known a priori.
小角散射（SAS）技术被应用于研究由混沌游戏表示（CGR）生成的空间图案的纳米和微观结构特性。使用德拜公式的简化版本，我们在动量空间中计算并分析了由随机取向且非相互作用的二维谢尔宾斯基垫片（SG）系统产生的单分散散射结构因子。我们表明，在CGR方法中，可以恢复主要的几何和分形特性，例如整体尺寸、缩放因子、散射单元之间的最小距离、分形维数以及构成SG的单元数量。通过开发一个理论模型来解析描述SG的结构因子，我们证实了数值结果。我们将我们的发现应用于单尺度质量分形的散射，以及分别应用于代表DNA序列的多尺度分形，对于后者，结构因子的解析描述事先并不清楚。
