广义Cantor分形的散射
The scattering from generalized Cantor fractals
摘要：
我们考虑一个具有可变分维的分形，它是著名的三分康托集的推广。与通常的康托集相比，分形维数是使用比例因子控制的，并且可以在一维中从零到一变化，在三维中从零到三变化。计算了三维广义Cantor分形小角散射的强度分布。该系统由一组迭代规则生成，每次迭代对应一定的分形生成。小角散射被认为是从单色散集，这是随机取向和放置。散射强度表示叠加在幂律衰减上的最小值和最大值，其指数等于散射体的分形维数，但最小值和最大值随着分形集的多分散性增加而衰减。它示出，对于有限代的分形，指数的变化在足够大的波矢量从分形维数为4，通常的Porod定律给出的值。它示出的分形组成的颗粒的数量可以估计从分形和Porod区域之间的边界值。用解析法计算了分形的回转半径。
英文摘要：
We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in one dimension and from zero to three in three dimensions. The intensity profile of small-angle scattering from the generalized Cantor fractal in three dimensions is calculated. The system is generated by a set of iterative rules, each iteration corresponding to a certain fractal generation. Small-angle scattering is considered from monodispersive sets, which are randomly oriented and placed. The scattering intensities represent minima and maxima superimposed on a power law decay, with the exponent equal to the fractal dimension of the scatterer, but the minima and maxima are damped with increasing polydispersity of the fractal sets. It is shown that for a finite generation of the fractal, the exponent changes at sufficiently large wave vectors from the fractal dimension to four, the value given by the usual Porod law. It is shown that the number of particles of which the fractal is composed can be estimated from the value of the boundary between the fractal and Porod regions. The radius of gyration of the fractal is calculated analytically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
