从毛发纤维中抽象出的分形几何与拓扑

基金项目: 国家自然科学基金资助项目(10572076;10872114);江苏省自然科学基金资助项目(BK2008370)

Fractal Geometry and Topology Abstracted From Hair Fibers

1.
Department of Engineering Mechanics, School of Aerospace, AML, Tsinghua University, Beijing 100084, P. R. China;

摘要: 以羊毛纤维和人类头发为原型，以超级分形纤维概念为基础，抽象出了(3)分圆和(9+2)分圆分形集，构造了(3,9+2)分圆和(9+2,3)分圆双重分形集．针对(9+2)拓扑花样，证明了这样的命题：(9+2)拓扑花样精确地存在，但不唯一，其总个数为9，其中有2种同素异构体，即9种拓扑花样中，只有2种是独立(或基本)的．另外证实了(3,9+2)或(9+2，3)分圆分形花样是一个对称性破缺的黄金分形．
- 毛发纤维 /
- (9+2)拓扑 /
- 对称性破缺 /
- 双重分形集 /
- 分形几何
Abstract: Based on the concepts of fractal super fibers, the (3, 9+2)-circle and (9+2, 3)-circle binary fractal sets were abstracted from such prototypes as wool fibers and human hairs, with the (3)circle and the (9+2)circle fractal sets as subsets. As far as the (9+2) topological patterns are concerned, the following propositions were proved: The (9+2) topological patterns accurately exist, but they are of no uniqueness. Their total number is 9. Among them there are only 2 allotropes. In another word, among the 9 topological patterns only 2 are independent (or fundamental). Besides, it was demonstrated that the (3, 9+2)-circle and (9+2, 3)-circle fractal sets are golden ones with symmetry breaking.
- hair fibers /
- (9+2) topological patterns /
- symmetry breaking /
- binary fractal sets /
- fractal geometry

[1]	YIN Ya-jun, ZHANG Tong, YANG Fan,et al. Geometric conditions for fractal super carbon nanotubes with strict self-similarities[J].Chaos, Solitons & Fractals,2008,37(5):1257-1266.
[2]	YIN Ya-jun, YANG Fan, ZHANG Tong,et al.Growth condition and growth limit for fractal super fibers and fractal super tubes[J].International Journal of Nonlinear Sciences and Numerical Simulations,2008,9(1):96-102.
[3]	YIN Ya-jun, YANG Fan, FAN Qin-shan,et al. Cell elements, growth modes and topology evolutions of fractal supper fibers[J].International Journal of Nonlinear Sciences and Numerical Simulation,2009,10(1):1-12. doi: 10.1515/IJNSNS.2009.10.1.1
[4]	YIN Ya-jun,YANG Fan,FAN Qin-shan.Isologous fractal super fibers or fractal super lattices[J].International Journal of Electrospun Nanofibers and Applications,2008,2(3):193-201.
[5]	FAN Jie, LIU Jun-fang, HE Ji-huan. Hierarchy of wool fibers and fractal dimensions[J].International Journal of Nonlinear Sciences and Numerical Simulation, 2008,9(3): 293-296.
[6]	HE Ji-huan, REN Zhong-fu, FAN Jie,et al. Hierarchy of wool fibers and its interpretation using E-infinity theory[J].Chaos, Solitons & Fractals,2009,41(4):1839-1841.