Fractal Geometry and Topology Abstracted From Hair Fibers

YIN Ya-jun; YANG Fan; LI Ying; FAN Qin-shan

doi:10.3879/j.issn.1000-0887.2009.08.004

Volume 30 Issue 8

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2009 > 30(8): 919-926

YIN Ya-jun, YANG Fan, LI Ying, FAN Qin-shan. Fractal Geometry and Topology Abstracted From Hair Fibers[J]. Applied Mathematics and Mechanics, 2009, 30(8): 919-926. doi: 10.3879/j.issn.1000-0887.2009.08.004

Citation:

PDF( 853 KB)

Fractal Geometry and Topology Abstracted From Hair Fibers

doi: 10.3879/j.issn.1000-0887.2009.08.004

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

Received Date: 2009-05-14
Rev Recd Date: 2009-06-29
Publish Date: 2009-08-15

Abstract

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

FullText(HTML)

References(6)

References

[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.