多重胞元和规则多重分形

殷雅俊; 李颖; 杨帆; 范钦珊

doi:10.3879/j.issn.1000-0887.2010.01.006

多重胞元和规则多重分形

doi: 10.3879/j.issn.1000-0887.2010.01.006

清华大学航天航空学院工程力学系,北京 100084;2.南京工业大学力学部,南京 211816

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

详细信息

作者简介:
殷雅俊(1964- ),男,河南人,教授,博士,博士生导师(联系人.Tel:+86-10-62795536;E-mail:yiny@jtsinghua.edu.cn).

中图分类号: Q811.6;O184
计量
- 文章访问数: 1211
- HTML全文浏览量: 91
- PDF下载量: 884
- 被引次数: 0
出版历程
- 收稿日期: 2009-07-09
- 修回日期: 2009-11-10
- 刊出日期: 2010-01-15

Multiple Cell Elements and Regular Multifractals

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

摘要

摘要: 以超级分形纤维和双重分形纤维的研究结果为基础，达成了如下目标：首先，归纳、抽象出了多重胞元概念；其次，基于多重胞元概念，证实：具有严格自相似性的规则多重分形，不仅是可构造的，而且其构造模式具有普遍性；再者，通过分析构造模式，发现：任何规则多重分形，都可以在多重胞元意义下，被精确地等价成具有多重精细结构的广义单重分形．而基于这种等价性，单重分形维数公式就能够推广至规则多重分形维数公式，单重分形几何就能够推广至规则多重分形几何；最后，借助规则多重分形，构造了几种黄金分形．
- 双重分形纤维 /
- 双重胞元 /
- 规则双重分形 /
- 多重胞元 /
- 规则多重分形
Abstract: Based on fractal super fibers and binary fractal fibers, the following objectives were approached: Firstly, the concept of multiple celle lements was induced and abstracted. Secondly, th rough multiple cell elements, regular multifractals with strict self-similarities were confirmed not only constructible, but also being of universal construction mode. Thirdly, through the construction mode, a regular multifractal was found to be equivalent to a generalized regular single fractal with multiple fine structures under the meaning of multiple cellelements. On the basis of this equivalence, the dimension of single fractals was extended to that of regular multifractals, and the geometry of single fractals was extended to that of regular multifractals. Fourthly, through regular multifractals a few golden fractals were constructed.
- binary fractal fibers /
- binary cell elements /
- regular binary fractals /
- multiple cellelements /
- multifractals

HTML全文

参考文献(20)

[1]	YIN Ya-jun, ZHANG Tong, YANG Fan, et al. Geometric conditions for fractal super carbon nanotubes with strict self-similarities [J]. Chaos, Solitons and Fractals, 2008, 37(5): 1257-1266. doi: 10.1016/j.chaos.2008.01.005
[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 and Fractals, 2009, 41(4):1839-1841. doi: 10.1016/j.chaos.2008.07.035
[7]	殷雅俊，杨帆，李颖，等.从毛发纤维中抽象出的分形几何与拓扑 [J].应用数学和力学, 2009, 30(8): 919-926.
[8]	黄立基，丁菊仁. 多标度分形理论及进展 [J].物理学进展，1991, 11(3): 69-330.
[9]	Mandelbrot B B. On the intermittent free turbulence [C]Weber E.Proc Symp Turbulence of Fluid and Plasma . New York: Interscience, 1969:483-492.
[10]	Grassberger P. Generalized dimensions of strange attractors [J]. Physics Letters A, 1983, 97(6): 227-230. doi: 10.1016/0375-9601(83)90753-3
[11]	Hentschel H, Procaccia I.The infinite number of generalized dimensions of fractals and strange attractors [J]. Physica D, 1983, 8(3): 435-444. doi: 10.1016/0167-2789(83)90235-X
[12]	Frisch U, Parisi G.On the singularity structure of fully developed turbulence [C] Ghil M, Benzi R, Parisi G. Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics. Amsterdam: North-Holland, 1985:84-87.
[13]	Benzi R, Paladin G, Parisi G, et al.On the multifractal nature of fully developed turbulence and chaotic systems [J]. J Phys A, 1984, 17(18): 3521-3531. doi: 10.1088/0305-4470/17/18/021
[14]	Helsey T, Jensen M H, Kadanoff L P,et al.Fractal measures and their singularities: the characterization of strange sets [J]. Phys Rev A, 1986, 33(2): 1141-1151. doi: 10.1103/PhysRevA.33.1141
[15]	Bensimon D, Jensen M H, Kadanoff L P.Renormalization-group analysis of the global structure of the period-doubling attractor [J]. Phys Rev A, 1986, 33(5): 3622-3624. doi: 10.1103/PhysRevA.33.3622
[16]	Feigenbaum M J, Jensen M H, Procaccia I I. Time ordering and the thermodynamics of strange sets: theory and experimental tests [J]. Phys Rev Lett, 1986, 57(13): 1503-1506. doi: 10.1103/PhysRevLett.57.1503
[17]	Feigenbaum M.Some characterizations of strange sets [J]. J Stat Phys, 1987, 46(5/6): 919-925. doi: 10.1007/BF01011148
[18]	成令忠，冯京生，冯子强，等.组织学彩色图鉴[M].北京：人民卫生出版社,2000.
[19]	周炜星，王延杰，于遵宏.多重分形奇异谱的几何特性（Ⅰ）：经典Renyi定义法[J]. 华东理工大学学报，2000, 26(4): 385-389.
[20]	周炜星，王延杰，于遵宏.多重分形奇异谱的几何特性（Ⅱ）：配分函数法 [J]. 华东理工大学学报，2000, 26(4): 390-395.