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fractal geometry and topology abstracted from hair fibers

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Applied Mathematics and Mechanics(English Edition) 2009年第8期30卷 983-990页

作者：殷雅俊杨帆李颖范钦珊 Department of Engineering Mechanics School of AerospaceAML Tsinghua University Division of Mechanics Nanjing University of Technology

Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form 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 are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.

关键词： hair fibers (9+2) topological patterns symmetry breaking binary fractal sets fractal geometry

Prediction of heat transfer of nanofluid on critical heat flux based on fractal geometry

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Chinese Physics B 2013年第1期22卷 344-349页

作者：肖波齐 School of Physics and Electromechanical Engineering Sanming University

Analytical expressions for nucleate pool boiling heat transfer of nanofluid in the critical heat flux （CHF） region are derived taking into account the effect of nanoparticles moving in liquid based on the fractal geometry theory. The proposed fractal model for the CHF of nanofluid is explicitly related to the average diameter of the nanoparticles, the volumetric nanoparticle concentration, the thermal conductivity of nanoparticles, the fractal dimension of nanoparticles, the fractal dimension of active cavities on the heated surfaces, the temperature, and the properties of the fluid. It is found that the CHF of nanofluid decreases with the increase of the average diameter of nanoparticles. Each parameter of the proposed formulas on CHF has a clear physical meaning. The model predictions are compared with the existing experimental data, and a good agreement between the model predictions and experimental data is found. The validity of the present model is thus verified. The proposed fractal model can reveal the mechanism of heat transfer in nanofluid.

关键词： nanofluid fractal geometry heat transfer

Synthesis of fractal geometry and CAGD models for multi-scale topography modelling of functional surfaces

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Journal of Central South University 2011年第5期18卷 1493-1501页

作者：王清辉李静蓉陈彦政潘敏强汤勇 School of Mechanical and Automotive Engineering South China University of Technology

In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified *** on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro *** issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case *** the consistent mathematic model,multi-scale surface geometries can be represented ***,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.

关键词： surface roughness microtopography fractal geometry functional surface

Restoration method of characters on Jiagu rubbings based on Poisson distribution and fractal geometry

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Science China(Information Sciences) 2010年第7期53卷 1296-1304页

作者： GU ShaoTong1,2,3, FENG GeFei1,2,3, MA XiaoHu1,2,4 & YANG YiMing1,2,3 1Institute of Linguistics, Xuzhou Normal University, Xuzhou 221009, China 2Jiangsu College Key Lab of Linguistic Sciences and Neuro-cognition Engineering, Xuzhou Normal University, Xuzhou 221009, China 3Linguistic Science College, Xuzhou Normal University, Xuzhou 221009, China 4School of Computer Science and Technology, Soochow University, Suzhou 215006, China Institute of Linguistics Xuzhou Normal University Xuzhou China Jiangsu College Key Lab of Linguistic Sciences and Neuro-cognition Engineering Xuzhou Normal University Xuzhou China Linguistic Science College Xuzhou Normal University Xuzhou China School of Computer Science and Technology Soochow University Suzhou China

A scheme for character restoration of Jiagu rubbings based on Poisson distribution and fractal geometry is proposed in this paper. The distribution characteristics of the connected regions on Jiagu rubbings is analyzed, and all the connected regions are recognized according to differences between these and their mathematical expectations. Regions are recognized as noise regions and filled if the differences are negative, while stroke regions are reserved. The attributes of the character image edges on Jiagu rubbings are also analyzed. The fractal dimensions of the character edge of Jiagu rubbings are calculated by means of statistics. The feature points are obtained using the cosine of the angle between the two vectors of the point and the consecutive two points. Different compression transformations with weighted coordinates are performed on different strokes and segments of the characters so as to smoothen the character edge of Jiagu rubbings images. Experimental results show that our scheme could successfully clear noise regions and polish the character edge of Jiagu rubbings.

关键词： Jiagu rubbings Poisson distribution fractal geometry fractal dimension compression transformation character restoration

Visual Evaluation of the Morphologic Structure of Nonwovens Using Image Analysis and fractal geometry

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Journal of Donghua University(English Edition) 2004年第3期21卷 162-165页

作者：杨旭红李栋高 College of Material Engeineering Soochow University China 215021

Nonwovens are fiber materials which are based on nonwoven technologies. For the complexity and randomness of nonwovens morphologic structures, it is difficult to express them effectively using classical method. fractal geometry gives us a new idea and a powerful tool to study on irregularity of geometric objects. Therefore, we studied on the pore size, pore shape, pore size distribution and fiber orientation distribution of real nonwovens using fractal geometry combined with computer image analysis to evaluate nonwovens’ morphologic structures.

关键词： nonwovens morphologic structure fractal geometry image analysis

A new proof of Honeycomb Conjecture by fractal geometry methods

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Frontiers of Mechanical Engineering 2013年第4期8卷 367-370页

作者： Tong ZHANG Kai DING Research Center for Solid Mechanics Beihang University School of Engineering Brown University School of Instrument Science and Optical Engineering Beihang University

Based on fractal geometry,we put forward a concise and straightforward method to prove Honeycomb Conjecture—a classical mathematic *** wins the most efficient covering unit in the twodimensional space,compared with the other two covering units—triangle and *** this point of view,honeycomb is treated as a hierarchical fractal structure that fully fills the ***,the total side length and area are easily calculated and from the results,the covering efficiency of each possible unit is provided quantitatively.

关键词： Honeycomb Conjecture fractal geometry hierarchical fractal structure

SOME PROBLEMS ON fractal geometry AND TOPOLOGICAL DYNAMICAL SYSTEMS

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Analysis in Theory and Applications 2009年第1期25卷 5-15页

作者： Zuoling Zhou Feng Li Lingnan Collge Sun Yat-sen University Guangzhou 510275 P. R. China Department of Mathematics and Computer Science Albany State University Albany GA 31705 USA

This paper is a continuation of [14], some new problems on fractal geometry and topological dynamical systems have been posed.

关键词： fractal geometry topological dynamical system

THE fractal geometry AND TRIGONOMETRIC SERIES

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Journal of Mathematical Study 1994年第1期 1-4页

作者： Yu Jiarong(Dept. of Math. Wuhan Univ,Wuhan 430070)

ＴＨＥＦＲＡＣＴＡＬＧＥＯＭＥＴＲＹＡＮＤＴＲＩＧＯＮＯＭＥＴＲＩＣＳＥＲＩＥＳ￥ＹｕＪｉａｒｏｎｇＤｅｐｔ．ｏｆＭａｔｈ．；ＷｕｈａｎＵｎｉｖ（Ｗｕｈａｎ４３００７０）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｉ... 详细信息

ＴＨＥＦＲＡＣＴＡＬＧＥＯＭＥＴＲＹＡＮＤＴＲＩＧＯＮＯＭＥＴＲＩＣＳＥＲＩＥＳ￥ＹｕＪｉａｒｏｎｇＤｅｐｔ．ｏｆＭａｔｈ．；ＷｕｈａｎＵｎｉｖ（Ｗｕｈａｎ４３００７０）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｉｎｄｒｏｄｕｃｅｓｏｍｅｒｅｃｅｎ...

关键词： fractal geometry Hausdorff dimension Bonligand dimension LacunaryTrigonometric series Random trigonometric series

Dual-band and polarization-insensitive terahertz absorber based on fractal Koch curves

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Chinese Physics B 2014年第5期23卷 594-599页

作者：马岩冰张怀武李元勋王艺程赖伟恩李颉 State Key Laboratory of Electronic Films and Integrated Devices University of Electronic Science and Technology of China Institute of Electronic and Information Engineering University of Electronic Science and Technology of China

We report the design, fabrication, and characterization of a dual-band and polarization-insensitive metamaterial ab-sorber （MA）, which consists of periodically arranged fractal Koch curves acting as the top resonator array and a metallic ground plane separated by a dielectric spacer. Compared with conventional MAs, a more compact size and multi-frequency operation are achieved by using fractal geometry as the unit cell of the MA. Both the effective medium theory and the multi- reflection interference theory are employed to investigate the underlying physical mechanism of the proposed terahertz MA, and results indicate that the latter theory is not suitable for explaining the absorption mechanism in our investigated struc-ture. Two absorption peaks are observed at 0.226 THz and 0.622 THz with absorptivities of 91.3% and 95.6% respectively and good agreements between the full-wave simulation and experimental results are achieved.

关键词： metamaterial absorber terahertz fractal geometry