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Hierarchical fractal structure of perfect single-layer graphene

T. Zhang, K. Ding

Frontiers of Mechanical Engineering 2013, Volume 8, Issue 4,   Pages 371-382 doi: 10.1007/s11465-013-0279-1

Abstract: structure from the perspective of fractal geometry was studied for the first time.The outer boundary curve had a fractal dimension equal to one, and a multi-fractal structure from a naturallyA series of strict self-similar hexagons comprised a rotating fractal set.existing regular fractal structures and sets.A fundamental example of a multi-fractal structure was also presented.

Keywords： hierarchical fractal structure     fractal dimension     the fifth space-filling curve     multi-fractal structure    

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A new proof of Honeycomb Conjecture by fractal geometry methods

Tong ZHANG, Kai DING

Frontiers of Mechanical Engineering 2013, Volume 8, Issue 4,   Pages 367-370 doi: 10.1007/s11465-013-0273-7

Abstract:

Based on fractal geometry, we put forward a concise and straightforward method to prove HoneycombFrom this point of view, honeycomb is treated as a hierarchical fractal structure that fully fills the

Keywords： Honeycomb Conjecture     fractal geometry     hierarchical fractal structure    

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Theoretical study on the confine-stiffening effect and fractal cracking of square concrete filled steel

Frontiers of Structural and Civil Engineering 2021, Volume 15, Issue 6,   Pages 1317-1336 doi: 10.1007/s11709-021-0763-3

Abstract: to accurately predict the tensile strength and stiffness enhancements and realistically simulate the fractal

Keywords： square concrete filled tubes     confine-stiffening     confine-strengthening     fractal cracking     fracture    

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Copper fractal growth during recycling from waste printed circuit boards by slurry electrolysis

Frontiers of Environmental Science & Engineering 2021, Volume 15, Issue 6, doi: 10.1007/s11783-021-1405-7

Abstract:

• Copper fractal growth was observed during WPCBs recycling by slurry

Keywords： Dendritic copper     Fractal growth     WPCBs     Slurry electrolysis    

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Fractal characteristic evaluation and interpolation reconstruction for surface topography of drilled

Frontiers of Mechanical Engineering 2021, Volume 16, Issue 4,   Pages 840-854 doi: 10.1007/s11465-021-0643-5

Abstract: In this paper, an improved fractal interpolation model is proposed to reconstruct the surface topographyFractal parameters are calculated to evaluate the measured surface profiles.The maximum and minimum fractal dimension of the hole wall are 1.36 and 1.07, whereas the maximum andminimum fractal roughness are 4.05 × 10 −5 and 4.36 × 10 −10 m, respectively.Fractal parameter D s and statistical parameters Sa, Sq, and Sz

Keywords： surface topography     fractal evaluation     fractal interpolation     reconstruction     composite    

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Permeability analysis and seepage process study on crystal layer in melt crystallization with fractal

Xiaobin JIANG, Baohong HOU, Yongli WANG, Jingkang WANG

Frontiers of Chemical Science and Engineering 2011, Volume 5, Issue 4,   Pages 435-441 doi: 10.1007/s11705-011-1139-3

Abstract: In this paper a porous media seepage model was applied to analyze the permeability and study the seepage process of crystal pillar formed in the preparation of electronic grade phosphoric acid (EGPA). By inspecting the seeping process, the structure parameter of crystal pillar could be obtained. Two basic ideal models (perfectly separated model and perfectly connected model) were presented and a characterized factor was introduced to modify the model. A good simulation result was obtained which met the experiment result well. The relationship between and permeability were also discussed. The characterized factor showed potential application on optimizing process.

Keywords： melt crystallization     porous media     fractal     permeability     hyperpure material     simulation    

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Aggregating structure in coal water slurry studied by eDLVO theory and fractal dimension

Qiang LI, Qian WANG, Jian HOU, Jiansheng ZHANG, Yang ZHANG

Frontiers in Energy 2023, Volume 17, Issue 2,   Pages 306-316 doi: 10.1007/s11708-021-0736-1

Abstract: this paper, the micro-structure in coal water slurry was studied by extended DLVO (eDLVO) theory and fractalstability between different types of coals are measured and explained by the aggregating structure and fractalThis aggregating structure can be described and characterized by fractal dimension.

Keywords： coal water slurry     extended DLVO (eDLVO)     fractal dimension     stability    

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Application of fractal theory to unsaturated soil mechanics

XU Yongfu, TONG Lixin

Frontiers of Structural and Civil Engineering 2007, Volume 1, Issue 4,   Pages 411-421 doi: 10.1007/s11709-007-0056-5

Abstract: The fractal approach seems to be a potentially useful tool to describe hierarchical systems and is suitableconductivity function, unsaturated shear strength, swelling deformation and compression were derived from the fractalfor the pore-size distribution, and were expressed by only two independent physical parameters, the fractalbetween the experimental results of unsaturated hydraulic conductivity and the predictions of the both fractaland the van Genuchten-Mualem model were also performed, and it was found that the predictions of the fractal

Keywords： selection     soil-water     independent physical     unsaturated     strength    

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Study of the Relationship Between Fractal Model Parameters and Roughness Parameter Ra

Pan Yuliang,Wu Liqun,Zhang Yundian

Strategic Study of CAE 2004, Volume 6, Issue 5,   Pages 49-51

Abstract:

The W-M fractal model and the physical meaning of fractal parameters (D, G，y) are briefly introduced

Keywords： W-M fractal model     fractal parameters     roughness Ra    

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A New Algorithm of Fractal Image Coding

Wang Xiuni,Jiang Wei,Wang Licun

Strategic Study of CAE 2006, Volume 8, Issue 1,   Pages 54-57

Abstract:

Because it takes too much of time in fractal image coding, the paper analyses the factors that affectthe speed of fractal image coding , and proposes a novel idea by using the reformed variance (tentatively) to improve image fractal compression performance .Moreover , it gives a novel fractal image compression method based on the reformed variance.

Keywords： fractal coding     image compression     variance    

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PD pattern recognition based on multi-fractal dimension in GIS

ZHANG Xiaoxing, YAO Yao, TANG Ju, ZHOU Qian, XU Zhongrong

Frontiers of Mechanical Engineering 2008, Volume 3, Issue 3,   Pages 270-275 doi: 10.1007/s11465-008-0042-1

Abstract: The multi-fractal dimension is founded on the box-counting dimension and multi-fractal theories.The GIS gray intensity images distillation methods, based on multi-fractal characteristics, is put forwardThe box-counting dimension, multi-fractal dimension, and discharge centrobaric characteristics of the

Keywords： substation     high-speed     discharge centrobaric     network     ultra-high frequency    

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Nonlinear Science and Its Medical Applications

Tu Chengyuan,Zeng Yanjun

Strategic Study of CAE 2003, Volume 5, Issue 8,   Pages 45-49

Abstract:

The fractal-dimension theory and the Shannom entropy theory of nonlinear science are briefly described

Keywords： complicated and large system     nonlinear     fractal theory     fractal-dimension     Shannom entropy     AF(atrial fibrillation    

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Fractal study on wood carbon storage of man-planted Pinus Koraiensis under different exposure

Qin Lei and Guo Minghui

Strategic Study of CAE 2014, Volume 16, Issue 4,   Pages 34-39

Abstract: Forestry University Laoshan Forest Farm in sunny slope and shady slope as research object，based on the fractaltheory，studied the Pinus Koraiensis wood carbon storage through fractal analysis from the nonlinearThe mean fractal dimension of juvenile wood and mature wood carbon storage of shady slope was obviously

Keywords： wood     man-planted Pinus Koraiensis     carbon storage     exposure     fractal    

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Improving the efficiency of magnetic coupling energy transfer by etching fractal patterns in the shielding

Qing-feng LI,Shao-bo CHEN,Wei-ming WANG,Hong-wei HAO,Lu-ming LI

Frontiers of Information Technology & Electronic Engineering 2016, Volume 17, Issue 1,   Pages 74-82 doi: 10.1631/FITEE.1500114

Abstract: This paper describes the use of etched fractal patterns in the metals to suppress the eddy currents andThe fractal patterns should satisfy three features, namely, breaking the metal edge, etching in the high-intensityDifferent fractal patterns lead to different results.By altering the eddy current distribution, the fractal pattern slots reduce the eddy current losses whenFractal pattern slots in multilayer high conductivity metals (e.g., Cu) reduce the induced magnetic field

Keywords： Fractal pattern     Metal-layer-shield     Eddy current     Magnetic coupling energy transfer    

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Analysis on the Machined Surface Profile Error Using Fractals and Wavelet

Liao Xiaoyun,Tang Qian,Zhao Ying,Zheng Shize

Strategic Study of CAE 2002, Volume 4, Issue 5,   Pages 75-78

Abstract: The fractal dimension algorithms, the analysis and reconstruction algorithms of surface profile based

Keywords： machining     machined error analysis     fractal geometry     wavelet analysis    

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Title Author Date Type Operation

Hierarchical fractal structure of perfect single-layer graphene

T. Zhang, K. Ding

Journal Article

A new proof of Honeycomb Conjecture by fractal geometry methods

Tong ZHANG, Kai DING

Journal Article

Theoretical study on the confine-stiffening effect and fractal cracking of square concrete filled steel

Journal Article

Copper fractal growth during recycling from waste printed circuit boards by slurry electrolysis

Journal Article

Fractal characteristic evaluation and interpolation reconstruction for surface topography of drilled

Journal Article

Permeability analysis and seepage process study on crystal layer in melt crystallization with fractal

Xiaobin JIANG, Baohong HOU, Yongli WANG, Jingkang WANG

Journal Article

Aggregating structure in coal water slurry studied by eDLVO theory and fractal dimension

Qiang LI, Qian WANG, Jian HOU, Jiansheng ZHANG, Yang ZHANG

Journal Article

Application of fractal theory to unsaturated soil mechanics

XU Yongfu, TONG Lixin

Journal Article

Study of the Relationship Between Fractal Model Parameters and Roughness Parameter Ra

Pan Yuliang,Wu Liqun,Zhang Yundian

Journal Article

A New Algorithm of Fractal Image Coding

Wang Xiuni,Jiang Wei,Wang Licun

Journal Article

PD pattern recognition based on multi-fractal dimension in GIS

ZHANG Xiaoxing, YAO Yao, TANG Ju, ZHOU Qian, XU Zhongrong

Journal Article

Nonlinear Science and Its Medical Applications

Tu Chengyuan,Zeng Yanjun

Journal Article

Fractal study on wood carbon storage of man-planted Pinus Koraiensis under different exposure

Qin Lei and Guo Minghui

Journal Article

Improving the efficiency of magnetic coupling energy transfer by etching fractal patterns in the shielding

Qing-feng LI,Shao-bo CHEN,Wei-ming WANG,Hong-wei HAO,Lu-ming LI

Journal Article

Analysis on the Machined Surface Profile Error Using Fractals and Wavelet

Liao Xiaoyun,Tang Qian,Zhao Ying,Zheng Shize

Journal Article