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Hierarchical fractal structure of perfect single-layer graphene

T. Zhang, K. Ding

《机械工程前沿（英文）》 2013年 第8卷 第4期   页码 371-382 doi: 10.1007/s11465-013-0279-1

摘要：

The atomic lattice structure of perfect single-layer graphene that can actually be regarded as a kind of hierarchical fractal structure from the perspective of fractal geometry was studied for the first time. Three novel and special discoveries on hierarchical fractal structure and sets were unveiled upon examination of the regular crystal lattices of the single-layer graphene. The interior fractal-type structure was discovered to be the fifth space-filling curve from physical realm. Two efficient methods for calculating the fractal dimension of this fresh member was also provided. The outer boundary curve had a fractal dimension equal to one, and a multi-fractal structure from a naturally existing material was found for the first time. A series of strict self-similar hexagons comprised a rotating fractal set. These hexagons slewed at a constant counterclockwise angle of 19.1° when observed from one level to the next higher level. From the perspective of fractal geometry, these pioneering discoveries added three new members to the existing regular fractal structures and sets. A fundamental example of a multi-fractal structure was also presented.

关键词： 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

《机械工程前沿（英文）》 2013年 第8卷 第4期   页码 367-370 doi: 10.1007/s11465-013-0273-7

摘要：

Based on fractal geometry, we put forward a concise and straightforward method to prove Honeycomb Conjecture—a classical mathematic problem. Hexagon wins the most efficient covering unit in the two- dimensional space, compared with the other two covering units—triangle and square. From this point of view, honeycomb is treated as a hierarchical fractal structure that fully fills the plane. Therefore, 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    

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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

《能源前沿（英文）》 2023年 第17卷 第2期   页码 306-316 doi: 10.1007/s11708-021-0736-1

摘要： Coal water slurry gasification is a main source of hydrogen in the developing hydrogen economy. Moreover, biomass and waste can be added, making gasification process greener. To expand the application of coal water slurry and gasification process, it is necessary to understand the micro-structure in this large particle suspension system. In this paper, the micro-structure in coal water slurry was studied by extended DLVO (eDLVO) theory and fractal dimension, which is used to explain the mechanism of stability in large particle suspension systems. The interaction between two coal particles was characterized from the interparticle potential and energy barrier based on the eDLVO theory. The rheology and stability between different types of coals are measured and explained by the aggregating structure and fractal dimension in coal water slurry. The results indicated that there would be an aggregating structure in high rank coals, due to the interparticle potential caused by the surface properties, but probably not in low rank coals. This aggregating structure can be described and characterized by fractal dimension. The aggregation of particles is the source of the stability for high rank coals, as the close-packed 3D network structure in large particle suspension can support coal particles from settling down. The results have demonstrated that the combination of the eDLVO theory and rheological measurement is an effective way to investigate the stability of large particle suspension systems.

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

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

《结构与土木工程前沿（英文）》 2021年 第15卷 第6期   页码 1317-1336 doi: 10.1007/s11709-021-0763-3

摘要： Tension stress in steel-concrete composite is widely observed in engineering design. Based on an experimental program on tension performance of three square concrete-filled tubes (SCFT), the tension theory of SCFT is proposed using a mechanics-based approach. The tension stiffening effect, the confining strengthening effect and the confining stiffening effect, observed in tests of SCFTs are included in the developed tension theory model. Subsequently, simplified constitutive models of steel and concrete are proposed for the axial tension performance of SCFT. Based on the MSC.MARC software, a special fiber beam-column element is proposed to include the confining effect of SCFTs under tension and verified. The proposed analytical theory, effective formulas, and equivalent constitutive laws are extensively verified against three available tests reported in the literature on both global level (e.g., load-displacement curves) and strain level. The experimental verification proves the accuracy of the proposed theory and formulations in simulating the performance of SCFT members under tension with the capability to accurately predict the tensile strength and stiffness enhancements and realistically simulate the fractal cracking phenomenon.

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

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The effect of hierarchical single-crystal ZSM-5 zeolites with different Si/Al ratios on its pore structure

Yuexin Hou, Xiaoyun Li, Minghui Sun, Chaofan Li, Syed ul Hasnain Bakhtiar, Kunhao Lei, Shen Yu, Zhao Wang, Zhiyi Hu, Lihua Chen, Bao-Lian Su

《化学科学与工程前沿（英文）》 2021年 第15卷 第2期   页码 269-278 doi: 10.1007/s11705-020-1948-3

摘要： Hierarchical single-crystal ZSM-5 zeolites with different Si/Al ratios (Hier-ZSM-5- , where = 50, 100, 150 and 200) were synthesized using an ordered mesoporous carbon-silica composite as hard template. Hier-ZSM-5- exhibits improved mass transport properties, excellent mechanical and hydrothermal stability, and higher catalytic activity than commercial bulk zeolites in the benzyl alcohol self-etherification reaction. Results show that a decrease in the Si/Al ratio in hierarchical single-crystal ZSM-5 zeolites leads to a significant increase in the acidity and the density of micropores, which increases the final catalytic conversion. The effect of porous hierarchy on the diffusion of active sites and the final catalytic activity was also studied by comparing the catalytic conversion after selectively designed poisoned acid sites. These poisoned Hier-ZSM-5- shows much higher catalytic conversion than the poisoned commercial ZSM-5 zeolite, which indicates that the numerous intracrystalline mesopores significantly reduce the diffusion path of the reactant, leading to the faster diffusion inside the zeolite to contact with the acid sites in the micropores predominating in ZSM-5 zeolites. This study can be extended to develop a series of hierarchical single-crystal zeolites with expected catalytic performance.

关键词： hierarchical zeolites     single crystalline     interconnected pores     improved diffusion performance     benzyl alcohol self-etherification reaction    

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

《环境科学与工程前沿（英文）》 2021年 第15卷 第6期 doi: 10.1007/s11783-021-1405-7

摘要：

• Copper fractal growth was observed during WPCBs recycling by slurry electrolysis.

关键词： Dendritic copper     Fractal growth     WPCBs     Slurry electrolysis    

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Fractal characteristic evaluation and interpolation reconstruction for surface topography of drilled

《机械工程前沿（英文）》 2021年 第16卷 第4期   页码 840-854 doi: 10.1007/s11465-021-0643-5

摘要： In this paper, an improved fractal interpolation model is proposed to reconstruct the surface topography of composite hole wall. This model adopts the maximum positive deviations and maximum negative deviations between the measured values and trend values to determine the contraction factors. Hole profiles in 24 directions are measured. Fractal 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 and minimum fractal roughness are 4.05 × 10 −5 and 4.36 × 10 −10 m, respectively. Based on the two-dimensional evaluation results, three-dimensional surface topographies in five typical angles (0°, 45°, 90°, 135°, and 165°) are reconstructed using the improved model. Fractal parameter D s and statistical parameters Sa, Sq, and Sz are used to evaluate the reconstructed surfaces. Average error of D s, Sa, Sq, and Sz between the measured surfaces and the reconstructed surfaces are 1.53%, 3.60%, 5.60%, and 9.47%, respectively. Compared with the model in published literature, the proposed model has equal reconstruction effect in relatively smooth surface and is more advanced in relatively rough surface. Comparative results prove that the proposed model for calculating contraction factors is more reasonable.

关键词： surface topography     fractal evaluation     fractal interpolation     reconstruction     composite    

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用于高风险环境安全监测和可调热管理的具有分层核壳结构的耐化学品纱线 Article

Duo Xu, Yingcun Liu, Can Ge, Chong Gao, Ze Chen, Ziyi Su, Haoran Gong, Weilin Xu, Jian Fang

《工程（英文）》 2024年 第32卷 第1期   页码 221-229 doi: 10.1016/j.eng.2023.06.018

摘要：

Chemical resistant textiles are vital for safeguarding humans against chemical hazards in various settings, such as industrial production, chemical accidents, laboratory activities, and road transportation. However, the ideal integration of chemical resistance, thermal and moisture management, and wearer condition monitoring in conventional chemically protective textiles remains challenging. Herein, the design, manufacturing, and use of stretchable hierarchical core–shell yarns (HCSYs) for integrated chemical resistance, moisture regulation, and smart sensing textiles are demonstrated. These yarns contain helically elastic spandex, wrapped silver-plated nylon, and surface-structured polytetrafluoroethylene (PTFE) yarns and are designed and manufactured based on a scalable fabrication process. In addition to their ideal chemical resistance performance, HCSYs can function as multifunctional stretchable electronics for real-time human motion monitoring and as the basic element of intelligent textiles. Furthermore, a desirable dynamic thermoregulation function is achieved by exploiting the fabric structure with stretching modulation. Our HCSYs may provide prospective opportunities for the future development of smart protective textiles with high durability, flexibility, and scalability.

关键词： Hierarchical core–shell structure     Chemical resistant yarn     Wearable strain sensor     Thermoregulation    

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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

《化学科学与工程前沿（英文）》 2011年 第5卷 第4期   页码 435-441 doi: 10.1007/s11705-011-1139-3

摘要： 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.

关键词： melt crystallization     porous media     fractal     permeability     hyperpure material     simulation    

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Application of fractal theory to unsaturated soil mechanics

XU Yongfu, TONG Lixin

《结构与土木工程前沿（英文）》 2007年 第1卷 第4期   页码 411-421 doi: 10.1007/s11709-007-0056-5

摘要： The mechanical properties of unsaturated soils are a function of the saturation degree or matric suction, and can be obtained based on currently available procedures. However, each procedure has its limitations and consequently, care should be taken in the selection of a proper procedure. The fractal approach seems to be a potentially useful tool to describe hierarchical systems and is suitable to model the structure and hydraulic properties of unsaturated soils. In this paper, the soil-water characteristics, unsaturated hydraulic conductivity function, unsaturated shear strength, swelling deformation and compression were derived from the fractal model for the pore-size distribution, and were expressed by only two independent physical parameters, the fractal dimension and the air entry value. The predictions of the proposed soil-water characteristics, unsaturated hydraulic conductivity, unsaturated shear strength, swelling deformation and compression were in good agreement with published experimental data. Comparisons between the experimental results of unsaturated hydraulic conductivity and the predictions of the both fractal model and the van Genuchten-Mualem model were also performed, and it was found that the predictions of the fractal model were better than that of the van Genuchten-Mualem model.

关键词： selection     soil-water     independent physical     unsaturated     strength    

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重复镜头视频基于分级B帧结构的长期预测编码方案 None

Xu-guang ZUO, Lu YU

《信息与电子工程前沿（英文）》 2018年 第19卷 第3期   页码 459-470 doi: 10.1631/FITEE.1601552

摘要： 最新视频编码标准——高效视频编码（HEVC）——获得了远高于之前视频编码标准的编码效率。特别是，在使用分级B帧预测结构时，HEVC可显著去除临近图像间的时间冗余。实际中，消费者使用的视频——例如电视剧、电影和脱口秀等——通常包含了很多重复镜头。据我们观察，这些视频在分级B帧结构下使用HEVC编码时，每个镜头的时域相关性可以得到很好利用。然而，重复镜头之间的长期相关性并未被使用。我们提出一种长期预测方案，以利用视频中重复镜头之间的长期时域相关性。首先，聚类源视频中的相似镜头并从中抽取代表性图像作为长期参考帧。然后，使用长期参考帧对分级B帧的编码结构进行调整，以实现长期时域预测。最后，为长期参考帧设计一种自适应量化方法，以提高整体的视频编码效率。实验表明，提出的新编码方案可获得高达22.86%的编码性能增益。

关键词： 高效视频编码（HEVC）；长期时域相关性；长期预测；分级B帧结构    

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分形模型参数与粗糙度参数Ra关系的研究

潘玉良,吴立群,张云电

《中国工程科学》 2004年 第6卷 第5期   页码 49-51

摘要：

介绍了W－M分形模型参数（D,G,γ）的物理含义，研究了分形参数（D,G,γ）与粗糙度参数Ra之间的联系，导出了分形参数（D,G,γ）与粗糙度参数Ra关系式，用数值分析拟合方法验证了关系式的正确性。

关键词： W－M分形模型     分形参数     粗糙度Ra    

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一种分形图像编码的新方法

王秀妮,姜威,王利村

《中国工程科学》 2006年 第8卷 第1期   页码 54-57

摘要：

由于分形图像编码过程非常费时，因此在前人的基础上，通过分析影响分形图像编码速度的相关因素，提出了使用图像块的改进方差来提高分形压缩性能的思想。在证明迭代函数系统不会改变图像块的改进方差的基础上，给出了基于改进方差的分形图像压缩方法。实验结果说明该方法在保证快速性的同时，重建图像的质量又得到了进一步的提高。

关键词： 分形编码     图像压缩     方差    

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Deep convolutional tree-inspired network: a decision-tree-structured neural network for hierarchical

《机械工程前沿（英文）》 2021年 第16卷 第4期   页码 814-828 doi: 10.1007/s11465-021-0650-6

摘要： The fault diagnosis of bearings is crucial in ensuring the reliability of rotating machinery. Deep neural networks have provided unprecedented opportunities to condition monitoring from a new perspective due to the powerful ability in learning fault-related knowledge. However, the inexplicability and low generalization ability of fault diagnosis models still bar them from the application. To address this issue, this paper explores a decision-tree-structured neural network, that is, the deep convolutional tree-inspired network (DCTN), for the hierarchical fault diagnosis of bearings. The proposed model effectively integrates the advantages of convolutional neural network (CNN) and decision tree methods by rebuilding the output decision layer of CNN according to the hierarchical structural characteristics of the decision tree, which is by no means a simple combination of the two models. The proposed DCTN model has unique advantages in 1) the hierarchical structure that can support more accuracy and comprehensive fault diagnosis, 2) the better interpretability of the model output with hierarchical decision making, and 3) more powerful generalization capabilities for the samples across fault severities. The multiclass fault diagnosis case and cross-severity fault diagnosis case are executed on a multicondition aeronautical bearing test rig. Experimental results can fully demonstrate the feasibility and superiority of the proposed method.

关键词： bearing     cross-severity fault diagnosis     hierarchical fault diagnosis     convolutional neural network     decision tree    

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PD pattern recognition based on multi-fractal dimension in GIS

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

《机械工程前沿（英文）》 2008年 第3卷 第3期   页码 270-275 doi: 10.1007/s11465-008-0042-1

摘要： This paper designs four types of gas insulated substation (GIS) defect models based on partial discharge (PD) characteristics and its defections. The GIS gray intensity images are constructed based on the mass specimens gathered by the ultra-high frequency and high-speed sampling systems. 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 forward. The box-counting dimension, multi-fractal dimension, and discharge centrobaric characteristics of the PD images are also extracted. The characteristic variables are then classified by the radial basis function (RBF) network. Identified results show that the methods can effectively elevate the discrimination of the four types of defects in GIS.

关键词： substation     high-speed     discharge centrobaric     network     ultra-high frequency    

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标题 作者 时间 类型 操作

Hierarchical fractal structure of perfect single-layer graphene

T. Zhang, K. Ding

期刊论文

A new proof of Honeycomb Conjecture by fractal geometry methods

Tong ZHANG, Kai DING

期刊论文

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

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

期刊论文

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

期刊论文

The effect of hierarchical single-crystal ZSM-5 zeolites with different Si/Al ratios on its pore structure

Yuexin Hou, Xiaoyun Li, Minghui Sun, Chaofan Li, Syed ul Hasnain Bakhtiar, Kunhao Lei, Shen Yu, Zhao Wang, Zhiyi Hu, Lihua Chen, Bao-Lian Su

期刊论文

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

期刊论文

Fractal characteristic evaluation and interpolation reconstruction for surface topography of drilled

期刊论文

用于高风险环境安全监测和可调热管理的具有分层核壳结构的耐化学品纱线

Duo Xu, Yingcun Liu, Can Ge, Chong Gao, Ze Chen, Ziyi Su, Haoran Gong, Weilin Xu, Jian Fang

期刊论文

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

Xiaobin JIANG, Baohong HOU, Yongli WANG, Jingkang WANG

期刊论文

Application of fractal theory to unsaturated soil mechanics

XU Yongfu, TONG Lixin

期刊论文

重复镜头视频基于分级B帧结构的长期预测编码方案

Xu-guang ZUO, Lu YU

期刊论文

分形模型参数与粗糙度参数Ra关系的研究

潘玉良,吴立群,张云电

期刊论文

一种分形图像编码的新方法

王秀妮,姜威,王利村

期刊论文

Deep convolutional tree-inspired network: a decision-tree-structured neural network for hierarchical

期刊论文

PD pattern recognition based on multi-fractal dimension in GIS

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

期刊论文