Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potentia...Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potential of fractals in traditional textile design,a fractal-based generative framework was proposed for efficiently creating drawnwork patterns suitable for practical handicraft production.The research was initiated with an analysis of the structural composition of center,skeleton,and filler motifs extracted from a pattern sample library.Based on this hierarchical classification,the box-counting method was employed to calculate their respective fractal dimensions.Building on fractal art theory,generative algorithms,and studies on the application of Ultra Fractal,a Chaoshan drawnwork fractal design model was established.Using this model,51 drawnwork fractal patterns and 153 handkerchief patterns were generated.These patterns were subsequently applied in real-world production to validate the feasibility and value of fractal techniques in textile design.展开更多
Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors i...Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors in rocks under the influence of cyclic heating is imperative for optimizing geothermal energy extraction. This study encompasses several critical aspects under cyclic heating conditions, including the assessment of stress distribution states, the characterization of two-dimensional fracture paths, the quantitative analysis of three-dimensional damage characteristics on fracture surfaces, and the determination of the fractal dimension of debris generated after the failure of granite. The test results demonstrate that cyclic heating has a pronounced adverse effect on the physical and mechanical properties of granite. Consequently, stress tends to develop and propagate in a direction perpendicular to the two-dimensional fracture path. This leads to an increase in the extent of tensile damage on the fracture surface and accelerates the overall rock failure process. This increases the number of small-sized debris, raises the fractal dimension, and enhances the rock’s rupture degree. In practical enhanced geothermal energy extraction, the real-time monitoring of fracture propagation within the reservoir rock mass is achieved through the analysis of rock debris generated during the staged fracturing process.展开更多
Nowadays,wireless communication devices turn out to be transportable owing to the execution of the current technologies.The antenna is the most important component deployed for communication purposes.The antenna plays...Nowadays,wireless communication devices turn out to be transportable owing to the execution of the current technologies.The antenna is the most important component deployed for communication purposes.The antenna plays an imperative role in receiving and transmitting the signals for any sensor network.Among varied antennas,micro strip fractal antenna(MFA)significantly contributes to increasing antenna gain.This study employs a hybrid optimization method known as the elephant clan updated grey wolf algorithm to introduce an optimized MFA design.This method optimizes antenna characteristics,including directivity and gain.Here,the factors,including length,width,ground plane length,height,and feed offset-X and feed offset-Y,are taken into account to achieve the best performance of gain and directivity.Ultimately,the superiority of the suggested technique over state-of-the-art strategies is calculated for various metrics such as cost and gain.The adopted model converges to a minimal value of 0.2872.Further,the spider monkey optimization(SMO)model accomplishes the worst performance over all other existing models like elephant herding optimization(EHO),grey wolf optimization(GWO),lion algorithm(LA),support vector regressor(SVR),bacterial foraging-particle swarm optimization(BF-PSO)and shark smell optimization(SSO).Effective MFA design is obtained using the suggested strategy regarding various parameters.展开更多
In Xikuangshan antimony ore-field, the western fracture zone is a composite of major fault, F75, and its secondary faults, such as F71, F72 and F3 etc.. On plane, the fracture zone scatters from southwest to northeast...In Xikuangshan antimony ore-field, the western fracture zone is a composite of major fault, F75, and its secondary faults, such as F71, F72 and F3 etc.. On plane, the fracture zone scatters from southwest to northeast, and concentrates from upper to deeper level on profile. All ore-bodies exist in the carbonate of footwall of the major fault or that of the footwall of its secondary faults. From 480 m and 320 m to 120 m level, the fractal dimensional number of the fault system decreases from 1.482 2 and 1.448 6 to 1.339 2, which indicates the form of fracture zone becoming more simple at deeper level. And in five sub-ranges, the III and IV sub-ranges are the known area, and the I, II and V sub-ranges are unknown. The fractal studies of the western fracture zone in these sub-ranges show that the fractal dimensional numbers of the I and II, being 1.201 5 and 1.278 0, respectively, are smaller than that of the III and IV, being 1.475 9 and 1.576 9, respectively; and that of the V, being 1.571 2, keeps with that of the III, IV sub-ranges. So mineralization is not well in I and II sub-ranges, and V sub-range is the best to benefit mineralization.展开更多
Some profile of a rock section and some isopleth of a fractured surface of the rock were divided each into three parts. Then three parts were measured by dividers method and lattice method. It was discovered that the...Some profile of a rock section and some isopleth of a fractured surface of the rock were divided each into three parts. Then three parts were measured by dividers method and lattice method. It was discovered that the fractal dimensions of the three parts were remarkably different, so the fractured surface of rock was not simple fractal but multi range fractals.展开更多
this paper, a more stable and accurate recursing equation and computing procedure are proposed to calculate scattering width of the multilayered cylinder. This procedure is applied to compute the distribution of the s...this paper, a more stable and accurate recursing equation and computing procedure are proposed to calculate scattering width of the multilayered cylinder. This procedure is applied to compute the distribution of the scattering width and to analyze the characteristic of scattering from fractal multilayered cylinder. The connection between the characteristic of scattering and fractal dimension is discussed, and some important results are obtained.展开更多
The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitativel...The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.展开更多
The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusio...The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusion process. Based on fractal geometry and the constitutive equation of Herschel-Bulkley fluid, an analytical model for Herschel-Bulkley fluid flowing in a porous geo-material with fractal characteristics is derived. The proposed model provides a theoretical basis for grouting design and helps to understand the chemical fluid flow in soil in real environments. The results indicate that the predictions from the proposed model show good consistency with the literature data and application results. Grouting pressure decreases with increasing diffusion distance. Under the condition that the chemical fluid flows the same distance, the grouting pressure undergoes almost no change at first and then decreases nonlinearly with increasing tortuosity dimension. With increasing rheological index, the pressure difference first decreases linearly, then presents a trend of nonlinear decrease, and then decreases linearly again. The pressure difference gradually increases with increasing viscosity and yield stress of the chemical fluid. The decreasing trend of the grouting pressure difference is non-linear and rapid for porosity Φ>0.4, while there is a linear and slow decrease in pressure difference for high porosity.展开更多
Stochastic noises of fiber optic gyroscope （FOG） mainly contain white noise and fractal noise whose long-term dependent component causes FOG a rather slow drift. In order to eliminate this component, a two-step filt...Stochastic noises of fiber optic gyroscope （FOG） mainly contain white noise and fractal noise whose long-term dependent component causes FOG a rather slow drift. In order to eliminate this component, a two-step filtering methodology is proposed. Firstly, fractional differencing （FD） method is introduced to trans-form fractal noise into fractional white noise based on the estima-tion of Hurst exponent for long-term dependent fractal process, which together with the existing white noise make up of a gener-alized white noise. Further, an improved denoising algorithm of wavelet maxima is developed to suppress the generalized white noise. Experimental results show that the basic noise terms of FOG greatly decrease, and especially the slow drift is restrained effectively. The proposed methodology provides a promising ap-proach for filtering long-term dependent fractal noise.展开更多
This paper addresses the existence detection of blanket jamming based on fractal features in fractional Fourier transform (FRET) domain. Firstly, the existences of fractal features of three typical jamming signals are...This paper addresses the existence detection of blanket jamming based on fractal features in fractional Fourier transform (FRET) domain. Firstly, the existences of fractal features of three typical jamming signals are analyzed, and box dimension and information dimension are employed to describe fractal features quantitatively. Then the differences of fractal characteristics between blanket jamming and white Gaussian noise (WGN) in FRFT domain are described, and a detector to detect the jamming is proposed. At last, simulations are done to verify that the algorithm is effective preferable.展开更多
文摘Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potential of fractals in traditional textile design,a fractal-based generative framework was proposed for efficiently creating drawnwork patterns suitable for practical handicraft production.The research was initiated with an analysis of the structural composition of center,skeleton,and filler motifs extracted from a pattern sample library.Based on this hierarchical classification,the box-counting method was employed to calculate their respective fractal dimensions.Building on fractal art theory,generative algorithms,and studies on the application of Ultra Fractal,a Chaoshan drawnwork fractal design model was established.Using this model,51 drawnwork fractal patterns and 153 handkerchief patterns were generated.These patterns were subsequently applied in real-world production to validate the feasibility and value of fractal techniques in textile design.
基金Project(52409132) supported by the National Natural Science Foundation of ChinaProject(ZR2024QE018) supported by the Natural Science Foundation of Shandong Province,China+2 种基金Project(BK20240431) supported by Basic Research Program of Jiangsu,ChinaProject(SNKJ2023A07-R14) supported by the Major Key Technical Research Projects of Shandong Energy Group,ChinaProject(2024M751813) supported by China Postdoctoral Science Foundation。
文摘Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors in rocks under the influence of cyclic heating is imperative for optimizing geothermal energy extraction. This study encompasses several critical aspects under cyclic heating conditions, including the assessment of stress distribution states, the characterization of two-dimensional fracture paths, the quantitative analysis of three-dimensional damage characteristics on fracture surfaces, and the determination of the fractal dimension of debris generated after the failure of granite. The test results demonstrate that cyclic heating has a pronounced adverse effect on the physical and mechanical properties of granite. Consequently, stress tends to develop and propagate in a direction perpendicular to the two-dimensional fracture path. This leads to an increase in the extent of tensile damage on the fracture surface and accelerates the overall rock failure process. This increases the number of small-sized debris, raises the fractal dimension, and enhances the rock’s rupture degree. In practical enhanced geothermal energy extraction, the real-time monitoring of fracture propagation within the reservoir rock mass is achieved through the analysis of rock debris generated during the staged fracturing process.
文摘Nowadays,wireless communication devices turn out to be transportable owing to the execution of the current technologies.The antenna is the most important component deployed for communication purposes.The antenna plays an imperative role in receiving and transmitting the signals for any sensor network.Among varied antennas,micro strip fractal antenna(MFA)significantly contributes to increasing antenna gain.This study employs a hybrid optimization method known as the elephant clan updated grey wolf algorithm to introduce an optimized MFA design.This method optimizes antenna characteristics,including directivity and gain.Here,the factors,including length,width,ground plane length,height,and feed offset-X and feed offset-Y,are taken into account to achieve the best performance of gain and directivity.Ultimately,the superiority of the suggested technique over state-of-the-art strategies is calculated for various metrics such as cost and gain.The adopted model converges to a minimal value of 0.2872.Further,the spider monkey optimization(SMO)model accomplishes the worst performance over all other existing models like elephant herding optimization(EHO),grey wolf optimization(GWO),lion algorithm(LA),support vector regressor(SVR),bacterial foraging-particle swarm optimization(BF-PSO)and shark smell optimization(SSO).Effective MFA design is obtained using the suggested strategy regarding various parameters.
文摘In Xikuangshan antimony ore-field, the western fracture zone is a composite of major fault, F75, and its secondary faults, such as F71, F72 and F3 etc.. On plane, the fracture zone scatters from southwest to northeast, and concentrates from upper to deeper level on profile. All ore-bodies exist in the carbonate of footwall of the major fault or that of the footwall of its secondary faults. From 480 m and 320 m to 120 m level, the fractal dimensional number of the fault system decreases from 1.482 2 and 1.448 6 to 1.339 2, which indicates the form of fracture zone becoming more simple at deeper level. And in five sub-ranges, the III and IV sub-ranges are the known area, and the I, II and V sub-ranges are unknown. The fractal studies of the western fracture zone in these sub-ranges show that the fractal dimensional numbers of the I and II, being 1.201 5 and 1.278 0, respectively, are smaller than that of the III and IV, being 1.475 9 and 1.576 9, respectively; and that of the V, being 1.571 2, keeps with that of the III, IV sub-ranges. So mineralization is not well in I and II sub-ranges, and V sub-range is the best to benefit mineralization.
文摘Some profile of a rock section and some isopleth of a fractured surface of the rock were divided each into three parts. Then three parts were measured by dividers method and lattice method. It was discovered that the fractal dimensions of the three parts were remarkably different, so the fractured surface of rock was not simple fractal but multi range fractals.
文摘this paper, a more stable and accurate recursing equation and computing procedure are proposed to calculate scattering width of the multilayered cylinder. This procedure is applied to compute the distribution of the scattering width and to analyze the characteristic of scattering from fractal multilayered cylinder. The connection between the characteristic of scattering and fractal dimension is discussed, and some important results are obtained.
基金Projects(51822403,51827901)supported by the National Natural Science Foundation of ChinaProject(2019ZT08G315)supported by the Department of Science and Technology of Guangdong Province,China。
文摘The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.
基金Project(2015CB060200)supported by the National Basic Research Program of ChinaProject supported by the R-D Program of Gangxi Province of ChinaProject(201622ts093)supported by the Fundamental Research Funds for the Central Universities,China
文摘The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusion process. Based on fractal geometry and the constitutive equation of Herschel-Bulkley fluid, an analytical model for Herschel-Bulkley fluid flowing in a porous geo-material with fractal characteristics is derived. The proposed model provides a theoretical basis for grouting design and helps to understand the chemical fluid flow in soil in real environments. The results indicate that the predictions from the proposed model show good consistency with the literature data and application results. Grouting pressure decreases with increasing diffusion distance. Under the condition that the chemical fluid flows the same distance, the grouting pressure undergoes almost no change at first and then decreases nonlinearly with increasing tortuosity dimension. With increasing rheological index, the pressure difference first decreases linearly, then presents a trend of nonlinear decrease, and then decreases linearly again. The pressure difference gradually increases with increasing viscosity and yield stress of the chemical fluid. The decreasing trend of the grouting pressure difference is non-linear and rapid for porosity Φ>0.4, while there is a linear and slow decrease in pressure difference for high porosity.
基金supported by Aviation Science Foundation(20070851011).
文摘Stochastic noises of fiber optic gyroscope （FOG） mainly contain white noise and fractal noise whose long-term dependent component causes FOG a rather slow drift. In order to eliminate this component, a two-step filtering methodology is proposed. Firstly, fractional differencing （FD） method is introduced to trans-form fractal noise into fractional white noise based on the estima-tion of Hurst exponent for long-term dependent fractal process, which together with the existing white noise make up of a gener-alized white noise. Further, an improved denoising algorithm of wavelet maxima is developed to suppress the generalized white noise. Experimental results show that the basic noise terms of FOG greatly decrease, and especially the slow drift is restrained effectively. The proposed methodology provides a promising ap-proach for filtering long-term dependent fractal noise.
基金supported by Key Laboratory of Science and Technology in Complex Electromagnetic Environment(201E-05-1)
文摘This paper addresses the existence detection of blanket jamming based on fractal features in fractional Fourier transform (FRET) domain. Firstly, the existences of fractal features of three typical jamming signals are analyzed, and box dimension and information dimension are employed to describe fractal features quantitatively. Then the differences of fractal characteristics between blanket jamming and white Gaussian noise (WGN) in FRFT domain are described, and a detector to detect the jamming is proposed. At last, simulations are done to verify that the algorithm is effective preferable.
