As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal...As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.展开更多
Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media withi...Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.展开更多
The separation of anomalies from geochemical background is an important part of data analysis because lack of such identifications might have profound influence on or even distort the final analysis results. In this a...The separation of anomalies from geochemical background is an important part of data analysis because lack of such identifications might have profound influence on or even distort the final analysis results. In this article, 1 672 geochemical analytical data of 11 elements, including Cu, Mo, Ag, Sn, and others, from a region within Tibet, South China, are used as one example. Together with the traditional anomaly recognition method of using the iterative mean ±2σ local multifractality theory has been utilized to delineate the ranges of geochemical anomalies of the elements. To different degrees, on the basis of original data mapping, C-A fractal analysis and singularity exponents, Sn differs from the other 10 elements. Moreover, geochemical mapping results based on values of the multifractal asymmetry index for all elements delineate the highly anomalous area. Similar to other 10 elements, the anomalous areas of Sn delineated by the asymmetry index distribute along the main structure orientations. According to the asymmetry indexes, the 11 elements could be classified into 3 groups： （1） Ag and Au, （2） As-Sb-Cu-Pb-Zn-Mo, and （3） Sn-Bi-W. This parageneflc association of elements can be used to interpret possible origins of mineralization, which is in agreement with petrological analysis and field survey results.展开更多
Fractal geometry is increasingly becoming a useful tool for modeling and quantifying the complex patterns of natural phenomena. The Earth's topography is one of these phenomena that have fractal characteristics. T...Fractal geometry is increasingly becoming a useful tool for modeling and quantifying the complex patterns of natural phenomena. The Earth's topography is one of these phenomena that have fractal characteristics. This paper investigates the relative sensitivity of topography to active tectonics using ASTER Global Digital Elevation Model. The covering divider method was used for direct extraction of surface fractal dimension(D surf) to estimate the roughness-surface of topography with aid of geographic information system(GIS)techniques. This evaluation let us highlight the role of the geomorphic and tectonic processes on the spatial variability of fractal properties of natural landforms.Geomorphic zones can be delineated using fractal dimension mapping in which variability of surface fractal dimension reflects the roughness of the landform surface and is a measure of topography texture. Obtained results showed this method can be a quick and easy way to assess the distribution of land surface deformation in different tectonic settings. The loose alluvial deposits and irregularities derived by tectonic activity have high fractal dimensions whereas the competent formations and higher wavelength folded surfaces have lower fractal dimensions.According to the obtained results, the Kazerun Fault Zone has a crucial role in the separation of the Zagros Mountain Ranges into the different lithological,geomorphological and structural zones.展开更多
AIM: To evaluate the fractal feature of the retinal vasculature of normal eyes on a stereographic projected and montaged ultra-wide field(UWF) fluorescein angiography(FA).METHODS: Prospective, observational, cross-sec...AIM: To evaluate the fractal feature of the retinal vasculature of normal eyes on a stereographic projected and montaged ultra-wide field(UWF) fluorescein angiography(FA).METHODS: Prospective, observational, cross-sectional study. Totally 59 eyes of 31 normal subjects were imaged using the Optos 200 Tx. Images obtained at different gaze angles stereographically projected and montaged. The early-phase UWF FA frames were processed to segment the retinal vasculature and the results were exported as binary masks. The fractal dimension(FD) was calculated using the box-counting method.RESULTS: The global FD for the entire retina was 1.6±0.04, with no difference between males and females(1.59±0.04 vs 1.61±0.04, P=0.084) or between right and left eyes(1.6±0.04 vs 1.6±0.05, P=0.61). FD was nonuniformly distributed among four quadrants(P<0.001) and decreased as the distance from the fovea increased(P<0.001). A negative association was observed between FD and age(R=-0.37, P=0.006), and this relationship was observed in the posterior and mid-peripheral retina(P<0.05) but absent in far-periphery(P>0.05).CONCLUSION: Fractal geometry is non-uniformly distributed across the retina in normal eyes and decreases from the fovea to the far-periphery. Subjects with an older age tend to have a smaller FD, however, the FD in the farperiphery does not appear to be influenced by age.展开更多
Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mo...Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks （MSNs） are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs.展开更多
The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently reported Saraswati supercluster and the Stripe 82 region containing it as an example.The report of 120 Mpc periodicity...The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently reported Saraswati supercluster and the Stripe 82 region containing it as an example.The report of 120 Mpc periodicity in the Abell galaxy clusters by power spectrum analysis is the motivation behind the study.The power spectral analysis across the central part of the Stripe 82 region shows a periodic variation of 3.09°or 71 Mpc in fractal dimension whereas an average angular periodicity of 3.45°or 94 Mpc is observed across the Stripe 82 region.This refers to the periodicity of complexity or cluster density of galaxy distribution.The texture of the distribution pattern understood through lacunarity analysis indicates a near symmetric distribution.Fractal dimensions like box-counting dimension,information dimension and correlation dimension are also found through multifractal analysis.While the information dimension tells about the distribution density of galactic points,the correlation dimension details the distribution of galaxies in the neighbourhood.展开更多
The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution ki...The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution kinetics of primary carbides during either heating or soaking.Dissolution of carbides proceeded in three stages(fast→slow→faster)as either temperature or holding time was increased.During the heating process and during the first and third stages of the soaking process,the original size of the carbides determined the steepness of the slope,but during the middle(“slow”)stage of the soaking process,the slope remained zero.The initial size of the carbides varied greatly,but their final dissolution temperature fell within the narrow range of 1210-1235℃,and the holding time remained within 50 min.Fractal analysis was used to study the morphological characteristics of small and medium-sized carbides during the dissolution process.According to changes in the fractal dimension before and after soaking,the carbides tended to evolve towards a more regular morphology.展开更多
Fractal geometry quantitatively analyzes the irregular distribution of geological features,highlighting the dynamic aspects of tectonics,seismic heterogeneity,and geological maturity.This study analyzed the active fau...Fractal geometry quantitatively analyzes the irregular distribution of geological features,highlighting the dynamic aspects of tectonics,seismic heterogeneity,and geological maturity.This study analyzed the active fault data along the Kuhbanan fault zone in southeastern Iran by applying the boxcounting method and observing the changes in Coulomb stress and tried to find the potential triggering parts.The entire region was divided into 16subzones with the box-counting method,and then the fractal dimension(D)in each zone was calculated.The analysis of the fractal dimension for active faults and earthquake epicenters along with the seismicity parameter(b)and their ratio in the Kuhbanan region indicates an imbalance between seismic fractals and faults.This finding suggests that the area may have the potential for future earthquakes or hidden faults.In conjunction with b-value and changes in Coulomb stress change,D-value analysis reveals intense tectonic activity and stress accumulation,particularly within the Ravar,Zarand,and Kianshahr sections.It may be considered a potential location for future earthquakes.The changes in Coulomb stress resulting from the 2005Dahuieh earthquake have also placed this region within the stress accumulation zone,potentially triggering the mentioned areas.This integrative approach,backed by historical earthquake data,highlights the impact of fault geometry and stress dynamics,offering an enhanced framework for earthquake forecasting and seismic risk mitigation applicable to other tectonically active areas within the Iranian plateau.展开更多
Boiling and fouling are taken as typical examples of new phase formation process to be analyzed and discussed in this paper. The process dynamics of nucleate boiling is analyzed and its mechanism is discussed from the...Boiling and fouling are taken as typical examples of new phase formation process to be analyzed and discussed in this paper. The process dynamics of nucleate boiling is analyzed and its mechanism is discussed from the view point of self-organization. Fouling, which is a more complicated phenomenon of new phase formation, involves series of underlying processes. The morphology and fractal analysis of fouling on low-energy surface and that with fouling inhibitors are studied and discussed. It is suggested that considering the process dynamics, fractal analysis and self-organization, a new avenue of research should be found.展开更多
Dear Sir,Iam Dr.Kavitha S,from the Department of Electronics and Communication Engineering,Nandha Engineering College,Erode,Tamil Nadu,India.I write to present the detection of glaucoma using extreme learning machine(...Dear Sir,Iam Dr.Kavitha S,from the Department of Electronics and Communication Engineering,Nandha Engineering College,Erode,Tamil Nadu,India.I write to present the detection of glaucoma using extreme learning machine(ELM)and fractal feature analysis.Glaucoma is the second most frequent cause of permanent blindness in industrial展开更多
Fractures running along a plane reflect the cracking progress.In this paper uniaxial and rockburst tests on a group of granite specimens from Sanya province are described.Scanning electron microscopic imaging was used...Fractures running along a plane reflect the cracking progress.In this paper uniaxial and rockburst tests on a group of granite specimens from Sanya province are described.Scanning electron microscopic imaging was used to characterize the fragments.Fractal fracture mechanics were used to analyze the microcracks in terms of both the crack type and the mineral constituent.A statistical analysis showed that the area of inter-granular cracking exceeds that of intra-granular cracking.Several types of crack were observed in the cracked areas.The percentage of intra-granular cracks in fragments from rockburst tests exceeds that from uniaxial compression tests.The results also showed that feldspar deformation was the main cause of fracture and that the consolidation along quartz grain boundaries was another weak area in the granite.Cracking along quartz grains had enough energy to enter the quartz crystal in the rockburst samples.All these results contribute to further research on rockburst mechanics.展开更多
The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of determini...The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of deterministic chaos theory. It involves the transition from study of the characteristics of the signal to the investigation of metric （and probabilistic） properties of the reconstructed attractor of the signal. It is shown that one of the most precise characteristics of the functional state of biological systems is the dynamical trend of correlation dimension and entropy of the reconstructed attractor. On the basis of this it is suggested that a complex programming apparatus be created for calculating these characteristics on line. A similar programming product is being created now with the support of RFBR. The first results of the working program, its adjustment, and further development, are also considered in the article.展开更多
Chinese calligraphy is a thousand-year-old writing art. The question of how Chinese calligraphy artworks convey emotion has cast its spell over people for millennia. Calligraphers' joys and sorrows were expressed ...Chinese calligraphy is a thousand-year-old writing art. The question of how Chinese calligraphy artworks convey emotion has cast its spell over people for millennia. Calligraphers' joys and sorrows were expressed in the complexity of the character strokes, style variations and general layouts. Determining how Chinese calligraphy aesthetic patterns emerged from the general layout of artworks is a challenging objective for researchers. Here we investigate the statistical fluctuation structure of Chinese calligraphy characters sizes using characters obtained from the calligraphy artwork "Preface to the Poems Collected from the Orchid Pavilion" which was praised as the best running script under heaven. We found that the character size distribution is a stretched exponential distribution. Moreover, the variations in the local correlation features in character size fluctuations can accurately reflect expressions of the calligrapher's complex feelings. The fractal dimensions of character size fluctuations are close to the Fibonacci sequence. The Fibonacci number is first discovered in the Chinese calligraphy artworks, which inspires the aesthetics of Chinese calligraphy artworks and maybe also provides an approach to creating Chinese calligraphy artworks in multiple genres.展开更多
The cyclic hydraulic stimulation(CHS) has proven as a prospective technology for enhancing the permeability of unconventional formations such as coalbeds. However, the effects of CHS on the microstructure and gas sorp...The cyclic hydraulic stimulation(CHS) has proven as a prospective technology for enhancing the permeability of unconventional formations such as coalbeds. However, the effects of CHS on the microstructure and gas sorption behavior of coal remain unclear. In this study, laboratory tests including the nuclear magnetic resonance(NMR), low-temperature nitrogen sorption(LTNS), and methane sorption isotherm measurement were conducted to explore changes in the pore structure and methane sorption characteristics caused by CHS on an anthracite coal from Qinshui Basin, China. The NMR and LTNS tests show that after CHS treatment, meso- and macro-pores tend to be enlarged, whereas micropores with larger sizes and transition-pores may be converted into smaller-sized micro-pores. After the coal samples treated with 1, 3, 5 and 7 hydraulic stimulation cycles, the total specific surface area(TSSA)decreased from 0.636 to 0.538, 0.516, 0.505, and 0.491 m^(2)/g, respectively. Fractal analysis based on the NMR and LTNS results show that the surface fractal dimensions increase with the increase in the number of hydraulic stimulation cycles, while the volume fractal dimensions exhibit an opposite trend to the surface fractal dimensions, indicating that the pore surface roughness and pore structure connectivity are both increased after CHS treatment. Methane sorption isothermal measurements show that both the Langmuir volume and Langmuir pressure decrease significantly with the increase in the number of hydraulic stimulation cycles. The Langmuir volume and the Langmuir pressure decrease from 33.47 cm^(3)/g and 0.205 MPa to 24.18 cm^(3)/g and 0.176 MPa after the coal samples treated with 7 hydraulic stimulation cycles, respectively. The increments of Langmuir volume and Langmuir pressure are positively correlated with the increment of TSSA and negatively correlated with the increments of surface fractal dimensions.展开更多
Multimodal medical image fusion has attained immense popularity in recent years due to its robust technology for clinical diagnosis.It fuses multiple images into a single image to improve the quality of images by reta...Multimodal medical image fusion has attained immense popularity in recent years due to its robust technology for clinical diagnosis.It fuses multiple images into a single image to improve the quality of images by retaining significant information and aiding diagnostic practitioners in diagnosing and treating many diseases.However,recent image fusion techniques have encountered several challenges,including fusion artifacts,algorithm complexity,and high computing costs.To solve these problems,this study presents a novel medical image fusion strategy by combining the benefits of pixel significance with edge-preserving processing to achieve the best fusion performance.First,the method employs a cross-bilateral filter(CBF)that utilizes one image to determine the kernel and the other for filtering,and vice versa,by considering both geometric closeness and the gray-level similarities of neighboring pixels of the images without smoothing edges.The outputs of CBF are then subtracted from the original images to obtain detailed images.It further proposes to use edge-preserving processing that combines linear lowpass filtering with a non-linear technique that enables the selection of relevant regions in detailed images while maintaining structural properties.These regions are selected using morphologically processed linear filter residuals to identify the significant regions with high-amplitude edges and adequate size.The outputs of low-pass filtering are fused with meaningfully restored regions to reconstruct the original shape of the edges.In addition,weight computations are performed using these reconstructed images,and these weights are then fused with the original input images to produce a final fusion result by estimating the strength of horizontal and vertical details.Numerous standard quality evaluation metrics with complementary properties are used for comparison with existing,well-known algorithms objectively to validate the fusion results.Experimental results from the proposed research article exhibit superior performance compared to other competing techniques in the case of both qualitative and quantitative evaluation.In addition,the proposed method advocates less computational complexity and execution time while improving diagnostic computing accuracy.Nevertheless,due to the lower complexity of the fusion algorithm,the efficiency of fusion methods is high in practical applications.The results reveal that the proposed method exceeds the latest state-of-the-art methods in terms of providing detailed information,edge contour,and overall contrast.展开更多
Early detection of pancreatic cancer has long eluded clinicians because of its insidious nature and onset.Often metastatic or locally invasive when symptomatic,most patients are deemed inoperable.In those who are symp...Early detection of pancreatic cancer has long eluded clinicians because of its insidious nature and onset.Often metastatic or locally invasive when symptomatic,most patients are deemed inoperable.In those who are symptomatic,multi-modal imaging modalities evaluate and confirm pancreatic ductal adenocarcinoma.In asymptomatic patients,detected pancreatic lesions can be either solid or cystic.The clinical implications of identifying small asymptomatic solid pancreatic lesions(SPLs)of<2 cm are tantamount to a better outcome.The accurate detection of SPLs undoubtedly promotes higher life expectancy when resected early,driving the development of existing imaging tools while promoting more comprehensive screening programs.An imaging tool that has matured in its reiterations and received many image-enhancing adjuncts is endoscopic ultrasound(EUS).It carries significant importance when risk stratifying cystic lesions and has substantial diagnostic value when combined with fine needle aspiration/biopsy(FNA/FNB).Adjuncts to EUS imaging include contrast-enhanced harmonic EUS and EUS-elastography,both having improved the specificity of FNA and FNB.This review intends to compile all existing enhancement modalities and explore ongoing research around the most promising of all adjuncts in the field of EUS imaging,artificial intelligence.展开更多
This study focuses on the non-linear rheological property and microstructure of peanut protein isolate(PPI)aggregation suspension.The impact of higher harmonics(I3 and I5)on fundamental stress wave during large amplit...This study focuses on the non-linear rheological property and microstructure of peanut protein isolate(PPI)aggregation suspension.The impact of higher harmonics(I3 and I5)on fundamental stress wave during large amplitude oscillatory shear test was studied.Rheological test show that storage modulus G′and loss modulus G″increased with increasing PPI concentration.The non-linear viscoelastic properties of PPI suspension with different concentration were investigated.Using confocal laser-scanning microscopy method,this research explored the microstructure of PPI suspension as well as the fractal dimensions.The new critical strain indirect method combined with Wu-Morbidelli model to calculate the fractal dimension(2.9225)is very close to the actual fractal dimension(2.9206).Fourier Transform Rheology was adopted to get the new critical strain for fractal dimension calculation,which was proved to be feasible.展开更多
Optical coherence tomography(OCT)is employed in the diagnosis of skin cancer.Particularly,quantitative image features extracted from OCT images might be used as indicators to classify the skin tumors.In the present pa...Optical coherence tomography(OCT)is employed in the diagnosis of skin cancer.Particularly,quantitative image features extracted from OCT images might be used as indicators to classify the skin tumors.In the present paper,we investigated intensity-based,texture-based and fractalbased features for automatically classifying the melanomas,basal cell carcinomas and pigment nevi.Generalized estimating equations were used to test for differences between the skin tumors.A modified p value of<0.001 was considered statistically significant.Significant increase of mean and median of intensity and significant decrease of mean and median of absolute gradient were observed in basal cell carcinomas and pigment nevi as compared with melanomas.Significant decrease of contrast,entropy and fractal dimension was also observed in basal cell carcinomas and pigment nevi as compared with melanomas.Our results suggest that the selected quantitative image features of OCT images could provide useful information to differentiate basal cell carcinomas and pigment nevi from the melanomas.Further research is warranted to determine how this approach may be used to improve the classification of skin tumors.展开更多
Quantitative analysis of populations having a geometric structure,which has developed into a special scientific subject called microstructology or stereology,is of great importance to the characterization and evaluati...Quantitative analysis of populations having a geometric structure,which has developed into a special scientific subject called microstructology or stereology,is of great importance to the characterization and evaluation of microstructures and their evolution in various processes.This paper, besides a brief discussion on those topics such as the recent developments of computer assisted image analysis,mathematical morphology,and fractal analysis,will mainly focus on the scope,fundamen- tals,present status,and perspectives of classical stereology.Several case examples of its application to materials science will also be given.展开更多
基金financially supported by the National Key R&D Program of China(No.2022YFE0121300)the National Natural Science Foundation of China(No.52374376)the Introduction Plan for High-end Foreign Experts(No.G2023105001L)。
文摘As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.
基金supported by the National Natural Science Foundation of China (Nos.52374078 and 52074043)the Fundamental Research Funds for the Central Universities (No.2023CDJKYJH021)。
文摘Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.
基金jointly supported by the National Natural Science Foundation of China (Nos. 40525009, 40638041, 40502029, and 40373003)
文摘The separation of anomalies from geochemical background is an important part of data analysis because lack of such identifications might have profound influence on or even distort the final analysis results. In this article, 1 672 geochemical analytical data of 11 elements, including Cu, Mo, Ag, Sn, and others, from a region within Tibet, South China, are used as one example. Together with the traditional anomaly recognition method of using the iterative mean ±2σ local multifractality theory has been utilized to delineate the ranges of geochemical anomalies of the elements. To different degrees, on the basis of original data mapping, C-A fractal analysis and singularity exponents, Sn differs from the other 10 elements. Moreover, geochemical mapping results based on values of the multifractal asymmetry index for all elements delineate the highly anomalous area. Similar to other 10 elements, the anomalous areas of Sn delineated by the asymmetry index distribute along the main structure orientations. According to the asymmetry indexes, the 11 elements could be classified into 3 groups： （1） Ag and Au, （2） As-Sb-Cu-Pb-Zn-Mo, and （3） Sn-Bi-W. This parageneflc association of elements can be used to interpret possible origins of mineralization, which is in agreement with petrological analysis and field survey results.
基金the Research Council of Shiraz University which has supported the project
文摘Fractal geometry is increasingly becoming a useful tool for modeling and quantifying the complex patterns of natural phenomena. The Earth's topography is one of these phenomena that have fractal characteristics. This paper investigates the relative sensitivity of topography to active tectonics using ASTER Global Digital Elevation Model. The covering divider method was used for direct extraction of surface fractal dimension(D surf) to estimate the roughness-surface of topography with aid of geographic information system(GIS)techniques. This evaluation let us highlight the role of the geomorphic and tectonic processes on the spatial variability of fractal properties of natural landforms.Geomorphic zones can be delineated using fractal dimension mapping in which variability of surface fractal dimension reflects the roughness of the landform surface and is a measure of topography texture. Obtained results showed this method can be a quick and easy way to assess the distribution of land surface deformation in different tectonic settings. The loose alluvial deposits and irregularities derived by tectonic activity have high fractal dimensions whereas the competent formations and higher wavelength folded surfaces have lower fractal dimensions.According to the obtained results, the Kazerun Fault Zone has a crucial role in the separation of the Zagros Mountain Ranges into the different lithological,geomorphological and structural zones.
文摘AIM: To evaluate the fractal feature of the retinal vasculature of normal eyes on a stereographic projected and montaged ultra-wide field(UWF) fluorescein angiography(FA).METHODS: Prospective, observational, cross-sectional study. Totally 59 eyes of 31 normal subjects were imaged using the Optos 200 Tx. Images obtained at different gaze angles stereographically projected and montaged. The early-phase UWF FA frames were processed to segment the retinal vasculature and the results were exported as binary masks. The fractal dimension(FD) was calculated using the box-counting method.RESULTS: The global FD for the entire retina was 1.6±0.04, with no difference between males and females(1.59±0.04 vs 1.61±0.04, P=0.084) or between right and left eyes(1.6±0.04 vs 1.6±0.05, P=0.61). FD was nonuniformly distributed among four quadrants(P<0.001) and decreased as the distance from the fovea increased(P<0.001). A negative association was observed between FD and age(R=-0.37, P=0.006), and this relationship was observed in the posterior and mid-peripheral retina(P<0.05) but absent in far-periphery(P>0.05).CONCLUSION: Fractal geometry is non-uniformly distributed across the retina in normal eyes and decreases from the fovea to the far-periphery. Subjects with an older age tend to have a smaller FD, however, the FD in the farperiphery does not appear to be influenced by age.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61501217,61363015,61501218 and 61262020the Natural Science Foundation of Jiangxi Province under Grant No 20142BAB206026
文摘Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks （MSNs） are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs.
文摘The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently reported Saraswati supercluster and the Stripe 82 region containing it as an example.The report of 120 Mpc periodicity in the Abell galaxy clusters by power spectrum analysis is the motivation behind the study.The power spectral analysis across the central part of the Stripe 82 region shows a periodic variation of 3.09°or 71 Mpc in fractal dimension whereas an average angular periodicity of 3.45°or 94 Mpc is observed across the Stripe 82 region.This refers to the periodicity of complexity or cluster density of galaxy distribution.The texture of the distribution pattern understood through lacunarity analysis indicates a near symmetric distribution.Fractal dimensions like box-counting dimension,information dimension and correlation dimension are also found through multifractal analysis.While the information dimension tells about the distribution density of galactic points,the correlation dimension details the distribution of galaxies in the neighbourhood.
基金supported by Independent Research Project of State Key Laboratory of Advanced Special Steel,Shanghai Key Laboratory of Advanced Ferrometallurgy,Shanghai University(SKLASS-2023-Z13)the Science and Technology Commission of Shanghai Municipality(No.19DZ2270200)+1 种基金A portion of the work was performed at US National High Magnetic Field Laboratory,which is supported by the National Science Foundation(Cooperative Agreement No.DMR-1157490 and DMR-1644779)the State of Florida.Thanks also to Mary Tyler for editing.
文摘The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution kinetics of primary carbides during either heating or soaking.Dissolution of carbides proceeded in three stages(fast→slow→faster)as either temperature or holding time was increased.During the heating process and during the first and third stages of the soaking process,the original size of the carbides determined the steepness of the slope,but during the middle(“slow”)stage of the soaking process,the slope remained zero.The initial size of the carbides varied greatly,but their final dissolution temperature fell within the narrow range of 1210-1235℃,and the holding time remained within 50 min.Fractal analysis was used to study the morphological characteristics of small and medium-sized carbides during the dissolution process.According to changes in the fractal dimension before and after soaking,the carbides tended to evolve towards a more regular morphology.
基金financial support received through a grant from the Vice-President's Research Office at Bu-Ali Sina University,Iran(Grant Number 09.99)。
文摘Fractal geometry quantitatively analyzes the irregular distribution of geological features,highlighting the dynamic aspects of tectonics,seismic heterogeneity,and geological maturity.This study analyzed the active fault data along the Kuhbanan fault zone in southeastern Iran by applying the boxcounting method and observing the changes in Coulomb stress and tried to find the potential triggering parts.The entire region was divided into 16subzones with the box-counting method,and then the fractal dimension(D)in each zone was calculated.The analysis of the fractal dimension for active faults and earthquake epicenters along with the seismicity parameter(b)and their ratio in the Kuhbanan region indicates an imbalance between seismic fractals and faults.This finding suggests that the area may have the potential for future earthquakes or hidden faults.In conjunction with b-value and changes in Coulomb stress change,D-value analysis reveals intense tectonic activity and stress accumulation,particularly within the Ravar,Zarand,and Kianshahr sections.It may be considered a potential location for future earthquakes.The changes in Coulomb stress resulting from the 2005Dahuieh earthquake have also placed this region within the stress accumulation zone,potentially triggering the mentioned areas.This integrative approach,backed by historical earthquake data,highlights the impact of fault geometry and stress dynamics,offering an enhanced framework for earthquake forecasting and seismic risk mitigation applicable to other tectonically active areas within the Iranian plateau.
文摘Boiling and fouling are taken as typical examples of new phase formation process to be analyzed and discussed in this paper. The process dynamics of nucleate boiling is analyzed and its mechanism is discussed from the view point of self-organization. Fouling, which is a more complicated phenomenon of new phase formation, involves series of underlying processes. The morphology and fractal analysis of fouling on low-energy surface and that with fouling inhibitors are studied and discussed. It is suggested that considering the process dynamics, fractal analysis and self-organization, a new avenue of research should be found.
文摘Dear Sir,Iam Dr.Kavitha S,from the Department of Electronics and Communication Engineering,Nandha Engineering College,Erode,Tamil Nadu,India.I write to present the detection of glaucoma using extreme learning machine(ELM)and fractal feature analysis.Glaucoma is the second most frequent cause of permanent blindness in industrial
基金the National Basic Research Program of China (No.2006CB202200)the Creative Team Development Project of the Ministry of Education of China (No.IRT0656)
文摘Fractures running along a plane reflect the cracking progress.In this paper uniaxial and rockburst tests on a group of granite specimens from Sanya province are described.Scanning electron microscopic imaging was used to characterize the fragments.Fractal fracture mechanics were used to analyze the microcracks in terms of both the crack type and the mineral constituent.A statistical analysis showed that the area of inter-granular cracking exceeds that of intra-granular cracking.Several types of crack were observed in the cracked areas.The percentage of intra-granular cracks in fragments from rockburst tests exceeds that from uniaxial compression tests.The results also showed that feldspar deformation was the main cause of fracture and that the consolidation along quartz grain boundaries was another weak area in the granite.Cracking along quartz grains had enough energy to enter the quartz crystal in the rockburst samples.All these results contribute to further research on rockburst mechanics.
文摘The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of deterministic chaos theory. It involves the transition from study of the characteristics of the signal to the investigation of metric （and probabilistic） properties of the reconstructed attractor of the signal. It is shown that one of the most precise characteristics of the functional state of biological systems is the dynamical trend of correlation dimension and entropy of the reconstructed attractor. On the basis of this it is suggested that a complex programming apparatus be created for calculating these characteristics on line. A similar programming product is being created now with the support of RFBR. The first results of the working program, its adjustment, and further development, are also considered in the article.
基金funded by the National Natural Science Foundation of China (No. 41465010, 41977245)。
文摘Chinese calligraphy is a thousand-year-old writing art. The question of how Chinese calligraphy artworks convey emotion has cast its spell over people for millennia. Calligraphers' joys and sorrows were expressed in the complexity of the character strokes, style variations and general layouts. Determining how Chinese calligraphy aesthetic patterns emerged from the general layout of artworks is a challenging objective for researchers. Here we investigate the statistical fluctuation structure of Chinese calligraphy characters sizes using characters obtained from the calligraphy artwork "Preface to the Poems Collected from the Orchid Pavilion" which was praised as the best running script under heaven. We found that the character size distribution is a stretched exponential distribution. Moreover, the variations in the local correlation features in character size fluctuations can accurately reflect expressions of the calligrapher's complex feelings. The fractal dimensions of character size fluctuations are close to the Fibonacci sequence. The Fibonacci number is first discovered in the Chinese calligraphy artworks, which inspires the aesthetics of Chinese calligraphy artworks and maybe also provides an approach to creating Chinese calligraphy artworks in multiple genres.
基金financially supported by the National Natural Science Foundation of China (51904319)the Fundamental Research Funds for the Central Universities (21CX06029A)。
文摘The cyclic hydraulic stimulation(CHS) has proven as a prospective technology for enhancing the permeability of unconventional formations such as coalbeds. However, the effects of CHS on the microstructure and gas sorption behavior of coal remain unclear. In this study, laboratory tests including the nuclear magnetic resonance(NMR), low-temperature nitrogen sorption(LTNS), and methane sorption isotherm measurement were conducted to explore changes in the pore structure and methane sorption characteristics caused by CHS on an anthracite coal from Qinshui Basin, China. The NMR and LTNS tests show that after CHS treatment, meso- and macro-pores tend to be enlarged, whereas micropores with larger sizes and transition-pores may be converted into smaller-sized micro-pores. After the coal samples treated with 1, 3, 5 and 7 hydraulic stimulation cycles, the total specific surface area(TSSA)decreased from 0.636 to 0.538, 0.516, 0.505, and 0.491 m^(2)/g, respectively. Fractal analysis based on the NMR and LTNS results show that the surface fractal dimensions increase with the increase in the number of hydraulic stimulation cycles, while the volume fractal dimensions exhibit an opposite trend to the surface fractal dimensions, indicating that the pore surface roughness and pore structure connectivity are both increased after CHS treatment. Methane sorption isothermal measurements show that both the Langmuir volume and Langmuir pressure decrease significantly with the increase in the number of hydraulic stimulation cycles. The Langmuir volume and the Langmuir pressure decrease from 33.47 cm^(3)/g and 0.205 MPa to 24.18 cm^(3)/g and 0.176 MPa after the coal samples treated with 7 hydraulic stimulation cycles, respectively. The increments of Langmuir volume and Langmuir pressure are positively correlated with the increment of TSSA and negatively correlated with the increments of surface fractal dimensions.
文摘Multimodal medical image fusion has attained immense popularity in recent years due to its robust technology for clinical diagnosis.It fuses multiple images into a single image to improve the quality of images by retaining significant information and aiding diagnostic practitioners in diagnosing and treating many diseases.However,recent image fusion techniques have encountered several challenges,including fusion artifacts,algorithm complexity,and high computing costs.To solve these problems,this study presents a novel medical image fusion strategy by combining the benefits of pixel significance with edge-preserving processing to achieve the best fusion performance.First,the method employs a cross-bilateral filter(CBF)that utilizes one image to determine the kernel and the other for filtering,and vice versa,by considering both geometric closeness and the gray-level similarities of neighboring pixels of the images without smoothing edges.The outputs of CBF are then subtracted from the original images to obtain detailed images.It further proposes to use edge-preserving processing that combines linear lowpass filtering with a non-linear technique that enables the selection of relevant regions in detailed images while maintaining structural properties.These regions are selected using morphologically processed linear filter residuals to identify the significant regions with high-amplitude edges and adequate size.The outputs of low-pass filtering are fused with meaningfully restored regions to reconstruct the original shape of the edges.In addition,weight computations are performed using these reconstructed images,and these weights are then fused with the original input images to produce a final fusion result by estimating the strength of horizontal and vertical details.Numerous standard quality evaluation metrics with complementary properties are used for comparison with existing,well-known algorithms objectively to validate the fusion results.Experimental results from the proposed research article exhibit superior performance compared to other competing techniques in the case of both qualitative and quantitative evaluation.In addition,the proposed method advocates less computational complexity and execution time while improving diagnostic computing accuracy.Nevertheless,due to the lower complexity of the fusion algorithm,the efficiency of fusion methods is high in practical applications.The results reveal that the proposed method exceeds the latest state-of-the-art methods in terms of providing detailed information,edge contour,and overall contrast.
文摘Early detection of pancreatic cancer has long eluded clinicians because of its insidious nature and onset.Often metastatic or locally invasive when symptomatic,most patients are deemed inoperable.In those who are symptomatic,multi-modal imaging modalities evaluate and confirm pancreatic ductal adenocarcinoma.In asymptomatic patients,detected pancreatic lesions can be either solid or cystic.The clinical implications of identifying small asymptomatic solid pancreatic lesions(SPLs)of<2 cm are tantamount to a better outcome.The accurate detection of SPLs undoubtedly promotes higher life expectancy when resected early,driving the development of existing imaging tools while promoting more comprehensive screening programs.An imaging tool that has matured in its reiterations and received many image-enhancing adjuncts is endoscopic ultrasound(EUS).It carries significant importance when risk stratifying cystic lesions and has substantial diagnostic value when combined with fine needle aspiration/biopsy(FNA/FNB).Adjuncts to EUS imaging include contrast-enhanced harmonic EUS and EUS-elastography,both having improved the specificity of FNA and FNB.This review intends to compile all existing enhancement modalities and explore ongoing research around the most promising of all adjuncts in the field of EUS imaging,artificial intelligence.
基金This research project was supported by General Project of Scientific Research Program of Beijing Education Commission(KM201910011003,KM201910011001)Joint Program of Beijing Natural Science Foundation Committee and Beijing Education Committee(KZ201810011017)and Beijing Excellent Talent Training Project(2017000020124G100).
文摘This study focuses on the non-linear rheological property and microstructure of peanut protein isolate(PPI)aggregation suspension.The impact of higher harmonics(I3 and I5)on fundamental stress wave during large amplitude oscillatory shear test was studied.Rheological test show that storage modulus G′and loss modulus G″increased with increasing PPI concentration.The non-linear viscoelastic properties of PPI suspension with different concentration were investigated.Using confocal laser-scanning microscopy method,this research explored the microstructure of PPI suspension as well as the fractal dimensions.The new critical strain indirect method combined with Wu-Morbidelli model to calculate the fractal dimension(2.9225)is very close to the actual fractal dimension(2.9206).Fourier Transform Rheology was adopted to get the new critical strain for fractal dimension calculation,which was proved to be feasible.
文摘Optical coherence tomography(OCT)is employed in the diagnosis of skin cancer.Particularly,quantitative image features extracted from OCT images might be used as indicators to classify the skin tumors.In the present paper,we investigated intensity-based,texture-based and fractalbased features for automatically classifying the melanomas,basal cell carcinomas and pigment nevi.Generalized estimating equations were used to test for differences between the skin tumors.A modified p value of<0.001 was considered statistically significant.Significant increase of mean and median of intensity and significant decrease of mean and median of absolute gradient were observed in basal cell carcinomas and pigment nevi as compared with melanomas.Significant decrease of contrast,entropy and fractal dimension was also observed in basal cell carcinomas and pigment nevi as compared with melanomas.Our results suggest that the selected quantitative image features of OCT images could provide useful information to differentiate basal cell carcinomas and pigment nevi from the melanomas.Further research is warranted to determine how this approach may be used to improve the classification of skin tumors.
文摘Quantitative analysis of populations having a geometric structure,which has developed into a special scientific subject called microstructology or stereology,is of great importance to the characterization and evaluation of microstructures and their evolution in various processes.This paper, besides a brief discussion on those topics such as the recent developments of computer assisted image analysis,mathematical morphology,and fractal analysis,will mainly focus on the scope,fundamen- tals,present status,and perspectives of classical stereology.Several case examples of its application to materials science will also be given.
