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
During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is ...During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is needed to replace the standard perturbation model of structure formation. Recently, we have been developing a model of cosmology that accounts for a large number of the observed properties of the universe. A key component of this model is that fractal structures that later regulated the creation of both matter and radiation came into existence during the initial Planck-era inflation. Initially, the vacuum was the only existence and since time, distance, and energy were uncertain, its only property, the curvature (or energy), was most likely distributed randomly. Everything that happened after the Planck era can be described by the known laws of physics so the remaining fundamental problem is to discover how such a random beginning could organize itself into the hierarchy of highly non-random self-similar structures on all length scales that are necessary to explain the existence of all cosmic structures. In this paper, we present a variation of the standard sandpile model that points to a solution. Incidental to our review of the distributions of cosmic structures, we discovered that the apparent transition from a fractal to a homogeneous distribution of structures at a distance of about 150 Mpc is a consequence of the finite size of the universe rather than a change in the underlying statistics of the distributions.展开更多
Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature ...Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.展开更多
For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fracti...For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.展开更多
Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle t...Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle that the number of network traffic can affect the degree ofself-similar traffic, the paper investigates the variety of self-similarity resulted fromunconventional network traffic. A network traffic model based on normal behaviors of user isproposed and the Hursl parameter of this model can be calculated. By comparing the Hurst parameterof normal traffic and the self-similar parameter, we ean judge whether the network is normal or notand alarm in time.展开更多
The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to ...The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to analyze the development of flow field.There is a linear scaling regarding the axial velocity of the jet and the scaling coefficient increases with the Froude number.展开更多
We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-k...We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.展开更多
A model of random particles constructed by the operation of self-similarity in fractalgeometry is presented.The correlation function of the number density has been obtained andcan be used conveniently in theoretical s...A model of random particles constructed by the operation of self-similarity in fractalgeometry is presented.The correlation function of the number density has been obtained andcan be used conveniently in theoretical study and computer simulation for wave interaction withrandom media.As an example,this model has been applied to calculate analytically the rangedependence of volume scattering in radar echoes.The result agrees with that of Rastogi andScheucher’s simulation.展开更多
In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.
A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes...A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.展开更多
Low profile antenna in communication is a new methodology. Fractal geometry is a methodology through which size reduction is achieved. A Self-similar fractal antenna using multicantor technique is proposed and experim...Low profile antenna in communication is a new methodology. Fractal geometry is a methodology through which size reduction is achieved. A Self-similar fractal antenna using multicantor technique is proposed and experimentally studied. Space-filling cantors and self-similarity properties of fractal geometry have been adopted in the proposed antenna to miniaturize the size of antenna. The antenna is designed in such a way to operate at MICS band (Medical Implant communication Service) for wireless telemedicine application. The prototype antenna exhibits wideband characteristics and provides a good agreement of return loss (S11). Experimental return loss has been compared with that which is obtained using method of moments. The objective of using self-similar concept in antenna makes it flexible in terms of controlling the resonance and bandwidth. In this paper, the Self-similar property of fractal geometry is examined by maintaining return loss (S11) more than –30 dB approximately in all the iterations (n) and the prototype antenna has return loss greater than –10 dB and exhibits wideband characteristics.展开更多
Based on similarity science and complex system theory,a new concept of characteristic self-diversity and corre- sponding relations between self-similarity and self-diversity for complex mechanical systems are presente...Based on similarity science and complex system theory,a new concept of characteristic self-diversity and corre- sponding relations between self-similarity and self-diversity for complex mechanical systems are presented in this paper.Methods of system self-similarity and self-diversity measure between main system and sub-system are studied.Numerical calculations show that the characteristic self-similarity and self-diversity measure method is validity.A new theory and method of self-similarity and self- diversity measure for complexity mechanical system is presented.展开更多
Real-world networks exhibit complex topological interactions that pose a significant computational challenge to analyses of such networks.Due to limited resources,there is an urgent need to develop dimensionality redu...Real-world networks exhibit complex topological interactions that pose a significant computational challenge to analyses of such networks.Due to limited resources,there is an urgent need to develop dimensionality reduction techniques that can significantly reduce the structural complexity of initial large-scale networks.In this paper,we propose a subgraph extraction method based on the node centrality measure to reduce the size of the initial network topology.Specifically,nodes with smaller centrality value are removed from the initial network to obtain a subgraph with a smaller size.Our results demonstrate that various real-world networks,including power grids,technology,transportation,biology,social,and language networks,exhibit self-similarity behavior during the reduction process.The present results reveal the selfsimilarity and scale invariance of real-world networks from a different perspective and also provide an effective guide for simplifying the topology of large-scale networks.展开更多
Pulmonary arterial hypertension (PAH) has become an important topic of basic and clinical research in recent years. Morphologic researches have shown that specific PAH-lesions are located in the lobular small muscular...Pulmonary arterial hypertension (PAH) has become an important topic of basic and clinical research in recent years. Morphologic researches have shown that specific PAH-lesions are located in the lobular small muscular arteries and correlate with hemodynamic measurements. However, it still remains to be shown how pathological changes of the small arteries in the lobule develop to PAH. Based on both fractal properties of pulmonary arterial tree and asynchronous phasic contractions of lobular arterial muscles under the evenness of the pulmonary capillary pressure (PCP) in the lung, the author has constructed an integrated model of pulmonary circulation which has produced a mathematical relationship between the mean pulmonary arterial pressure (MPAP) and the cardiac output (CO). By use of the expression between MPAP and CO, it has been able to explain the pathogenesis of PAH in terms of statistical changes among regional and temporal perfusions in the lung. In order to detect clinically the early stage of PAH, the author has suggested that it is important to establish the pulmonary functional imaging of regional and temporal perfusions.展开更多
Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system （UIFS） on R^d. Denote by D the Hausdorff dimension, by H^D（E） the Hausdorff measu...Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system （UIFS） on R^d. Denote by D the Hausdorff dimension, by H^D（E） the Hausdorff measure and by diam（E） the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H^O（E） = diam（E）^D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present a parametrised UIFS, where ω depends on c and show the inequatily H^D（E） 〈 diam（E）^D, if c is small enough.展开更多
Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal...Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal synergistically affected by solvents have not been fully understood.Ultrasonic testing,nuclear magnetic resonance analysis,liquid phase mass spectrometry was adopted to comprehensively analyze pore-fracture change characteristics of lean coal treated by combined solvent(NMP and CS_(2)).Meanwhile,quantitative characterization of above changing properties was conducted using geometric fractal theory.Relationship model between permeability,fractal dimension and porosity were established.Results indicate that the end face fractures of coal are well developed after CS2and combined solvent treatments,of which,end face box-counting fractal dimensions range from 1.1227 to 1.4767.Maximum decreases in ultrasonic longitudinal wave velocity of coal affected by NMP,CS_(2)and combined solvent are 2.700%,20.521%,22.454%,respectively.Solvent treatments could lead to increasing amount of both mesopores and macropores.Decrease ratio of fractal dimension Dsis 0.259%–2.159%,while permeability increases ratio of NMR ranges from 0.1904 to 6.4486.Meanwhile,combined solvent could dissolve coal polar and non-polar small molecules and expand flow space.Results could provide reference for solvent selection and parameter optimization of permeability-enhancement technology.展开更多
Decelerating open-channel flow is a type of flow that gradually moves forward with decreasing velocity and increasing water depth.Although all flow parameters change along the streamwise direction,previous studies hav...Decelerating open-channel flow is a type of flow that gradually moves forward with decreasing velocity and increasing water depth.Although all flow parameters change along the streamwise direction,previous studies have revealed that these parameters’vertical distributions at different sections can be universally described with a single profile when being nondimensionalised by appropriate scales.This study focuses on the population trends of spanwise rotational motions at various sections along the main flow direction by particle imaging velocimetry(PIV)measurement.The wall-normal population distributions of density,radius,swirling strength,and convection velocity of the prograde and retrograde motions show similar trends in uniform open-channel flows.The dimensionless representation is invariant along the main flow direction.This study’s results indicate the self-similar characteristic of population trends of spanwise rotational motions prevails in decelerating open-channel flow.展开更多
This paper presents an inexpensive method for self-similarity based editing of real-world 3D surface textures by using height and albedo maps. Unlike self-similarity based 2D texture editing approaches which only make...This paper presents an inexpensive method for self-similarity based editing of real-world 3D surface textures by using height and albedo maps. Unlike self-similarity based 2D texture editing approaches which only make changes to pixel color or inten- sity values, this technique also allows surface geometry and reflectance of the captured 3D surface textures to be edited and relit us- ing illumination conditions and viewing angles that differ from those of the original. A single editing operation at a given location affects all similar areas and produces changes on all images of the sample rendered under different conditions. Since surface height and albedo maps can be used to describe seabed topography and geologic features, which play important roles in many oceanic proc- esses, the proposed method can be effectively employed in applications regarding visualization and simulation of oceanic phenom- ena.展开更多
Fabric defect detection has been an indispensable and important link in fabric production,many studies on the development of vision based automated inspection techniques have been reported.The main drawback of existin...Fabric defect detection has been an indispensable and important link in fabric production,many studies on the development of vision based automated inspection techniques have been reported.The main drawback of existing methods is that they can only inspect a particular type of fabric pattern in controlled environment.Recently,nonlocal self-similarity(NSS)based method is used for fabric defect detection.This method achieves good defect detection performance for small defects with uneven illumination,the disadvantage of NNS based method is poor for detecting linear defects.Based on this reason,we improve NSS based defect detection method by introducing a gray density function,namely an enhanced NSS(ENSS)based defect detection method.Meanwhile,mean filter is applied to smooth images and suppress noise.Experimental results prove the validity and feasibility of the proposed NLRA algorithm.展开更多
Layering detection is an important step in petroleum engineering.Time series of post-stack seismic data and wire-line log data belong to subsurface layering.They exhibit multifractal properties with complex patterns b...Layering detection is an important step in petroleum engineering.Time series of post-stack seismic data and wire-line log data belong to subsurface layering.They exhibit multifractal properties with complex patterns because of the heterogeneity and different genetic properties in the earth layers.In a multifractal configuration,any piece of a series has a distinct Hurst exponent that reflects its nature and can be used for zone detection.Time series are post-stack seismic traces and wire-line log data near the well-bores.Self-similar Autoregressive Exogenous(SAE)model is a modified method which can place self-similar post-stack seismic and wire-line log segments across layers with the same lithology.The results satisfy the capability of layering identification from seismic data by SAE model.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.
文摘During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is needed to replace the standard perturbation model of structure formation. Recently, we have been developing a model of cosmology that accounts for a large number of the observed properties of the universe. A key component of this model is that fractal structures that later regulated the creation of both matter and radiation came into existence during the initial Planck-era inflation. Initially, the vacuum was the only existence and since time, distance, and energy were uncertain, its only property, the curvature (or energy), was most likely distributed randomly. Everything that happened after the Planck era can be described by the known laws of physics so the remaining fundamental problem is to discover how such a random beginning could organize itself into the hierarchy of highly non-random self-similar structures on all length scales that are necessary to explain the existence of all cosmic structures. In this paper, we present a variation of the standard sandpile model that points to a solution. Incidental to our review of the distributions of cosmic structures, we discovered that the apparent transition from a fractal to a homogeneous distribution of structures at a distance of about 150 Mpc is a consequence of the finite size of the universe rather than a change in the underlying statistics of the distributions.
基金supported by The National Natural Science Foundation of China(Grant Nos.12272411 and 42007259).
文摘Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.
文摘For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.
文摘Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle that the number of network traffic can affect the degree ofself-similar traffic, the paper investigates the variety of self-similarity resulted fromunconventional network traffic. A network traffic model based on normal behaviors of user isproposed and the Hursl parameter of this model can be calculated. By comparing the Hurst parameterof normal traffic and the self-similar parameter, we ean judge whether the network is normal or notand alarm in time.
基金supported by the National Natural Science Founda-tion of China(Grant Nos.12122214,12272382,12293000,12293003,and 12293004)the Youth Innovation Promotion Association CAS(Grant No.2022019)High-level Innovation Research Institute Program of Guangdong Province(Grant Nos.2020B0909010003 and GARA2022002000).
文摘The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to analyze the development of flow field.There is a linear scaling regarding the axial velocity of the jet and the scaling coefficient increases with the Froude number.
文摘We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.
基金Supported by National Natural Science Foundation of China(68971020)
文摘A model of random particles constructed by the operation of self-similarity in fractalgeometry is presented.The correlation function of the number density has been obtained andcan be used conveniently in theoretical study and computer simulation for wave interaction withrandom media.As an example,this model has been applied to calculate analytically the rangedependence of volume scattering in radar echoes.The result agrees with that of Rastogi andScheucher’s simulation.
文摘In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.
基金This study was supported by the National Natural Science Foundation of China(U22B2075,52274056,51974356).
文摘A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.
文摘Low profile antenna in communication is a new methodology. Fractal geometry is a methodology through which size reduction is achieved. A Self-similar fractal antenna using multicantor technique is proposed and experimentally studied. Space-filling cantors and self-similarity properties of fractal geometry have been adopted in the proposed antenna to miniaturize the size of antenna. The antenna is designed in such a way to operate at MICS band (Medical Implant communication Service) for wireless telemedicine application. The prototype antenna exhibits wideband characteristics and provides a good agreement of return loss (S11). Experimental return loss has been compared with that which is obtained using method of moments. The objective of using self-similar concept in antenna makes it flexible in terms of controlling the resonance and bandwidth. In this paper, the Self-similar property of fractal geometry is examined by maintaining return loss (S11) more than –30 dB approximately in all the iterations (n) and the prototype antenna has return loss greater than –10 dB and exhibits wideband characteristics.
基金Supported by National Natural Science Foundation of China(50475072)
文摘Based on similarity science and complex system theory,a new concept of characteristic self-diversity and corre- sponding relations between self-similarity and self-diversity for complex mechanical systems are presented in this paper.Methods of system self-similarity and self-diversity measure between main system and sub-system are studied.Numerical calculations show that the characteristic self-similarity and self-diversity measure method is validity.A new theory and method of self-similarity and self- diversity measure for complexity mechanical system is presented.
基金the Science and Technology Project of State Grid Corporation of China(Grant No.5100-202199557A-0-5-ZN)。
文摘Real-world networks exhibit complex topological interactions that pose a significant computational challenge to analyses of such networks.Due to limited resources,there is an urgent need to develop dimensionality reduction techniques that can significantly reduce the structural complexity of initial large-scale networks.In this paper,we propose a subgraph extraction method based on the node centrality measure to reduce the size of the initial network topology.Specifically,nodes with smaller centrality value are removed from the initial network to obtain a subgraph with a smaller size.Our results demonstrate that various real-world networks,including power grids,technology,transportation,biology,social,and language networks,exhibit self-similarity behavior during the reduction process.The present results reveal the selfsimilarity and scale invariance of real-world networks from a different perspective and also provide an effective guide for simplifying the topology of large-scale networks.
文摘Pulmonary arterial hypertension (PAH) has become an important topic of basic and clinical research in recent years. Morphologic researches have shown that specific PAH-lesions are located in the lobular small muscular arteries and correlate with hemodynamic measurements. However, it still remains to be shown how pathological changes of the small arteries in the lobule develop to PAH. Based on both fractal properties of pulmonary arterial tree and asynchronous phasic contractions of lobular arterial muscles under the evenness of the pulmonary capillary pressure (PCP) in the lung, the author has constructed an integrated model of pulmonary circulation which has produced a mathematical relationship between the mean pulmonary arterial pressure (MPAP) and the cardiac output (CO). By use of the expression between MPAP and CO, it has been able to explain the pathogenesis of PAH in terms of statistical changes among regional and temporal perfusions in the lung. In order to detect clinically the early stage of PAH, the author has suggested that it is important to establish the pulmonary functional imaging of regional and temporal perfusions.
文摘Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system （UIFS） on R^d. Denote by D the Hausdorff dimension, by H^D（E） the Hausdorff measure and by diam（E） the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H^O（E） = diam（E）^D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present a parametrised UIFS, where ω depends on c and show the inequatily H^D（E） 〈 diam（E）^D, if c is small enough.
基金financially supported by National Natural Science Foundation of China(No.52274171)Joint National-Local Engineering Research Centre for Safe and Precise Coal Mining Fund(No.EC2023015)+1 种基金Excellent Youth Project of Universities in Anhui Province(No.2023AH030042)Unveiled List of Bidding Projects of Shanxi Province(No.20201101001)。
文摘Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal synergistically affected by solvents have not been fully understood.Ultrasonic testing,nuclear magnetic resonance analysis,liquid phase mass spectrometry was adopted to comprehensively analyze pore-fracture change characteristics of lean coal treated by combined solvent(NMP and CS_(2)).Meanwhile,quantitative characterization of above changing properties was conducted using geometric fractal theory.Relationship model between permeability,fractal dimension and porosity were established.Results indicate that the end face fractures of coal are well developed after CS2and combined solvent treatments,of which,end face box-counting fractal dimensions range from 1.1227 to 1.4767.Maximum decreases in ultrasonic longitudinal wave velocity of coal affected by NMP,CS_(2)and combined solvent are 2.700%,20.521%,22.454%,respectively.Solvent treatments could lead to increasing amount of both mesopores and macropores.Decrease ratio of fractal dimension Dsis 0.259%–2.159%,while permeability increases ratio of NMR ranges from 0.1904 to 6.4486.Meanwhile,combined solvent could dissolve coal polar and non-polar small molecules and expand flow space.Results could provide reference for solvent selection and parameter optimization of permeability-enhancement technology.
基金the National Natural Science Foundation of China(Grant No.51679020)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202100731).
文摘Decelerating open-channel flow is a type of flow that gradually moves forward with decreasing velocity and increasing water depth.Although all flow parameters change along the streamwise direction,previous studies have revealed that these parameters’vertical distributions at different sections can be universally described with a single profile when being nondimensionalised by appropriate scales.This study focuses on the population trends of spanwise rotational motions at various sections along the main flow direction by particle imaging velocimetry(PIV)measurement.The wall-normal population distributions of density,radius,swirling strength,and convection velocity of the prograde and retrograde motions show similar trends in uniform open-channel flows.The dimensionless representation is invariant along the main flow direction.This study’s results indicate the self-similar characteristic of population trends of spanwise rotational motions prevails in decelerating open-channel flow.
文摘This paper presents an inexpensive method for self-similarity based editing of real-world 3D surface textures by using height and albedo maps. Unlike self-similarity based 2D texture editing approaches which only make changes to pixel color or inten- sity values, this technique also allows surface geometry and reflectance of the captured 3D surface textures to be edited and relit us- ing illumination conditions and viewing angles that differ from those of the original. A single editing operation at a given location affects all similar areas and produces changes on all images of the sample rendered under different conditions. Since surface height and albedo maps can be used to describe seabed topography and geologic features, which play important roles in many oceanic proc- esses, the proposed method can be effectively employed in applications regarding visualization and simulation of oceanic phenom- ena.
文摘Fabric defect detection has been an indispensable and important link in fabric production,many studies on the development of vision based automated inspection techniques have been reported.The main drawback of existing methods is that they can only inspect a particular type of fabric pattern in controlled environment.Recently,nonlocal self-similarity(NSS)based method is used for fabric defect detection.This method achieves good defect detection performance for small defects with uneven illumination,the disadvantage of NNS based method is poor for detecting linear defects.Based on this reason,we improve NSS based defect detection method by introducing a gray density function,namely an enhanced NSS(ENSS)based defect detection method.Meanwhile,mean filter is applied to smooth images and suppress noise.Experimental results prove the validity and feasibility of the proposed NLRA algorithm.
文摘Layering detection is an important step in petroleum engineering.Time series of post-stack seismic data and wire-line log data belong to subsurface layering.They exhibit multifractal properties with complex patterns because of the heterogeneity and different genetic properties in the earth layers.In a multifractal configuration,any piece of a series has a distinct Hurst exponent that reflects its nature and can be used for zone detection.Time series are post-stack seismic traces and wire-line log data near the well-bores.Self-similar Autoregressive Exogenous(SAE)model is a modified method which can place self-similar post-stack seismic and wire-line log segments across layers with the same lithology.The results satisfy the capability of layering identification from seismic data by SAE model.
