The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the...The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.展开更多
After exposure to freeze-thaw cycles, scanning electron microscopy(SEM) and nuclear magnetic resonance(NMR) were used to test the four mixtures. The microstructure is qualitatively analyzed from the 2D SEM image and t...After exposure to freeze-thaw cycles, scanning electron microscopy(SEM) and nuclear magnetic resonance(NMR) were used to test the four mixtures. The microstructure is qualitatively analyzed from the 2D SEM image and the 3D pore distribution curve before and after freezing and thawing. The fractal dimension is utilized to characterize the two-dimensional topography image and the three-dimensional pore distribution, quantitatively. The results reveal that the surface porosity and volume porosity increase as the freeze-thaw action increases. Self-similarity characteristics exist in micro-damage inside the concrete. In the fractal dimension, it is possible to characterize pore evolution quantitatively. The fractal dimension correlates with pore damage evolution. The fractal dimension effectively quantitatively characterizes micro-damage features at various scales from the local to the global level.展开更多
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
The microscopic characterization of isolated bubbles in gassy soil plays an important role in the macroscopic physical properties of sediments and is a key factor in the study of geological hazards in gas-bearing stra...The microscopic characterization of isolated bubbles in gassy soil plays an important role in the macroscopic physical properties of sediments and is a key factor in the study of geological hazards in gas-bearing strata.Based on the box-counting method and the pore fractal features in porous media,a fractal model of bubble microstructure parameters in gassy soil under different gas con-tents and vertical load conditions is established by using an industrial X-ray CT scanning system.The results show that the fractal di-mension of bubbles in the sample is correlated with the volume fraction of bubbles,and it is also restricted by the vertical load.The three-dimensional fractal dimension of the sample is about 1 larger than the average two-dimensional fractal dimension of all the slices from the same sample.The uniform porous media fractal model is used to test the equivalent diameter,and the results show that the variation of the measured pore diameter ratio is jointly restricted by the volume fraction and the vertical load.In addition,the measured self-similarity interval of the bubble area distribution is tested by the porous media fractal capillary bundle model,and the fitting curve of measured pore area ratio in a small loading range is obtained in this paper.展开更多
Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied usin...Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.展开更多
This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus.A series of fluid fl...This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus.A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm,3 mm,5 mm,7 mm and 10 mm under a normal stress of 0.5 MPa.Four granite fractures with different roughnesses are selected and quantified using variogram fractal dimensions.The obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture surface.The flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact spots.As the shear displacement continues to increase,preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation;yet the area of single contacts in-creases.Based on the experimental results,an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension.展开更多
The morphological complexity of cells and tissues,whether normal or pathological,is characterized by two primary attributes:Irregularity and self-similarity across different scales.When an object exhibits self-similar...The morphological complexity of cells and tissues,whether normal or pathological,is characterized by two primary attributes:Irregularity and self-similarity across different scales.When an object exhibits self-similarity,its shape remains unchanged as the scales of measurement vary because any part of it resembles the whole.On the other hand,the size and geometric characteristics of an irregular object vary as the resolution increases,revealing more intricate details.Despite numerous attempts,a reliable and accurate method for quantifying the morphological features of gastrointestinal organs,tissues,cells,their dynamic changes,and pathological disorders has not yet been established.However,fractal geometry,which studies shapes and patterns that exhibit self-similarity,holds promise in providing a quantitative measure of the irregularly shaped morphologies and their underlying self-similar temporal behaviors.In this context,we explore the fractal nature of the gastrointestinal system and the potential of fractal geometry as a robust descriptor of its complex forms and functions.Additionally,we examine the practical applications of fractal geometry in clinical gastroenterology and hepatology practice.展开更多
Motivated by the mathematical beauty and the recent experimental realizations of fractal systems,we study the spin-1/2 antiferromagnetic Heisenberg model on a Sierpiński gasket.The fractal porous feature generates ne...Motivated by the mathematical beauty and the recent experimental realizations of fractal systems,we study the spin-1/2 antiferromagnetic Heisenberg model on a Sierpiński gasket.The fractal porous feature generates new kinds of frustration to exhibit exotic quantum states.Using advanced tensor network techniques,we identify a quantum gapless-spin-liquid ground state in fractional spatial dimension.This fractal spin system also demonstrates nontrivial nonlocal properties.While the extremely short-range correlation causes a highly degenerate spin form factor,the entanglement in this fractal system suggests a long-range scaling behavior.We also study the dynamic structure factor and clearly identify the gapless excitation with a stable corner excitation emerged from the ground-state entanglement.Our results unambiguously point out multiple essential properties of this fractal spin system,and open a new route to explore spin liquid and frustrated magnetism.展开更多
In this study,X-ray diffraction,N_(2)adsorption(N_(2)A),and mercury intrusion(MI)experiments were used to investigate the influence of acid treatment on pore structure and fractal characterization of tight sandstones....In this study,X-ray diffraction,N_(2)adsorption(N_(2)A),and mercury intrusion(MI)experiments were used to investigate the influence of acid treatment on pore structure and fractal characterization of tight sandstones.The results showed that acid treatment generated a certain number of ink-bottle pores in fine sandstone,aggravated the ink-bottle effect in the sandy mudstone,and transformed some smaller pores into larger ones.After the acid treatment,both the pore volume in the range of 2–11 nm and 0.271–8μm for the fine sandstone and the entire pore size range for the sandy mudstone significantly increased.The dissolution of sandstone cement causes the fine sandstone particles to fall off and fill the pores;the porosity increased at first but then decreased with acid treatment time.The fractal dimension obtained using the Frenkel-Halsey-Hill model was positively correlated with acid treatment time.However,the total fractal dimensions obtained by MI tests showed different changes with acid treatment time in fine sandstone and sandy mudstone.These results provide good guiding significance for reservoir acidification stimulation.展开更多
The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich str...The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich structure was designed.The generation mechanism and recurrence formula of theHilbert fractal were expressed by Lin’s language,and the second-orderHilbert sandwich structure was constructed fromthermoplastic polyurethane.The constitutive model of the hyperelastic body was established by using the finite element method.With the unit mass energy absorption as the optimization goal,the fractal sandwich structure was optimized,and the best result was obtained when the order was 2.5 and the unit layer thickness was 0.75 mm.TheHilbert sandwich structure was compared with the rice-shaped sandwich structure commonly used in industry,and the Hilbert fractal structure had better energy absorption.This has practical significance for the development and application of newcushioning packaging structures.展开更多
The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in pe...The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T_(2) spectra and T_(2) cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T_(2) cut-off values, ranging from 7 to 50 ms. Additionally, the T_(2) spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T_(2) spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T_(2) cut-off value were separately developed based on the classified T_(2) spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T_(2) spectral shift. However, the T_(2) spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T_(2) spectrum and pore types, as well as to predict the T_(2) cut-off value of low-permeability rocks using machine learning and data augmentation techniques.展开更多
Activation functions play an essential role in converting the output of the artificial neural network into nonlinear results,since without this nonlinearity,the results of the network will be less accurate.Nonlinearity...Activation functions play an essential role in converting the output of the artificial neural network into nonlinear results,since without this nonlinearity,the results of the network will be less accurate.Nonlinearity is the mission of all nonlinear functions,except for polynomials.The activation function must be dif-ferentiable for backpropagation learning.This study’s objective is to determine the best activation functions for the approximation of each fractal image.Different results have been attained using Matlab and Visual Basic programs,which indi-cate that the bounded function is more helpful than other functions.The non-lin-earity of the activation function is important when using neural networks for coding fractal images because the coefficients of the Iterated Function System are different according to the different types of fractals.The most commonly cho-sen activation function is the sigmoidal function,which produces a positive value.Other functions,such as tansh or arctan,whose values can be positive or negative depending on the network input,tend to train neural networks faster.The coding speed of the fractal image is different depending on the appropriate activation function chosen for each fractal shape.In this paper,we have provided the appro-priate activation functions for each type of system of iterated functions that help the network to identify the transactions of the system.展开更多
Next-generation networks,including the Internet of Things(IoT),fifth-generation cellular systems(5G),and sixth-generation cellular systems(6G),suf-fer from the dramatic increase of the number of deployed devices.This p...Next-generation networks,including the Internet of Things(IoT),fifth-generation cellular systems(5G),and sixth-generation cellular systems(6G),suf-fer from the dramatic increase of the number of deployed devices.This puts high constraints and challenges on the design of such networks.Structural changing of the network is one of such challenges that affect the network performance,includ-ing the required quality of service(QoS).The fractal dimension(FD)is consid-ered one of the main indicators used to represent the structure of the communication network.To this end,this work analyzes the FD of the network and its use for telecommunication networks investigation and planning.The clus-ter growing method for assessing the FD is introduced and analyzed.The article proposes a novel method for estimating the FD of a communication network,based on assessing the network’s connectivity,by searching for the shortest routes.Unlike the cluster growing method,the proposed method does not require multiple iterations,which reduces the number of calculations,and increases the stability of the results obtained.Thus,the proposed method requires less compu-tational cost than the cluster growing method and achieves higher stability.The method is quite simple to implement and can be used in the tasks of research and planning of modern and promising communication networks.The developed method is evaluated for two different network structures and compared with the cluster growing method.Results validate the developed method.展开更多
The accurate prediction of energy consumption has effective role in decision making and risk management for individuals and governments.Meanwhile,the accurate prediction can be realized using the recent advances in ma...The accurate prediction of energy consumption has effective role in decision making and risk management for individuals and governments.Meanwhile,the accurate prediction can be realized using the recent advances in machine learning and predictive models.This research proposes a novel approach for energy consumption forecasting based on a new optimization algorithm and a new forecasting model consisting of a set of long short-term memory(LSTM)units.The proposed optimization algorithm is used to optimize the parameters of the LSTM-based model to boost its forecasting accuracy.This optimization algorithm is based on the recently emerged dipper-throated optimization(DTO)and stochastic fractal search(SFS)algo-rithm and is referred to as dynamic DTOSFS.To prove the effectiveness and superiority of the proposed approach,five standard benchmark algorithms,namely,stochastic fractal search(SFS),dipper throated optimization(DTO),whale optimization algorithm(WOA),particle swarm optimization(PSO),and grey wolf optimization(GWO),are used to optimize the parameters of the LSTM-based model,and the results are compared with that of the proposed approach.Experimental results show that the proposed DDTOSFS+LSTM can accurately forecast the energy consumption with root mean square error RMSE of 0.00013,which is the best among the recorded results of the other methods.In addition,statistical experiments are conducted to prove the statistical difference of the proposed model.The results of these tests confirmed the expected outcomes.展开更多
Pore structure is the key element of tight sandstone reservoir, which restricts the accumulation and flow of oil and gas in the reservoir. At present, reservoir pore structure is the focus and difficulty of unconventi...Pore structure is the key element of tight sandstone reservoir, which restricts the accumulation and flow of oil and gas in the reservoir. At present, reservoir pore structure is the focus and difficulty of unconventional oil and gas exploration and development research. The tight sandstone reservoir in the Chang 4 + 5 member of the Upper Triassic Yanchang Formation is the main reservoir for oil and gas exploration in G area. At present, there is little research on its pore structure and fractal characteristics, which to some extent affects the progress of exploration and development. This paper selects the tight core samples of the Chang 4 + 5 member in the southern edge of the Ordos Basin, and based on the high-pressure mercury intrusion experiment, uses fractal theory to study the pore structure and fractal characteristics of the reservoir in the study area, thus providing theoretical basis for the evaluation and exploration and development of the Chang 4 + 5 tight reservoir in the G area. The research results show that the lithology of the Chang 4 + 5 tight sandstone reservoir in the southern edge of the Ordos Basin is mainly feldspathic sandstone, with the highest feldspar content, followed by quartz, and the clay mineral is mainly chlorite. The reservoir has poor physical properties and strong heterogeneity. There are three main fractal characteristics in Chang 4 + 5 reservoir in G area: the fractal curve of Type I reservoir sample is in two segments, the relatively large pore has certain fractal characteristics, the pore structure is relatively regular, and the heterogeneity is weak;Relatively small pores have no fractal characteristics and pore structure is irregular. The fractal curve of Type II reservoir samples shows a three-segment pattern, and each pore size range has certain fractal characteristics, and it gradually gets better with the increase of pore size. The fractal curve of Type III reservoir samples presents a similar one-segment pattern, and the fractal dimension exceeds the upper limit of 3. It is considered that the full pore size of this type of reservoir does not have fractal characteristics, the pore throat is completely irregular or the surface is rough, and the heterogeneity is very strong.展开更多
Because of the developed economy and lush vegetation in southern China, the following obstacles or difficulties exist in remote sensing land surface classification: 1) Diverse surface composition types;2) Undulating t...Because of the developed economy and lush vegetation in southern China, the following obstacles or difficulties exist in remote sensing land surface classification: 1) Diverse surface composition types;2) Undulating terrains;3) Small fragmented land;4) Indistinguishable shadows of surface objects. It is our top priority to clarify how to use the concept of big data (Data mining technology) and various new technologies and methods to make complex surface remote sensing information extraction technology develop in the direction of automation, refinement and intelligence. In order to achieve the above research objectives, the paper takes the Gaofen-2 satellite data produced in China as the data source, and takes the complex surface remote sensing information extraction technology as the research object, and intelligently analyzes the remote sensing information of complex surface on the basis of completing the data collection and preprocessing. The specific extraction methods are as follows: 1) extraction research on fractal texture features of Brownian motion;2) extraction research on color features;3) extraction research on vegetation index;4) research on vectors and corresponding classification. In this paper, fractal texture features, color features, vegetation features and spectral features of remote sensing images are combined to form a combination feature vector, which improves the dimension of features, and the feature vector improves the difference of remote sensing features, and it is more conducive to the classification of remote sensing features, and thus it improves the classification accuracy of remote sensing images. It is suitable for remote sensing information extraction of complex surface in southern China. This method can be extended to complex surface area in the future.展开更多
Deep neural networks often outperform classical machine learning algorithms in solving real-world problems.However,designing better networks usually requires domain expertise and consumes significant time and com-puti...Deep neural networks often outperform classical machine learning algorithms in solving real-world problems.However,designing better networks usually requires domain expertise and consumes significant time and com-puting resources.Moreover,when the task changes,the original network architecture becomes outdated and requires redesigning.Thus,Neural Architecture Search(NAS)has gained attention as an effective approach to automatically generate optimal network architectures.Most NAS methods mainly focus on achieving high performance while ignoring architectural complexity.A myriad of research has revealed that network performance and structural complexity are often positively correlated.Nevertheless,complex network structures will bring enormous computing resources.To cope with this,we formulate the neural architecture search task as a multi-objective optimization problem,where an optimal architecture is learned by minimizing the classification error rate and the number of network parameters simultaneously.And then a decomposition-based multi-objective stochastic fractal search method is proposed to solve it.In view of the discrete property of the NAS problem,we discretize the stochastic fractal search step size so that the network architecture can be optimized more effectively.Additionally,two distinct update methods are employed in step size update stage to enhance the global and local search abilities adaptively.Furthermore,an information exchange mechanism between architectures is raised to accelerate the convergence process and improve the efficiency of the algorithm.Experimental studies show that the proposed algorithm has competitive performance comparable to many existing manual and automatic deep neural network generation approaches,which achieved a parameter-less and high-precision architecture with low-cost on each of the six benchmark datasets.展开更多
After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organiz...After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.展开更多
The seepage characteristics of multiscale porous media is of considerable significance in many scientific and engineering fields.The Darcy permeability is one of the key macroscopic physical properties to characterize...The seepage characteristics of multiscale porous media is of considerable significance in many scientific and engineering fields.The Darcy permeability is one of the key macroscopic physical properties to characterize the seepage capacity of porous media.Therefore,based on the statistically fractal scaling law of porous media,fractal geometry is applied to model the multiscale pore structures.And a two-dimensional fractal orifice-throat model with multiscale and tortuous characteristics is proposed for the seepage flow through porous media.The analytical expression for Darcy permeability of porous media is derived,which is validated by comparing with available experimental data.The results show that the Darcy permeability is significantly influenced by porosity,orifice-throat fractal dimension,minimum to maximum diameter ratio,orifice-throat ratio and tortuosity fractal dimension.The present results are helpful for understanding the seepage mechanism of multiscale porous media,and may provide theoretical basis for unconventional oil and gas exploration and development,porous phase transition energy storage composites,CO2 geological sequestration,environmental protection and nuclear waste treatment,etc.展开更多
文摘The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.
基金Funded by the Key Project of Science and Technology Research in Higher Educational Institutions of Inner Mongolia Autonomous Region (No.NJZZ22518)Inner Mongolia Natural Science Foundation Project (No.2022MS05043)Inner Mongolia Autonomous Region Water Conservancy Research Special Project(No.NSK2016-S11)。
文摘After exposure to freeze-thaw cycles, scanning electron microscopy(SEM) and nuclear magnetic resonance(NMR) were used to test the four mixtures. The microstructure is qualitatively analyzed from the 2D SEM image and the 3D pore distribution curve before and after freezing and thawing. The fractal dimension is utilized to characterize the two-dimensional topography image and the three-dimensional pore distribution, quantitatively. The results reveal that the surface porosity and volume porosity increase as the freeze-thaw action increases. Self-similarity characteristics exist in micro-damage inside the concrete. In the fractal dimension, it is possible to characterize pore evolution quantitatively. The fractal dimension correlates with pore damage evolution. The fractal dimension effectively quantitatively characterizes micro-damage features at various scales from the local to the global level.
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.
基金supported by the Open Research Fund Program of State Key Laboratory of Hydroscience and Engineering(No.sk lhse-2022-D-03)the National Natural Science Foundation of China(Nos.U2006213,42277139)the Taishan Scholars Program(No.tsqn202306297).
文摘The microscopic characterization of isolated bubbles in gassy soil plays an important role in the macroscopic physical properties of sediments and is a key factor in the study of geological hazards in gas-bearing strata.Based on the box-counting method and the pore fractal features in porous media,a fractal model of bubble microstructure parameters in gassy soil under different gas con-tents and vertical load conditions is established by using an industrial X-ray CT scanning system.The results show that the fractal di-mension of bubbles in the sample is correlated with the volume fraction of bubbles,and it is also restricted by the vertical load.The three-dimensional fractal dimension of the sample is about 1 larger than the average two-dimensional fractal dimension of all the slices from the same sample.The uniform porous media fractal model is used to test the equivalent diameter,and the results show that the variation of the measured pore diameter ratio is jointly restricted by the volume fraction and the vertical load.In addition,the measured self-similarity interval of the bubble area distribution is tested by the porous media fractal capillary bundle model,and the fitting curve of measured pore area ratio in a small loading range is obtained in this paper.
基金The first author would like to express sincere appreciation for the scholarship provided by China Scholarship Council(No.202006430006)and University of Wollongongfinancially supported by the ACARP Project C28006+1 种基金the National Key Research and Development Program of China(No.2018YFC0808301)the Natural Science Foundation of Beijing Municipality,China(No.8192036)。
文摘Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.
基金This study has been partially funded by National Key Research and Development Program of China(Grant No.2020YFA0711800)the National Natural Science Foundation of China(Grant No.51979272)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021QE069).
文摘This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus.A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm,3 mm,5 mm,7 mm and 10 mm under a normal stress of 0.5 MPa.Four granite fractures with different roughnesses are selected and quantified using variogram fractal dimensions.The obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture surface.The flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact spots.As the shear displacement continues to increase,preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation;yet the area of single contacts in-creases.Based on the experimental results,an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension.
文摘The morphological complexity of cells and tissues,whether normal or pathological,is characterized by two primary attributes:Irregularity and self-similarity across different scales.When an object exhibits self-similarity,its shape remains unchanged as the scales of measurement vary because any part of it resembles the whole.On the other hand,the size and geometric characteristics of an irregular object vary as the resolution increases,revealing more intricate details.Despite numerous attempts,a reliable and accurate method for quantifying the morphological features of gastrointestinal organs,tissues,cells,their dynamic changes,and pathological disorders has not yet been established.However,fractal geometry,which studies shapes and patterns that exhibit self-similarity,holds promise in providing a quantitative measure of the irregularly shaped morphologies and their underlying self-similar temporal behaviors.In this context,we explore the fractal nature of the gastrointestinal system and the potential of fractal geometry as a robust descriptor of its complex forms and functions.Additionally,we examine the practical applications of fractal geometry in clinical gastroenterology and hepatology practice.
基金the National Natural Science Foundation of China(Grant No.12274126)carried out during the virtual program“Tensor Networks in Many Body and Quantum Field Theory”held at the Institute for Nuclear Theory,University of Washington,Seattle(INT 21–1c)。
文摘Motivated by the mathematical beauty and the recent experimental realizations of fractal systems,we study the spin-1/2 antiferromagnetic Heisenberg model on a Sierpiński gasket.The fractal porous feature generates new kinds of frustration to exhibit exotic quantum states.Using advanced tensor network techniques,we identify a quantum gapless-spin-liquid ground state in fractional spatial dimension.This fractal spin system also demonstrates nontrivial nonlocal properties.While the extremely short-range correlation causes a highly degenerate spin form factor,the entanglement in this fractal system suggests a long-range scaling behavior.We also study the dynamic structure factor and clearly identify the gapless excitation with a stable corner excitation emerged from the ground-state entanglement.Our results unambiguously point out multiple essential properties of this fractal spin system,and open a new route to explore spin liquid and frustrated magnetism.
基金supported by the National Natural Science Foundation of China(51674049,52074044,and 51874053)the Scientific Research Foundation of Hunan Provincial Education Department,China(22B0854)。
文摘In this study,X-ray diffraction,N_(2)adsorption(N_(2)A),and mercury intrusion(MI)experiments were used to investigate the influence of acid treatment on pore structure and fractal characterization of tight sandstones.The results showed that acid treatment generated a certain number of ink-bottle pores in fine sandstone,aggravated the ink-bottle effect in the sandy mudstone,and transformed some smaller pores into larger ones.After the acid treatment,both the pore volume in the range of 2–11 nm and 0.271–8μm for the fine sandstone and the entire pore size range for the sandy mudstone significantly increased.The dissolution of sandstone cement causes the fine sandstone particles to fall off and fill the pores;the porosity increased at first but then decreased with acid treatment time.The fractal dimension obtained using the Frenkel-Halsey-Hill model was positively correlated with acid treatment time.However,the total fractal dimensions obtained by MI tests showed different changes with acid treatment time in fine sandstone and sandy mudstone.These results provide good guiding significance for reservoir acidification stimulation.
基金supported by the Natural Science Foundation of Tianjin Munici-pality[21YDTPJC00480]the Science and Technology Project of Tianjin[20YDTPJC00830].
文摘The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich structure was designed.The generation mechanism and recurrence formula of theHilbert fractal were expressed by Lin’s language,and the second-orderHilbert sandwich structure was constructed fromthermoplastic polyurethane.The constitutive model of the hyperelastic body was established by using the finite element method.With the unit mass energy absorption as the optimization goal,the fractal sandwich structure was optimized,and the best result was obtained when the order was 2.5 and the unit layer thickness was 0.75 mm.TheHilbert sandwich structure was compared with the rice-shaped sandwich structure commonly used in industry,and the Hilbert fractal structure had better energy absorption.This has practical significance for the development and application of newcushioning packaging structures.
基金supported by National Natural Science Foundation of China(Nos.42002171,42172159)China Postdoctoral Science Foundation(Nos.2020TQ0299,2020M682520)Postdoctoral Innovation Science Foundation of Hubei Province of China.
文摘The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T_(2) spectra and T_(2) cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T_(2) cut-off values, ranging from 7 to 50 ms. Additionally, the T_(2) spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T_(2) spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T_(2) cut-off value were separately developed based on the classified T_(2) spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T_(2) spectral shift. However, the T_(2) spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T_(2) spectrum and pore types, as well as to predict the T_(2) cut-off value of low-permeability rocks using machine learning and data augmentation techniques.
文摘Activation functions play an essential role in converting the output of the artificial neural network into nonlinear results,since without this nonlinearity,the results of the network will be less accurate.Nonlinearity is the mission of all nonlinear functions,except for polynomials.The activation function must be dif-ferentiable for backpropagation learning.This study’s objective is to determine the best activation functions for the approximation of each fractal image.Different results have been attained using Matlab and Visual Basic programs,which indi-cate that the bounded function is more helpful than other functions.The non-lin-earity of the activation function is important when using neural networks for coding fractal images because the coefficients of the Iterated Function System are different according to the different types of fractals.The most commonly cho-sen activation function is the sigmoidal function,which produces a positive value.Other functions,such as tansh or arctan,whose values can be positive or negative depending on the network input,tend to train neural networks faster.The coding speed of the fractal image is different depending on the appropriate activation function chosen for each fractal shape.In this paper,we have provided the appro-priate activation functions for each type of system of iterated functions that help the network to identify the transactions of the system.
基金supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2022R66),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘Next-generation networks,including the Internet of Things(IoT),fifth-generation cellular systems(5G),and sixth-generation cellular systems(6G),suf-fer from the dramatic increase of the number of deployed devices.This puts high constraints and challenges on the design of such networks.Structural changing of the network is one of such challenges that affect the network performance,includ-ing the required quality of service(QoS).The fractal dimension(FD)is consid-ered one of the main indicators used to represent the structure of the communication network.To this end,this work analyzes the FD of the network and its use for telecommunication networks investigation and planning.The clus-ter growing method for assessing the FD is introduced and analyzed.The article proposes a novel method for estimating the FD of a communication network,based on assessing the network’s connectivity,by searching for the shortest routes.Unlike the cluster growing method,the proposed method does not require multiple iterations,which reduces the number of calculations,and increases the stability of the results obtained.Thus,the proposed method requires less compu-tational cost than the cluster growing method and achieves higher stability.The method is quite simple to implement and can be used in the tasks of research and planning of modern and promising communication networks.The developed method is evaluated for two different network structures and compared with the cluster growing method.Results validate the developed method.
基金funded by the Deanship of Scientific Research,Princess Nourah bint Abdulrahman University,through the Program of Research Project Funding After Publication,Grant No (43-PRFA-P-52).
文摘The accurate prediction of energy consumption has effective role in decision making and risk management for individuals and governments.Meanwhile,the accurate prediction can be realized using the recent advances in machine learning and predictive models.This research proposes a novel approach for energy consumption forecasting based on a new optimization algorithm and a new forecasting model consisting of a set of long short-term memory(LSTM)units.The proposed optimization algorithm is used to optimize the parameters of the LSTM-based model to boost its forecasting accuracy.This optimization algorithm is based on the recently emerged dipper-throated optimization(DTO)and stochastic fractal search(SFS)algo-rithm and is referred to as dynamic DTOSFS.To prove the effectiveness and superiority of the proposed approach,five standard benchmark algorithms,namely,stochastic fractal search(SFS),dipper throated optimization(DTO),whale optimization algorithm(WOA),particle swarm optimization(PSO),and grey wolf optimization(GWO),are used to optimize the parameters of the LSTM-based model,and the results are compared with that of the proposed approach.Experimental results show that the proposed DDTOSFS+LSTM can accurately forecast the energy consumption with root mean square error RMSE of 0.00013,which is the best among the recorded results of the other methods.In addition,statistical experiments are conducted to prove the statistical difference of the proposed model.The results of these tests confirmed the expected outcomes.
文摘Pore structure is the key element of tight sandstone reservoir, which restricts the accumulation and flow of oil and gas in the reservoir. At present, reservoir pore structure is the focus and difficulty of unconventional oil and gas exploration and development research. The tight sandstone reservoir in the Chang 4 + 5 member of the Upper Triassic Yanchang Formation is the main reservoir for oil and gas exploration in G area. At present, there is little research on its pore structure and fractal characteristics, which to some extent affects the progress of exploration and development. This paper selects the tight core samples of the Chang 4 + 5 member in the southern edge of the Ordos Basin, and based on the high-pressure mercury intrusion experiment, uses fractal theory to study the pore structure and fractal characteristics of the reservoir in the study area, thus providing theoretical basis for the evaluation and exploration and development of the Chang 4 + 5 tight reservoir in the G area. The research results show that the lithology of the Chang 4 + 5 tight sandstone reservoir in the southern edge of the Ordos Basin is mainly feldspathic sandstone, with the highest feldspar content, followed by quartz, and the clay mineral is mainly chlorite. The reservoir has poor physical properties and strong heterogeneity. There are three main fractal characteristics in Chang 4 + 5 reservoir in G area: the fractal curve of Type I reservoir sample is in two segments, the relatively large pore has certain fractal characteristics, the pore structure is relatively regular, and the heterogeneity is weak;Relatively small pores have no fractal characteristics and pore structure is irregular. The fractal curve of Type II reservoir samples shows a three-segment pattern, and each pore size range has certain fractal characteristics, and it gradually gets better with the increase of pore size. The fractal curve of Type III reservoir samples presents a similar one-segment pattern, and the fractal dimension exceeds the upper limit of 3. It is considered that the full pore size of this type of reservoir does not have fractal characteristics, the pore throat is completely irregular or the surface is rough, and the heterogeneity is very strong.
文摘Because of the developed economy and lush vegetation in southern China, the following obstacles or difficulties exist in remote sensing land surface classification: 1) Diverse surface composition types;2) Undulating terrains;3) Small fragmented land;4) Indistinguishable shadows of surface objects. It is our top priority to clarify how to use the concept of big data (Data mining technology) and various new technologies and methods to make complex surface remote sensing information extraction technology develop in the direction of automation, refinement and intelligence. In order to achieve the above research objectives, the paper takes the Gaofen-2 satellite data produced in China as the data source, and takes the complex surface remote sensing information extraction technology as the research object, and intelligently analyzes the remote sensing information of complex surface on the basis of completing the data collection and preprocessing. The specific extraction methods are as follows: 1) extraction research on fractal texture features of Brownian motion;2) extraction research on color features;3) extraction research on vegetation index;4) research on vectors and corresponding classification. In this paper, fractal texture features, color features, vegetation features and spectral features of remote sensing images are combined to form a combination feature vector, which improves the dimension of features, and the feature vector improves the difference of remote sensing features, and it is more conducive to the classification of remote sensing features, and thus it improves the classification accuracy of remote sensing images. It is suitable for remote sensing information extraction of complex surface in southern China. This method can be extended to complex surface area in the future.
基金supported by the China Postdoctoral Science Foundation Funded Project(Grant Nos.2017M613054 and 2017M613053)the Shaanxi Postdoctoral Science Foundation Funded Project(Grant No.2017BSHYDZZ33)the National Science Foundation of China(Grant No.62102239).
文摘Deep neural networks often outperform classical machine learning algorithms in solving real-world problems.However,designing better networks usually requires domain expertise and consumes significant time and com-puting resources.Moreover,when the task changes,the original network architecture becomes outdated and requires redesigning.Thus,Neural Architecture Search(NAS)has gained attention as an effective approach to automatically generate optimal network architectures.Most NAS methods mainly focus on achieving high performance while ignoring architectural complexity.A myriad of research has revealed that network performance and structural complexity are often positively correlated.Nevertheless,complex network structures will bring enormous computing resources.To cope with this,we formulate the neural architecture search task as a multi-objective optimization problem,where an optimal architecture is learned by minimizing the classification error rate and the number of network parameters simultaneously.And then a decomposition-based multi-objective stochastic fractal search method is proposed to solve it.In view of the discrete property of the NAS problem,we discretize the stochastic fractal search step size so that the network architecture can be optimized more effectively.Additionally,two distinct update methods are employed in step size update stage to enhance the global and local search abilities adaptively.Furthermore,an information exchange mechanism between architectures is raised to accelerate the convergence process and improve the efficiency of the algorithm.Experimental studies show that the proposed algorithm has competitive performance comparable to many existing manual and automatic deep neural network generation approaches,which achieved a parameter-less and high-precision architecture with low-cost on each of the six benchmark datasets.
文摘After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.
文摘The seepage characteristics of multiscale porous media is of considerable significance in many scientific and engineering fields.The Darcy permeability is one of the key macroscopic physical properties to characterize the seepage capacity of porous media.Therefore,based on the statistically fractal scaling law of porous media,fractal geometry is applied to model the multiscale pore structures.And a two-dimensional fractal orifice-throat model with multiscale and tortuous characteristics is proposed for the seepage flow through porous media.The analytical expression for Darcy permeability of porous media is derived,which is validated by comparing with available experimental data.The results show that the Darcy permeability is significantly influenced by porosity,orifice-throat fractal dimension,minimum to maximum diameter ratio,orifice-throat ratio and tortuosity fractal dimension.The present results are helpful for understanding the seepage mechanism of multiscale porous media,and may provide theoretical basis for unconventional oil and gas exploration and development,porous phase transition energy storage composites,CO2 geological sequestration,environmental protection and nuclear waste treatment,etc.
