Considering the urban characteristics, a customized multi-scale numerical modeling system is established to simulate the urban meteorological environment. The system mainly involves three spatial scales: the urban sca...Considering the urban characteristics, a customized multi-scale numerical modeling system is established to simulate the urban meteorological environment. The system mainly involves three spatial scales: the urban scale, urban sub-domain scale, and single to few buildings scale. In it, different underlying surface types are employed, the building drag factor is used to replace its roughness in the influence on the urban wind field, the effects of building distribution, azimuth and screening of shortwave radiation are added, and the influence of anthropogenic heating is also taken into account. All the numerical tests indicate that the simulated results are reasonably in agreement with the observational data, so the system can be used to simulate the urban meteorological environment. Making use of it, the characteristics of the meteorological environment from the urban to urban sub-domain scales, even the among-buildings scale, can be recognized. As long as the urban planning scheme is given, the corresponding simulated results can be obtained so as to meet the need of optimizing urban planning.展开更多
The multi-scale modeling combined with the cohesive zone model(CZM)and the molecular dynamics(MD)method were preformed to simulate the crack propagation in NiTi shape memory alloys(SMAs).The metallographic microscope ...The multi-scale modeling combined with the cohesive zone model(CZM)and the molecular dynamics(MD)method were preformed to simulate the crack propagation in NiTi shape memory alloys(SMAs).The metallographic microscope and image processing technology were employed to achieve a quantitative grain size distribution of NiTi alloys so as to provide experimental data for molecular dynamics modeling at the atomic scale.Considering the size effect of molecular dynamics model on material properties,a reasonable modeling size was provided by taking into account three characteristic dimensions from the perspective of macro,meso,and micro scales according to the Buckinghamπtheorem.Then,the corresponding MD simulation on deformation and fracture behavior was investigated to derive a parameterized traction-separation(T-S)law,and then it was embedded into cohesive elements of finite element software.Thus,the crack propagation behavior in NiTi alloys was reproduced by the finite element method(FEM).The experimental results show that the predicted initiation fracture toughness is in good agreement with experimental data.In addition,it is found that the dynamics initiation fracture toughness increases with decreasing grain size and increasing loading velocity.展开更多
Previous failure analyses of bridges typically focus on substructure failure or superstructure failure separately. However, in an actual bridge, the seismic induced substructure failure and superstructure failure may ...Previous failure analyses of bridges typically focus on substructure failure or superstructure failure separately. However, in an actual bridge, the seismic induced substructure failure and superstructure failure may influence each other. Moreover, previous studies typically use simplified models to analyze the bridge failure; however, there are inherent defects in the calculation accuracy compared with using a detailed three-dimensional （3D） finite element （FE） model. Conversely, a detailed 3D FE model requires more computational costs, and a proper erosion criterion of the 3D elements is necessary. In this paper, a multi-scale FE model, including a corresponding erosion criterion, is proposed and validated that can significantly reduce computational costs with high precision by modelling a pseudo-dynamic test of an reinforced concrete （RC） pier. Numerical simulations of the seismic failures of a continuous RC bridge based on the multi-scale FE modeling method using LS-DYNA are performed. The nonlinear properties of the bridge, various connection strengths and bidirectional excitations are considered. The numerical results demonstrate that the failure of the connections will induce large pounding responses of the girders. The nonlinear deformation of the piers will aggravate the pounding damages. Furthermore, bidirectional earthquakes will induce eccentric poundingsto the girders and different failure modes to the adjacent piers.展开更多
A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and...A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.展开更多
Water electrolyzers play a crucial role in green hydrogen production.However,their efficiency and scalability are often compromised by bubble dynamics across various scales,from nanoscale to macroscale components.This...Water electrolyzers play a crucial role in green hydrogen production.However,their efficiency and scalability are often compromised by bubble dynamics across various scales,from nanoscale to macroscale components.This review explores multi-scale modeling as a tool to visualize multi-phase flow and improve mass transport in water electrolyzers.At the nanoscale,molecular dynamics(MD)simulations reveal how electrode surface features and wettability influence nanobubble nucleation and stability.Moving to the mesoscale,models such as volume of fluid(VOF)and lattice Boltzmann method(LBM)shed light on bubble transport in porous transport layers(PTLs).These insights inform innovative designs,including gradient porosity and hydrophilic-hydrophobic patterning,aimed at minimizing gas saturation.At the macroscale,VOF simulations elucidate two-phase flow regimes within channels,showing how flow field geometry and wettability affect bubble discharging.Moreover,artificial intelligence(AI)-driven surrogate models expedite the optimization process,allowing for rapid exploration of structural parameters in channel-rib flow fields and porous flow field designs.By integrating these approaches,we can bridge theoretical insights with experimental validation,ultimately enhancing water electrolyzer performance,reducing costs,and advancing affordable,high-efficiency hydrogen production.展开更多
Rock is geometrically and mechanically multiscale in nature,and the traditional phenomenological laws at the macroscale cannot render a quantitative relationship between microscopic damage of rocks and overall rock st...Rock is geometrically and mechanically multiscale in nature,and the traditional phenomenological laws at the macroscale cannot render a quantitative relationship between microscopic damage of rocks and overall rock structural degradation.This may lead to problems in the evaluation of rock structure stability and safe life.Multiscale numerical modeling is regarded as an effective way to gain insight into factors affecting rock properties from a cross-scale view.This study compiles the history of theoretical developments and numerical techniques related to rock multiscale issues according to different modeling architectures,that is,the homogenization theory,the hierarchical approach,and the concurrent approach.For these approaches,their benefits,drawbacks,and application scope are underlined.Despite the considerable attempts that have been made,some key issues still result in multiple challenges.Therefore,this study points out the perspectives of rock multiscale issues so as to provide a research direction for the future.The review results show that,in addition to numerical techniques,for example,high-performance computing,more attention should be paid to the development of an advanced constitutive model with consideration of fine geometrical descriptions of rock to facilitate solutions to multiscale problems in rock mechanics and rock engineering.展开更多
Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implemen...Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implementation,or configuration.To guarantee the durability&robustness of the software,vulnerability identification and fixation have become crucial areas of focus for developers,cybersecurity experts and industries.This paper presents a thorough multi-phase mathematical model for efficient patch management and vulnerability detection.To uniquely model these processes,the model incorporated the notion of the learning phenomenon in describing vulnerability fixation using a logistic learning function.Furthermore,the authors have used numerical methods to approximate the solution of the proposed framework where an analytical solution is difficult to attain.The suggested systematic architecture has been demonstrated through statistical analysis using patch datasets,which offers a solid basis for the research conclusions.According to computational research,learning dynamics improves security response and results in more effective vulnerability management.The suggested model offers a systematic approach to proactive vulnerability mitigation and has important uses in risk assessment,software maintenance,and cybersecurity.This study helps create more robust software systems by increasing patch management effectiveness,which benefits developers,cybersecurity experts,and sectors looking to reduce security threats in a growing digital world.展开更多
With the increasing development of deepburied engineering projects,rockburst disasters have become a frequent concern.Studies have indicated that tunnel diameter is a critical factor influencing the occurrence of rock...With the increasing development of deepburied engineering projects,rockburst disasters have become a frequent concern.Studies have indicated that tunnel diameter is a critical factor influencing the occurrence of rockbursts.To investigate the influence of tunnel diameter on the deformation and failure characteristics of surrounding rock,large-sized rocklike gypsum specimens were tested using a selfdeveloped true triaxial rockburst loading system containing circular tunnels with three different diameters(D=0.07 m,0.11 m,and 0.15 m).Acoustic emission monitoring,together with a miniature intelligent camera,was employed to analyze the entire process,focusing on macroscopic failure patterns,fragment characteristics,and underlying failure mechanisms.In addition,theoretical analyses were carried out and combined with numerical simulations to investigate the differences in energy evolution associated with rockburst physical models.The results indicate that:(1)The rockburst process with different tunnel diameters consistently evolved through three distinct stages—initial particle ejection,crack propagation accompanied by flake spalling,and,finally,fragment ejection leading to the formation of a‘V'-shaped notch.(2)Increasing tunnel diameter reduces rockburst failure load while increasing surrounding rock damage extent,total mass and average size of ejected fragments.Additionally,shear failure proportion decreases with tensile failure becoming increasingly dominant.(3)Larger tunnel diameters reduce the attenuation rate of elastic strain energy,thereby expanding the zone of elastic strain energy accumulation and disturbance and creating conditions for larger volume rockburst.(4)Larger tunnel diameters result in a smaller principal stress ratio at equivalent distances in the surrounding rock,indicating a higher likelihood of tensile failure.(5)Numerical analyses further reveal that larger tunnel diameters reduce the maximum elastic strain energy density around the tunnel,lowering the energy released per unit volume of rockburst fragments and their ejection velocities.However,both the total failure volume and overall energy release from rockburst increase.Model experiments with different tunnel diameters are of great significance for optimizing engineering design and parameter selection,as well as guiding tunnel construction under complex geological conditions.展开更多
The nozzle is a critical component responsible for generating most of the net thrust in a scramjet engine.The quality of its design directly affects the performance of the entire propulsion system.However,most turbule...The nozzle is a critical component responsible for generating most of the net thrust in a scramjet engine.The quality of its design directly affects the performance of the entire propulsion system.However,most turbulence models struggle to make accurate predictions for subsonic and supersonic flows in nozzles.In this study,we explored a novel model,the algebraic stress model k-kL-ARSM+J,to enhance the accuracy of turbulence numerical simulations.This new model was used to conduct numerical simulations of the design and off-design performance of a 3D supersonic asymmetric truncated nozzle designed in our laboratory,with the aim of providing a realistic pattern of changes.The research indicates that,compared to linear eddy viscosity turbulence models such as k-kL and shear stress transport(SST),the k-kL-ARSM+J algebraic stress model shows better accuracy in predicting the performance of supersonic nozzles.Its predictions were identical to the experimental values,enabling precise calculations of the nozzle.The performance trends of the nozzle are as follows:as the inlet Mach number increases,both thrust and pitching moment increase,but the rate of increase slows down.Lift peaks near the design Mach number and then rapidly decreases.With increasing inlet pressure,the nozzle thrust,lift,and pitching moment all show linear growth.As the flight altitude rises,the internal flow field within the nozzle remains relatively consistent due to the same supersonic nozzle inlet flow conditions.However,external to the nozzle,the change in external flow pressure results in the nozzle exit transitioning from over-expanded to under-expanded,leading to a shear layer behind the nozzle that initially converges towards the nozzle center and then diverges.展开更多
Systematic bias is a type of model error that can affect the accuracy of data assimilation and forecasting that must be addressed.An online bias correction scheme called the sequential bias correction scheme(SBCS),was...Systematic bias is a type of model error that can affect the accuracy of data assimilation and forecasting that must be addressed.An online bias correction scheme called the sequential bias correction scheme(SBCS),was developed using the6 h average bias to correct the systematic bias during model integration.The primary purpose of this study is to investigate the impact of the SBCS in the high-resolution China Meteorological Administration Meso-scale(CMA-MESO)numerical weather prediction(NWP)model to reduce the systematic bias and to improve the data assimilation and forecast results through this method.The SBCS is improved upon and applied to the CMA-MESO 3-km model in this study.Four-week sequential data assimilation and forecast experiments,driven by rapid update and cycling(RUC),were conducted for the period from 2–29 May 2022.In terms of the characteristics of systematic bias,both the background and analysis show diurnal bias,and these large biases are affected by complex underlying surfaces(e.g.,oceans,coasts,and mountains).After the application of the SBCS,the results of the data assimilation show that the SBCS can reduce the systematic bias of the background and yield a neutral to slightly positive result for the analysis fields.In addition,the SBCS can reduce forecast errors and improve forecast results,especially for surface variables.The above results indicate that this scheme has good prospects for high-resolution regional NWP models.展开更多
Coral reef limestone(CRL)constitutes a distinctive marine carbonate formation with complex mechanical properties.This study investigates the multiscale damage and fracture mechanisms of CRL through integrated experime...Coral reef limestone(CRL)constitutes a distinctive marine carbonate formation with complex mechanical properties.This study investigates the multiscale damage and fracture mechanisms of CRL through integrated experimental testing,digital core technology,and theoretical modelling.Two CRL types with contrasting mesostructures were characterized across three scales.Macroscopically,CRL-I and CRL-II exhibited mean compressive strengths of 8.46 and 5.17 MPa,respectively.Mesoscopically,CRL-I featured small-scale highly interconnected pores,whilst CRL-II developed larger stratified pores with diminished connectivity.Microscopically,both CRL matrices demonstrated remarkable similarity in mineral composition and mechanical properties.A novel voxel average-based digital core scaling methodology was developed to facilitate numerical simulation of cross-scale damage processes,revealing network-progressive failure in CRL-I versus directional-brittle failure in CRL-II.Furthermore,a damage statistical constitutive model based on digital core technology and mesoscopic homogenisation theory established quantitative relationships between microelement strength distribution and macroscopic mechanical behavior.These findings illuminate the fundamental mechanisms through which mesoscopic structure governs the macroscopic mechanical properties of CRL.展开更多
Oilfields worldwide are increasingly grappling with challenges such as early water breakthrough and high water production,yet direct,targeted solutions remain elusive.In recent years,chemical flooding techniques desig...Oilfields worldwide are increasingly grappling with challenges such as early water breakthrough and high water production,yet direct,targeted solutions remain elusive.In recent years,chemical flooding techniques designed for tertiary oil recovery have garnered significant attention,with microgel flooding emerging as a particularly prominent area of research.Despite its promise,the complex mechanisms underlying microgel flooding have been rarely investigated numerically.This study aims to address these gaps by characterizing the distribution of microgel concentration and viscosity within different pore structures.To enhance the accuracy of these characterizations,the viscosity of microgels is adjusted to account for the shear effects induced by flow rate and the swelling effects driven by salinity variations.The absolute permeability of the rock and the relative permeability of both oil and microgel are also analyzed to elucidate the mechanisms of microgel flooding.Additionally,a connectivity model is employed to achieve a quantitative representation of fluid flow capacity.The proposed model is validated through conceptual examples and applied to real oilfield blocks,demonstrating its accuracy and practical applicability.展开更多
Polymer flooding is an important means of improving oil recovery and is widely used in Daqing,Xinjiang,and Shengli oilfields,China.Different from conventional injection media such as water and gas,viscoelastic polymer...Polymer flooding is an important means of improving oil recovery and is widely used in Daqing,Xinjiang,and Shengli oilfields,China.Different from conventional injection media such as water and gas,viscoelastic polymer solutions exhibit non-Newtonian and nonlinear flow behavior including shear thinning and shear thickening,polymer convection,diffusion,adsorption,retention,inaccessible pore volume,and reduced effective permeability.However,available well test model of polymer flooding wells generally simplifies these characteristics on pressure transient response,which may lead to inaccurate results.This work proposes a novel two-phase numerical well test model to better describe the polymer viscoelasticity and nonlinear flow behavior.Different influence factors that related to near-well blockage during polymer flooding process,including the degree of blockage(inner zone permeability),the extent of blockage(composite radius),and polymer flooding front radius are explored to investigate these impacts on bottom hole pressure responses.Results show that polymer viscoelasticity has a significant impact on the transitional flow segment of type curves,and the effects of near-well formation blockage and polymer concentration distribution on well test curves are very similar.Thus,to accurately interpret the degree of near-well blockage in injection wells,it is essential to first eliminate the influence of polymer viscoelasticity.Finally,a field case is comprehensively analyzed and discussed to illustrate the applicability of the proposed model.展开更多
A three-dimensional numerical model of laser-arc hybrid plasma for aluminum alloy fillet joints is developed in this study.This mod-el accounts for the geometric complexity of fillet joints,the physical properties of ...A three-dimensional numerical model of laser-arc hybrid plasma for aluminum alloy fillet joints is developed in this study.This mod-el accounts for the geometric complexity of fillet joints,the physical properties of shielding gases with varying He-Ar ratios,and the coupling between arc plasma and laser-induced metal plume.The accuracy of the model is validated using a high-speed camera.The effects of varying He contents in the shielding gas on both the temperature and flow velocity of hybrid plasma,as well as the distribu-tion of laser-induced metal vapor mass,were investigated separately.The maximum temperature and size of arc plasma decrease as the He volume ratio increases,the arc distribution becomes more concentrated,and its flow velocity initially decreases and then sharply increases.At high helium content,both the flow velocity of hybrid plasma and metal vapor are high,the metal vapor is con-centrated on the right side of keyhole,and its flow appears chaotic.The flow state of arc plasma is most stable when the shielding gas consists of 50%He+50%Ar.展开更多
The Regional Atmospheric Modeling System （RAMS） and the computational fluid dynamics （CFD） codes known as FLUENT are combinatorially applied in a multi-scale numerical simulation of the urban surface layer （USL）...The Regional Atmospheric Modeling System （RAMS） and the computational fluid dynamics （CFD） codes known as FLUENT are combinatorially applied in a multi-scale numerical simulation of the urban surface layer （USL）. RAMS and FLUENT are combined as a multi-scale numerical modeling system, in which the RAMS simulated data are delivered to the computational model for FLUENT simulation in an offline way. Numerical simulations are performed to present and preliminarily validate the capability of the multi-scale modeling system, and the results show that the modeling system can reasonably provide information on the meteorological elements in an urban area from the urban scale to the city-block scale, especially the details of the turbulent flows within the USL.展开更多
The cretaceous gas reservoir in Kelasu Gas Field of the Tarim Basin is a rare ultra-deep and ultra-high pressure fractured tight sandstone gas reservoir where multi-scale discrete fractures of matrix,fracture and faul...The cretaceous gas reservoir in Kelasu Gas Field of the Tarim Basin is a rare ultra-deep and ultra-high pressure fractured tight sandstone gas reservoir where multi-scale discrete fractures of matrix,fracture and fault are developed,so its development cannot be conducted just based on static and dynamic reservoir description.In order to solve this problem,this paper establishes a numerical well test model of vertical wells based on matrix,fractures and faults(large fractures and small faults)by combining the random generation of natural fracture networks with the unstructured discrete fracture modeling method to break through the traditional continuous medium well test model.In addition,the model is solved by using the finite element method with mixed element,and the typical well test type curves under different random fracture networks are obtained.And the following research results are obtained.First,based on the observed data,the fracture network distribution modes of fractured tight sandstone gas reservoirs are classified into three categories.The influence of random generation of fracture networks on typical well test type curves is discussed.The results of discrete fracture well test model are compared with those of the traditional continuous medium well test model,and the applicable conditions of the traditional continuous medium well test model is determined.Second,there are great differences between the results of discrete fracture model and those of dual porosity medium model.1 The dual porosity medium model is a special case of the discrete fracture model,in which the fractures are evenly distributed within infinitely small spacing.Third,the characteristics of well test type curves under three fracture network distribution modes are discussed.The well test type curves that cannot be interpreted by the conventional dual/triple porosity continuous medium model are successfully interpreted by using the established well test interpretation model of random discrete fracture.The curve matching effect is ideal and the interpreted parameters are reasonable.In conclusion,the new model and the new method reveal the development mechanism of step-by-step production and coordinated gas supply between media of different scales,explain the development characteristics of large inter-well productivity difference and abnormal rapid inter-well pressure response,and provide a reference for the development of similar gas reservoirs.展开更多
In order to investigate the fatigue behavior of asphalt concrete, a new numerical approach based on a bi-linear cohesive zone model （CZM） is developed. Integrated with the CZM, a fatigue damage evolution model is es...In order to investigate the fatigue behavior of asphalt concrete, a new numerical approach based on a bi-linear cohesive zone model （CZM） is developed. Integrated with the CZM, a fatigue damage evolution model is established to indicate the gradual degradation of cohesive properties of asphalt concrete under cyclic loading. Then the model is implemented in the finite element software ABAQUS through a user-defined subroutine. Based on the proposed model, an indirect tensile fatigue test is finally simulated. The fatigue lives obtained through numerical analysis show good agreement with laboratory results. Fatigue damage accumulates in a nonlinear manner during the cyclic loading process and damage initiation phase is the major part of fatigue failure. As the stress ratio increases, the time of the steady damage growth stage decreases significantly. It is found that the proposed fatigue damage evolution model can serve as an accurate and efficient tool for the prediction of fatigue damage of asphalt concrete.展开更多
Biot-flow and squirt-flow are the two most important fluid flow mechanisms in porous media containing fluids. Based on the BISQ （Biot-Squirt） model where the two mechanisms are treated simultaneously, the elastic wa...Biot-flow and squirt-flow are the two most important fluid flow mechanisms in porous media containing fluids. Based on the BISQ （Biot-Squirt） model where the two mechanisms are treated simultaneously, the elastic wave-field simulation in the porous medium is limited to two-dimensions and two-components （2D2C） or two-dimensions and three-components （2D3C）. There is no previous report on wave simulation in three- dimensions and three-components. Only through three dimensional numerical simulations can we have an overall understanding of wave field coupling relations and the spatial distribution characteristics between the solid and fluid phases in the dual-phase anisotropic medium. In this paper, based on the BISQ equation, we present elastic wave propagation in a three dimensional dual-phase anisotropic medium simulated by the staggered-grid high-order finite-difference method. We analyze the resulting wave fields and show that the results are an improvement.展开更多
To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional （2D） time- domain transient electromagnetic secondary field of t...To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional （2D） time- domain transient electromagnetic secondary field of the line source based on the DuFort- Frankel finite-difference method. In the proposed method, we included the treatment of the earth-air boundary conductivity, calculated the normalized partial derivative of the induced electromotive force （Emf）, and determined the forward time step. By extending upward the earth-air interface to the air grid nodes and the zero-value boundary conditions, not only we have a method that is more efficient but also simpler than the total field solution. We computed and analyzed the homogeneous half-space model and the fiat layered model with high precision--the maximum relative error is less than 0.01% between our method and the analytical method--and the solution speed is roughly three times faster than the total-field solution. Lastly, we used the model of a thin body embedded in a homogeneous half-space at different delay times to depict the downward and upward spreading characteristics of the induced eddy current, and the physical interaction processes between the electromagnetic field and the underground low-resistivity body.展开更多
This study focuses on the factors that may affect the feasibility of performing elliptical anisotropy analysis on azimuthal PP and PS-wave data in HTI media, with the aim of using the modeling results as guidance in r...This study focuses on the factors that may affect the feasibility of performing elliptical anisotropy analysis on azimuthal PP and PS-wave data in HTI media, with the aim of using the modeling results as guidance in real seismic data application. Our results reveal that there is an offset limitation for both PP- and PS-waves in elliptical anisotropy fitting, and that PS-waves show a wider applicable offset range and larger observable azimuthal anisotropy than PP-waves. The major axis of the elliptical fit to the amplitudes of the R-component is perpendicular to the fracture strike, which is opposite to that in PP-wave analysis. The azimuthal interval travel time of PS-waves shows a nearly elliptical distribution and the major axis of the fit ellipse is perpendicular to the fracture strike, which is same as that in PP-wave analysis. For data within the applicable offset range, the anisotropic magnitude obtained from amplitude and travel time attributes of PP- and PS-waves exhibits a dependence on fracture density, and the major to minor axis ratio of the fit ellipse may be used to infer the relative distribution of fracture densities.展开更多
基金sponsored by the Key Project(96-920-34-07)of the Ministry of Science and Technology,Chinathe Nationa1 Natura1 Science Foundation of China(40333027).
文摘Considering the urban characteristics, a customized multi-scale numerical modeling system is established to simulate the urban meteorological environment. The system mainly involves three spatial scales: the urban scale, urban sub-domain scale, and single to few buildings scale. In it, different underlying surface types are employed, the building drag factor is used to replace its roughness in the influence on the urban wind field, the effects of building distribution, azimuth and screening of shortwave radiation are added, and the influence of anthropogenic heating is also taken into account. All the numerical tests indicate that the simulated results are reasonably in agreement with the observational data, so the system can be used to simulate the urban meteorological environment. Making use of it, the characteristics of the meteorological environment from the urban to urban sub-domain scales, even the among-buildings scale, can be recognized. As long as the urban planning scheme is given, the corresponding simulated results can be obtained so as to meet the need of optimizing urban planning.
基金Funded by the National Natural Science Foundation of China Academy of Engineering Physics and Jointly Setup"NSAF"Joint Fund(No.U1430119)。
文摘The multi-scale modeling combined with the cohesive zone model(CZM)and the molecular dynamics(MD)method were preformed to simulate the crack propagation in NiTi shape memory alloys(SMAs).The metallographic microscope and image processing technology were employed to achieve a quantitative grain size distribution of NiTi alloys so as to provide experimental data for molecular dynamics modeling at the atomic scale.Considering the size effect of molecular dynamics model on material properties,a reasonable modeling size was provided by taking into account three characteristic dimensions from the perspective of macro,meso,and micro scales according to the Buckinghamπtheorem.Then,the corresponding MD simulation on deformation and fracture behavior was investigated to derive a parameterized traction-separation(T-S)law,and then it was embedded into cohesive elements of finite element software.Thus,the crack propagation behavior in NiTi alloys was reproduced by the finite element method(FEM).The experimental results show that the predicted initiation fracture toughness is in good agreement with experimental data.In addition,it is found that the dynamics initiation fracture toughness increases with decreasing grain size and increasing loading velocity.
基金National Program on Key Basic Research Project of China(973) under Grant No.2011CB013603the National Natural Science Foundation of China under Grant Nos.51427901,91315301 and 51408410the Natural Science Foundation of Tianjin,China under Grant No.15JCQNJC07200
文摘Previous failure analyses of bridges typically focus on substructure failure or superstructure failure separately. However, in an actual bridge, the seismic induced substructure failure and superstructure failure may influence each other. Moreover, previous studies typically use simplified models to analyze the bridge failure; however, there are inherent defects in the calculation accuracy compared with using a detailed three-dimensional （3D） finite element （FE） model. Conversely, a detailed 3D FE model requires more computational costs, and a proper erosion criterion of the 3D elements is necessary. In this paper, a multi-scale FE model, including a corresponding erosion criterion, is proposed and validated that can significantly reduce computational costs with high precision by modelling a pseudo-dynamic test of an reinforced concrete （RC） pier. Numerical simulations of the seismic failures of a continuous RC bridge based on the multi-scale FE modeling method using LS-DYNA are performed. The nonlinear properties of the bridge, various connection strengths and bidirectional excitations are considered. The numerical results demonstrate that the failure of the connections will induce large pounding responses of the girders. The nonlinear deformation of the piers will aggravate the pounding damages. Furthermore, bidirectional earthquakes will induce eccentric poundingsto the girders and different failure modes to the adjacent piers.
基金supported by the National Natural Science Foundation of China(Grant Nos.42150204 and 2288101)supported by the China National Postdoctoral Program for Innovative Talents(BX20230045)the China Postdoctoral Science Foundation(2023M730279)。
文摘A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.15308024)a grant from Research Centre for Carbon-Strategic Catalysis,The Hong Kong Polytechnic University(CE2X).
文摘Water electrolyzers play a crucial role in green hydrogen production.However,their efficiency and scalability are often compromised by bubble dynamics across various scales,from nanoscale to macroscale components.This review explores multi-scale modeling as a tool to visualize multi-phase flow and improve mass transport in water electrolyzers.At the nanoscale,molecular dynamics(MD)simulations reveal how electrode surface features and wettability influence nanobubble nucleation and stability.Moving to the mesoscale,models such as volume of fluid(VOF)and lattice Boltzmann method(LBM)shed light on bubble transport in porous transport layers(PTLs).These insights inform innovative designs,including gradient porosity and hydrophilic-hydrophobic patterning,aimed at minimizing gas saturation.At the macroscale,VOF simulations elucidate two-phase flow regimes within channels,showing how flow field geometry and wettability affect bubble discharging.Moreover,artificial intelligence(AI)-driven surrogate models expedite the optimization process,allowing for rapid exploration of structural parameters in channel-rib flow fields and porous flow field designs.By integrating these approaches,we can bridge theoretical insights with experimental validation,ultimately enhancing water electrolyzer performance,reducing costs,and advancing affordable,high-efficiency hydrogen production.
基金National Natural Science Foundation of China,Grant/Award Numbers:52192691,52192690。
文摘Rock is geometrically and mechanically multiscale in nature,and the traditional phenomenological laws at the macroscale cannot render a quantitative relationship between microscopic damage of rocks and overall rock structural degradation.This may lead to problems in the evaluation of rock structure stability and safe life.Multiscale numerical modeling is regarded as an effective way to gain insight into factors affecting rock properties from a cross-scale view.This study compiles the history of theoretical developments and numerical techniques related to rock multiscale issues according to different modeling architectures,that is,the homogenization theory,the hierarchical approach,and the concurrent approach.For these approaches,their benefits,drawbacks,and application scope are underlined.Despite the considerable attempts that have been made,some key issues still result in multiple challenges.Therefore,this study points out the perspectives of rock multiscale issues so as to provide a research direction for the future.The review results show that,in addition to numerical techniques,for example,high-performance computing,more attention should be paid to the development of an advanced constitutive model with consideration of fine geometrical descriptions of rock to facilitate solutions to multiscale problems in rock mechanics and rock engineering.
基金supported by grants received by the first author and third author from the Institute of Eminence,Delhi University,Delhi,India,as part of the Faculty Research Program via Ref.No./IoE/2024-25/12/FRP.
文摘Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implementation,or configuration.To guarantee the durability&robustness of the software,vulnerability identification and fixation have become crucial areas of focus for developers,cybersecurity experts and industries.This paper presents a thorough multi-phase mathematical model for efficient patch management and vulnerability detection.To uniquely model these processes,the model incorporated the notion of the learning phenomenon in describing vulnerability fixation using a logistic learning function.Furthermore,the authors have used numerical methods to approximate the solution of the proposed framework where an analytical solution is difficult to attain.The suggested systematic architecture has been demonstrated through statistical analysis using patch datasets,which offers a solid basis for the research conclusions.According to computational research,learning dynamics improves security response and results in more effective vulnerability management.The suggested model offers a systematic approach to proactive vulnerability mitigation and has important uses in risk assessment,software maintenance,and cybersecurity.This study helps create more robust software systems by increasing patch management effectiveness,which benefits developers,cybersecurity experts,and sectors looking to reduce security threats in a growing digital world.
基金funded by the National Natural Science Foundation of China(Nos.42077228,52174085)。
文摘With the increasing development of deepburied engineering projects,rockburst disasters have become a frequent concern.Studies have indicated that tunnel diameter is a critical factor influencing the occurrence of rockbursts.To investigate the influence of tunnel diameter on the deformation and failure characteristics of surrounding rock,large-sized rocklike gypsum specimens were tested using a selfdeveloped true triaxial rockburst loading system containing circular tunnels with three different diameters(D=0.07 m,0.11 m,and 0.15 m).Acoustic emission monitoring,together with a miniature intelligent camera,was employed to analyze the entire process,focusing on macroscopic failure patterns,fragment characteristics,and underlying failure mechanisms.In addition,theoretical analyses were carried out and combined with numerical simulations to investigate the differences in energy evolution associated with rockburst physical models.The results indicate that:(1)The rockburst process with different tunnel diameters consistently evolved through three distinct stages—initial particle ejection,crack propagation accompanied by flake spalling,and,finally,fragment ejection leading to the formation of a‘V'-shaped notch.(2)Increasing tunnel diameter reduces rockburst failure load while increasing surrounding rock damage extent,total mass and average size of ejected fragments.Additionally,shear failure proportion decreases with tensile failure becoming increasingly dominant.(3)Larger tunnel diameters reduce the attenuation rate of elastic strain energy,thereby expanding the zone of elastic strain energy accumulation and disturbance and creating conditions for larger volume rockburst.(4)Larger tunnel diameters result in a smaller principal stress ratio at equivalent distances in the surrounding rock,indicating a higher likelihood of tensile failure.(5)Numerical analyses further reveal that larger tunnel diameters reduce the maximum elastic strain energy density around the tunnel,lowering the energy released per unit volume of rockburst fragments and their ejection velocities.However,both the total failure volume and overall energy release from rockburst increase.Model experiments with different tunnel diameters are of great significance for optimizing engineering design and parameter selection,as well as guiding tunnel construction under complex geological conditions.
基金supported by the Zhejiang Provincial Key Research and Development Program of China(No.2020C01020).
文摘The nozzle is a critical component responsible for generating most of the net thrust in a scramjet engine.The quality of its design directly affects the performance of the entire propulsion system.However,most turbulence models struggle to make accurate predictions for subsonic and supersonic flows in nozzles.In this study,we explored a novel model,the algebraic stress model k-kL-ARSM+J,to enhance the accuracy of turbulence numerical simulations.This new model was used to conduct numerical simulations of the design and off-design performance of a 3D supersonic asymmetric truncated nozzle designed in our laboratory,with the aim of providing a realistic pattern of changes.The research indicates that,compared to linear eddy viscosity turbulence models such as k-kL and shear stress transport(SST),the k-kL-ARSM+J algebraic stress model shows better accuracy in predicting the performance of supersonic nozzles.Its predictions were identical to the experimental values,enabling precise calculations of the nozzle.The performance trends of the nozzle are as follows:as the inlet Mach number increases,both thrust and pitching moment increase,but the rate of increase slows down.Lift peaks near the design Mach number and then rapidly decreases.With increasing inlet pressure,the nozzle thrust,lift,and pitching moment all show linear growth.As the flight altitude rises,the internal flow field within the nozzle remains relatively consistent due to the same supersonic nozzle inlet flow conditions.However,external to the nozzle,the change in external flow pressure results in the nozzle exit transitioning from over-expanded to under-expanded,leading to a shear layer behind the nozzle that initially converges towards the nozzle center and then diverges.
基金supported by the National Natural Science Foundation of China(Grant Nos.U2242213,U2142213,42305167,42175105)。
文摘Systematic bias is a type of model error that can affect the accuracy of data assimilation and forecasting that must be addressed.An online bias correction scheme called the sequential bias correction scheme(SBCS),was developed using the6 h average bias to correct the systematic bias during model integration.The primary purpose of this study is to investigate the impact of the SBCS in the high-resolution China Meteorological Administration Meso-scale(CMA-MESO)numerical weather prediction(NWP)model to reduce the systematic bias and to improve the data assimilation and forecast results through this method.The SBCS is improved upon and applied to the CMA-MESO 3-km model in this study.Four-week sequential data assimilation and forecast experiments,driven by rapid update and cycling(RUC),were conducted for the period from 2–29 May 2022.In terms of the characteristics of systematic bias,both the background and analysis show diurnal bias,and these large biases are affected by complex underlying surfaces(e.g.,oceans,coasts,and mountains).After the application of the SBCS,the results of the data assimilation show that the SBCS can reduce the systematic bias of the background and yield a neutral to slightly positive result for the analysis fields.In addition,the SBCS can reduce forecast errors and improve forecast results,especially for surface variables.The above results indicate that this scheme has good prospects for high-resolution regional NWP models.
基金the National Key Research and Development Program of China(No.2021YFC3100800)the National Natural Science Foundation of China(Nos.42407235 and 42271026)the Project of Sanya Yazhou Bay Science and Technology City(No.SCKJ-JYRC-2023-54).
文摘Coral reef limestone(CRL)constitutes a distinctive marine carbonate formation with complex mechanical properties.This study investigates the multiscale damage and fracture mechanisms of CRL through integrated experimental testing,digital core technology,and theoretical modelling.Two CRL types with contrasting mesostructures were characterized across three scales.Macroscopically,CRL-I and CRL-II exhibited mean compressive strengths of 8.46 and 5.17 MPa,respectively.Mesoscopically,CRL-I featured small-scale highly interconnected pores,whilst CRL-II developed larger stratified pores with diminished connectivity.Microscopically,both CRL matrices demonstrated remarkable similarity in mineral composition and mechanical properties.A novel voxel average-based digital core scaling methodology was developed to facilitate numerical simulation of cross-scale damage processes,revealing network-progressive failure in CRL-I versus directional-brittle failure in CRL-II.Furthermore,a damage statistical constitutive model based on digital core technology and mesoscopic homogenisation theory established quantitative relationships between microelement strength distribution and macroscopic mechanical behavior.These findings illuminate the fundamental mechanisms through which mesoscopic structure governs the macroscopic mechanical properties of CRL.
基金supported by the National Natural Science Foundation project“Micro-Scale Effect of Oil-Gas Flow and the Mechanism of Enhancing Shale Oil Recovery by Natural Gas Injection”(No.52074317)。
文摘Oilfields worldwide are increasingly grappling with challenges such as early water breakthrough and high water production,yet direct,targeted solutions remain elusive.In recent years,chemical flooding techniques designed for tertiary oil recovery have garnered significant attention,with microgel flooding emerging as a particularly prominent area of research.Despite its promise,the complex mechanisms underlying microgel flooding have been rarely investigated numerically.This study aims to address these gaps by characterizing the distribution of microgel concentration and viscosity within different pore structures.To enhance the accuracy of these characterizations,the viscosity of microgels is adjusted to account for the shear effects induced by flow rate and the swelling effects driven by salinity variations.The absolute permeability of the rock and the relative permeability of both oil and microgel are also analyzed to elucidate the mechanisms of microgel flooding.Additionally,a connectivity model is employed to achieve a quantitative representation of fluid flow capacity.The proposed model is validated through conceptual examples and applied to real oilfield blocks,demonstrating its accuracy and practical applicability.
基金supported by the National Natural Science Foundation of China(52104049)the Young Elite Scientist Sponsorship Program by Beijing Association for Science and Technology(BYESS2023262)。
文摘Polymer flooding is an important means of improving oil recovery and is widely used in Daqing,Xinjiang,and Shengli oilfields,China.Different from conventional injection media such as water and gas,viscoelastic polymer solutions exhibit non-Newtonian and nonlinear flow behavior including shear thinning and shear thickening,polymer convection,diffusion,adsorption,retention,inaccessible pore volume,and reduced effective permeability.However,available well test model of polymer flooding wells generally simplifies these characteristics on pressure transient response,which may lead to inaccurate results.This work proposes a novel two-phase numerical well test model to better describe the polymer viscoelasticity and nonlinear flow behavior.Different influence factors that related to near-well blockage during polymer flooding process,including the degree of blockage(inner zone permeability),the extent of blockage(composite radius),and polymer flooding front radius are explored to investigate these impacts on bottom hole pressure responses.Results show that polymer viscoelasticity has a significant impact on the transitional flow segment of type curves,and the effects of near-well formation blockage and polymer concentration distribution on well test curves are very similar.Thus,to accurately interpret the degree of near-well blockage in injection wells,it is essential to first eliminate the influence of polymer viscoelasticity.Finally,a field case is comprehensively analyzed and discussed to illustrate the applicability of the proposed model.
基金supported by the National Natural Science Foundation of China(Grant No.52375340,51975263,52405366).
文摘A three-dimensional numerical model of laser-arc hybrid plasma for aluminum alloy fillet joints is developed in this study.This mod-el accounts for the geometric complexity of fillet joints,the physical properties of shielding gases with varying He-Ar ratios,and the coupling between arc plasma and laser-induced metal plume.The accuracy of the model is validated using a high-speed camera.The effects of varying He contents in the shielding gas on both the temperature and flow velocity of hybrid plasma,as well as the distribu-tion of laser-induced metal vapor mass,were investigated separately.The maximum temperature and size of arc plasma decrease as the He volume ratio increases,the arc distribution becomes more concentrated,and its flow velocity initially decreases and then sharply increases.At high helium content,both the flow velocity of hybrid plasma and metal vapor are high,the metal vapor is con-centrated on the right side of keyhole,and its flow appears chaotic.The flow state of arc plasma is most stable when the shielding gas consists of 50%He+50%Ar.
基金This study was supported by the National Natural Science Foundation of China （Grant Nos. 40233030, 40405004, 40405014）.
文摘The Regional Atmospheric Modeling System （RAMS） and the computational fluid dynamics （CFD） codes known as FLUENT are combinatorially applied in a multi-scale numerical simulation of the urban surface layer （USL）. RAMS and FLUENT are combined as a multi-scale numerical modeling system, in which the RAMS simulated data are delivered to the computational model for FLUENT simulation in an offline way. Numerical simulations are performed to present and preliminarily validate the capability of the multi-scale modeling system, and the results show that the modeling system can reasonably provide information on the meteorological elements in an urban area from the urban scale to the city-block scale, especially the details of the turbulent flows within the USL.
基金supported by the Major Science and Technology Project of PetroChina Company Limited“Research and application of key technologies for development of deep and ultra-deep gas reservoirs in Kuqa Depression(No.2018E-1803).
文摘The cretaceous gas reservoir in Kelasu Gas Field of the Tarim Basin is a rare ultra-deep and ultra-high pressure fractured tight sandstone gas reservoir where multi-scale discrete fractures of matrix,fracture and fault are developed,so its development cannot be conducted just based on static and dynamic reservoir description.In order to solve this problem,this paper establishes a numerical well test model of vertical wells based on matrix,fractures and faults(large fractures and small faults)by combining the random generation of natural fracture networks with the unstructured discrete fracture modeling method to break through the traditional continuous medium well test model.In addition,the model is solved by using the finite element method with mixed element,and the typical well test type curves under different random fracture networks are obtained.And the following research results are obtained.First,based on the observed data,the fracture network distribution modes of fractured tight sandstone gas reservoirs are classified into three categories.The influence of random generation of fracture networks on typical well test type curves is discussed.The results of discrete fracture well test model are compared with those of the traditional continuous medium well test model,and the applicable conditions of the traditional continuous medium well test model is determined.Second,there are great differences between the results of discrete fracture model and those of dual porosity medium model.1 The dual porosity medium model is a special case of the discrete fracture model,in which the fractures are evenly distributed within infinitely small spacing.Third,the characteristics of well test type curves under three fracture network distribution modes are discussed.The well test type curves that cannot be interpreted by the conventional dual/triple porosity continuous medium model are successfully interpreted by using the established well test interpretation model of random discrete fracture.The curve matching effect is ideal and the interpreted parameters are reasonable.In conclusion,the new model and the new method reveal the development mechanism of step-by-step production and coordinated gas supply between media of different scales,explain the development characteristics of large inter-well productivity difference and abnormal rapid inter-well pressure response,and provide a reference for the development of similar gas reservoirs.
基金The Open Research Fund of Key Laboratory of Highway Engineering of Sichuan Province of Southw est Jiaotong University (No.LHTE002201102)
文摘In order to investigate the fatigue behavior of asphalt concrete, a new numerical approach based on a bi-linear cohesive zone model （CZM） is developed. Integrated with the CZM, a fatigue damage evolution model is established to indicate the gradual degradation of cohesive properties of asphalt concrete under cyclic loading. Then the model is implemented in the finite element software ABAQUS through a user-defined subroutine. Based on the proposed model, an indirect tensile fatigue test is finally simulated. The fatigue lives obtained through numerical analysis show good agreement with laboratory results. Fatigue damage accumulates in a nonlinear manner during the cyclic loading process and damage initiation phase is the major part of fatigue failure. As the stress ratio increases, the time of the steady damage growth stage decreases significantly. It is found that the proposed fatigue damage evolution model can serve as an accurate and efficient tool for the prediction of fatigue damage of asphalt concrete.
基金National Natural Science Foundation (Project number 40604013).
文摘Biot-flow and squirt-flow are the two most important fluid flow mechanisms in porous media containing fluids. Based on the BISQ （Biot-Squirt） model where the two mechanisms are treated simultaneously, the elastic wave-field simulation in the porous medium is limited to two-dimensions and two-components （2D2C） or two-dimensions and three-components （2D3C）. There is no previous report on wave simulation in three- dimensions and three-components. Only through three dimensional numerical simulations can we have an overall understanding of wave field coupling relations and the spatial distribution characteristics between the solid and fluid phases in the dual-phase anisotropic medium. In this paper, based on the BISQ equation, we present elastic wave propagation in a three dimensional dual-phase anisotropic medium simulated by the staggered-grid high-order finite-difference method. We analyze the resulting wave fields and show that the results are an improvement.
基金supported by the National High Technology Research and Development Program (863 Program)(2009AA06Z108)
文摘To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional （2D） time- domain transient electromagnetic secondary field of the line source based on the DuFort- Frankel finite-difference method. In the proposed method, we included the treatment of the earth-air boundary conductivity, calculated the normalized partial derivative of the induced electromotive force （Emf）, and determined the forward time step. By extending upward the earth-air interface to the air grid nodes and the zero-value boundary conditions, not only we have a method that is more efficient but also simpler than the total field solution. We computed and analyzed the homogeneous half-space model and the fiat layered model with high precision--the maximum relative error is less than 0.01% between our method and the analytical method--and the solution speed is roughly three times faster than the total-field solution. Lastly, we used the model of a thin body embedded in a homogeneous half-space at different delay times to depict the downward and upward spreading characteristics of the induced eddy current, and the physical interaction processes between the electromagnetic field and the underground low-resistivity body.
文摘This study focuses on the factors that may affect the feasibility of performing elliptical anisotropy analysis on azimuthal PP and PS-wave data in HTI media, with the aim of using the modeling results as guidance in real seismic data application. Our results reveal that there is an offset limitation for both PP- and PS-waves in elliptical anisotropy fitting, and that PS-waves show a wider applicable offset range and larger observable azimuthal anisotropy than PP-waves. The major axis of the elliptical fit to the amplitudes of the R-component is perpendicular to the fracture strike, which is opposite to that in PP-wave analysis. The azimuthal interval travel time of PS-waves shows a nearly elliptical distribution and the major axis of the fit ellipse is perpendicular to the fracture strike, which is same as that in PP-wave analysis. For data within the applicable offset range, the anisotropic magnitude obtained from amplitude and travel time attributes of PP- and PS-waves exhibits a dependence on fracture density, and the major to minor axis ratio of the fit ellipse may be used to infer the relative distribution of fracture densities.
