The data processing technique and the method determining the optimal number of measured points are studied aiming at the sphericity error measured on a coordinate measurement machine(CMM).The consummate criterion for ...The data processing technique and the method determining the optimal number of measured points are studied aiming at the sphericity error measured on a coordinate measurement machine(CMM).The consummate criterion for the minimum zone of spherical surface is analyzed first,and then an approximation technique searching for the minimum sphericity error from the form data is studied.In order to obtain the minimum zone of spherical surface,the radial separation is reduced gradually by moving the center of the concentric spheres along certain directions with certain steps.Therefore the algorithm is precise and efficient.After the appropriate mathematical model for the approximation technique is created,a data processing program is developed accordingly.By processing the metrical data with the developed program,the spherical errors are evaluated when different numbers of measured points are taken from the same sample,and then the corresponding scatter diagram and fit curve for the sample are graphically represented.The optimal number of measured points is determined through regression analysis.Experiment shows that both the data processing technique and the method for determining the optimal number of measured points are effective.On average,the obtained sphericity error is 5.78μm smaller than the least square solution,whose accuracy is increased by 8.63%;The obtained optimal number of measured points is half of the number usually measured.展开更多
This article presents a statistic for testing the sphericity in a GMANOVA- MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in seri...This article presents a statistic for testing the sphericity in a GMANOVA- MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in series form of beta distributions.展开更多
The mathematical modeling for evaluation of the sphericity error is proposed with minimum radial separation center. To obtain the minimum sphericity error from the form data, a geometric approximation technique was de...The mathematical modeling for evaluation of the sphericity error is proposed with minimum radial separation center. To obtain the minimum sphericity error from the form data, a geometric approximation technique was devised. The technique regarded the least square sphere center as the initial center of the concentric spheres containing all measurement points, and then the center was moved gradually to reduce the radial separation till the minimum radial separation center was got where the constructed concentric spheres conformed to the minimum zone condition. The method was modeled firstly, then the geometric approximation process was analyzed, and finally,the software for data processing was programmed. As evaluation example, five steel balls were measured and the measurement data were processed with the developed program. The average iteration times of the approximation technique is 4.2, and on average the obtained sphericity error is 0. 529μm smaller than the least square solution,with accuracy increased by 7. 696%.展开更多
The present study aims to plumb blockage of the deep-sea mining pump transporting large particles with different shapes. A numerical work was performed through combining the computational fluid dynamics(CFD) technique...The present study aims to plumb blockage of the deep-sea mining pump transporting large particles with different shapes. A numerical work was performed through combining the computational fluid dynamics(CFD) technique and the discrete element method(DEM). Six particle shapes with sphericity ranging from 0.67 to 1.0 were selected. A velocity triangle is built with the absolute, relative, and circumferential velocities of particles. Velocity triangles with absolute velocity angles ranging from 90° to 180° prevail in the first-stage impeller. With declining sphericity, more particles follow the velocity triangle with absolute velocity angles ranging from 0° to 90°, which weakens the ability of particles to pass through the flow passage. Furthermore, the forces acting on the particles traveling in the impeller passage are analyzed. Large particles, especially non-spherical ones, suffer from high centrifugal force and therefore move along the suction surface of the impeller blades. Non-spherical particles undergo great drag force as a result of large surface area. The distribution of drag force angles is featured by two peaks, and one vanishes due to blockage.As particle sphericity declines, both magnitude and angle of the pressure gradient force decrease. Variation of the drag force and the pressure gradient force causes clockwise deflection of the centripetal force, resulting in deflection and elongation of particle trajectory, which increases the possibility of blockage.展开更多
BACKGROUND The sphericity of the femoral head is a metric used to evaluate hip pathologies and is associated with the development of osteoarthritis and femoral-acetabular impingement.AIM To analyze the three-dimension...BACKGROUND The sphericity of the femoral head is a metric used to evaluate hip pathologies and is associated with the development of osteoarthritis and femoral-acetabular impingement.AIM To analyze the three-dimensional asphericity of the femoral head of asymptomatic pediatric hips.We hypothesized that femoral head asphericity will vary significantly between male and female pediatric hips and increase with age in both sexes.METHODS Computed tomography scans were obtained on 158 children and adolescents from a single institution in the United States(8-18 years;50%male)without hip pain.Proximal femoral measurements including the femoral head diameter,femoral head volume,residual volume,asphericity index,and local diameter difference were used to evaluate femoral head sphericity.RESULTS In both sexes,the residual volume increased by age(P<0.05).Despite significantly smaller femoral head size in older ages(>13 years)in females,there were no sex-differences in residual volume and aspherity index.There were no age-related changes in mean diameter difference in both sexes(P=0.07)with no significant sex-differences across different age groups(P=0.06).In contrast,there were significant increases in local aspherity(maximum diameter difference)across whole surface of the femoral head and all quadrants except the inferior regions in males(P=0.03).There were no sex-differences in maximum diameter difference at any regions and age group(P>0.05).Increased alpha angle was only correlated to increased mean diameter difference across overall surface of the femoral head(P=0.024).CONCLUSION There is a substantial localized asphericity in asymptomatic hips which increases with age in.While 2D measured alpha angle can capture overall asphericity of the femoral head,it may not be sensitive enough to represent regional asphericity patterns.展开更多
A comparison of sphericity and Zingg factor for particle morphology and description of fluidized-bed dynamics are presented. It is found that Zingg factor Fz = LH/B2 （where L, H and B are, respectively, the length, b...A comparison of sphericity and Zingg factor for particle morphology and description of fluidized-bed dynamics are presented. It is found that Zingg factor Fz = LH/B2 （where L, H and B are, respectively, the length, breadth and height of a particle） well describes the effect of particle morphology. Experimental results show that non-spherical particles give poor fluidizing quality as compared to spherical particles in terms of pressure drop, Umf, etc. With the same volume-equivalent diameter, non-spherical particles have lower Umf and fluidizing coefficient 8. Some smooth curves have been obtained between the parameters 8, Umf and Fz. The quality of fluidization could be evaluated by fluidizing coefficient, which has been correlated to the Zingg factor and minimum fluidizing velocity in this paper.展开更多
This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds the sample size.The central limit theorem of the first four moments of...This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds the sample size.The central limit theorem of the first four moments of eigenvalues of sample covariance matrix is derived using random matrix theory for generally distributed populations.Further,some desirable asymptotic properties of the proposed test statistics are provided under the null hypothesis as data dimension and sample size both tend to infinity.Simulations show that the proposed tests have a greater power than existing methods for the spiked covariance model.展开更多
Sphericity,a measure of how much a particle’s shape deviates from spherical,is useful as a shape factorwhen characterizing particulate materials.However,particle surface areas,required when determiningthe sphericity,...Sphericity,a measure of how much a particle’s shape deviates from spherical,is useful as a shape factorwhen characterizing particulate materials.However,particle surface areas,required when determiningthe sphericity,are very difficult to measure.As a result,the circularity,derivable from microscopic views,is often measured instead and assumed to be equal to the sphericity.This paper shows that the twoquantities are generally not equal for simple non-spherical shapes and provides advice on improving theestimation of sphericity from circularity.展开更多
Fertilizer sphericity is an important assessment index of appearance quality that affects the fertilization effect.A fertilizer sphericity measuring device based on machine vision was designed aimed at low precision a...Fertilizer sphericity is an important assessment index of appearance quality that affects the fertilization effect.A fertilizer sphericity measuring device based on machine vision was designed aimed at low precision and heavy workload of manual fertilizer measurement,and high cost and complicated operation of high precision measuring instruments.A fertilizer sphericity measuring method based on equatorial and meridian circles was proposed.The device works in an intermittent static acquisition mode to simultaneously obtain both top and side images of a single fertilizer.First,the method performs gamma correction on the top and side images of the single fertilizer,and uses the Canny operator to detect the edge of the image to obtain the equatorial and meridian circular contour images of the fertilizer.Second,based on the fertilizer equatorial and meridian circular contour,the Least Squares Circle method was used to evaluate the roundness of the single fertilizer.Finally,the average roundness value of the equatorial and meridian circles was used as the final sphericity value of the fertilizer.The sphericity measurement test was carried out on the same batch of compound,organic and biological fertilizers by using the sphericity measuring device.The fertilizer sphericity data were obtained by different measurement and evaluation methods.The variation coefficient was used to evaluate the difference in fertilizer sphericity measured by different sphericity measurement and evaluation methods.The results show that among the different measurement and evaluation methods,the coefficient of variation of fertilizer sphericity measured by the equatorial and meridian circle method was the smallest,and the coefficient of variation of sphericity measured by the Least Squares Circle method was the smallest and accurate.This study shows that the sphericity measuring device and method can accurately measure the fertilizer sphericity,and has a significant potential to facilitate fertilizer production and quality inspection.展开更多
Carbon superstructures with multiscale hierarchies and functional attributes represent an appealing cathode candidate for zinc hybrid capacitors,but their tailor-made design to optimize the capacitive activity remains...Carbon superstructures with multiscale hierarchies and functional attributes represent an appealing cathode candidate for zinc hybrid capacitors,but their tailor-made design to optimize the capacitive activity remains a confusing topic.Here we develop a hydrogen-bond-oriented interfacial super-assembly strategy to custom-tailor nanosheet-intertwined spherical carbon superstructures(SCSs)for Zn-ion storage with double-high capacitive activity and durability.Tetrachlorobenzoquinone(H-bond acceptor)and dimethylbenzidine(H-bond donator)can interact to form organic nanosheet modules,which are sequentially assembled,orientally compacted and densified into well-orchestrated superstructures through multiple H-bonds(N-H···O).Featured with rich surface-active heterodiatomic motifs,more exposed nanoporous channels,and successive charge migration paths,SCSs cathode promises high accessibility of built-in zincophilic sites and rapid ion diffusion with low energy barriers(3.3Ωs-0.5).Consequently,the assembled Zn||SCSs capacitor harvests all-round improvement in Zn-ion storage metrics,including high energy density(166 Wh kg-1),high-rate performance(172 m Ah g^(-1)at 20 A g^(-1)),and long-lasting cycling lifespan(95.5%capacity retention after 500,000 cycles).An opposite chargecarrier storage mechanism is rationalized for SCSs cathode to maximize spatial capacitive charge storage,involving high-kinetics physical Zn^(2+)/CF_(3)SO_(3)-adsorption and chemical Zn^(2+)redox with carbonyl/pyridine groups.This work gives insights into H-bond-guided interfacial superassembly design of superstructural carbons toward advanced energy storage.展开更多
The melting process of a phase change material(PCM) inside a capsule can be promising in the thermal management of spacecraft. Such spacecraft operate under various gravity conditions, but previous studies have mostly...The melting process of a phase change material(PCM) inside a capsule can be promising in the thermal management of spacecraft. Such spacecraft operate under various gravity conditions, but previous studies have mostly considered the influence of gravity conditions on the constrained melting process of a PCM and not on its unconstrained melting process. In this study, a numerical model was constructed to comprehensively analyze the constrained and unconstrained melting processes of a PCM inside a spherical capsule under low-gravity conditions. After validation, the model was then applied to investigating the effects of low-gravity conditions on the evolution of velocity, temperature, melt layer thickness, heat transfer, liquid fraction, and total melting time. For the unconstrained melting process, low-gravity conditions weaken buoyancy-driven natural convection and slow down the solid PCM downward trend, thereby limiting the melting rate. In addition, the melt layer thickness does not increase linearly with decreasing gravity. Specifically, the increase in melt layer thickness is smaller by about 1.06 mm when the gravity drops from 0.4g to 0.2g compared to when it drops from 0.2g to 0.1g. The local heat flux in the contact melting area gradually decreases with the reduction of gravity during the unconstrained melting process. During the constrained melting process, notable oscillations in the local heat flux were observed. Decreasing the gravity from g to 0g increased the total melting times of the constrained and unconstrained melting processes by 417% and 621%, respectively.展开更多
For mission-oriented unmanned aerial vehicle(UAV)swarms,mission capability assessment provides an important reference in the design and development process,and is a precondition for mission success.For this multi-crit...For mission-oriented unmanned aerial vehicle(UAV)swarms,mission capability assessment provides an important reference in the design and development process,and is a precondition for mission success.For this multi-criteria decisionmaking(MCDM)problem,the current literature lacks a way to unambiguously present criteria and the popular fuzzy analytic network process(ANP)approaches neglect the hesitancy of subjective judgments.To fill these research gaps,an MCDM method based on unified architecture framework(UAF)and interval-valued spherical fuzzy ANP(IVSF-ANP)is proposed in this paper.Firstly,selected viewpoints in UAF are extended to construct criteria models with standardized representation.Secondly,interval-valued spherical fuzzy sets are introduced to ANP to weight interdependent criteria,handling fuzziness and hesitancy in pairwise comparisons.A method of adjusting weights of experts based on their decision similarities is also included in this process to reduce ambiguity brought by multiple experts.Next,performance characteristics are non-linearly transformed regarding to expectations to get final results.This proposition is applied to assess the mission capability of UAV swarms to search and strike surface vessels.Comparative analysis shows that the proposed method is valid and reasonable.展开更多
For a general linear model, spherical distributions are often considered whenerrors do not have normal distribution. Several authors[1-3] studied the least squaresand James-Stein estimations for a linear model whose e...For a general linear model, spherical distributions are often considered whenerrors do not have normal distribution. Several authors[1-3] studied the least squaresand James-Stein estimations for a linear model whose errors follow multivariate t or moregeneral spherical distributions. In this paper the test problem for sphericity of errors isconsidered. We propose an exact test for the sphericity by using the conditional probabilityintegral transformation and another transformation. As an important special case, thecorresponding test statistics for multivariate t distribution are obtained.展开更多
To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fract...To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.展开更多
To accurately analyze proppant transport in rough intersecting fractures and elucidate the interaction mechanisms among liquid,particles,and rough walls,this study reconstructed a numerical model of fractures in inhom...To accurately analyze proppant transport in rough intersecting fractures and elucidate the interaction mechanisms among liquid,particles,and rough walls,this study reconstructed a numerical model of fractures in inhomogeneous reservoirs with varying brittleness index(BI).Various auto-correlation Gaussian rough fracture models were created using Matlab to assess roughness through the fractal dimension method.This research innovatively combined Boolean operations to establish three-dimensional rough fracture models,incorporating(Computational Fluid Dynamics)CFD-DEM(Discrete Element Method)with a bidirectional method for cosimulation.The proppant transport in fractures was categorized into three zones based on the difference in the turbulent kinetic energy.Artificially induced fracture roughness increases fluid retention and turbulence,causing plugging effects and limiting proppant flow into branch fractures.Additionally,compared with the superior deposition and significant support effects of the spherical proppant,the low-sphericity proppant traveled farther under fracturing fluid,inducing more pronounced plugging near curved fracture intersections;the variation in fracture intersection angles primarily impacted the wall shear stress within the flow field,indicating smaller angles led to higher shear energy at the intersection.Compared with the intersection angle of 30°,the height and area deposited in the 90 branch fracture increased by 52.25%and 65.33%,respectively:notably,injecting proppant from smaller to larger particles(S:M:L)and a low velocity effectively ensured fracture conductivity near the wellbore at joint roughness coefficient(JRC)≥46 while achieving satis-factory placement in the branch fracture,making it a recommended approach.展开更多
Rectangular explosive charges are usually used in military or civilian explosive transportation and storage.The effects of shape parameters and detonation positions on the peak overpressure and maximum impulse of blas...Rectangular explosive charges are usually used in military or civilian explosive transportation and storage.The effects of shape parameters and detonation positions on the peak overpressure and maximum impulse of blasts lack comprehensive investigation,which is significant for the design of blast-resistant structures.In this paper,the side-length ratio of the rectangle,orientation,and detonation position of the charge are chosen as controlling parameters to investigate their influence on blast loads in the scaled distances of the gauges ranging from 0.63 to 10.54 m/kg^(1/3) with well validated 3D numerical simulations.The results show that there is a large difference in the near-field spatial distribution of the blast load of the rectangular charge;if the blast load of the rectangular charge is simply evaluated with the spherical charge,the maximum peak overpressure(maximum impulse)will be underestimated by a factor of 7.46(4.84).This must be taken seriously by blast-resistant structure designers.With the increase in the scaled distance,when the critical scaled distance is greater than 6.32(7.38)m/kg^(1/3),the influence of the charge shape on the maximum peak overpressure(maximum impulse)of the spatial blast load can be ignored.In general,the impact of detonation of the charge at the end on the maximum peak overpressure is greater compared with central detonation,but for the impact of the maximum impulse,it is necessary to pay attention to the side-length ratio of the rectangular charge and the specific detonation position on the end face.Furthermore,the structural response of steel plates placed at different azimuths under the blast load of a rectangular charge is preliminarily analyzed,and the results show that the deformation and energy of the plates are consistent with the distribution of the blast load.These analysis results provide a reference for the explosion protection design in near-field air explosions.展开更多
As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal vari...As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal variations in the lithosphere.Traditional approaches either do not consider the non-axial dipolar terms of the inducing field and its radial variation or do so by means of complicated formulae.Moreover,existing methods treat the magnetic lithosphere either as an infinitesimally thin layer or as a radially uniform spherical shell of constant thickness.Here,we present alternative forward formulae that account for an arbitrarily high maximum degree of the inducing field and for a magnetic lithosphere of variable thickness.Our simulations based on these formulae suggest that the satellite magnetic anomaly field is sensitive to the non-axial dipolar terms of the inducing field but not to its radial variation.Therefore,in forward and inverse calculations of satellite magnetic anomaly data,the non-axial dipolar terms of the inducing field should not be ignored.Furthermore,our results show that the satellite magnetic anomaly field is sensitive to variability in the lateral thickness of the magnetized shell.In particular,we show that for a given vertically integrated susceptibility distribution,underestimating the thickness of the magnetic layer overestimates the induced magnetic field.This discovery bridges the greatest part of the alleged gap between the susceptibility values measured from rock samples and the susceptibility values required to match the observed magnetic field signal.We expect the formulae and conclusions of this study to be a valuable tool for the quantitative interpretation of the Earth's global lithospheric magnetic field,through an inverse or forward modelling approach.展开更多
The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.Howeve...The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.However,the inversion for the ES model suffers from nonuniqueness and instability,which remain unresolved.To mitigate these issues,we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method.We first present the methods,then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data.The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region.Finally,we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1(CSES-1)and Macao Science Satellite-1(MSS-1)magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field.Compared with existing global lithospheric magnetic field models,our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes.Furthermore,we derive the reduction to the pole(RTP)magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model.The latter correlates well with the regional tectonic framework in Africa and surroundings.展开更多
Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including at...Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including atmospheric, hydrological, and nontidal ocean loading. Continuous improvements in the accuracy of surface mass loading products, performance of Earth models, and precise data-processing technologies have significantly advanced research on the effects of environmental loading on nonlinear variations in GNSS coordinate time series. However, owing to theoretical limitations, the lack of high spatiotemporal resolution surface mass observations, and the coupling of GNSS technology-related systematic errors, environmental loading and nonlinear GNSS reference station displacements remain inconsistent. The applicability and capability of these loading products across different regions also require further evaluation. This paper outlines methods for modeling environmental loading, surface mass loading products, and service organizations. In addition, it summarizes recent advances in applying environmental loading to address nonlinear variations in global and regional GNSS coordinate time series. Moreover, the scientific questions of existing studies are summarized, and insights into future research directions are provided. The complex nonlinear motion of reference stations is a major factor limiting the accuracy of the current terrestrial reference frame. Further refining the environmental load modeling method, establishing a surface mass distribution model with high spatiotemporal resolution and reliability, exploring other environmental load factors such as ice sheet and artificial mass-change effects, and developing an optimal data-processing model and strategy for reprocessing global reference station data consistently could contribute to the development of a millimeter-level nonlinear motion model for GNSS reference stations with actual physical significance and provide theoretical support for establishing a terrestrial reference frame with 1 mm accuracy by 2050.展开更多
The CUG_CLMFM3D series comprises high-resolution three-dimensional lithospheric magnetic field models for China and its surroundings.The first version,CUG_CLMFM3Dv1,is a spherical cap harmonic model integrating the WD...The CUG_CLMFM3D series comprises high-resolution three-dimensional lithospheric magnetic field models for China and its surroundings.The first version,CUG_CLMFM3Dv1,is a spherical cap harmonic model integrating the WDMAMv2(World Digital Magnetic Anomaly Map version 2)global magnetic anomaly grid and nearly a decade of CHAMP(Challenging Minisatellite Payload for Geophysical Research and Application)satellite vector data.It achieves a~5.7 km resolution but has limitations:the WDMAMv2 grid lacks high-resolution data in the southern Xinjiang and Tibet regions,which leads to missing small-to medium-scale anomalies,and unfiltered CHAMP data introduce low-frequency conflicts with global spherical harmonic models.Above the altitude of 150 km,correlations with global models drop below 0.9.The second version,CUG_CLMFM3Dv2,addresses these issues by incorporating 5-km-resolution aeromagnetic data and rigorously processed satellite data from CHAMP,Swarm,CSES-1(China Seismo-Electromagnetic Satellite 1),and MSS-1(Macao Science Satellite 1).The comparison analysis shows that the CUG_CLMFM3Dv2 captures finer high-frequency details and more stable long-wavelength signals,offering improved magnetic anomaly maps for further geological and geophysical studies.展开更多
基金This project is supported by National Natural Science Foundation of China(No.50475117)Municipal Science and Technology Commission of,Tianjin China(No.0431835116).
文摘The data processing technique and the method determining the optimal number of measured points are studied aiming at the sphericity error measured on a coordinate measurement machine(CMM).The consummate criterion for the minimum zone of spherical surface is analyzed first,and then an approximation technique searching for the minimum sphericity error from the form data is studied.In order to obtain the minimum zone of spherical surface,the radial separation is reduced gradually by moving the center of the concentric spheres along certain directions with certain steps.Therefore the algorithm is precise and efficient.After the appropriate mathematical model for the approximation technique is created,a data processing program is developed accordingly.By processing the metrical data with the developed program,the spherical errors are evaluated when different numbers of measured points are taken from the same sample,and then the corresponding scatter diagram and fit curve for the sample are graphically represented.The optimal number of measured points is determined through regression analysis.Experiment shows that both the data processing technique and the method for determining the optimal number of measured points are effective.On average,the obtained sphericity error is 5.78μm smaller than the least square solution,whose accuracy is increased by 8.63%;The obtained optimal number of measured points is half of the number usually measured.
基金the National Natural Science Foundation of China (10761010, 10771185)the Mathematics Tianyuan Youth Foundation of China
文摘This article presents a statistic for testing the sphericity in a GMANOVA- MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in series form of beta distributions.
基金Supported by National Natural Science Foundation of China(No.50175081) andTianjin Municipal Science and Technology Commission (No.0431835116).
文摘The mathematical modeling for evaluation of the sphericity error is proposed with minimum radial separation center. To obtain the minimum sphericity error from the form data, a geometric approximation technique was devised. The technique regarded the least square sphere center as the initial center of the concentric spheres containing all measurement points, and then the center was moved gradually to reduce the radial separation till the minimum radial separation center was got where the constructed concentric spheres conformed to the minimum zone condition. The method was modeled firstly, then the geometric approximation process was analyzed, and finally,the software for data processing was programmed. As evaluation example, five steel balls were measured and the measurement data were processed with the developed program. The average iteration times of the approximation technique is 4.2, and on average the obtained sphericity error is 0. 529μm smaller than the least square solution,with accuracy increased by 7. 696%.
基金financially supported by the Science and Technology Plan Project of State Administration for Market Regulation of China (Grant No. 2021MK060)the National Key Research and Development Program of China (Grant No. 2021YFC2801600)+1 种基金the Postgraduate Research and Practice Innovation Program of Jiangsu Province (Grant No. KYCX20_3082)the Science and Technology Innovation Project from China State Shipbuilding Corporation Limited。
文摘The present study aims to plumb blockage of the deep-sea mining pump transporting large particles with different shapes. A numerical work was performed through combining the computational fluid dynamics(CFD) technique and the discrete element method(DEM). Six particle shapes with sphericity ranging from 0.67 to 1.0 were selected. A velocity triangle is built with the absolute, relative, and circumferential velocities of particles. Velocity triangles with absolute velocity angles ranging from 90° to 180° prevail in the first-stage impeller. With declining sphericity, more particles follow the velocity triangle with absolute velocity angles ranging from 0° to 90°, which weakens the ability of particles to pass through the flow passage. Furthermore, the forces acting on the particles traveling in the impeller passage are analyzed. Large particles, especially non-spherical ones, suffer from high centrifugal force and therefore move along the suction surface of the impeller blades. Non-spherical particles undergo great drag force as a result of large surface area. The distribution of drag force angles is featured by two peaks, and one vanishes due to blockage.As particle sphericity declines, both magnitude and angle of the pressure gradient force decrease. Variation of the drag force and the pressure gradient force causes clockwise deflection of the centripetal force, resulting in deflection and elongation of particle trajectory, which increases the possibility of blockage.
文摘BACKGROUND The sphericity of the femoral head is a metric used to evaluate hip pathologies and is associated with the development of osteoarthritis and femoral-acetabular impingement.AIM To analyze the three-dimensional asphericity of the femoral head of asymptomatic pediatric hips.We hypothesized that femoral head asphericity will vary significantly between male and female pediatric hips and increase with age in both sexes.METHODS Computed tomography scans were obtained on 158 children and adolescents from a single institution in the United States(8-18 years;50%male)without hip pain.Proximal femoral measurements including the femoral head diameter,femoral head volume,residual volume,asphericity index,and local diameter difference were used to evaluate femoral head sphericity.RESULTS In both sexes,the residual volume increased by age(P<0.05).Despite significantly smaller femoral head size in older ages(>13 years)in females,there were no sex-differences in residual volume and aspherity index.There were no age-related changes in mean diameter difference in both sexes(P=0.07)with no significant sex-differences across different age groups(P=0.06).In contrast,there were significant increases in local aspherity(maximum diameter difference)across whole surface of the femoral head and all quadrants except the inferior regions in males(P=0.03).There were no sex-differences in maximum diameter difference at any regions and age group(P>0.05).Increased alpha angle was only correlated to increased mean diameter difference across overall surface of the femoral head(P=0.024).CONCLUSION There is a substantial localized asphericity in asymptomatic hips which increases with age in.While 2D measured alpha angle can capture overall asphericity of the femoral head,it may not be sensitive enough to represent regional asphericity patterns.
基金The authors acknowledge with gratitude the financial support from the National Natural Science Foundation of China （Contract no. 50476082）.
文摘A comparison of sphericity and Zingg factor for particle morphology and description of fluidized-bed dynamics are presented. It is found that Zingg factor Fz = LH/B2 （where L, H and B are, respectively, the length, breadth and height of a particle） well describes the effect of particle morphology. Experimental results show that non-spherical particles give poor fluidizing quality as compared to spherical particles in terms of pressure drop, Umf, etc. With the same volume-equivalent diameter, non-spherical particles have lower Umf and fluidizing coefficient 8. Some smooth curves have been obtained between the parameters 8, Umf and Fz. The quality of fluidization could be evaluated by fluidizing coefficient, which has been correlated to the Zingg factor and minimum fluidizing velocity in this paper.
基金supported by the National Natural Science Foundation of China(Nos.61374027,11871357)the Sichuan Science and Technology Program(Nos.2019YJ0122)。
文摘This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds the sample size.The central limit theorem of the first four moments of eigenvalues of sample covariance matrix is derived using random matrix theory for generally distributed populations.Further,some desirable asymptotic properties of the proposed test statistics are provided under the null hypothesis as data dimension and sample size both tend to infinity.Simulations show that the proposed tests have a greater power than existing methods for the spiked covariance model.
基金The authors acknowledge the financial support of the Natural Science and Engineering Research Council of Canada(NSERC)via their CREATE and Discovery Grant programs.
文摘Sphericity,a measure of how much a particle’s shape deviates from spherical,is useful as a shape factorwhen characterizing particulate materials.However,particle surface areas,required when determiningthe sphericity,are very difficult to measure.As a result,the circularity,derivable from microscopic views,is often measured instead and assumed to be equal to the sphericity.This paper shows that the twoquantities are generally not equal for simple non-spherical shapes and provides advice on improving theestimation of sphericity from circularity.
基金This work was supported in part by the National Key Research and Development Plan of China(2016YFD0201104),National Apple Industry Technology System Project.
文摘Fertilizer sphericity is an important assessment index of appearance quality that affects the fertilization effect.A fertilizer sphericity measuring device based on machine vision was designed aimed at low precision and heavy workload of manual fertilizer measurement,and high cost and complicated operation of high precision measuring instruments.A fertilizer sphericity measuring method based on equatorial and meridian circles was proposed.The device works in an intermittent static acquisition mode to simultaneously obtain both top and side images of a single fertilizer.First,the method performs gamma correction on the top and side images of the single fertilizer,and uses the Canny operator to detect the edge of the image to obtain the equatorial and meridian circular contour images of the fertilizer.Second,based on the fertilizer equatorial and meridian circular contour,the Least Squares Circle method was used to evaluate the roundness of the single fertilizer.Finally,the average roundness value of the equatorial and meridian circles was used as the final sphericity value of the fertilizer.The sphericity measurement test was carried out on the same batch of compound,organic and biological fertilizers by using the sphericity measuring device.The fertilizer sphericity data were obtained by different measurement and evaluation methods.The variation coefficient was used to evaluate the difference in fertilizer sphericity measured by different sphericity measurement and evaluation methods.The results show that among the different measurement and evaluation methods,the coefficient of variation of fertilizer sphericity measured by the equatorial and meridian circle method was the smallest,and the coefficient of variation of sphericity measured by the Least Squares Circle method was the smallest and accurate.This study shows that the sphericity measuring device and method can accurately measure the fertilizer sphericity,and has a significant potential to facilitate fertilizer production and quality inspection.
基金financially supported by the National Natural Science Foundation of China(Nos.22272118,22172111,and 22309134)the Science and Technology Commission of Shanghai Municipality,China(Nos.22ZR1464100,20ZR1460300,and 19DZ2271500)+2 种基金the China Postdoctoral Science Foundation(2022M712402),the Shanghai Rising-Star Program(23YF1449200)the Zhejiang Provincial Science and Technology Project(2022C01182)the Fundamental Research Funds for the Central Universities(2023-3-YB-07)。
文摘Carbon superstructures with multiscale hierarchies and functional attributes represent an appealing cathode candidate for zinc hybrid capacitors,but their tailor-made design to optimize the capacitive activity remains a confusing topic.Here we develop a hydrogen-bond-oriented interfacial super-assembly strategy to custom-tailor nanosheet-intertwined spherical carbon superstructures(SCSs)for Zn-ion storage with double-high capacitive activity and durability.Tetrachlorobenzoquinone(H-bond acceptor)and dimethylbenzidine(H-bond donator)can interact to form organic nanosheet modules,which are sequentially assembled,orientally compacted and densified into well-orchestrated superstructures through multiple H-bonds(N-H···O).Featured with rich surface-active heterodiatomic motifs,more exposed nanoporous channels,and successive charge migration paths,SCSs cathode promises high accessibility of built-in zincophilic sites and rapid ion diffusion with low energy barriers(3.3Ωs-0.5).Consequently,the assembled Zn||SCSs capacitor harvests all-round improvement in Zn-ion storage metrics,including high energy density(166 Wh kg-1),high-rate performance(172 m Ah g^(-1)at 20 A g^(-1)),and long-lasting cycling lifespan(95.5%capacity retention after 500,000 cycles).An opposite chargecarrier storage mechanism is rationalized for SCSs cathode to maximize spatial capacitive charge storage,involving high-kinetics physical Zn^(2+)/CF_(3)SO_(3)-adsorption and chemical Zn^(2+)redox with carbonyl/pyridine groups.This work gives insights into H-bond-guided interfacial superassembly design of superstructural carbons toward advanced energy storage.
基金supported by the National Natural Science Foundation of China (Grant No.52376181)。
文摘The melting process of a phase change material(PCM) inside a capsule can be promising in the thermal management of spacecraft. Such spacecraft operate under various gravity conditions, but previous studies have mostly considered the influence of gravity conditions on the constrained melting process of a PCM and not on its unconstrained melting process. In this study, a numerical model was constructed to comprehensively analyze the constrained and unconstrained melting processes of a PCM inside a spherical capsule under low-gravity conditions. After validation, the model was then applied to investigating the effects of low-gravity conditions on the evolution of velocity, temperature, melt layer thickness, heat transfer, liquid fraction, and total melting time. For the unconstrained melting process, low-gravity conditions weaken buoyancy-driven natural convection and slow down the solid PCM downward trend, thereby limiting the melting rate. In addition, the melt layer thickness does not increase linearly with decreasing gravity. Specifically, the increase in melt layer thickness is smaller by about 1.06 mm when the gravity drops from 0.4g to 0.2g compared to when it drops from 0.2g to 0.1g. The local heat flux in the contact melting area gradually decreases with the reduction of gravity during the unconstrained melting process. During the constrained melting process, notable oscillations in the local heat flux were observed. Decreasing the gravity from g to 0g increased the total melting times of the constrained and unconstrained melting processes by 417% and 621%, respectively.
基金supported by the National Natural Science Foundation of China(62073267,61903305)the Fundamental Research Funds for the Central Universities(HXGJXM202214)。
文摘For mission-oriented unmanned aerial vehicle(UAV)swarms,mission capability assessment provides an important reference in the design and development process,and is a precondition for mission success.For this multi-criteria decisionmaking(MCDM)problem,the current literature lacks a way to unambiguously present criteria and the popular fuzzy analytic network process(ANP)approaches neglect the hesitancy of subjective judgments.To fill these research gaps,an MCDM method based on unified architecture framework(UAF)and interval-valued spherical fuzzy ANP(IVSF-ANP)is proposed in this paper.Firstly,selected viewpoints in UAF are extended to construct criteria models with standardized representation.Secondly,interval-valued spherical fuzzy sets are introduced to ANP to weight interdependent criteria,handling fuzziness and hesitancy in pairwise comparisons.A method of adjusting weights of experts based on their decision similarities is also included in this process to reduce ambiguity brought by multiple experts.Next,performance characteristics are non-linearly transformed regarding to expectations to get final results.This proposition is applied to assess the mission capability of UAV swarms to search and strike surface vessels.Comparative analysis shows that the proposed method is valid and reasonable.
文摘For a general linear model, spherical distributions are often considered whenerrors do not have normal distribution. Several authors[1-3] studied the least squaresand James-Stein estimations for a linear model whose errors follow multivariate t or moregeneral spherical distributions. In this paper the test problem for sphericity of errors isconsidered. We propose an exact test for the sphericity by using the conditional probabilityintegral transformation and another transformation. As an important special case, thecorresponding test statistics for multivariate t distribution are obtained.
基金funded by the project of the Major Scientific and Technological Projects of CNOOC in the 14th Five-Year Plan(No.KJGG2022-0701)the CNOOC Research Institute(No.2020PFS-03).
文摘To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.
文摘To accurately analyze proppant transport in rough intersecting fractures and elucidate the interaction mechanisms among liquid,particles,and rough walls,this study reconstructed a numerical model of fractures in inhomogeneous reservoirs with varying brittleness index(BI).Various auto-correlation Gaussian rough fracture models were created using Matlab to assess roughness through the fractal dimension method.This research innovatively combined Boolean operations to establish three-dimensional rough fracture models,incorporating(Computational Fluid Dynamics)CFD-DEM(Discrete Element Method)with a bidirectional method for cosimulation.The proppant transport in fractures was categorized into three zones based on the difference in the turbulent kinetic energy.Artificially induced fracture roughness increases fluid retention and turbulence,causing plugging effects and limiting proppant flow into branch fractures.Additionally,compared with the superior deposition and significant support effects of the spherical proppant,the low-sphericity proppant traveled farther under fracturing fluid,inducing more pronounced plugging near curved fracture intersections;the variation in fracture intersection angles primarily impacted the wall shear stress within the flow field,indicating smaller angles led to higher shear energy at the intersection.Compared with the intersection angle of 30°,the height and area deposited in the 90 branch fracture increased by 52.25%and 65.33%,respectively:notably,injecting proppant from smaller to larger particles(S:M:L)and a low velocity effectively ensured fracture conductivity near the wellbore at joint roughness coefficient(JRC)≥46 while achieving satis-factory placement in the branch fracture,making it a recommended approach.
基金supported by the National Science Foundation of China(Grant No.14102428)the Fundamental Research Funds for the Central Universities(Grant Nos.WK2090000019 and YD2480002002)the Open Research Fund of Anhui Province Key Laboratory of Green Building and Assembly Construction,Anhui Institute of Building Research&Design(Grant No.2021-JKYL-005).
文摘Rectangular explosive charges are usually used in military or civilian explosive transportation and storage.The effects of shape parameters and detonation positions on the peak overpressure and maximum impulse of blasts lack comprehensive investigation,which is significant for the design of blast-resistant structures.In this paper,the side-length ratio of the rectangle,orientation,and detonation position of the charge are chosen as controlling parameters to investigate their influence on blast loads in the scaled distances of the gauges ranging from 0.63 to 10.54 m/kg^(1/3) with well validated 3D numerical simulations.The results show that there is a large difference in the near-field spatial distribution of the blast load of the rectangular charge;if the blast load of the rectangular charge is simply evaluated with the spherical charge,the maximum peak overpressure(maximum impulse)will be underestimated by a factor of 7.46(4.84).This must be taken seriously by blast-resistant structure designers.With the increase in the scaled distance,when the critical scaled distance is greater than 6.32(7.38)m/kg^(1/3),the influence of the charge shape on the maximum peak overpressure(maximum impulse)of the spatial blast load can be ignored.In general,the impact of detonation of the charge at the end on the maximum peak overpressure is greater compared with central detonation,but for the impact of the maximum impulse,it is necessary to pay attention to the side-length ratio of the rectangular charge and the specific detonation position on the end face.Furthermore,the structural response of steel plates placed at different azimuths under the blast load of a rectangular charge is preliminarily analyzed,and the results show that the deformation and energy of the plates are consistent with the distribution of the blast load.These analysis results provide a reference for the explosion protection design in near-field air explosions.
基金supported by the National Natural Science Foundation of China(Grant Nos.42250103 and 42174090)the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(Grant No.GLAB2023ZR02)the Ministry of Science and Technology(MOST)Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources(Grant No.MSFGPMR2022-4)。
文摘As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal variations in the lithosphere.Traditional approaches either do not consider the non-axial dipolar terms of the inducing field and its radial variation or do so by means of complicated formulae.Moreover,existing methods treat the magnetic lithosphere either as an infinitesimally thin layer or as a radially uniform spherical shell of constant thickness.Here,we present alternative forward formulae that account for an arbitrarily high maximum degree of the inducing field and for a magnetic lithosphere of variable thickness.Our simulations based on these formulae suggest that the satellite magnetic anomaly field is sensitive to the non-axial dipolar terms of the inducing field but not to its radial variation.Therefore,in forward and inverse calculations of satellite magnetic anomaly data,the non-axial dipolar terms of the inducing field should not be ignored.Furthermore,our results show that the satellite magnetic anomaly field is sensitive to variability in the lateral thickness of the magnetized shell.In particular,we show that for a given vertically integrated susceptibility distribution,underestimating the thickness of the magnetic layer overestimates the induced magnetic field.This discovery bridges the greatest part of the alleged gap between the susceptibility values measured from rock samples and the susceptibility values required to match the observed magnetic field signal.We expect the formulae and conclusions of this study to be a valuable tool for the quantitative interpretation of the Earth's global lithospheric magnetic field,through an inverse or forward modelling approach.
基金supported by the National Natural Science Foundation of China(Grant Nos.42250103 and 42174090)the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(Grant No.GLAB2023ZR02)the MOST Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources(Grant No.MSFGPMR2022-4).
文摘The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.However,the inversion for the ES model suffers from nonuniqueness and instability,which remain unresolved.To mitigate these issues,we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method.We first present the methods,then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data.The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region.Finally,we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1(CSES-1)and Macao Science Satellite-1(MSS-1)magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field.Compared with existing global lithospheric magnetic field models,our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes.Furthermore,we derive the reduction to the pole(RTP)magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model.The latter correlates well with the regional tectonic framework in Africa and surroundings.
基金supported by the Basic Science Center Project of the National Natural Science Foundation of China(42388102)the National Natural Science Foundation of China(42174030)+2 种基金the Special Fund of Hubei Luojia Laboratory(220100020)the Major Science and Technology Program for Hubei Province(2022AAA002)the Fundamental Research Funds for the Central Universities of China(2042022dx0001 and 2042023kfyq01)。
文摘Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including atmospheric, hydrological, and nontidal ocean loading. Continuous improvements in the accuracy of surface mass loading products, performance of Earth models, and precise data-processing technologies have significantly advanced research on the effects of environmental loading on nonlinear variations in GNSS coordinate time series. However, owing to theoretical limitations, the lack of high spatiotemporal resolution surface mass observations, and the coupling of GNSS technology-related systematic errors, environmental loading and nonlinear GNSS reference station displacements remain inconsistent. The applicability and capability of these loading products across different regions also require further evaluation. This paper outlines methods for modeling environmental loading, surface mass loading products, and service organizations. In addition, it summarizes recent advances in applying environmental loading to address nonlinear variations in global and regional GNSS coordinate time series. Moreover, the scientific questions of existing studies are summarized, and insights into future research directions are provided. The complex nonlinear motion of reference stations is a major factor limiting the accuracy of the current terrestrial reference frame. Further refining the environmental load modeling method, establishing a surface mass distribution model with high spatiotemporal resolution and reliability, exploring other environmental load factors such as ice sheet and artificial mass-change effects, and developing an optimal data-processing model and strategy for reprocessing global reference station data consistently could contribute to the development of a millimeter-level nonlinear motion model for GNSS reference stations with actual physical significance and provide theoretical support for establishing a terrestrial reference frame with 1 mm accuracy by 2050.
基金supported by the National Natural Science Foundation of China(Grant Nos.42250103,42174090,42250101,42250102,and 41774091)the Macao Foundation+1 种基金the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(Grant No.GLAB2023ZR02)the MOST Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources(Grant No.MSFGPMR2022-4)。
文摘The CUG_CLMFM3D series comprises high-resolution three-dimensional lithospheric magnetic field models for China and its surroundings.The first version,CUG_CLMFM3Dv1,is a spherical cap harmonic model integrating the WDMAMv2(World Digital Magnetic Anomaly Map version 2)global magnetic anomaly grid and nearly a decade of CHAMP(Challenging Minisatellite Payload for Geophysical Research and Application)satellite vector data.It achieves a~5.7 km resolution but has limitations:the WDMAMv2 grid lacks high-resolution data in the southern Xinjiang and Tibet regions,which leads to missing small-to medium-scale anomalies,and unfiltered CHAMP data introduce low-frequency conflicts with global spherical harmonic models.Above the altitude of 150 km,correlations with global models drop below 0.9.The second version,CUG_CLMFM3Dv2,addresses these issues by incorporating 5-km-resolution aeromagnetic data and rigorously processed satellite data from CHAMP,Swarm,CSES-1(China Seismo-Electromagnetic Satellite 1),and MSS-1(Macao Science Satellite 1).The comparison analysis shows that the CUG_CLMFM3Dv2 captures finer high-frequency details and more stable long-wavelength signals,offering improved magnetic anomaly maps for further geological and geophysical studies.
