Recently unstructured dense point sets have become a new representation of geometric shapes. In this paper we introduce a novel framework within which several usable error metrics are analyzed and the most basic prope...Recently unstructured dense point sets have become a new representation of geometric shapes. In this paper we introduce a novel framework within which several usable error metrics are analyzed and the most basic properties of the pro- gressive point-sampled geometry are characterized. Another distinct feature of the proposed framework is its compatibility with most previously proposed surface inference engines. Given the proposed framework, the performances of four representative well-reputed engines are studied and compared.展开更多
We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection(LOP) operator.Our algorithm includes two new developments.First,a weight term related to s...We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection(LOP) operator.Our algorithm includes two new developments.First,a weight term related to surface variation at each point is introduced to the classic LOP operator.It produces output points with a spatially adaptive distribution.Second,for speeding up the convergence of our method,an initialization process is proposed based on geometry-aware stochastic sampling.Owing to the initialization,the relaxation process achieves a faster convergence rate than those initialized by uniform sampling.Our simplification method possesses a number of distinguishing features.In particular,it provides resilience to noise and outliers,and an intuitively controllable distribution of simplification.Finally,we show the results of our approach with publicly available point cloud data,and compare the results with those obtained using previous methods.Our method outperforms these methods on raw scanned data.展开更多
The shallow slip deficit(SSD)during strike-slip earthquakes raises a question of how the strain budget is accommodated over multiple cycles.However,the origin of variable SSD observed in different earthquakes is still...The shallow slip deficit(SSD)during strike-slip earthquakes raises a question of how the strain budget is accommodated over multiple cycles.However,the origin of variable SSD observed in different earthquakes is still under debate because each earthquake has its unique initial stress condition.Here,we derive the slip model of the 2021 M W 7.4 Maduo earthquake in Qinghai,China,using multi-track radar images.Our results revealed that,in contrast to the large SSD on segments close to the epicenter,a much smaller SSD was observed at the west terminus of the rupture,where aftershock distribution indicates that the fault changes dip direction at 6 km depth.The 2021 Maduo earthquake thus represents an extraordinary case of significant along-strike SSD variation.After accounting for interseismic,postseismic,and diffuse off-fault deformation,we find that this variation is likely contributed by the along-dipping geometrical variation,implying that a multi-segment earthquake may leave heterogeneous stress condition on the fault with different amounts of SSD.展开更多
The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor...The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor(QGT),another important concept in the field of quantum geometry.The DWZC is Hermitian with respect to the two integer indices,just like the original Hermitian WZC.Based on the symmetric logarithmic derivative operator,we propose a mixed-state quantum geometric tensor.Using the symmetric properties of the DWZC,we find that the real part of the QGT is connected to the real part of the DWZC and the square of eigenvalue differences of the density matrix,whereas the imaginary part can be given in terms of the imaginary part of the DWZC and the cube of the eigenvalue differences.For density matrices with full rank or no full rank,the QGT can be given in terms of real and imaginary parts of the DWZC.展开更多
The calculation of viewing and solar geometry angles is a critical first step in retrieving atmospheric and surface variables from geostationary satellite observations.Whereas the viewing angles for geostationary sate...The calculation of viewing and solar geometry angles is a critical first step in retrieving atmospheric and surface variables from geostationary satellite observations.Whereas the viewing angles for geostationary satellites are not timevarying,a primary source of inaccuracy in solar positioning is the use of a single timestamp.Since pixel scanning times can differ significantly across the field-of-view disk(e.g.,by approximately 13 min for Fengyun-4B),this practice leads to errors of up to±2°in solar zenith angle,which translates to±50 W m^(−2) in extraterrestrial irradiance;the errors in solar azimuth angle can exceed±100°.Beyond scanning time,this work also quantifies the impact of other inputs—including altitude,surface pressure,air temperature,difference between Terrestrial Time and Universal Time,and atmospheric refraction—on the resulting angles.A comparison of our precise calculations with the official National Satellite Meteorological Center L1_GEO product shows an accuracy within 0.1°,confirming its utility for most retrieval tasks.To facilitate higher precision when required,this work releases the corresponding satellite and solar positioning codes in both R and Python.展开更多
A non-local denoising (NLD) algorithm for point-sampled surfaces (PSSs) is presented based on similarities, including geometry intensity and features of sample points. By using the trilateral filtering operator, the d...A non-local denoising (NLD) algorithm for point-sampled surfaces (PSSs) is presented based on similarities, including geometry intensity and features of sample points. By using the trilateral filtering operator, the differential signal of each sample point is determined and called "geometry intensity". Based on covariance analysis, a regular grid of geometry intensity of a sample point is constructed, and the geometry-intensity similarity of two points is measured according to their grids. Based on mean shift clustering, the PSSs are clustered in terms of the local geometry-features similarity. The smoothed geometry intensity, i.e., offset distance, of the sample point is estimated according to the two similarities. Using the resulting intensity, the noise component from PSSs is finally removed by adjusting the position of each sample point along its own normal direction. Ex- perimental results demonstrate that the algorithm is robust and can produce a more accurate denoising result while having better feature preservation.展开更多
This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New ...This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New Geometric Theory of Phyllotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci λ-Goniometry (λ > 0 is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-the “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—the “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.展开更多
Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geomet...Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geometry.In modem scientific literature often write from a firm that"there is no strict definition of fractals",to the more moderate that"objects in a certain sense,fractal and similar."We show that fractal geometry is a strict mathematical theory,defined by their axioms.This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials.Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension,geometri-cal interpretation of fractal derivative gain and open dual symmetry.展开更多
The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fed...The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.展开更多
To overcome the limitations of low efficiency and reliance on manual processes in the measurement of geometric parameters for bridge prefabricated components,a method based on deep learning and computer vision is deve...To overcome the limitations of low efficiency and reliance on manual processes in the measurement of geometric parameters for bridge prefabricated components,a method based on deep learning and computer vision is developed to identify the geometric parameters.The study utilizes a common precast element for highway bridges as the research subject.First,edge feature points of the bridge component section are extracted from images of the precast component cross-sections by combining the Canny operator with mathematical morphology.Subsequently,a deep learning model is developed to identify the geometric parameters of the precast components using the extracted edge coordinates from the images as input and the predefined control parameters of the bridge section as output.A dataset is generated by varying the control parameters and noise levels for model training.Finally,field measurements are conducted to validate the accuracy of the developed method.The results indicate that the developed method effectively identifies the geometric parameters of bridge precast components,with an error rate maintained within 5%.展开更多
The Taishan Antineutrino Observatory(TAO)is a satellite experiment of the Jiangmen Underground Neutrino Observatory,located near the Taishan nuclear power plant(NPP).The TAO aims to measure the energy spectrum of reac...The Taishan Antineutrino Observatory(TAO)is a satellite experiment of the Jiangmen Underground Neutrino Observatory,located near the Taishan nuclear power plant(NPP).The TAO aims to measure the energy spectrum of reactor antineutrinos with unprecedented precision,which would benefit both reactor neutrino physics and the nuclear database.A detector geometry and event visualization system was developed for the TAO.The software was based on ROOT packages and embedded in the TAO offline software framework.This provided an intuitive tool for visualizing the detector geometry,tuning the reconstruction algorithm,understanding neutrino physics,and monitoring the operation of reactors at NPP.Further applications of the visualization system in the experimental operation of TAO and its future development are discussed.展开更多
The fracture surfaces of coal-rock masses formed under mining-induced stress generally exhibit complex geometries, and the fracture geometry is one of the primary factors affecting the seepage characteristics of coal-...The fracture surfaces of coal-rock masses formed under mining-induced stress generally exhibit complex geometries, and the fracture geometry is one of the primary factors affecting the seepage characteristics of coal-rock penetrating fracture. This paper investigates the seepage characteristics of 5 groups of coal penetrating fracture(CPF) with different joint roughness coefficients(JRCs). Based on 3D morphology scanner tests and hydraulic coupling tests, a characterization method of effective geometric parameters in fracture surfaces under various confining pressures was improved, and a relationship between effective geometric parameters and the confining pressure is established. The results indicate that the nonlinear flow behavior in a CPF primarily includes three types: non-Newtonian fluid seepage under high confining pressure and low JRC, non-Darcy seepage under low confining pressure and high JRC, and the whole process of seepage characteristics between these two conditions. Among them, nonNewtonian fluid seepage is caused by significant fracture expansion, while non-Darcy seepage can be attributed to turbulence effects. During the seepage process, the geometric parameters with different JRC fracture samples all exhibit exponential changes with the increase of confining pressure. In addition,under high confining pressure, the effective contact ratio, effective fracture aperture, and void deviation ratio with high JRC fracture samples under high confining pressure increase by 93.5%, 67.4%, and 24.9%,respectively, compared with those of low JRC fracture samples. According to the variation of geometric parameters in a CPF with external stress, a seepage model considering geometric parameters in a CPF is proposed. By introducing the root mean square error(RMSE) and coefficient of determination(R2) to evaluate the error and goodness of fit between model curves and experimental data, it is found that the theoretical curves of model in this paper have the best matching with the experimental data. The average values of RMSE and R2for model in this paper are 0.002 and 0.70, respectively, which are better than models in the existing literature.展开更多
Soft electronics,which are designed to function under mechanical deformation(such as bending,stretching,and folding),have become essential in applications like wearable electronics,artificial skin,and brain-machine in...Soft electronics,which are designed to function under mechanical deformation(such as bending,stretching,and folding),have become essential in applications like wearable electronics,artificial skin,and brain-machine interfaces.Crystalline silicon is one of the most mature and reliable materials for high-performance electronics;however,its intrinsic brittleness and rigidity pose challenges for integrating it into soft electronics.Recent research has focused on overcoming these limitations by utilizing structural design techniques to impart flexibility and stretchability to Si-based materials,such as transforming them into thin nanomembranes or nanowires.This review summarizes key strategies in geometry engineering for integrating crystalline silicon into soft electronics,from the use of hard silicon islands to creating out-of-plane foldable silicon nanofilms on flexible substrates,and ultimately to shaping silicon nanowires using vapor-liquid-solid or in-plane solid-liquid-solid techniques.We explore the latest developments in Si-based soft electronic devices,with applications in sensors,nanoprobes,robotics,and brain-machine interfaces.Finally,the paper discusses the current challenges in the field and outlines future research directions to enable the widespread adoption of silicon-based flexible electronics.展开更多
This paper delves into the visual teaching of analytic geometry facilitated by GeoGebra software.Through a meticulous analysis of the current landscape of analytic geometry instruction and the distinct advantages of G...This paper delves into the visual teaching of analytic geometry facilitated by GeoGebra software.Through a meticulous analysis of the current landscape of analytic geometry instruction and the distinct advantages of GeoGebra software,it expounds upon the imperative and feasibility of its application within the realm of analytic geometry teaching.Furthermore,it presents a detailed account of the teaching practice process grounded in this software,encompassing teaching design and the demonstration of teaching cases,and conducts an in-depth investigation and analysis of the teaching outcomes.The research findings indicate that the GeoGebra software can effectively elevate the level of visualization in analytic geometry teaching,thereby augmenting students’learning enthusiasm and comprehension capabilities.It thus offers novel perspectives and methodologies for the pedagogical reform of analytic geometry.展开更多
We have developed a class of charged,anisotropic,and spherically symmetric solutions,described by the function f(R,A)=R+a A,where R represents the Ricci scalar,A is the anticurvature scalar,andαis the coupling consta...We have developed a class of charged,anisotropic,and spherically symmetric solutions,described by the function f(R,A)=R+a A,where R represents the Ricci scalar,A is the anticurvature scalar,andαis the coupling constant.The model was constructed using the Karmarkar condition to obtain the radial metric component,while the time metric component followed the approach proposed by Adler.We assumed a specific charge distribution inside the star to build the model.To ensure a smooth spacetime transition,we established boundary conditions,considering Bardeen?s solution for the exterior spacetime.Additionally,we examined various physical aspects,such as energy density,pressure components,pressure anisotropy,energy conditions,the equation of state,surface redshift,compactness factor,adiabatic index,sound speed,and the Tolman-Oppenheimer-Volkoff equilibrium condition.All these conditions were met,demonstrating that the solutions we obtained are physically viable.展开更多
Fatigue failure continues to be a significant challenge in designing structural and mechanical components subjected to repeated and complex loading.While earlier studies mainly examined material properties and how str...Fatigue failure continues to be a significant challenge in designing structural and mechanical components subjected to repeated and complex loading.While earlier studies mainly examined material properties and how stress affects lifespan,this review offers the first comprehensive,multiscale comparison of strategies that optimize geometry to improve fatigue performance.This includes everything from microscopic features like the shape of graphite nodules to large-scale design elements such as fillets,notches,and overall structural layouts.We analyze and combine various methods,including topology and shape optimization,the ability of additive manufacturing to finetune internal geometries,and reliability-based design approaches.A key new contribution is our proposal of a standard way to evaluate geometry-focused fatigue design,allowing for consistent comparison and encouraging validation across different fields.Furthermore,we highlight important areas for future research,such as incorporating manufacturing flaws,using multiscale models,and integrating machine learning techniques.This work is the first to provide a broad geometric viewpoint in fatigue engineering,laying the groundwork for future design methods that are driven by data and centered on reliability.展开更多
In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional tran...In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional transverse integrated equations using the transverse integration procedure over 3D hexagonal geometry and denoted the solutions as a nodal Green's functions under the Neumann boundary condition.By applying a quadratic polynomial expansion of the transverse-averaged quantities,we derived the net neutron current coupling equation,equation for the expansion coefficients of the transverse-averaged neutron flux,and formulas for the coefficient matrix of these equations.We formulated the closed system of equations in correspondence with the boundary conditions.The proposed model was tested by comparing it with the benchmark for the VVER-440 reactor,and the numerical results were in good agreement with the reference solutions.展开更多
The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a ...The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a six-dimensional search is huge.To solve this problem,the differential-geometry-based Multi-dimensional Joint Position-Velocity Estimation(MJPVE)using Crab pulsar profile distortion is proposed in this paper.Firstly,through theoretical analysis,it is found that the pulsar profile distortion caused by the initial state error in some joint positionvelocity directions is very small.In other words,the accuracies of estimation in these directions are very low.Namely,the search dimension can be reduced,which in turn greatly reduces the computational load.Then,we construct the chi-squared function of the pulsar profile with respect to the estimation error in joint position-velocity direction and use differential geometry to find the joint position-velocity directions corresponding to different degrees of distortion.Finally,we utilize the grid search based on directory folding in these joint position-velocity directions corresponding to large degrees of distortion to obtain the joint position-velocity estimation.The experimental results show that compared with the grouping bi-chi-squared inversion method,MJPVE has high precision and extensive navigation information.展开更多
Fluid imbibition from hydraulic fractures into shale formations is mainly affected by a combination of capillary forces and viscous resistance,both of which are closely related to the pore geometry.This study establis...Fluid imbibition from hydraulic fractures into shale formations is mainly affected by a combination of capillary forces and viscous resistance,both of which are closely related to the pore geometry.This study established five self-imbibition models with idealized pore structures and conducted a comparative analysis of these models.These models include circular,square,and equilateral triangular capillaries;a triangular star-shaped cross-section formed by three tangent spherical particles;and a traditional porous medium representation method.All these models are derived based on Newton’s second law,where capillary pressure is described by the Young-Laplace equation and viscous resistance is characterized by the Hagen-Poiret equation and Darcy’s law.All derived models predict that the fluid imbibition distance is proportional to the square root of time,in accordance with the classical Lucas-Washburn law.However,different pore structures exhibit significantly different characteristic imbibition rates.Compared to the single pore model,the conventional Darcy’s law-based model for porous media predicts significantly lower imbibition rates,which is consistent with the relatively slower uptake rates in actual shale nanoscale pore networks.These findings emphasize the important role played by pore geometry in fluid imbibition dynamics and further point to the need for optimizing pore structure to extend fluid imbibition duration in shale reservoirs in practical operations.展开更多
Reasonable field acquisition geometry can not only guide seismic exploration to obtain sufficient geological information of target body,but also reduce acquisition cost to the maximum.In this study,building on convent...Reasonable field acquisition geometry can not only guide seismic exploration to obtain sufficient geological information of target body,but also reduce acquisition cost to the maximum.In this study,building on conventional ray-based geometry design methods,we incorporate imaging results as a constraint to optimize the geometry design and evaluate its effectiveness.Firstly,the geological model of the target layer is established based on the geological data of the study area and surface seismic data combined with exploration tasks.Then,the ray-tracing method is employed to simulate and assess the proposed geometry design,verifying whether its parameters meet the exploration requirements.Finally,the imaging effect of the designed geometry on the target layer is tested by the cross-well seismic reverse time migration method.This methodology was applied to design the cross-well seismic acquisition geometry for offshore deviated wells in the X Oilfield.The simulation results demonstrate that the imaging-driven geometry design approach effectively guides field operations,enhances the imaging quality of the target layer,and reduces acquisition costs.展开更多
文摘Recently unstructured dense point sets have become a new representation of geometric shapes. In this paper we introduce a novel framework within which several usable error metrics are analyzed and the most basic properties of the pro- gressive point-sampled geometry are characterized. Another distinct feature of the proposed framework is its compatibility with most previously proposed surface inference engines. Given the proposed framework, the performances of four representative well-reputed engines are studied and compared.
基金Project (Nos. 60673006 and U0935004) supported by the National Natural Science Foundation of Chinaan INBRE grant from NIH,USA (No. 5P20RR01647206)
文摘We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection(LOP) operator.Our algorithm includes two new developments.First,a weight term related to surface variation at each point is introduced to the classic LOP operator.It produces output points with a spatially adaptive distribution.Second,for speeding up the convergence of our method,an initialization process is proposed based on geometry-aware stochastic sampling.Owing to the initialization,the relaxation process achieves a faster convergence rate than those initialized by uniform sampling.Our simplification method possesses a number of distinguishing features.In particular,it provides resilience to noise and outliers,and an intuitively controllable distribution of simplification.Finally,we show the results of our approach with publicly available point cloud data,and compare the results with those obtained using previous methods.Our method outperforms these methods on raw scanned data.
基金the Deep Earth Probe and Mineral Resources Exploration-National Science and Technology Major Project under Grant 2024ZD1000500。
文摘The shallow slip deficit(SSD)during strike-slip earthquakes raises a question of how the strain budget is accommodated over multiple cycles.However,the origin of variable SSD observed in different earthquakes is still under debate because each earthquake has its unique initial stress condition.Here,we derive the slip model of the 2021 M W 7.4 Maduo earthquake in Qinghai,China,using multi-track radar images.Our results revealed that,in contrast to the large SSD on segments close to the epicenter,a much smaller SSD was observed at the west terminus of the rupture,where aftershock distribution indicates that the fault changes dip direction at 6 km depth.The 2021 Maduo earthquake thus represents an extraordinary case of significant along-strike SSD variation.After accounting for interseismic,postseismic,and diffuse off-fault deformation,we find that this variation is likely contributed by the along-dipping geometrical variation,implying that a multi-segment earthquake may leave heterogeneous stress condition on the fault with different amounts of SSD.
基金Project supported by Quantum Science and Technology–National Science and Technology Major Project(Grant No.2024ZD0301000)the National Natural Science Foundation of China(Grant No.12305031)+1 种基金the Hangzhou Joint Fund of the Natural Science Foundation of Zhejiang Province,China(Grant No.LHZSD24A050001)the Science Foundation of Zhejiang Sci-Tech University(Grant Nos.23062088Y and 23062153-Y)。
文摘The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor(QGT),another important concept in the field of quantum geometry.The DWZC is Hermitian with respect to the two integer indices,just like the original Hermitian WZC.Based on the symmetric logarithmic derivative operator,we propose a mixed-state quantum geometric tensor.Using the symmetric properties of the DWZC,we find that the real part of the QGT is connected to the real part of the DWZC and the square of eigenvalue differences of the density matrix,whereas the imaginary part can be given in terms of the imaginary part of the DWZC and the cube of the eigenvalue differences.For density matrices with full rank or no full rank,the QGT can be given in terms of real and imaginary parts of the DWZC.
基金supported by the National Natural Science Foundation of China(Grant No.42375192).
文摘The calculation of viewing and solar geometry angles is a critical first step in retrieving atmospheric and surface variables from geostationary satellite observations.Whereas the viewing angles for geostationary satellites are not timevarying,a primary source of inaccuracy in solar positioning is the use of a single timestamp.Since pixel scanning times can differ significantly across the field-of-view disk(e.g.,by approximately 13 min for Fengyun-4B),this practice leads to errors of up to±2°in solar zenith angle,which translates to±50 W m^(−2) in extraterrestrial irradiance;the errors in solar azimuth angle can exceed±100°.Beyond scanning time,this work also quantifies the impact of other inputs—including altitude,surface pressure,air temperature,difference between Terrestrial Time and Universal Time,and atmospheric refraction—on the resulting angles.A comparison of our precise calculations with the official National Satellite Meteorological Center L1_GEO product shows an accuracy within 0.1°,confirming its utility for most retrieval tasks.To facilitate higher precision when required,this work releases the corresponding satellite and solar positioning codes in both R and Python.
基金the Hi-Tech Research and Development Pro-gram (863) of China (Nos. 2007AA01Z311 and 2007AA04Z1A5)the Research Fund for the Doctoral Program of Higher Education of China (No. 20060335114)
文摘A non-local denoising (NLD) algorithm for point-sampled surfaces (PSSs) is presented based on similarities, including geometry intensity and features of sample points. By using the trilateral filtering operator, the differential signal of each sample point is determined and called "geometry intensity". Based on covariance analysis, a regular grid of geometry intensity of a sample point is constructed, and the geometry-intensity similarity of two points is measured according to their grids. Based on mean shift clustering, the PSSs are clustered in terms of the local geometry-features similarity. The smoothed geometry intensity, i.e., offset distance, of the sample point is estimated according to the two similarities. Using the resulting intensity, the noise component from PSSs is finally removed by adjusting the position of each sample point along its own normal direction. Ex- perimental results demonstrate that the algorithm is robust and can produce a more accurate denoising result while having better feature preservation.
文摘This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New Geometric Theory of Phyllotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci λ-Goniometry (λ > 0 is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-the “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—the “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.
文摘Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geometry.In modem scientific literature often write from a firm that"there is no strict definition of fractals",to the more moderate that"objects in a certain sense,fractal and similar."We show that fractal geometry is a strict mathematical theory,defined by their axioms.This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials.Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension,geometri-cal interpretation of fractal derivative gain and open dual symmetry.
文摘The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.
基金The National Natural Science Foundation of China(No.52338011,52378291)Young Elite Scientists Sponsorship Program by CAST(No.2022-2024QNRC0101).
文摘To overcome the limitations of low efficiency and reliance on manual processes in the measurement of geometric parameters for bridge prefabricated components,a method based on deep learning and computer vision is developed to identify the geometric parameters.The study utilizes a common precast element for highway bridges as the research subject.First,edge feature points of the bridge component section are extracted from images of the precast component cross-sections by combining the Canny operator with mathematical morphology.Subsequently,a deep learning model is developed to identify the geometric parameters of the precast components using the extracted edge coordinates from the images as input and the predefined control parameters of the bridge section as output.A dataset is generated by varying the control parameters and noise levels for model training.Finally,field measurements are conducted to validate the accuracy of the developed method.The results indicate that the developed method effectively identifies the geometric parameters of bridge precast components,with an error rate maintained within 5%.
基金supported by the National Natural Science Foundation of China(Nos.12175321,11975021,and 11675275)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDA10010900)。
文摘The Taishan Antineutrino Observatory(TAO)is a satellite experiment of the Jiangmen Underground Neutrino Observatory,located near the Taishan nuclear power plant(NPP).The TAO aims to measure the energy spectrum of reactor antineutrinos with unprecedented precision,which would benefit both reactor neutrino physics and the nuclear database.A detector geometry and event visualization system was developed for the TAO.The software was based on ROOT packages and embedded in the TAO offline software framework.This provided an intuitive tool for visualizing the detector geometry,tuning the reconstruction algorithm,understanding neutrino physics,and monitoring the operation of reactors at NPP.Further applications of the visualization system in the experimental operation of TAO and its future development are discussed.
基金supported by the National Natural Science Foundation of China (Nos. 52474161, and 52404093)Fundamental Research Program of Shanxi Province (Nos. 202303021222168 and 202203021221143)+1 种基金Taiyuan University of Science and Technology Scientific Research Initial Funding (No. 20242103)the Postdoctoral Research Foundation of China(No. 2023M733778)。
文摘The fracture surfaces of coal-rock masses formed under mining-induced stress generally exhibit complex geometries, and the fracture geometry is one of the primary factors affecting the seepage characteristics of coal-rock penetrating fracture. This paper investigates the seepage characteristics of 5 groups of coal penetrating fracture(CPF) with different joint roughness coefficients(JRCs). Based on 3D morphology scanner tests and hydraulic coupling tests, a characterization method of effective geometric parameters in fracture surfaces under various confining pressures was improved, and a relationship between effective geometric parameters and the confining pressure is established. The results indicate that the nonlinear flow behavior in a CPF primarily includes three types: non-Newtonian fluid seepage under high confining pressure and low JRC, non-Darcy seepage under low confining pressure and high JRC, and the whole process of seepage characteristics between these two conditions. Among them, nonNewtonian fluid seepage is caused by significant fracture expansion, while non-Darcy seepage can be attributed to turbulence effects. During the seepage process, the geometric parameters with different JRC fracture samples all exhibit exponential changes with the increase of confining pressure. In addition,under high confining pressure, the effective contact ratio, effective fracture aperture, and void deviation ratio with high JRC fracture samples under high confining pressure increase by 93.5%, 67.4%, and 24.9%,respectively, compared with those of low JRC fracture samples. According to the variation of geometric parameters in a CPF with external stress, a seepage model considering geometric parameters in a CPF is proposed. By introducing the root mean square error(RMSE) and coefficient of determination(R2) to evaluate the error and goodness of fit between model curves and experimental data, it is found that the theoretical curves of model in this paper have the best matching with the experimental data. The average values of RMSE and R2for model in this paper are 0.002 and 0.70, respectively, which are better than models in the existing literature.
基金the National Natural Science Foundation of China under granted No.62104100National Key Research Program of China under No.92164201+1 种基金National Natural Science Foundation of China for Distinguished Young Scholars under No.62325403National Natural Science Foundation of China under No.61934004.
文摘Soft electronics,which are designed to function under mechanical deformation(such as bending,stretching,and folding),have become essential in applications like wearable electronics,artificial skin,and brain-machine interfaces.Crystalline silicon is one of the most mature and reliable materials for high-performance electronics;however,its intrinsic brittleness and rigidity pose challenges for integrating it into soft electronics.Recent research has focused on overcoming these limitations by utilizing structural design techniques to impart flexibility and stretchability to Si-based materials,such as transforming them into thin nanomembranes or nanowires.This review summarizes key strategies in geometry engineering for integrating crystalline silicon into soft electronics,from the use of hard silicon islands to creating out-of-plane foldable silicon nanofilms on flexible substrates,and ultimately to shaping silicon nanowires using vapor-liquid-solid or in-plane solid-liquid-solid techniques.We explore the latest developments in Si-based soft electronic devices,with applications in sensors,nanoprobes,robotics,and brain-machine interfaces.Finally,the paper discusses the current challenges in the field and outlines future research directions to enable the widespread adoption of silicon-based flexible electronics.
基金The 2024 Undergraduate Education Teaching Research and Reform Project of Colleges and Universities in the Autonomous Region“Construction of School-based Digital Resources for Ideological and Political Education in the Course of Analytic Geometry”(XJGXJGPTB-2024104)。
文摘This paper delves into the visual teaching of analytic geometry facilitated by GeoGebra software.Through a meticulous analysis of the current landscape of analytic geometry instruction and the distinct advantages of GeoGebra software,it expounds upon the imperative and feasibility of its application within the realm of analytic geometry teaching.Furthermore,it presents a detailed account of the teaching practice process grounded in this software,encompassing teaching design and the demonstration of teaching cases,and conducts an in-depth investigation and analysis of the teaching outcomes.The research findings indicate that the GeoGebra software can effectively elevate the level of visualization in analytic geometry teaching,thereby augmenting students’learning enthusiasm and comprehension capabilities.It thus offers novel perspectives and methodologies for the pedagogical reform of analytic geometry.
基金Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under Grant No.RGP2/30/45。
文摘We have developed a class of charged,anisotropic,and spherically symmetric solutions,described by the function f(R,A)=R+a A,where R represents the Ricci scalar,A is the anticurvature scalar,andαis the coupling constant.The model was constructed using the Karmarkar condition to obtain the radial metric component,while the time metric component followed the approach proposed by Adler.We assumed a specific charge distribution inside the star to build the model.To ensure a smooth spacetime transition,we established boundary conditions,considering Bardeen?s solution for the exterior spacetime.Additionally,we examined various physical aspects,such as energy density,pressure components,pressure anisotropy,energy conditions,the equation of state,surface redshift,compactness factor,adiabatic index,sound speed,and the Tolman-Oppenheimer-Volkoff equilibrium condition.All these conditions were met,demonstrating that the solutions we obtained are physically viable.
文摘Fatigue failure continues to be a significant challenge in designing structural and mechanical components subjected to repeated and complex loading.While earlier studies mainly examined material properties and how stress affects lifespan,this review offers the first comprehensive,multiscale comparison of strategies that optimize geometry to improve fatigue performance.This includes everything from microscopic features like the shape of graphite nodules to large-scale design elements such as fillets,notches,and overall structural layouts.We analyze and combine various methods,including topology and shape optimization,the ability of additive manufacturing to finetune internal geometries,and reliability-based design approaches.A key new contribution is our proposal of a standard way to evaluate geometry-focused fatigue design,allowing for consistent comparison and encouraging validation across different fields.Furthermore,we highlight important areas for future research,such as incorporating manufacturing flaws,using multiscale models,and integrating machine learning techniques.This work is the first to provide a broad geometric viewpoint in fatigue engineering,laying the groundwork for future design methods that are driven by data and centered on reliability.
文摘In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional transverse integrated equations using the transverse integration procedure over 3D hexagonal geometry and denoted the solutions as a nodal Green's functions under the Neumann boundary condition.By applying a quadratic polynomial expansion of the transverse-averaged quantities,we derived the net neutron current coupling equation,equation for the expansion coefficients of the transverse-averaged neutron flux,and formulas for the coefficient matrix of these equations.We formulated the closed system of equations in correspondence with the boundary conditions.The proposed model was tested by comparing it with the benchmark for the VVER-440 reactor,and the numerical results were in good agreement with the reference solutions.
基金supported in part by the National Natural Science Foundation of China(Nos.61873196,62373030,61772187)the Innovation Program for Quantum Science and Technology(No.2021ZD0303400)。
文摘The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a six-dimensional search is huge.To solve this problem,the differential-geometry-based Multi-dimensional Joint Position-Velocity Estimation(MJPVE)using Crab pulsar profile distortion is proposed in this paper.Firstly,through theoretical analysis,it is found that the pulsar profile distortion caused by the initial state error in some joint positionvelocity directions is very small.In other words,the accuracies of estimation in these directions are very low.Namely,the search dimension can be reduced,which in turn greatly reduces the computational load.Then,we construct the chi-squared function of the pulsar profile with respect to the estimation error in joint position-velocity direction and use differential geometry to find the joint position-velocity directions corresponding to different degrees of distortion.Finally,we utilize the grid search based on directory folding in these joint position-velocity directions corresponding to large degrees of distortion to obtain the joint position-velocity estimation.The experimental results show that compared with the grouping bi-chi-squared inversion method,MJPVE has high precision and extensive navigation information.
文摘Fluid imbibition from hydraulic fractures into shale formations is mainly affected by a combination of capillary forces and viscous resistance,both of which are closely related to the pore geometry.This study established five self-imbibition models with idealized pore structures and conducted a comparative analysis of these models.These models include circular,square,and equilateral triangular capillaries;a triangular star-shaped cross-section formed by three tangent spherical particles;and a traditional porous medium representation method.All these models are derived based on Newton’s second law,where capillary pressure is described by the Young-Laplace equation and viscous resistance is characterized by the Hagen-Poiret equation and Darcy’s law.All derived models predict that the fluid imbibition distance is proportional to the square root of time,in accordance with the classical Lucas-Washburn law.However,different pore structures exhibit significantly different characteristic imbibition rates.Compared to the single pore model,the conventional Darcy’s law-based model for porous media predicts significantly lower imbibition rates,which is consistent with the relatively slower uptake rates in actual shale nanoscale pore networks.These findings emphasize the important role played by pore geometry in fluid imbibition dynamics and further point to the need for optimizing pore structure to extend fluid imbibition duration in shale reservoirs in practical operations.
基金funded by the Young Scientists Fund of the National Natural Science Foundation of China(42304135)the scientific research project of Gansu Coal Geology Bureau(2023-07).
文摘Reasonable field acquisition geometry can not only guide seismic exploration to obtain sufficient geological information of target body,but also reduce acquisition cost to the maximum.In this study,building on conventional ray-based geometry design methods,we incorporate imaging results as a constraint to optimize the geometry design and evaluate its effectiveness.Firstly,the geological model of the target layer is established based on the geological data of the study area and surface seismic data combined with exploration tasks.Then,the ray-tracing method is employed to simulate and assess the proposed geometry design,verifying whether its parameters meet the exploration requirements.Finally,the imaging effect of the designed geometry on the target layer is tested by the cross-well seismic reverse time migration method.This methodology was applied to design the cross-well seismic acquisition geometry for offshore deviated wells in the X Oilfield.The simulation results demonstrate that the imaging-driven geometry design approach effectively guides field operations,enhances the imaging quality of the target layer,and reduces acquisition costs.
