Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine fini...Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.展开更多
Precast concrete pavements(PCPs)represent an innovative solution in the construction industry,addressing the need for rapid,intelligent,and low-carbon pavement technologies that significantly reduce construction time ...Precast concrete pavements(PCPs)represent an innovative solution in the construction industry,addressing the need for rapid,intelligent,and low-carbon pavement technologies that significantly reduce construction time and environmental impact.However,the integration of prefabricated technology in pavement surface and base layers lacks systematic classification and understanding.This paper aims to fill this gap by introducing a detailed analysis of discretization and assembly connection technology for cement concrete pavement(CCP)structures.Through a comprehensive review of domestic and international literature,the study classifies prefabricated pavement technology based on discrete assembly structural layers and presents specific conclusions(i)surface layer discrete units are categorized into bottom plates,top plates,plate-rod separated assemblies,and prestressed connections,with optimal material compositions identified to enhance mechanical properties;(ii)base layer discrete units include block-type,plate-type,and beam-type elements,highlighting their contributions to sustainability by incorporating recycled materials(iii)planar assembly connection types are assessed,ranking them by load transfer efficiency,with specific dimensions provided for optimal performance;and(iv)vertical assembly connections are defined by their leveling and sealing layers,suitable for both new constructions and repairs of existing roads.The insights gained from this review not only clarify the distinctions between various structural layers but also provide practical guidelines for enhancing the design and implementation of PCP.This work contributes to advancing sustainable and resilient road construction practices,making it a significant reference for researchers and practitioners in the field.展开更多
This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint proble...This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.展开更多
In this paper,we extend the work of Brenner and Sung[Math.Comp.59,321–338(1992)]and present a regularity estimate for the elastic equations in concave domains.Based on the regularity estimate we prove that the consta...In this paper,we extend the work of Brenner and Sung[Math.Comp.59,321–338(1992)]and present a regularity estimate for the elastic equations in concave domains.Based on the regularity estimate we prove that the constants in the error estimates of the nonconforming Crouzeix-Raviart element approximations for the elastic equations/eigenvalue problem are independent of Laméconstant,which means the nonconforming Crouzeix-Raviart element approximations are locking-free.We also establish two kinds of two-grid discretization schemes for the elastic eigenvalue problem,and analyze that when the mesh sizes of coarse grid and fine grid satisfy some relationship,the resulting solutions can achieve the optimal accuracy.Numerical examples are provided to show the efficiency of two-grid schemes for the elastic eigenvalue problem.展开更多
This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou （Math. Comput., 70 （2001）, pp.17-25） to the nonconforming finite elements for eigenvalue problems. In...This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou （Math. Comput., 70 （2001）, pp.17-25） to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is reduced to that on a much coarser mesh together with the solution of a linear algebraic system on the fine mesh. The resulting solution still maintains an asymptotically optimal accuracy. Comparing with the two-grid discretization scheme of the conforming finite elements, the main advantages of our new schemes are twofold when the mesh size is small enough. First, the lower bounds of the exact eigenvalues in our two-grid discretization schemes can be obtained. Second, the first eigenvalue given by the new schemes has much better accuracy than that obtained by solving the eigenvalue problems on the fine mesh directly.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
In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.T...In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.展开更多
In this paper,we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods.We mainly concern the case when pressure coefficients and source terms are nonlinear.To...In this paper,we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods.We mainly concern the case when pressure coefficients and source terms are nonlinear.To linearize the nonlinear mixed equations,we use the two-grid algorithm.We first solve the nonlinear equations on the coarse grid,then,on the fine mesh,we solve a linearized problem using Newton iteration once.It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h 1/2).As a result,solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.展开更多
We introduce CURDIS,a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc.In this template,algorithms proceed by finding the tangent quadra...We introduce CURDIS,a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc.In this template,algorithms proceed by finding the tangent quadrant at each point of the arc and determining which side the curve exits the pixel according to a tailored criterion.These two elements can be adapted for any type of curve,leading to algorithms dedicated to the shape of specific curves.While the calculation of the tangent quadrant for various curves,such as lines,conics,or cubics,is simple,it is more complex to analyze how pixels are traversed by the curve.In the case of conic arcs,we found a criterion for determining the pixel exit side.This leads us to present a new algorithm,called CURDIS-C,specific to the discretization of conics,for which we provide all the details.Surprisingly,the criterion for conics requires between one and three sign tests and four additions per pixel,making the algorithm efficient for resource-constrained systems and feasible for fixed-point or integer arithmetic implementations.Our algorithm also perfectly handles the pathological cases in which the conic intersects a pixel twice or changes quadrants multiple times within this pixel,achieving this generality at the cost of potentially computing up to two square roots per arc.We illustrate the use of CURDIS for the discretization of different curves,such as ellipses,hyperbolas,and parabolas,even when they degenerate into lines or corners.展开更多
Discrete fracture network(DFN)commonly existing in natural rock masses plays an important role in geological complexity which can influence rock fracturing behaviour during fluid injection.This paper simulated the hyd...Discrete fracture network(DFN)commonly existing in natural rock masses plays an important role in geological complexity which can influence rock fracturing behaviour during fluid injection.This paper simulated the hydraulic fracturing process in lab-scale coal samples with DFNs and the induced seismic activities by the discrete element method(DEM).The effects of DFNs on hydraulic fracturing,induced seismicity and elastic property changes have been concluded.Denser DFNs can comprehensively decrease the peak injection pressure and injection duration.The proportion of strong seismic events increases first and then decreases with increasing DFN density.In addition,the relative modulus of the rock mass is derived innovatively from breakdown pressure,breakdown fracture length and the related initiation time.Increasing DFN densities among large(35–60 degrees)and small(0–30 degrees)fracture dip angles show opposite evolution trends in relative modulus.The transitional point(dip angle)for the opposite trends is also proportionally affected by the friction angle of the rock mass.The modelling results have much practical meaning to infer the density and geometry of pre-existing fractures and the elastic property of rock mass in the field,simply based on the hydraulic fracturing and induced seismicity monitoring data.展开更多
With the development of cyber-physical systems,system security faces more risks from cyber-attacks.In this work,we study the problem that an external attacker implements covert sensor and actuator attacks with resourc...With the development of cyber-physical systems,system security faces more risks from cyber-attacks.In this work,we study the problem that an external attacker implements covert sensor and actuator attacks with resource constraints(the total resource consumption of the attacks is not greater than a given initial resource of the attacker)to mislead a discrete event system under supervisory control to reach unsafe states.We consider that the attacker can implement two types of attacks:One by modifying the sensor readings observed by a supervisor and the other by enabling the actuator commands disabled by the supervisor.Each attack has its corresponding resource consumption and remains covert.To solve this problem,we first introduce a notion of combined-attackability to determine whether a closedloop system may reach an unsafe state after receiving attacks with resource constraints.We develop an algorithm to construct a corrupted supervisor under attacks,provide a verification method for combined-attackability in polynomial time based on a plant,a corrupted supervisor,and an attacker's initial resource,and propose a corresponding attack synthesis algorithm.The effectiveness of the proposed method is illustrated by an example.展开更多
Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embe...Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embedding a unique identifier that identifies the owner of the content.Image watermarking can also be used to verify the authenticity of digital media,such as images or videos,by ascertaining the watermark information.In this paper,a mathematical chaos-based image watermarking technique is proposed using discrete wavelet transform(DWT),chaotic map,and Laplacian operator.The DWT can be used to decompose the image into its frequency components,chaos is used to provide extra security defense by encrypting the watermark signal,and the Laplacian operator with optimization is applied to the mid-frequency bands to find the sharp areas in the image.These mid-frequency bands are used to embed the watermarks by modifying the coefficients in these bands.The mid-sub-band maintains the invisible property of the watermark,and chaos combined with the second-order derivative Laplacian is vulnerable to attacks.Comprehensive experiments demonstrate that this approach is effective for common signal processing attacks,i.e.,compression,noise addition,and filtering.Moreover,this approach also maintains image quality through peak signal-to-noise ratio(PSNR)and structural similarity index metrics(SSIM).The highest achieved PSNR and SSIM values are 55.4 dB and 1.In the same way,normalized correlation(NC)values are almost 10%–20%higher than comparative research.These results support assistance in copyright protection in multimedia content.展开更多
Objective This study explored the job choice preferences of Center for Disease Prevention and Control(CDC)workers to provide CDC management information and recommendations for optimizing employee retention and motivat...Objective This study explored the job choice preferences of Center for Disease Prevention and Control(CDC)workers to provide CDC management information and recommendations for optimizing employee retention and motivation policies.Methods A discrete choice experiment was conducted in nine provinces across China.Seven key attributes were identified to analyze the job preferences of CDC workers.Mixed logit models,latent class models,and policy simulation tools were used.Results A valid sample of 5,944 cases was included in the analysis.All seven attributes significantly influenced the job choices of CDC workers.Heterogeneity analyses identified two main groups based on different levels of preference for attribute utility.Income-prioritizers were concerned with income and opportunities for career development,whereas bianzhi-prioritizers were concerned with bianzhi and welfare benefits.The policy simulation analysis revealed that income-prioritizers had a relatively higher sensitivity to multiple job preference incentives.Conclusion Income and bianzhi were the two key attributes influencing the job choices and retention preferences of CDC workers.Heterogeneity in job preferences was also identified.Based on the preference characteristics of different subgroups,policy content should be skewed to differentiate the importance of incentives.展开更多
This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density...This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density of prey species with interval parameters.The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature.The equilibria of the model are obtained,and the dynamic behaviours of the proposed system are examined.Simulations of the model are performed for different parameters of the model.Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.Our study,through analytical derivation and numerical example,presents the effect of refuge on population dynamics under imprecise biological parameters.展开更多
The homogeneity of aggregate blend has a significant influence on the performance of asphalt mixture.The composition of aggregate blend,including the size combination and the mass ratio between each size particles(MRE...The homogeneity of aggregate blend has a significant influence on the performance of asphalt mixture.The composition of aggregate blend,including the size combination and the mass ratio between each size particles(MRESP),is an important factor affecting the homogeneity.This study investigated the influence of the size combination and MRESP on the distribution homogeneity of particles in aggregate blend using discrete element method(DEM).An indicator quantifying the distribution homogeneity was established according to the coefficient of variation(CV)for particle number.Two-size,three-size,and four-size aggregate blends with various compositions were designed.Laboratory tests show the DEM simulation is feasible.The particle distribution homogeneity in various blends was analyzed.The results showed the distribution homogeneity of each size particles in a blend is closely related to their mass fraction.The higher the mass fraction of the particles,the more homogeneous the distribution of them.The MRESP has no significant influence on the homogeneity of the blend composed of only coarse aggregates.However,the homogeneity of the blend composed of coarse and fine aggregates improves gradually with the increase of the mass fraction of fine aggregates.The smaller the maximum particle size in a blend,the better the homogeneity.It is suggested that the mass fraction of fine aggregates should be between 33%and 50%for achieving good homogeneity of aggregate blends.The research results can provide a reference for gradation design of asphalt mixture.展开更多
Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and...Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and their applications.Therefore,in this paper,a new NDM is constructed,and a non-autonomous hyperchaotic map is proposed by connecting this non-autonomous memristor in parallel with an autonomous memristor.This map exhibits complex dynamical behaviors,including infinitely many fixed points,initial-boosted attractors,initial-boosted bifurcations,and the size of the attractors being controlled by the initial value.In addition,a simple pseudo-random number generator(PRNG)was designed using the non-autonomous hyperchaotic map,and the pseudo-random numbers(PRNs)generated by it were tested using the National Institute of Standards and Technology(NIST)SP800-22 test suite.Finally,the non-autonomous hyperchaotic map is implemented on the STM32 hardware experimental platform.展开更多
The mechanical properties of solid oxide fuel cells(SOFCs)can limit their mechanical stability and lifespan.Understanding the correlation between the microstructure and mechanical properties of porous electrode is ess...The mechanical properties of solid oxide fuel cells(SOFCs)can limit their mechanical stability and lifespan.Understanding the correlation between the microstructure and mechanical properties of porous electrode is essential for enhancing the performance and durability of SOFCs.Accurate prediction of mechanical properties of porous electrode can be achieved by microscale finite element modeling based on three-dimensional(3D)microstructures,which requires expensive 3D tomography techniques and massive computational resources.In this study,we proposed a cost-effective alternative approach to access the mechanical properties of porous electrodes,with the elastic properties of La_(0.6)Sr_(0.4)Co_(0.2)Fe_(0.8)O_(3-δc)athode serving as a case study.Firstly,a stochastic modeling was used to reconstruct 3D microstructures from two-dimensional(2D)cross-sections as an alternative to expensive tomography.Then,the discrete element method(DEM)was used to predict the elastic properties of porous ceramics based on the discretized 3D microstructures reconstructed by stochastic modeling.Based on 2D microstructure and the elastic properties calculated by the DEM modeling of the 3D reconstructed porous microstructures,a convolutional neural network(CNN)based deep learning model was built to predict the elastic properties rapidly from 2D microstructures.The proposed combined framework can be implemented with limited computational resources and provide a basis for rapid prediction of mechanical properties and parameter estimation for multiscale modeling of SOFCs.展开更多
Shield tunnel,composed of several segments,is widely used in urban underground engineering.When the tunnel is under load,relative displacement occurs between adjacent segments.In the past,distributed optical fiber sen...Shield tunnel,composed of several segments,is widely used in urban underground engineering.When the tunnel is under load,relative displacement occurs between adjacent segments.In the past,distributed optical fiber sensing technology was used to perform strain monitoring,but there is an urgent need to determine how to transform strain into displacement.In this study,optical frequency domain reflectometry was applied in laboratory tests.Aiming at the shear process and center settlement process of shield tunnel segments,two kinds of quantitative calculation methods were put forward to carry out a quantitative analysis.Meanwhile,the laboratory test process was simulated numerically utilizing the discrete element numerical analysis method.Optical fiber,an atypical geotechnical material,was innovatively applied for discrete element modeling and numerical simulation.The results show that the measured displacement of the dial gauge,the calculated results of the numerical model,and the displacement quantitatively calculated from the optical fiber data agree with each other in general.The latter two methods can potentially be utilized in engineering application of deformation monitoring at shield tunnel joints,but need to be further calibrated and adjusted in detail.展开更多
The nonlinear dynamic characteristics of a two-peak discrete chaotic system are studied.Through the study of the nonlinear dy‐namic behavior of the system,it is found that with the change of the system parameters,the...The nonlinear dynamic characteristics of a two-peak discrete chaotic system are studied.Through the study of the nonlinear dy‐namic behavior of the system,it is found that with the change of the system parameters,the system starts from a chaotic state,and then goes through intermittent chaos,stable region,period-doubling bifurcation to a chaotic state again.The systems critical conditions and pro‐cess to generate intermittent chaos are analyzed.The feedback control method sets linear and nonlinear controllers for the system to control the chaos.By adjusting the value of control parameters,the intermittent chaos can be delayed or disappear,and the stability region and period-doubling bifurcation process of the system can be expanded.Both linear controllers and nonlinear controllers have the same control effect.The numerical simulation analysis verifies the correctness of the theoretical analysis.展开更多
The flexible satellite batch production line is a complex discrete production system with multiple cross-disciplinary fields and mixed serial parallel tasks.As the source of the satellite batch production line process...The flexible satellite batch production line is a complex discrete production system with multiple cross-disciplinary fields and mixed serial parallel tasks.As the source of the satellite batch production line process,the warehousing system has urgent needs such as uncertain production scale and rapid iteration and optimization of business processes.Therefore,the requirements and architecture of complex discrete warehousing systems such as flexible satellite batch production lines are studied.The physical system of intelligent equipment is abstracted as a digital model to form the underlying module,and a digital fusion framework of“business domain+middleware platform+intelligent equipment information model”is constructed.The granularity of microservice splitting is calculated based on the dynamic correlation relationship between user access instances and database table structures.The general warehousing functions of the platform are divided to achieve module customization,addition,and configuration.An open discrete warehousing system based on microservices is designed.Software architecture and design develop complex discrete warehousing systems based on the SpringCloud framework.This architecture achieves the decoupling of business logic and physical hardware,enhances the maintainability and scalability of the system,and greatly improves the system’s adaptability to different complex discrete warehousing business scenarios.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10371096)
文摘Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.
基金supported by the Research Program of Wuhan Building Energy Efficiency Office(grant number 202331).
文摘Precast concrete pavements(PCPs)represent an innovative solution in the construction industry,addressing the need for rapid,intelligent,and low-carbon pavement technologies that significantly reduce construction time and environmental impact.However,the integration of prefabricated technology in pavement surface and base layers lacks systematic classification and understanding.This paper aims to fill this gap by introducing a detailed analysis of discretization and assembly connection technology for cement concrete pavement(CCP)structures.Through a comprehensive review of domestic and international literature,the study classifies prefabricated pavement technology based on discrete assembly structural layers and presents specific conclusions(i)surface layer discrete units are categorized into bottom plates,top plates,plate-rod separated assemblies,and prestressed connections,with optimal material compositions identified to enhance mechanical properties;(ii)base layer discrete units include block-type,plate-type,and beam-type elements,highlighting their contributions to sustainability by incorporating recycled materials(iii)planar assembly connection types are assessed,ranking them by load transfer efficiency,with specific dimensions provided for optimal performance;and(iv)vertical assembly connections are defined by their leveling and sealing layers,suitable for both new constructions and repairs of existing roads.The insights gained from this review not only clarify the distinctions between various structural layers but also provide practical guidelines for enhancing the design and implementation of PCP.This work contributes to advancing sustainable and resilient road construction practices,making it a significant reference for researchers and practitioners in the field.
基金supported by National Natural Science Foundation of China (Grant No.10761003) the Governor's Special Foundation of Guizhou Province for Outstanding Scientific Education Personnel (Grant No.[2005]155)
文摘This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
基金supported by the National Natural Science Foundation of China (Grant No.11761022)。
文摘In this paper,we extend the work of Brenner and Sung[Math.Comp.59,321–338(1992)]and present a regularity estimate for the elastic equations in concave domains.Based on the regularity estimate we prove that the constants in the error estimates of the nonconforming Crouzeix-Raviart element approximations for the elastic equations/eigenvalue problem are independent of Laméconstant,which means the nonconforming Crouzeix-Raviart element approximations are locking-free.We also establish two kinds of two-grid discretization schemes for the elastic eigenvalue problem,and analyze that when the mesh sizes of coarse grid and fine grid satisfy some relationship,the resulting solutions can achieve the optimal accuracy.Numerical examples are provided to show the efficiency of two-grid schemes for the elastic eigenvalue problem.
基金supported by National Natural Science Foundation of China (No. 10761003)by the Foundation of Guizhou Province Scientific Research for Senior Personnel, China
文摘This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou （Math. Comput., 70 （2001）, pp.17-25） to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is reduced to that on a much coarser mesh together with the solution of a linear algebraic system on the fine mesh. The resulting solution still maintains an asymptotically optimal accuracy. Comparing with the two-grid discretization scheme of the conforming finite elements, the main advantages of our new schemes are twofold when the mesh size is small enough. First, the lower bounds of the exact eigenvalues in our two-grid discretization schemes can be obtained. Second, the first eigenvalue given by the new schemes has much better accuracy than that obtained by solving the eigenvalue problems on the fine mesh directly.
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.
基金The authors gratefully acknowledge the support provided by the Postgraduate Research&Practice Program of Jiangsu Province(Grant No.KYCX18_0526)the Fundamental Research Funds for the Central Universities(Grant No.2018B682X14)Guangdong Basic and Applied Basic Research Foundation(No.2021A1515110807).
文摘In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.
基金National Science Foundation of China(11271145)Foundation for Talent Introduction of Guangdong Provincial University,Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009)the Project of Department of Education of Guangdong Province(2012KJCX0036).
文摘In this paper,we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods.We mainly concern the case when pressure coefficients and source terms are nonlinear.To linearize the nonlinear mixed equations,we use the two-grid algorithm.We first solve the nonlinear equations on the coarse grid,then,on the fine mesh,we solve a linearized problem using Newton iteration once.It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h 1/2).As a result,solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.
文摘We introduce CURDIS,a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc.In this template,algorithms proceed by finding the tangent quadrant at each point of the arc and determining which side the curve exits the pixel according to a tailored criterion.These two elements can be adapted for any type of curve,leading to algorithms dedicated to the shape of specific curves.While the calculation of the tangent quadrant for various curves,such as lines,conics,or cubics,is simple,it is more complex to analyze how pixels are traversed by the curve.In the case of conic arcs,we found a criterion for determining the pixel exit side.This leads us to present a new algorithm,called CURDIS-C,specific to the discretization of conics,for which we provide all the details.Surprisingly,the criterion for conics requires between one and three sign tests and four additions per pixel,making the algorithm efficient for resource-constrained systems and feasible for fixed-point or integer arithmetic implementations.Our algorithm also perfectly handles the pathological cases in which the conic intersects a pixel twice or changes quadrants multiple times within this pixel,achieving this generality at the cost of potentially computing up to two square roots per arc.We illustrate the use of CURDIS for the discretization of different curves,such as ellipses,hyperbolas,and parabolas,even when they degenerate into lines or corners.
基金Australian Research Council Linkage Program(LP200301404)for sponsoring this researchthe financial support provided by the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection(Chengdu University of Technology,SKLGP2021K002)National Natural Science Foundation of China(52374101,32111530138).
文摘Discrete fracture network(DFN)commonly existing in natural rock masses plays an important role in geological complexity which can influence rock fracturing behaviour during fluid injection.This paper simulated the hydraulic fracturing process in lab-scale coal samples with DFNs and the induced seismic activities by the discrete element method(DEM).The effects of DFNs on hydraulic fracturing,induced seismicity and elastic property changes have been concluded.Denser DFNs can comprehensively decrease the peak injection pressure and injection duration.The proportion of strong seismic events increases first and then decreases with increasing DFN density.In addition,the relative modulus of the rock mass is derived innovatively from breakdown pressure,breakdown fracture length and the related initiation time.Increasing DFN densities among large(35–60 degrees)and small(0–30 degrees)fracture dip angles show opposite evolution trends in relative modulus.The transitional point(dip angle)for the opposite trends is also proportionally affected by the friction angle of the rock mass.The modelling results have much practical meaning to infer the density and geometry of pre-existing fractures and the elastic property of rock mass in the field,simply based on the hydraulic fracturing and induced seismicity monitoring data.
基金partially supported by the Science Technology Development Fund,Macao Special Administrative Region(0029/2023/RIA1)the National Research Foundation Singapore under its AI Singapore Programme(AISG2-GC-2023-007)
文摘With the development of cyber-physical systems,system security faces more risks from cyber-attacks.In this work,we study the problem that an external attacker implements covert sensor and actuator attacks with resource constraints(the total resource consumption of the attacks is not greater than a given initial resource of the attacker)to mislead a discrete event system under supervisory control to reach unsafe states.We consider that the attacker can implement two types of attacks:One by modifying the sensor readings observed by a supervisor and the other by enabling the actuator commands disabled by the supervisor.Each attack has its corresponding resource consumption and remains covert.To solve this problem,we first introduce a notion of combined-attackability to determine whether a closedloop system may reach an unsafe state after receiving attacks with resource constraints.We develop an algorithm to construct a corrupted supervisor under attacks,provide a verification method for combined-attackability in polynomial time based on a plant,a corrupted supervisor,and an attacker's initial resource,and propose a corresponding attack synthesis algorithm.The effectiveness of the proposed method is illustrated by an example.
基金supported by the researcher supporting Project number(RSPD2025R636),King Saud University,Riyadh,Saudi Arabia.
文摘Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embedding a unique identifier that identifies the owner of the content.Image watermarking can also be used to verify the authenticity of digital media,such as images or videos,by ascertaining the watermark information.In this paper,a mathematical chaos-based image watermarking technique is proposed using discrete wavelet transform(DWT),chaotic map,and Laplacian operator.The DWT can be used to decompose the image into its frequency components,chaos is used to provide extra security defense by encrypting the watermark signal,and the Laplacian operator with optimization is applied to the mid-frequency bands to find the sharp areas in the image.These mid-frequency bands are used to embed the watermarks by modifying the coefficients in these bands.The mid-sub-band maintains the invisible property of the watermark,and chaos combined with the second-order derivative Laplacian is vulnerable to attacks.Comprehensive experiments demonstrate that this approach is effective for common signal processing attacks,i.e.,compression,noise addition,and filtering.Moreover,this approach also maintains image quality through peak signal-to-noise ratio(PSNR)and structural similarity index metrics(SSIM).The highest achieved PSNR and SSIM values are 55.4 dB and 1.In the same way,normalized correlation(NC)values are almost 10%–20%higher than comparative research.These results support assistance in copyright protection in multimedia content.
基金supported by the Major Program of the National Social Science Foundation of China(no.2022YFC3600801)the Operation of Public Health Emergency Response Mechanisms of the Chinese Center for Disease Control and Prevention(no.102393220020010000017)。
文摘Objective This study explored the job choice preferences of Center for Disease Prevention and Control(CDC)workers to provide CDC management information and recommendations for optimizing employee retention and motivation policies.Methods A discrete choice experiment was conducted in nine provinces across China.Seven key attributes were identified to analyze the job preferences of CDC workers.Mixed logit models,latent class models,and policy simulation tools were used.Results A valid sample of 5,944 cases was included in the analysis.All seven attributes significantly influenced the job choices of CDC workers.Heterogeneity analyses identified two main groups based on different levels of preference for attribute utility.Income-prioritizers were concerned with income and opportunities for career development,whereas bianzhi-prioritizers were concerned with bianzhi and welfare benefits.The policy simulation analysis revealed that income-prioritizers had a relatively higher sensitivity to multiple job preference incentives.Conclusion Income and bianzhi were the two key attributes influencing the job choices and retention preferences of CDC workers.Heterogeneity in job preferences was also identified.Based on the preference characteristics of different subgroups,policy content should be skewed to differentiate the importance of incentives.
文摘This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density of prey species with interval parameters.The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature.The equilibria of the model are obtained,and the dynamic behaviours of the proposed system are examined.Simulations of the model are performed for different parameters of the model.Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.Our study,through analytical derivation and numerical example,presents the effect of refuge on population dynamics under imprecise biological parameters.
基金funded by the National Natural Science Foundation of China(No.51978048).
文摘The homogeneity of aggregate blend has a significant influence on the performance of asphalt mixture.The composition of aggregate blend,including the size combination and the mass ratio between each size particles(MRESP),is an important factor affecting the homogeneity.This study investigated the influence of the size combination and MRESP on the distribution homogeneity of particles in aggregate blend using discrete element method(DEM).An indicator quantifying the distribution homogeneity was established according to the coefficient of variation(CV)for particle number.Two-size,three-size,and four-size aggregate blends with various compositions were designed.Laboratory tests show the DEM simulation is feasible.The particle distribution homogeneity in various blends was analyzed.The results showed the distribution homogeneity of each size particles in a blend is closely related to their mass fraction.The higher the mass fraction of the particles,the more homogeneous the distribution of them.The MRESP has no significant influence on the homogeneity of the blend composed of only coarse aggregates.However,the homogeneity of the blend composed of coarse and fine aggregates improves gradually with the increase of the mass fraction of fine aggregates.The smaller the maximum particle size in a blend,the better the homogeneity.It is suggested that the mass fraction of fine aggregates should be between 33%and 50%for achieving good homogeneity of aggregate blends.The research results can provide a reference for gradation design of asphalt mixture.
基金supported by the National Natural Science Foundation of China(Grant No.62071411).
文摘Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and their applications.Therefore,in this paper,a new NDM is constructed,and a non-autonomous hyperchaotic map is proposed by connecting this non-autonomous memristor in parallel with an autonomous memristor.This map exhibits complex dynamical behaviors,including infinitely many fixed points,initial-boosted attractors,initial-boosted bifurcations,and the size of the attractors being controlled by the initial value.In addition,a simple pseudo-random number generator(PRNG)was designed using the non-autonomous hyperchaotic map,and the pseudo-random numbers(PRNs)generated by it were tested using the National Institute of Standards and Technology(NIST)SP800-22 test suite.Finally,the non-autonomous hyperchaotic map is implemented on the STM32 hardware experimental platform.
基金supported by the National Natural Science Foundation of China(Grant Nos.12172104 and 11932005)the Talent Recruitment Project of Guangdong(2021QN02L892)+3 种基金the Stable Supporting Fund of Shenzhen(GXWD20231130153335002)the Shccig-Qinling Program(SMYJY202300140C)the program of Innovation Team in Universities and Colleges in Guangdong(2021KCXTD006)Development and Reform Commission of Shenzhen(XMHT20220103004).
文摘The mechanical properties of solid oxide fuel cells(SOFCs)can limit their mechanical stability and lifespan.Understanding the correlation between the microstructure and mechanical properties of porous electrode is essential for enhancing the performance and durability of SOFCs.Accurate prediction of mechanical properties of porous electrode can be achieved by microscale finite element modeling based on three-dimensional(3D)microstructures,which requires expensive 3D tomography techniques and massive computational resources.In this study,we proposed a cost-effective alternative approach to access the mechanical properties of porous electrodes,with the elastic properties of La_(0.6)Sr_(0.4)Co_(0.2)Fe_(0.8)O_(3-δc)athode serving as a case study.Firstly,a stochastic modeling was used to reconstruct 3D microstructures from two-dimensional(2D)cross-sections as an alternative to expensive tomography.Then,the discrete element method(DEM)was used to predict the elastic properties of porous ceramics based on the discretized 3D microstructures reconstructed by stochastic modeling.Based on 2D microstructure and the elastic properties calculated by the DEM modeling of the 3D reconstructed porous microstructures,a convolutional neural network(CNN)based deep learning model was built to predict the elastic properties rapidly from 2D microstructures.The proposed combined framework can be implemented with limited computational resources and provide a basis for rapid prediction of mechanical properties and parameter estimation for multiscale modeling of SOFCs.
基金National Natural Science Foundation of China,Grant/Award Numbers:41977218,42222707State Key Laboratory for GeoMechanics and Deep Underground Engineering,Grant/Award Number:SKLGDUEK2117。
文摘Shield tunnel,composed of several segments,is widely used in urban underground engineering.When the tunnel is under load,relative displacement occurs between adjacent segments.In the past,distributed optical fiber sensing technology was used to perform strain monitoring,but there is an urgent need to determine how to transform strain into displacement.In this study,optical frequency domain reflectometry was applied in laboratory tests.Aiming at the shear process and center settlement process of shield tunnel segments,two kinds of quantitative calculation methods were put forward to carry out a quantitative analysis.Meanwhile,the laboratory test process was simulated numerically utilizing the discrete element numerical analysis method.Optical fiber,an atypical geotechnical material,was innovatively applied for discrete element modeling and numerical simulation.The results show that the measured displacement of the dial gauge,the calculated results of the numerical model,and the displacement quantitatively calculated from the optical fiber data agree with each other in general.The latter two methods can potentially be utilized in engineering application of deformation monitoring at shield tunnel joints,but need to be further calibrated and adjusted in detail.
基金Supported by the Guiding Project of Science and Technology Research Plan of Hubei Provincial Department of Education(B2022458)。
文摘The nonlinear dynamic characteristics of a two-peak discrete chaotic system are studied.Through the study of the nonlinear dy‐namic behavior of the system,it is found that with the change of the system parameters,the system starts from a chaotic state,and then goes through intermittent chaos,stable region,period-doubling bifurcation to a chaotic state again.The systems critical conditions and pro‐cess to generate intermittent chaos are analyzed.The feedback control method sets linear and nonlinear controllers for the system to control the chaos.By adjusting the value of control parameters,the intermittent chaos can be delayed or disappear,and the stability region and period-doubling bifurcation process of the system can be expanded.Both linear controllers and nonlinear controllers have the same control effect.The numerical simulation analysis verifies the correctness of the theoretical analysis.
文摘The flexible satellite batch production line is a complex discrete production system with multiple cross-disciplinary fields and mixed serial parallel tasks.As the source of the satellite batch production line process,the warehousing system has urgent needs such as uncertain production scale and rapid iteration and optimization of business processes.Therefore,the requirements and architecture of complex discrete warehousing systems such as flexible satellite batch production lines are studied.The physical system of intelligent equipment is abstracted as a digital model to form the underlying module,and a digital fusion framework of“business domain+middleware platform+intelligent equipment information model”is constructed.The granularity of microservice splitting is calculated based on the dynamic correlation relationship between user access instances and database table structures.The general warehousing functions of the platform are divided to achieve module customization,addition,and configuration.An open discrete warehousing system based on microservices is designed.Software architecture and design develop complex discrete warehousing systems based on the SpringCloud framework.This architecture achieves the decoupling of business logic and physical hardware,enhances the maintainability and scalability of the system,and greatly improves the system’s adaptability to different complex discrete warehousing business scenarios.
