This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi...This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.展开更多
Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmande...Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander＇s condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω.展开更多
In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=(X1,X2,…,Xm)is a system of real smooth vector fields which satisfy the H?rmander’s condition,...In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=(X1,X2,…,Xm)is a system of real smooth vector fields which satisfy the H?rmander’s condition,and△X=∑j=1m Xj2 is a finitely degenerate elliptic operator.Using potential well method,we first prove the invariance of some sets and vacuum isolating of solutions.Finally,by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy,and also we discuss the asymptotic behavior of the global solutions.展开更多
Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi ar...Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.展开更多
Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax i...Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.展开更多
In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated...In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.展开更多
Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) contain...Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.展开更多
In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the ...In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the question:When is an essential extension of a finitely presented module(an almost finitely presented module)also finitely presented(almost finitely presented)?In Section 2,we study the C-excellent extensions and the finitely presented dimensions.We obtain some results on the homological dimensions of matrix rings and group rings.展开更多
In this paper, we study the initial-boundary value problem for the semilinear pseudoparabolic equations ut —△xut —△xu =|u|^p-1u, where X =(X1, X2,..., Xm) is a system of real smooth vector fields which satisfy the...In this paper, we study the initial-boundary value problem for the semilinear pseudoparabolic equations ut —△xut —△xu =|u|^p-1u, where X =(X1, X2,..., Xm) is a system of real smooth vector fields which satisfy the Hormander's condition, and △x =∑j=1^m Xj^2 is a finitely degenera te elliptic operator. By using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy. The asymptotic behavior of the global solutions and a lower bound for blow-up time of local solution are also given.展开更多
A gradient structure was introduced into a metal laminated target plate,and the anti-penetration simulation of the gradient structure was compared with that of a uniform-layer-thickness target plate by finite element ...A gradient structure was introduced into a metal laminated target plate,and the anti-penetration simulation of the gradient structure was compared with that of a uniform-layer-thickness target plate by finite element simulation.The analysis was verified by an impact experiment.Results show that the high-level thickness and appropriate percentage of Ti alloy at the upper side of the gradient structure provide greater impact resistance against the bullet,which increases the warhead breakage and enhances the anti-penetration performance.In addition,during the impact process,the stress is transmitted and reflected in the form of waves in each layer of the target plate,and the interaction between the compression and tension waves causes non-synergistic deformation of the target plate and leads to delamination.The gradient target plate takes penetration resistance a step further through the higher energy absorption rate and more consumption of the bullet kinetic energy.This research provides a theoretical basis for the application of gradient structures in metallic laminated armor.展开更多
A multi-physics approach was used to quantify the effect of process parameters (laser power, scanning speed, hatch spacing, and scanning strategy) on the thermal history and corresponding microstructure evolution of T...A multi-physics approach was used to quantify the effect of process parameters (laser power, scanning speed, hatch spacing, and scanning strategy) on the thermal history and corresponding microstructure evolution of Ti-25Nb (at%) alloy during the dual-track selective laser melting (SLM) process. Simulation results reveal that during the dual-track SLM process, increasing laser power results in greater thermal accumulation, leading to a molten pool of larger volume and coarser grains. Reducing scanning speed enhances remelting and promotes cellular growth at the top of molten pool, whereas faster scanning speed leads to rougher melt tracks and finer grains. Notably, hatch spacing significantly influences the molten pool dimensions and microstructures, and smaller hatch spacing promotes remelting. Furthermore, the orientations of grains in the second track during zigzag scanning differ markedly from those in the first track. More importantly, compared with those after the first track, both the temperature gradient and cooling rate at the boundaries of remelting molten pool are reduced after the second track scanning, resulting in slower interface velocity and significant change in solidification microstructure. This research provides a theoretical foundation for controlling non-equilibrium microstructure and offering novel insights into the optimization of SLM process parameters of titanium alloys.展开更多
In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results i...In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results in increased leakage current,decreased breakdown voltage,and lower nonlinearity,ultimately compromising their protective performance.To investigate the evolution in electrical properties during DC aging,this work developed a finite element model based on Voronoi networks and conducted accelerated aging tests on commercial varistors.Throughout the aging process,current-voltage characteristics and Schottky barrier parameters were measured and analyzed.The results indicate that when subjected to constant voltage,current flows through regions with larger grain sizes,forming discharge channels.As aging progresses,the current focus increases on these channels,leading to a decline in the varistor’s overall performance.Furthermore,analysis of the Schottky barrier parameters shows that the changes in electrical performance during aging are non-monotonic.These findings offer theoretical support for understanding the aging mechanisms and condition assessment of modern stable ZnO varistors.展开更多
This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit...This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.展开更多
In the present paper,we prove the 1/2-Holder continuity of spectral measures for the C^k Schrodinger operators.This result is based on the quantitative almost reducibility and an estimate for the growth of the Schrodi...In the present paper,we prove the 1/2-Holder continuity of spectral measures for the C^k Schrodinger operators.This result is based on the quantitative almost reducibility and an estimate for the growth of the Schrodinger cocycles in[5].展开更多
The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling,arterial stents,and energy harvesting.This has attracted widespread att...The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling,arterial stents,and energy harvesting.This has attracted widespread attention from researchers.In this paper,the deformation and buckling behaviors of a circular arch subject to compression by a rigid plate are investigated with a planar elastic rod model that incorporates tension,shearing,and bending.In comparison with the existing models that solely consider the bending energy,the deflection curve,the internal force distribution,and the critical load of the present model show good agreement with the finite element results.Through the dimensional analysis and order-of-magnitude estimation,we examine the factors influencing the critical load.The study reveals that the semi-central angle of the arch has the most significant effect.The dimensionless geometric parameter describing arch slenderness becomes prominent when the semi-central angle is less than 30°,while Poisson's ratio and the cross-sectional shear correction factor exhibit negligible influence.Furthermore,the variation in the proportions of strain energy components during critical buckling is presented with respect to the semi-central angle and the geometric parameter,thereby delineating the applicable ranges of both the original model(OM)and the modified model(MM).展开更多
Slopes are likely to fail in areas with frequent rainfall and earthquakes.The deformation characteristics of unsaturated slopes subjected to post-rainfall earthquakes are investigated using centrifuge model tests and ...Slopes are likely to fail in areas with frequent rainfall and earthquakes.The deformation characteristics of unsaturated slopes subjected to post-rainfall earthquakes are investigated using centrifuge model tests and finite element analyses.Three tests of the slope deformation under earthquake and post-rainfall earthquakes are first studied using image analysis techniques.Then,based on an elastoplastic constitutive model,numerical simulations are carried out using the finite element method and compared with the centrifuge test results.Finally,a parametric study is performed to clarify the effects of antecedent rainfall on earthquake-induced slope deformation.The results show that slope deformation caused by post-rainfall earthquakes differs from that caused by earthquakes without antecedent rainfall.The seepage flow and soil strength of the slope are affected by previous rainfall conditions,such as intensity and duration,which directly influence the slope deformation caused by the subsequent earthquake.Soil displacement and strain become greater and the slip surface is more noticeable during the post-rainfall earthquake of higher intensity.In addition,the time interval between the rainfall and the earthquake has a considerable impact on the detailed characteristics of the slope deformation,and the significant deformation occurs at the time of lowest soil strength when seepage flow reaches the lower part of the slope.Moreover,the repeated intermittent rainfall greatly affects the subsequent earthquake-induced slope deformation,the main characteristics of which are closely related to the changes in saturation and strength of the slope.However,with the prolonged time gap between each round of rainfall,the earthquake-induced slope deformation becomes insignificant.展开更多
Most failures in component operation occur due to cyclic loads.Validation has been performed under quasistatic loads,but the fatigue life of components under dynamic loads should be predicted to prevent failures durin...Most failures in component operation occur due to cyclic loads.Validation has been performed under quasistatic loads,but the fatigue life of components under dynamic loads should be predicted to prevent failures during component service life.Fatigue is a damage accumulation process where loads degrade the material,depending on the characteristics and number of repetitions of the load.Studies on themechanical fatigue of 3D-printedOnyx are limited.In this paper,the strength of 3D-printed Onyx components under dynamic conditions(repetitive loads)is estimated.Fatigue life prediction is influenced bymanufacturing processes,material properties,and applied loads,which can cause scatter in the results due to the interplay of these factors.By utilizing synthetic parameters derived from mechanical properties,the accuracy of fatigue life predictions has been improved significantly,from 23.13%to 98.33%.Additive manufacturing is flexible,but this flexibility generates scatter in the mechanical properties of produced components.This work also proposes the use of synthetic data with a neural network to improve the fatigue life prediction of printedOnyx subjected to tension–tension loads.Experimental uniaxial loads were used to characterize themechanical behaviorofprinted specimens.The experimental datawereused to evaluate thenumerical predictionsobtainedthrough finite element analysis using commercial software and an artificial neural network.The results showed that the use of synthetic data helped improve fatigue life prediction.展开更多
In our study,we tackle a linear advection-diffusion equation that varies with time and is constrained to one dimension,under the framework of homogeneous Dirichlet boundary conditions.We employ two distinct approaches...In our study,we tackle a linear advection-diffusion equation that varies with time and is constrained to one dimension,under the framework of homogeneous Dirichlet boundary conditions.We employ two distinct approaches for solving this equation:an analytical solution through the method of separation of variables,and a numerical solution utilizing the finite difference method.The computational output includes three dimensional(3D)plots for solutions,focusing on pollutants such as Ammonia,Carbon monoxide,Carbon dioxide,and Sulphur dioxide.Concentrations,along with their respective diffusivities,are analyzed through 3D plots and actual calculations.To comprehend the diffusivity-concentration relationship for predicting pollutant movement in the air,the domain is divided into two halves.The study explores the behavior of pollutants with higher diffusivity entering regions with lower diffusivity,and vice versa,using 2D and 3D plots.This task is crucial for effective pollution control strategies,and safeguarding the environment and public health.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
文摘This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.
基金partially supported by the NSFC(11631011,11626251)
文摘Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander＇s condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω.
基金supported by National Natural Science Foundation of China(11631011 and 11626251)
文摘In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=(X1,X2,…,Xm)is a system of real smooth vector fields which satisfy the H?rmander’s condition,and△X=∑j=1m Xj2 is a finitely degenerate elliptic operator.Using potential well method,we first prove the invariance of some sets and vacuum isolating of solutions.Finally,by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy,and also we discuss the asymptotic behavior of the global solutions.
基金Climb-Up (Pan Deng) Project of Department of Science and Technology of China，国家自然科学基金，Doctoral Programme Foundation of Institution of Higher Education of China
文摘Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.
基金Project supported by the National Natural Science Foundation of China(No.11126346)
文摘Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.
文摘In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.
文摘Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.
基金Supported by the Natural Science Foundation of China
文摘In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the question:When is an essential extension of a finitely presented module(an almost finitely presented module)also finitely presented(almost finitely presented)?In Section 2,we study the C-excellent extensions and the finitely presented dimensions.We obtain some results on the homological dimensions of matrix rings and group rings.
基金Supported by National Natural Science Foundation of China(Grants Nos.11631011 and 11626251)
文摘In this paper, we study the initial-boundary value problem for the semilinear pseudoparabolic equations ut —△xut —△xu =|u|^p-1u, where X =(X1, X2,..., Xm) is a system of real smooth vector fields which satisfy the Hormander's condition, and △x =∑j=1^m Xj^2 is a finitely degenera te elliptic operator. By using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy. The asymptotic behavior of the global solutions and a lower bound for blow-up time of local solution are also given.
基金National Defense Basic Scientific Research Program of China(JCKY2020408B002,WDZC2022-12)Key Research and Development Program of Shanxi Province(202102050201011,202202050201014)Fundamental Research Program of Shanxi Province(20210302124178,20210302123061,202103021224183)。
文摘A gradient structure was introduced into a metal laminated target plate,and the anti-penetration simulation of the gradient structure was compared with that of a uniform-layer-thickness target plate by finite element simulation.The analysis was verified by an impact experiment.Results show that the high-level thickness and appropriate percentage of Ti alloy at the upper side of the gradient structure provide greater impact resistance against the bullet,which increases the warhead breakage and enhances the anti-penetration performance.In addition,during the impact process,the stress is transmitted and reflected in the form of waves in each layer of the target plate,and the interaction between the compression and tension waves causes non-synergistic deformation of the target plate and leads to delamination.The gradient target plate takes penetration resistance a step further through the higher energy absorption rate and more consumption of the bullet kinetic energy.This research provides a theoretical basis for the application of gradient structures in metallic laminated armor.
基金Guangdong Basic and Applied Basic Research Foundation (2024A1515011873)Shenzhen Basic Research Project (JCYJ20241202123504007)Shenzhen Science and Technology Innovation Commission (KJZD20240903101400001, KJZD20240903102006009)。
文摘A multi-physics approach was used to quantify the effect of process parameters (laser power, scanning speed, hatch spacing, and scanning strategy) on the thermal history and corresponding microstructure evolution of Ti-25Nb (at%) alloy during the dual-track selective laser melting (SLM) process. Simulation results reveal that during the dual-track SLM process, increasing laser power results in greater thermal accumulation, leading to a molten pool of larger volume and coarser grains. Reducing scanning speed enhances remelting and promotes cellular growth at the top of molten pool, whereas faster scanning speed leads to rougher melt tracks and finer grains. Notably, hatch spacing significantly influences the molten pool dimensions and microstructures, and smaller hatch spacing promotes remelting. Furthermore, the orientations of grains in the second track during zigzag scanning differ markedly from those in the first track. More importantly, compared with those after the first track, both the temperature gradient and cooling rate at the boundaries of remelting molten pool are reduced after the second track scanning, resulting in slower interface velocity and significant change in solidification microstructure. This research provides a theoretical foundation for controlling non-equilibrium microstructure and offering novel insights into the optimization of SLM process parameters of titanium alloys.
文摘In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results in increased leakage current,decreased breakdown voltage,and lower nonlinearity,ultimately compromising their protective performance.To investigate the evolution in electrical properties during DC aging,this work developed a finite element model based on Voronoi networks and conducted accelerated aging tests on commercial varistors.Throughout the aging process,current-voltage characteristics and Schottky barrier parameters were measured and analyzed.The results indicate that when subjected to constant voltage,current flows through regions with larger grain sizes,forming discharge channels.As aging progresses,the current focus increases on these channels,leading to a decline in the varistor’s overall performance.Furthermore,analysis of the Schottky barrier parameters shows that the changes in electrical performance during aging are non-monotonic.These findings offer theoretical support for understanding the aging mechanisms and condition assessment of modern stable ZnO varistors.
文摘This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.
基金supported by National Nature Science Foundation of China grant(No.71774070)。
文摘In the present paper,we prove the 1/2-Holder continuity of spectral measures for the C^k Schrodinger operators.This result is based on the quantitative almost reducibility and an estimate for the growth of the Schrodinger cocycles in[5].
基金Project supported by the National Natural Science Foundation of China(Nos.124B2043,U2241267,12172155,and 12302278)the Science and Technology Leading Talent Project of Gansu Province of China(No.23ZDKA0009)the Natural Science Foundation of Gansu Province of China(Nos.24JRRA473 and 24JRRA489)。
文摘The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling,arterial stents,and energy harvesting.This has attracted widespread attention from researchers.In this paper,the deformation and buckling behaviors of a circular arch subject to compression by a rigid plate are investigated with a planar elastic rod model that incorporates tension,shearing,and bending.In comparison with the existing models that solely consider the bending energy,the deflection curve,the internal force distribution,and the critical load of the present model show good agreement with the finite element results.Through the dimensional analysis and order-of-magnitude estimation,we examine the factors influencing the critical load.The study reveals that the semi-central angle of the arch has the most significant effect.The dimensionless geometric parameter describing arch slenderness becomes prominent when the semi-central angle is less than 30°,while Poisson's ratio and the cross-sectional shear correction factor exhibit negligible influence.Furthermore,the variation in the proportions of strain energy components during critical buckling is presented with respect to the semi-central angle and the geometric parameter,thereby delineating the applicable ranges of both the original model(OM)and the modified model(MM).
基金supported by the China Postdoctoral Science Foundation(CPSF)(Grant No.2024M762769)the Natural Science Basic Research Program of Shaanxi(Grant No.2024JC-YBQN-0333)the Postdoctoral Fellowship Program of CPSF(Grant No.GZC20232230).
文摘Slopes are likely to fail in areas with frequent rainfall and earthquakes.The deformation characteristics of unsaturated slopes subjected to post-rainfall earthquakes are investigated using centrifuge model tests and finite element analyses.Three tests of the slope deformation under earthquake and post-rainfall earthquakes are first studied using image analysis techniques.Then,based on an elastoplastic constitutive model,numerical simulations are carried out using the finite element method and compared with the centrifuge test results.Finally,a parametric study is performed to clarify the effects of antecedent rainfall on earthquake-induced slope deformation.The results show that slope deformation caused by post-rainfall earthquakes differs from that caused by earthquakes without antecedent rainfall.The seepage flow and soil strength of the slope are affected by previous rainfall conditions,such as intensity and duration,which directly influence the slope deformation caused by the subsequent earthquake.Soil displacement and strain become greater and the slip surface is more noticeable during the post-rainfall earthquake of higher intensity.In addition,the time interval between the rainfall and the earthquake has a considerable impact on the detailed characteristics of the slope deformation,and the significant deformation occurs at the time of lowest soil strength when seepage flow reaches the lower part of the slope.Moreover,the repeated intermittent rainfall greatly affects the subsequent earthquake-induced slope deformation,the main characteristics of which are closely related to the changes in saturation and strength of the slope.However,with the prolonged time gap between each round of rainfall,the earthquake-induced slope deformation becomes insignificant.
文摘Most failures in component operation occur due to cyclic loads.Validation has been performed under quasistatic loads,but the fatigue life of components under dynamic loads should be predicted to prevent failures during component service life.Fatigue is a damage accumulation process where loads degrade the material,depending on the characteristics and number of repetitions of the load.Studies on themechanical fatigue of 3D-printedOnyx are limited.In this paper,the strength of 3D-printed Onyx components under dynamic conditions(repetitive loads)is estimated.Fatigue life prediction is influenced bymanufacturing processes,material properties,and applied loads,which can cause scatter in the results due to the interplay of these factors.By utilizing synthetic parameters derived from mechanical properties,the accuracy of fatigue life predictions has been improved significantly,from 23.13%to 98.33%.Additive manufacturing is flexible,but this flexibility generates scatter in the mechanical properties of produced components.This work also proposes the use of synthetic data with a neural network to improve the fatigue life prediction of printedOnyx subjected to tension–tension loads.Experimental uniaxial loads were used to characterize themechanical behaviorofprinted specimens.The experimental datawereused to evaluate thenumerical predictionsobtainedthrough finite element analysis using commercial software and an artificial neural network.The results showed that the use of synthetic data helped improve fatigue life prediction.
文摘In our study,we tackle a linear advection-diffusion equation that varies with time and is constrained to one dimension,under the framework of homogeneous Dirichlet boundary conditions.We employ two distinct approaches for solving this equation:an analytical solution through the method of separation of variables,and a numerical solution utilizing the finite difference method.The computational output includes three dimensional(3D)plots for solutions,focusing on pollutants such as Ammonia,Carbon monoxide,Carbon dioxide,and Sulphur dioxide.Concentrations,along with their respective diffusivities,are analyzed through 3D plots and actual calculations.To comprehend the diffusivity-concentration relationship for predicting pollutant movement in the air,the domain is divided into two halves.The study explores the behavior of pollutants with higher diffusivity entering regions with lower diffusivity,and vice versa,using 2D and 3D plots.This task is crucial for effective pollution control strategies,and safeguarding the environment and public health.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
