By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin(DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin(IE...By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin(DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin(IEFG) method is used for 2D transient heat conduction problems, and the finite difference method is applied in the splitting direction. The discretized system equation is obtained based on the Galerkin weak form of 2D problem;the essential boundary conditions are imposed with the penalty method;and the finite difference method is employed in the time domain. Four exemplary problems are chosen to verify the efficiency of the DSEFG method. The numerical solutions show that the efficiency and precision of the DSEFG method are greater than ones of the IEFG method for 3D problems.展开更多
Accurate calculation of the natural frequencies of permanent magnet synchronous motors (PMSMs) is essential to the prediction of vibration and noise of PMSMs. The analytical and numerical methods are respectively used...Accurate calculation of the natural frequencies of permanent magnet synchronous motors (PMSMs) is essential to the prediction of vibration and noise of PMSMs. The analytical and numerical methods are respectively used to calculate natural frequencies of stator yoke, stator core, stator core with windings, motor casing and stator system. It is found that the relative errors between calculated results with traditional analytical formulas and numerical results are very large. For the sake of reducing relative errors, novel analytical formulas of calculating circumferential modal frequencies of stator core, stator core with windings, motor casing and stator system are proposed. Compared with the results of numerical and experimental modal analysis, the effectiveness of novel analytical formulas is verified.展开更多
The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed w...The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects;2) upper-bound solutions;3) accurate solutions and higher convergence rates;4) insensitivity to mesh distortion;5) Jacobian?free;6) volumetric-locking-free;and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on Al-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.展开更多
Permeability is a key parameter to describe fluid transport properties of porous medium;however,the permeability measurement is extremely difficult for tight porous medium,e.g.fine-grained rock or dense soil.In this p...Permeability is a key parameter to describe fluid transport properties of porous medium;however,the permeability measurement is extremely difficult for tight porous medium,e.g.fine-grained rock or dense soil.In this paper,three methods for gas permeability measurement,i.e.steady state method,pulse decay method(PDM)and pressure oscillation method(POM),are first reviewed and then their advantages and drawbacks are discussed.Both analytical and numerical solutions of gas permeability are presented for the tight porous medium.The results show that the analytical method is relatively simple but only valid under certain conditions,whilst the numerical method is more robust and generic,which can take into account several factors such as porosity,saturation,gas leakage,and unconventional boundary conditions.The influence of the effective porosity on the permeability determination is further analyzed using the proposed numerical method.In this study,new pressure data interpretation procedures for PDM and POM are proposed,and the obtained results can serve as a guidance to define a proper method for permeability measurement of the tight porous medium.展开更多
Three processing techniques,split-squaring(SS),V-grooving(VG),and split-edging(SE),were evaluated and compared in terms of their processing time and recovery.Semantan bamboo(Gigantochloa scortechinii Gamble)was used a...Three processing techniques,split-squaring(SS),V-grooving(VG),and split-edging(SE),were evaluated and compared in terms of their processing time and recovery.Semantan bamboo(Gigantochloa scortechinii Gamble)was used as a raw material and the results showed that the VG-method required the longest processing time(32.1 min),followed by the SS-method(18.2 min),and the SE-method(17.9 min).However,the VG-method showed the highest recovery(82.0%)compared to the SS-method and SE-method,31.0 and 49.4%,respectively.When both processing time and recovery factors were combined with the same weighing factor,the highest value was recorded with the VG-method(49.1),while the SE-method had values of 31.1 and the SS-method 12.8.The results suggest that the VG-method is the best option.However,the V-grooving machine is still a prototype and therefore the SE-method could be an alternative option until the improved V-grooving machine is available.展开更多
A modified domain reduction method(MDRM) that introduces damping terms to the original DRM is presented in this paper. To verify the proposed MDRM and compare the computational accuracy of these two methods, a numeric...A modified domain reduction method(MDRM) that introduces damping terms to the original DRM is presented in this paper. To verify the proposed MDRM and compare the computational accuracy of these two methods, a numerical test is designed. The numerical results of the MDRM and DRM are compared using an extended meshed model. The results show that the MDRM significantly improved the computational accuracy of the DRM. Then, the MDRM is compared with two existing conventional methods, namely Liao’s transmitting boundary and viscous-spring boundary with Liu’s method. The MDRM shows its great advancement in computational accuracy, stability and range of applications. This paper also discusses the influence of boundary location on computational accuracy. It can be concluded that smaller models tend to have larger errors. By introducing two dimensionless parameters, φ1 and φ2, the rational distance between the observation point and the MDRM boundary is suggested. When φ1 >2 or φ2>13, the relative PGA error can be limited to 5%. In practice, the appropriate model size can be chosen based on these two parameters to achieve desired computational accuracy.展开更多
In this paper, a hybrid method based on the collocation and Newton-Kantorovich methods is used for solving the nonlinear singular Thomas-Fermi equation. At first, by using the Newton-Kantorovich method, the nonlinear ...In this paper, a hybrid method based on the collocation and Newton-Kantorovich methods is used for solving the nonlinear singular Thomas-Fermi equation. At first, by using the Newton-Kantorovich method, the nonlinear problem is converted to a sequence of linear differential equations, and then, the fractional order of rational Legendre functions are introduced and used for solving linear differential equations at each iteration based on the collocation method. Moreover, the boundary conditions of the problem by using Ritz method without domain truncation method are satisfied. In the end, the obtained results compare with other published in the literature to show the performance of the method, and the amounts of residual error are very small, which indicates the convergence of the method.展开更多
The algebraic methods represented by Wu's method have made significant breakthroughs in the field of geometric theorem proving.Algebraic proofs usually involve large amounts of calcula- tions,thus making it diffic...The algebraic methods represented by Wu's method have made significant breakthroughs in the field of geometric theorem proving.Algebraic proofs usually involve large amounts of calcula- tions,thus making it difficult to understand intuitively.However,if the authors look at Wu's method from the perspective of identity,Wu's method can be understood easily and can be used to generate new geometric propositions.To make geometric reasoning simpler,more expressive,and richer in geometric meaning,the authors establish a geometric algebraic system (point geometry built on nearly 20 basic properties/formulas about operations on points)while maintaining the advantages of the coordinate method,vector method,and particle geometry method and avoiding their disadvantages.Geometric relations in the propositions and conclusions of a geometric problem are expressed as identical equations of vector polynomials according to point geometry.Thereafter,a proof method that maintains the essence of Wu's method is introduced to find the relationships between these equations.A test on more than 400 geometry statements shows that the proposed proof method,which is based on identical equations of vector polynomials,is simple and effective.Furthermore,when solving the original problem,this proof method can also help the authors recognize the relationship between the propositions of the problem and help the authors generate new geometric propositions.展开更多
The pseudo-excitation method combined with the integral transform method (PEM-ITM) is presented to investigate the ground vibration of a coupled track-soil system induced by moving random loads. Commonly in the track ...The pseudo-excitation method combined with the integral transform method (PEM-ITM) is presented to investigate the ground vibration of a coupled track-soil system induced by moving random loads. Commonly in the track model, the rail, sleepers, rail pads, and ballast are modelled as an infinite Euler beam, discretely distributed masses, discretely distributed vertical springs, and a viscoelastic layer, respectively. The soil is regarded as a homogenous isotropic half-space coupled with the track using the boundary condition at the surface of the ground. By introducing a pseudo-excitation, the random vibration analysis of the coupled system is converted into a harmonic analysis. The analytical form of evolutionary power spectral density responses of the simplified coupled track-soil system under a random moving load is derived in the frequency/wavenumber domain by PEM-ITM. In the numerical examples, the effects of different parameters, such as the moving speed, the soil properties, and the coherence of moving loads, on the ground response are investigated.展开更多
The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green’s function method, some ingenious energy estimates are given. Then the global existence and...The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green’s function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L~p convergence rate of the solution is obtained.展开更多
Basis of explosion’s responsive analysis and anti-explosion’s structure design is the relation among thin explosive mass, impulse and plate deformation. In this paper, the limitations of theoretical calculation and ...Basis of explosion’s responsive analysis and anti-explosion’s structure design is the relation among thin explosive mass, impulse and plate deformation. In this paper, the limitations of theoretical calculation and experimental methods are analyzed according to the relation between impulse loading and deformation of steel plate in thin explosive experiment. The time histories of deformation for the square steel plate under the impulse of thin explosive are calculated by the fluid-solid coupling method and the pressure loading method. The advantages of the pressure loading method and the fluid-solid coupling method are compared. The results show that the steel plate deformation can be estimated accurately using the fluid-solid coupling method when the explosive impulse is unknown, while the theoretical calculation and the pressure loading method provide quick and accurate prediction on the steel plate deformation when the explosive impulse is known.展开更多
The methods of determination of 6-methyl coumarin in cosmetics by HPLC-DAD and GC-FID were compared. The positive samples were confirmed by GC-MS. Methanol was used to extract 6-methyl coumarin from cosmetics. The chr...The methods of determination of 6-methyl coumarin in cosmetics by HPLC-DAD and GC-FID were compared. The positive samples were confirmed by GC-MS. Methanol was used to extract 6-methyl coumarin from cosmetics. The chromatographic conditions of the two methods were optimized and the samples were determined. The recovery, precision, correlation coefficient, detection limit and quantitative limit of the two methods were compared. The results showed that the linear relationship between the two methods was good. The percentage recovery of standard addition by HPLC-DAD was 92.20%~102.80%, by RSD was 0.77%~2.00%;the detection limit was 0.05 mg/kg, the quantitative limit was 0.17 mg/kg. The percentage recovery of standard addition by GC-FID was 97.30%~103.28%, by RSD was 0.47%~4.87%;the detection limit was 1.3 mg/kg, the quantitative limit was 5.0 mg/kg. The detection limit by HPLC-DAD was lower and more sensitive than that by GC-FID , which also shows that HPLC-DAD has more advantages for the detection of low content samples.展开更多
An implicit higher-order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Ins...An implicit higher-order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher-order simulations (fourth-and fifth-order accuracy) are adopted. Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher-order DG method’s better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom (DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.展开更多
The Mn-Ce-Nb-Ox/P84 catalytic filter for removal of particulates and NO simultaneous was prepared by a novel method(foam coating method). The process parameters including the concentrations of PTFE emulsion, particle ...The Mn-Ce-Nb-Ox/P84 catalytic filter for removal of particulates and NO simultaneous was prepared by a novel method(foam coating method). The process parameters including the concentrations of PTFE emulsion, particle size of catalyst and calcination temperature for preparation of catalytic filters were analyzed. In addition, the physical properties and performance for removal of NO(NH3-SCR) and particulates of Mn-Ce-Nb-Ox/P84 catalytic filter prepared under the optimized parameters, were also systematic studied. Results show that the process parameters had significant influences on stability and performance of catalytic filter, The Mn-Ce-Nb-Ox/P84 catalytic filter prepared by foam coating method under the optimized parameters, has satisfactory physical properties and catalytic performance for removal of NO and particulates at 140-220 ℃. The NO removal efficiency of catalytic filter can reach95.3% at 200 ℃ as the catalyst loading amount is 450 g/m2, Moreover,the dust removal efficiency of MnGe-Nb-Ox/P84 catalytic filter reaches as high as 99.98%, and the PM2.5 removal efficiency also reaches99.98%. The anti-sulfur performance of Mn-Ce-Nb-Ox catalytic filter is also attractive, after injecting150 ppm SO2, the NO removal efficiency still retains up to 85%. It is indicated that the foam coating method can not only make a bond of high strength between catalyst and filter, but also make the catalytic filter possessing an excellent and stable performance for removal of NO and particulates.展开更多
In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these fu...In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.展开更多
The transfer matrix method for multibody systems, namely the 'Rui method', is a new method for studying multibody system dynamics, which avoids the global dynamics equations of the system, keeps high computati...The transfer matrix method for multibody systems, namely the 'Rui method', is a new method for studying multibody system dynamics, which avoids the global dynamics equations of the system, keeps high computational speed, and allows highly formalized programming. It has been widely applied to scientific research and key engineering of lots of complex mechanical systems in 52 research directions. The following aspects regarding the transfer matrix method for multibody systems are reviewed systematically in this paper: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, highlights, tendency, and applications in 52 research directions in over 100 key engineering products.展开更多
We investigate the Cauchy problem for the 3D magneto-hydrodynamics equations with only horizontal dissipation for the small initial data. With the help of the dissipation in the horizontal direction and the structure ...We investigate the Cauchy problem for the 3D magneto-hydrodynamics equations with only horizontal dissipation for the small initial data. With the help of the dissipation in the horizontal direction and the structure of the system, we analyze the properties of the decay of the solution and apply these decay properties to get the global regularity of the solution. In the process, we mainly use the frequency decomposition in Green's function method and energy method.展开更多
In order to make assessment on urbanization coordination, we developed a comprehensive model by integrating entropy weight method(EWM), coupling degree model(CDM), coupling coordination degree model(CCDM), multi-index...In order to make assessment on urbanization coordination, we developed a comprehensive model by integrating entropy weight method(EWM), coupling degree model(CDM), coupling coordination degree model(CCDM), multi-index grading method(MIGM) and Remote Sensing & Geographic Information System(RS & GIS) technology. Then we applied this integrated model to a case study in Jiangxi Province, China. Our study finds that: 1) EWM, CDM and CCDM can evaluate the temporal dynamic of urbanization. Urbanization process of Jiangxi Province can be divided into three periods, the stable development period(1990–2001), the accelerated development period(2002–2009) and the rapid development period(2010–2015). Coordinated development of urbanization in Jiangxi Province can be divided into two phases, an increasingly coordinated phase(1990–2003) and an increasingly incongruous phase(2003–2015). The state transition was due to low development rate of population urbanization. 2) RS & GIS technology is an effective tool for detecting urban growth. Urban construction land area of Jiangxi Province increased from 615.8 km~2 in 1990 to 2896.8 km~2 in2015, and the per capita urban construction land area(PCUCLA) reached 122.9 m~2, with the maximum value of 343 m~2 in Gongqingcheng City. 3) MIGM and RS & GIS technology can analyze spatial difference of urbanization. There is a significant spatial difference in socioeconomic development at county scale, with the maximum value six times the minimum value for both PCUCLA and per capita GDP in 2015. Population urbanization lag and excessive land use are the main reasons for uncoordinated urbanization. There were 15 counties with a lag in demographic urbanization and 33 counties where PCUCLA exceeded the national standard in 2015, among which 20 exceeded the national standard of PCUCLA by 50%(≥165 m~2). Since there are significant spatio-temporal differences in urbanization, it is necessary to carry out a comprehensive assessment to facilitate differential urbanization strategy making.展开更多
Sample preparation by fusion for XRF analysis is all about knowing the exact weights of the sample and the flux (sample-to-flux ratio). The whole analytical chain, including the weighing step in sample preparation pri...Sample preparation by fusion for XRF analysis is all about knowing the exact weights of the sample and the flux (sample-to-flux ratio). The whole analytical chain, including the weighing step in sample preparation prior to fusion, is of crucial importance to get precise and accurate x-ray fluorescence (XRF) results. Consequently, the weighing method will affect the quality of the analytical results given by the spectrometer. In this study, the effects of different weighing methods on the precision (RSD) of the obtained XRF results are compared to determine the best weighing method for sample preparation by fusion in terms of comparable precisions in the XRF results.展开更多
基金the National Natural Science Foundation of China (Grant Nos.11571223.and 51404160)the Science and Technology Innovation Foundation of Higher Education of Shanxi Province (Grant No.2016163).
文摘By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin(DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin(IEFG) method is used for 2D transient heat conduction problems, and the finite difference method is applied in the splitting direction. The discretized system equation is obtained based on the Galerkin weak form of 2D problem;the essential boundary conditions are imposed with the penalty method;and the finite difference method is employed in the time domain. Four exemplary problems are chosen to verify the efficiency of the DSEFG method. The numerical solutions show that the efficiency and precision of the DSEFG method are greater than ones of the IEFG method for 3D problems.
基金National Natural Science Foundation of China (Grant No. 51175350).
文摘Accurate calculation of the natural frequencies of permanent magnet synchronous motors (PMSMs) is essential to the prediction of vibration and noise of PMSMs. The analytical and numerical methods are respectively used to calculate natural frequencies of stator yoke, stator core, stator core with windings, motor casing and stator system. It is found that the relative errors between calculated results with traditional analytical formulas and numerical results are very large. For the sake of reducing relative errors, novel analytical formulas of calculating circumferential modal frequencies of stator core, stator core with windings, motor casing and stator system are proposed. Compared with the results of numerical and experimental modal analysis, the effectiveness of novel analytical formulas is verified.
文摘The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects;2) upper-bound solutions;3) accurate solutions and higher convergence rates;4) insensitivity to mesh distortion;5) Jacobian?free;6) volumetric-locking-free;and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on Al-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.
基金the National Natural Science Foundation of China(Grant Nos.41572290,51479190 and 51879260)the Chinese Fundamental Research(973)Program(Grant No.2015CB057906)Hubei Provincial Natural Science Foundation of China(Grant No.2018CFA012).
文摘Permeability is a key parameter to describe fluid transport properties of porous medium;however,the permeability measurement is extremely difficult for tight porous medium,e.g.fine-grained rock or dense soil.In this paper,three methods for gas permeability measurement,i.e.steady state method,pulse decay method(PDM)and pressure oscillation method(POM),are first reviewed and then their advantages and drawbacks are discussed.Both analytical and numerical solutions of gas permeability are presented for the tight porous medium.The results show that the analytical method is relatively simple but only valid under certain conditions,whilst the numerical method is more robust and generic,which can take into account several factors such as porosity,saturation,gas leakage,and unconventional boundary conditions.The influence of the effective porosity on the permeability determination is further analyzed using the proposed numerical method.In this study,new pressure data interpretation procedures for PDM and POM are proposed,and the obtained results can serve as a guidance to define a proper method for permeability measurement of the tight porous medium.
基金Fundamental Research Grant Scheme(FRGS),Ministry of Higher Education,MalaysiaHigher Institutions’Centre of Excellence(HICoE).
文摘Three processing techniques,split-squaring(SS),V-grooving(VG),and split-edging(SE),were evaluated and compared in terms of their processing time and recovery.Semantan bamboo(Gigantochloa scortechinii Gamble)was used as a raw material and the results showed that the VG-method required the longest processing time(32.1 min),followed by the SS-method(18.2 min),and the SE-method(17.9 min).However,the VG-method showed the highest recovery(82.0%)compared to the SS-method and SE-method,31.0 and 49.4%,respectively.When both processing time and recovery factors were combined with the same weighing factor,the highest value was recorded with the VG-method(49.1),while the SE-method had values of 31.1 and the SS-method 12.8.The results suggest that the VG-method is the best option.However,the V-grooving machine is still a prototype and therefore the SE-method could be an alternative option until the improved V-grooving machine is available.
基金National Natural Science Foundation of China under Grant Nos. 91315301, 51478279the State Key Laboratory Basic Theory Foundation of the Ministry of Science and Technology of China under the Grant SLDRCE08-A-07。
文摘A modified domain reduction method(MDRM) that introduces damping terms to the original DRM is presented in this paper. To verify the proposed MDRM and compare the computational accuracy of these two methods, a numerical test is designed. The numerical results of the MDRM and DRM are compared using an extended meshed model. The results show that the MDRM significantly improved the computational accuracy of the DRM. Then, the MDRM is compared with two existing conventional methods, namely Liao’s transmitting boundary and viscous-spring boundary with Liu’s method. The MDRM shows its great advancement in computational accuracy, stability and range of applications. This paper also discusses the influence of boundary location on computational accuracy. It can be concluded that smaller models tend to have larger errors. By introducing two dimensionless parameters, φ1 and φ2, the rational distance between the observation point and the MDRM boundary is suggested. When φ1 >2 or φ2>13, the relative PGA error can be limited to 5%. In practice, the appropriate model size can be chosen based on these two parameters to achieve desired computational accuracy.
文摘In this paper, a hybrid method based on the collocation and Newton-Kantorovich methods is used for solving the nonlinear singular Thomas-Fermi equation. At first, by using the Newton-Kantorovich method, the nonlinear problem is converted to a sequence of linear differential equations, and then, the fractional order of rational Legendre functions are introduced and used for solving linear differential equations at each iteration based on the collocation method. Moreover, the boundary conditions of the problem by using Ritz method without domain truncation method are satisfied. In the end, the obtained results compare with other published in the literature to show the performance of the method, and the amounts of residual error are very small, which indicates the convergence of the method.
基金the National Key Research and Development Program of China under Grant No.2017YFB1401302the National Natural Science Foundation of China under Grant No.41671377.
文摘The algebraic methods represented by Wu's method have made significant breakthroughs in the field of geometric theorem proving.Algebraic proofs usually involve large amounts of calcula- tions,thus making it difficult to understand intuitively.However,if the authors look at Wu's method from the perspective of identity,Wu's method can be understood easily and can be used to generate new geometric propositions.To make geometric reasoning simpler,more expressive,and richer in geometric meaning,the authors establish a geometric algebraic system (point geometry built on nearly 20 basic properties/formulas about operations on points)while maintaining the advantages of the coordinate method,vector method,and particle geometry method and avoiding their disadvantages.Geometric relations in the propositions and conclusions of a geometric problem are expressed as identical equations of vector polynomials according to point geometry.Thereafter,a proof method that maintains the essence of Wu's method is introduced to find the relationships between these equations.A test on more than 400 geometry statements shows that the proposed proof method,which is based on identical equations of vector polynomials,is simple and effective.Furthermore,when solving the original problem,this proof method can also help the authors recognize the relationship between the propositions of the problem and help the authors generate new geometric propositions.
基金the National Basic Research Program of China (Grant 2014CB046803)the National Natural Science Foundation of China (Grant 11772084).
文摘The pseudo-excitation method combined with the integral transform method (PEM-ITM) is presented to investigate the ground vibration of a coupled track-soil system induced by moving random loads. Commonly in the track model, the rail, sleepers, rail pads, and ballast are modelled as an infinite Euler beam, discretely distributed masses, discretely distributed vertical springs, and a viscoelastic layer, respectively. The soil is regarded as a homogenous isotropic half-space coupled with the track using the boundary condition at the surface of the ground. By introducing a pseudo-excitation, the random vibration analysis of the coupled system is converted into a harmonic analysis. The analytical form of evolutionary power spectral density responses of the simplified coupled track-soil system under a random moving load is derived in the frequency/wavenumber domain by PEM-ITM. In the numerical examples, the effects of different parameters, such as the moving speed, the soil properties, and the coherence of moving loads, on the ground response are investigated.
基金supported by the National Natural Science Foundation of China(11271141)Chongqing Science&Technology Commission(cstc2018jcyjAX0787).
文摘The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green’s function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L~p convergence rate of the solution is obtained.
文摘Basis of explosion’s responsive analysis and anti-explosion’s structure design is the relation among thin explosive mass, impulse and plate deformation. In this paper, the limitations of theoretical calculation and experimental methods are analyzed according to the relation between impulse loading and deformation of steel plate in thin explosive experiment. The time histories of deformation for the square steel plate under the impulse of thin explosive are calculated by the fluid-solid coupling method and the pressure loading method. The advantages of the pressure loading method and the fluid-solid coupling method are compared. The results show that the steel plate deformation can be estimated accurately using the fluid-solid coupling method when the explosive impulse is unknown, while the theoretical calculation and the pressure loading method provide quick and accurate prediction on the steel plate deformation when the explosive impulse is known.
文摘The methods of determination of 6-methyl coumarin in cosmetics by HPLC-DAD and GC-FID were compared. The positive samples were confirmed by GC-MS. Methanol was used to extract 6-methyl coumarin from cosmetics. The chromatographic conditions of the two methods were optimized and the samples were determined. The recovery, precision, correlation coefficient, detection limit and quantitative limit of the two methods were compared. The results showed that the linear relationship between the two methods was good. The percentage recovery of standard addition by HPLC-DAD was 92.20%~102.80%, by RSD was 0.77%~2.00%;the detection limit was 0.05 mg/kg, the quantitative limit was 0.17 mg/kg. The percentage recovery of standard addition by GC-FID was 97.30%~103.28%, by RSD was 0.47%~4.87%;the detection limit was 1.3 mg/kg, the quantitative limit was 5.0 mg/kg. The detection limit by HPLC-DAD was lower and more sensitive than that by GC-FID , which also shows that HPLC-DAD has more advantages for the detection of low content samples.
基金the National High Technology Research and Development Program of China(No. 2015AA015303)the National Natural Science Foundation of China(No.11272152)+1 种基金the Aeronautical Science Foundation of China(No. 20152752033)the Open Project of Key Laboratory of Aerodynamic Noise Control.
文摘An implicit higher-order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher-order simulations (fourth-and fifth-order accuracy) are adopted. Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher-order DG method’s better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom (DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.
基金Project supported by the National Natural Science Foundation of China(21501097,21272118,21577065)the Natural Science Foundation of Jiangsu Province(BK20170954)+2 种基金the Startup Foundation for Introducing Talent of NUIST(2017r073)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China,China(18KJB430019)University Science Research Project of Jiangsu Province(18KJB430019).
文摘The Mn-Ce-Nb-Ox/P84 catalytic filter for removal of particulates and NO simultaneous was prepared by a novel method(foam coating method). The process parameters including the concentrations of PTFE emulsion, particle size of catalyst and calcination temperature for preparation of catalytic filters were analyzed. In addition, the physical properties and performance for removal of NO(NH3-SCR) and particulates of Mn-Ce-Nb-Ox/P84 catalytic filter prepared under the optimized parameters, were also systematic studied. Results show that the process parameters had significant influences on stability and performance of catalytic filter, The Mn-Ce-Nb-Ox/P84 catalytic filter prepared by foam coating method under the optimized parameters, has satisfactory physical properties and catalytic performance for removal of NO and particulates at 140-220 ℃. The NO removal efficiency of catalytic filter can reach95.3% at 200 ℃ as the catalyst loading amount is 450 g/m2, Moreover,the dust removal efficiency of MnGe-Nb-Ox/P84 catalytic filter reaches as high as 99.98%, and the PM2.5 removal efficiency also reaches99.98%. The anti-sulfur performance of Mn-Ce-Nb-Ox catalytic filter is also attractive, after injecting150 ppm SO2, the NO removal efficiency still retains up to 85%. It is indicated that the foam coating method can not only make a bond of high strength between catalyst and filter, but also make the catalytic filter possessing an excellent and stable performance for removal of NO and particulates.
文摘In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.
基金supported by the Science Challenge Project of China(Grant No.TZ2016006-0104)the National Program on Key Basic Research Project(Grant No.613308)the National Natural Science Foundation of China(Grant No.11472135).
文摘The transfer matrix method for multibody systems, namely the 'Rui method', is a new method for studying multibody system dynamics, which avoids the global dynamics equations of the system, keeps high computational speed, and allows highly formalized programming. It has been widely applied to scientific research and key engineering of lots of complex mechanical systems in 52 research directions. The following aspects regarding the transfer matrix method for multibody systems are reviewed systematically in this paper: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, highlights, tendency, and applications in 52 research directions in over 100 key engineering products.
基金National Natural Science Foundation of China (Grant No. 11771284).
文摘We investigate the Cauchy problem for the 3D magneto-hydrodynamics equations with only horizontal dissipation for the small initial data. With the help of the dissipation in the horizontal direction and the structure of the system, we analyze the properties of the decay of the solution and apply these decay properties to get the global regularity of the solution. In the process, we mainly use the frequency decomposition in Green's function method and energy method.
基金Under the auspices of open foundation of The Key Laboratory of Poyang Lake Environment and Resource Utilization(Nanchang University)Ministry of Education,China(No.PYH2015-02).
文摘In order to make assessment on urbanization coordination, we developed a comprehensive model by integrating entropy weight method(EWM), coupling degree model(CDM), coupling coordination degree model(CCDM), multi-index grading method(MIGM) and Remote Sensing & Geographic Information System(RS & GIS) technology. Then we applied this integrated model to a case study in Jiangxi Province, China. Our study finds that: 1) EWM, CDM and CCDM can evaluate the temporal dynamic of urbanization. Urbanization process of Jiangxi Province can be divided into three periods, the stable development period(1990–2001), the accelerated development period(2002–2009) and the rapid development period(2010–2015). Coordinated development of urbanization in Jiangxi Province can be divided into two phases, an increasingly coordinated phase(1990–2003) and an increasingly incongruous phase(2003–2015). The state transition was due to low development rate of population urbanization. 2) RS & GIS technology is an effective tool for detecting urban growth. Urban construction land area of Jiangxi Province increased from 615.8 km~2 in 1990 to 2896.8 km~2 in2015, and the per capita urban construction land area(PCUCLA) reached 122.9 m~2, with the maximum value of 343 m~2 in Gongqingcheng City. 3) MIGM and RS & GIS technology can analyze spatial difference of urbanization. There is a significant spatial difference in socioeconomic development at county scale, with the maximum value six times the minimum value for both PCUCLA and per capita GDP in 2015. Population urbanization lag and excessive land use are the main reasons for uncoordinated urbanization. There were 15 counties with a lag in demographic urbanization and 33 counties where PCUCLA exceeded the national standard in 2015, among which 20 exceeded the national standard of PCUCLA by 50%(≥165 m~2). Since there are significant spatio-temporal differences in urbanization, it is necessary to carry out a comprehensive assessment to facilitate differential urbanization strategy making.
文摘Sample preparation by fusion for XRF analysis is all about knowing the exact weights of the sample and the flux (sample-to-flux ratio). The whole analytical chain, including the weighing step in sample preparation prior to fusion, is of crucial importance to get precise and accurate x-ray fluorescence (XRF) results. Consequently, the weighing method will affect the quality of the analytical results given by the spectrometer. In this study, the effects of different weighing methods on the precision (RSD) of the obtained XRF results are compared to determine the best weighing method for sample preparation by fusion in terms of comparable precisions in the XRF results.
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