In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both...In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both stochastically C-stable and stochastically B-consistent,is convergent has been proved in a previous paper.In order to analyze the convergence of the split-step theta method(θ∈[1/2,1]),the stochastic C-stability and stochastic B-consistency under the condition of global monotonicity have been researched,and the rate of convergence 1/2 has been explored in this paper.It can be seen that the convergence does not require the drift function should satisfy the linear growth condition whenθ=1/2 Furthermore,the rate of the convergence of the split-step scheme for stochastic differential equations with additive noise has been researched and found to be 1.Finally,an example is given to illustrate the convergence with the theoretical results.展开更多
Noble metal-loaded layered hydroxides exhibit high efficiency in electrocatalyzing water splitting.However,their widespread use as bifunctional electrocatalysts is hindered by low metal loading,inefficient yield,and c...Noble metal-loaded layered hydroxides exhibit high efficiency in electrocatalyzing water splitting.However,their widespread use as bifunctional electrocatalysts is hindered by low metal loading,inefficient yield,and complex synthesis processes.In this work,platinum atoms were anchored onto nickel-iron layered double hydroxide/carbon nanotube(LDH/CNT)hybrid electrocatalysts by using a straightforward milling technique with K_(2)Pt Cl_(6)·6H_(2)O as the Pt source.By adjusting the Pt-to-Fe ratio to 1/2 and 1/10,excellent electrocatalysts—Pt_(1/6)-Ni_(2/3)Fe_(1/3)-LDH/CNT and Pt_(1/30)-Ni_(2/3)Fe_(1/3)-LDH/CNT—were achieved with superior performance in hydrogen evolution reaction(HER)and oxygen evolution reaction(OER),outperforming the corresponding commercial Pt/C(20 wt%)and Ru O_(2)electrocatalysts.The enhanced electrochemical performance is attributed to the modification of Pt's electronic structure,which exhibits electron-rich states for HER and electrondeficient states for OER,significantly boosting Pt's electrochemical activity.Furthermore,the simple milling technology for controlling Pt loading offers a promising approach for scaling up the production of electrocatalysts.展开更多
A new numerical approach, called the “subdomain Chebyshev spectral method” is presented for calculation of the spatial derivatives in a curved coordinate system, which may be employed for numerical solutions of part...A new numerical approach, called the “subdomain Chebyshev spectral method” is presented for calculation of the spatial derivatives in a curved coordinate system, which may be employed for numerical solutions of partial differential equations defined in a 2D or 3D geological model. The new approach refers to a “strong version” against the “weak version” of the subspace spectral method based on the variational principle or Galerkin’s weighting scheme. We incorporate local nonlinear transformations and global spline interpolations in a curved coordinate system and make the discrete grid exactly matches geometry of the model so that it is achieved to convert the global domain into subdomains and apply Chebyshev points to locally sampling physical quantities and globally computing the spatial derivatives. This new approach not only remains exponential convergence of the standard spectral method in subdomains, but also yields a sparse assembled matrix when applied for the global domain simulations. We conducted 2D and 3D synthetic experiments and compared accuracies of the numerical differentiations with traditional finite difference approaches. The results show that as the points of differentiation vector are larger than five, the subdomain Chebyshev spectral method significantly improve the accuracies of the finite difference approaches.展开更多
In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor depos...In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.展开更多
Based on the propagation characteristics of shear wave in the anisotropic layers,thecorrelation among several splitting shear-wave identification methods hasbeen studied.Thispaper puts forward the method estimating sp...Based on the propagation characteristics of shear wave in the anisotropic layers,thecorrelation among several splitting shear-wave identification methods hasbeen studied.Thispaper puts forward the method estimating splitting shear-wave phases and its reliability byusing of the assumption that variance of noise and useful signal data obey normaldistribution.To check the validity of new method,the identification results and errorestimation corresponding to 95% confidence level by analyzing simulation signals have beengiven.展开更多
Computed tomography(CT) blurring caused by point spread function leads to errors in quantification and visualization. In this paper, multichannel blind CT image restoration is proposed to overcome the effect of point ...Computed tomography(CT) blurring caused by point spread function leads to errors in quantification and visualization. In this paper, multichannel blind CT image restoration is proposed to overcome the effect of point spread function. The main advantage from multichannel blind CT image restoration is to exploit the diversity and redundancy of information in different acquisitions. The proposed approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is addressed with the alternating direction method of multipliers and simply implemented in the Fourier domain. Numerical experiments illustrate that our method obtains a higher average gain value of at least 1.21 d B in terms of Q metric than the other methods, and it requires only 7 iterations of alternating minimization to obtain a fast convergence.展开更多
Due to the intrinsic interaction between piezoelectric effects and semiconducting properties,piezoelectric semiconductors(PSs)have great promise for applications in multi-functional electronic devices,requiring a deep...Due to the intrinsic interaction between piezoelectric effects and semiconducting properties,piezoelectric semiconductors(PSs)have great promise for applications in multi-functional electronic devices,requiring a deep understanding of the multi-field coupling behavior.This work investigates the free vibration and buckling characteristics of a PS beam under different mechanical boundary conditions.The coupling fields of a PS beam are modeled by combining the Timoshenko beam theory for mechanical fields with a high-order expansion along the beam thickness for electric fields and carrier distributions.Based on the hypothesis of small perturbation of carrier density,the governing equations and boundary conditions are derived with the principle of virtual work.The differential quadrature method(DQM)is used to solve the boundary-value problem.The analytical solutions for a simply supported-simply supported(SS)PS beam are also obtained for verification.The convergence and correctness of the solutions obtained with the DQM are first evaluated.Subsequently,the effects of initial electron density,boundary conditions,and geometric parameters on the vibration and buckling characteristics are explored through numerical examples,where the finite element simulations are also included.The interaction mechanism of multi-physics fields is revealed.The scale effect on the static and dynamic responses of a PS beam is demonstrated.The derived model and findings are useful for the analysis and design of PS-based devices.展开更多
In this study, housing prices data for residential quarters from the period 2001-2012 were used and Global Differentiation Index （GDI） was established to measure the overall differentiation trend in housing prices i...In this study, housing prices data for residential quarters from the period 2001-2012 were used and Global Differentiation Index （GDI） was established to measure the overall differentiation trend in housing prices in Yangzhou City, eastern China. Then the influence of the natural landscape and environment on prices of global housing market and housing submarkets was evaluated by the hedonic price model. The results are shown as follows. （1） There have been increasing gaps among housing prices since 2001. In this period, the differentiation trend has shown an upward fluctuation, which has been coupled with the annual growth rate of housing prices. （2） The spatial distribution of residential quarters of homogenous prices has changed from clustered in 2001 into dispersed in 2012. （3） Natural landscape and environmental externalities clearly influence spatial differentiation of housing prices. （4） In different housing submarkets, the influence of natural landscape and environmental eternalities are varied. Natural landscape characteristics have significant impact on housing prices of ordinary commercial houses and indemnificatory houses, while the impact of environmental characteristics have obvious influence on housing prices of cottages and villas.展开更多
In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the B...In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.展开更多
In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes eq...In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.展开更多
The quasi-static and dynamic responses of a thermoviscoelastic Timoshenko beam subject to thermal loads are analyzed. First, based on the small geometric deformation assumption and Boltzmann constitutive relation, the...The quasi-static and dynamic responses of a thermoviscoelastic Timoshenko beam subject to thermal loads are analyzed. First, based on the small geometric deformation assumption and Boltzmann constitutive relation, the governing equations for the beam are presented. Second, an extended differential quadrature method(DQM)in the spatial domain and a differential method in the temporal domain are combined to transform the integro-partial-differential governing equations into the ordinary differential equations. Third, the accuracy of the present discrete method is verified by elastic/viscoelastic examples, and the effects of thermal load parameters, material and geometrical parameters on the quasi-static and dynamic responses of the beam are discussed. Numerical results show that the thermal function parameter has a great effect on quasi-static and dynamic responses of the beam. Compared with the thermal relaxation time, the initial vibrational responses of the beam are more sensitive to the mechanical relaxation time of the thermoviscoelastic material.展开更多
LiMnOand LiNiAlyMnO（x= 0.50;y = 0.05-0.50） powders have been synthesized via facile solgel method using Behenic acid as active cheiating agent.The synthesized samples are subjected to physical characterizations such...LiMnOand LiNiAlyMnO（x= 0.50;y = 0.05-0.50） powders have been synthesized via facile solgel method using Behenic acid as active cheiating agent.The synthesized samples are subjected to physical characterizations such as thermo gravimetric analysis（TG/DTA）,X-ray diffraction（XRD）,Fourier transform infrared spectroscopy（FT-IR）,field-emission scanning electron microscopy（FESEM）,transmission electron microscopy（TEM） and electrochemical studies viz.,galvanostatic cycling properties,electrochemical impedance spectroscopy（EIS） and differential capacity curves（dQ/dE）.Finger print XRD patterns of LiMnOand LiNiAlMnOfortify the high degree of crystallinity with better phase purity.FESEM images of the undoped pristine spinel illustrate uniform spherical grains surface morphology with an average particle size of 0.5 μm while Ni doped particles depict the spherical grains growth（50nm） with ice-cube surface morphology.TEM images of the spinel LiMnOshows the uniform spherical morphology with particle size of（100 nm） while low level of Al-doping spinel（LiNio.5Alo.05Mn1.45O4） displaying cloudy particles with agglomerated particles of（50nm）.The LiMnOsamples calcined at 850℃ deliver the discharge capacity of 130 mAh/g in the first cycle corresponds to 94%coiumbic efficiency with capacity fade of 1.5 mAh/g/cycle over the investigated 10 cycles.Among all four dopant compositions investigated,LiNiAlMnOdelivers the maximum discharge capacity of 126 mAh/g during the first cycle and shows the stable cycling performance with low capacity fade of 1 mAh/g/cycle（capacity retention of 92%） over the investigated 10 cycles.Electrochemical impedance studies of spinel LiMnOand LiNiAlMnOdepict the high and low real polarization of 1562 and 1100 Ω.展开更多
In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on...In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface,a nonlinear initial-boundary value problem satisfies by stream function is obtained,existence and uniqueness of its solution are proven.Based this theory we proposal a new method called"dimension split method"to solve 3D NSE.展开更多
This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the...This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.展开更多
This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence ...This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.展开更多
The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear...The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.展开更多
Recent years have witnessed growing interests in solving partial differential equations by deep neural networks,especially in the high-dimensional case.Unlike classical numerical methods,such as finite difference meth...Recent years have witnessed growing interests in solving partial differential equations by deep neural networks,especially in the high-dimensional case.Unlike classical numerical methods,such as finite difference method and finite element method,the enforcement of boundary conditions in deep neural networks is highly nontrivial.One general strategy is to use the penalty method.In the work,we conduct a comparison study for elliptic problems with four different boundary conditions,i.e.,Dirichlet,Neumann,Robin,and periodic boundary conditions,using two representative methods:deep Galerkin method and deep Ritz method.In the former,the PDE residual is minimized in the least-squares sense while the corresponding variational problem is minimized in the latter.Therefore,it is reasonably expected that deep Galerkin method works better for smooth solutions while deep Ritz method works better for low-regularity solutions.However,by a number of examples,we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions.Besides,in some cases,when the boundary condition can be implemented in an exact manner,we find that such a strategy not only provides a better approximate solution but also facilitates the training process.展开更多
The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation wit...The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.展开更多
The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditi...The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory （FSDT）. The equations of motion are obtained applying Hamilton＇s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.展开更多
In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the...In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 12301521)the Natural Science Foundation of Shanxi Province (Grant No. 20210302124081)。
文摘In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both stochastically C-stable and stochastically B-consistent,is convergent has been proved in a previous paper.In order to analyze the convergence of the split-step theta method(θ∈[1/2,1]),the stochastic C-stability and stochastic B-consistency under the condition of global monotonicity have been researched,and the rate of convergence 1/2 has been explored in this paper.It can be seen that the convergence does not require the drift function should satisfy the linear growth condition whenθ=1/2 Furthermore,the rate of the convergence of the split-step scheme for stochastic differential equations with additive noise has been researched and found to be 1.Finally,an example is given to illustrate the convergence with the theoretical results.
基金supported by the Natural Science Foundation of Henan(242300421230)the Young Teacher Fundamental Research Cultivation Program of Zhengzhou University(JC23557030)the National Natural Science Foundation of China(U21A20281 and 22208322)。
文摘Noble metal-loaded layered hydroxides exhibit high efficiency in electrocatalyzing water splitting.However,their widespread use as bifunctional electrocatalysts is hindered by low metal loading,inefficient yield,and complex synthesis processes.In this work,platinum atoms were anchored onto nickel-iron layered double hydroxide/carbon nanotube(LDH/CNT)hybrid electrocatalysts by using a straightforward milling technique with K_(2)Pt Cl_(6)·6H_(2)O as the Pt source.By adjusting the Pt-to-Fe ratio to 1/2 and 1/10,excellent electrocatalysts—Pt_(1/6)-Ni_(2/3)Fe_(1/3)-LDH/CNT and Pt_(1/30)-Ni_(2/3)Fe_(1/3)-LDH/CNT—were achieved with superior performance in hydrogen evolution reaction(HER)and oxygen evolution reaction(OER),outperforming the corresponding commercial Pt/C(20 wt%)and Ru O_(2)electrocatalysts.The enhanced electrochemical performance is attributed to the modification of Pt's electronic structure,which exhibits electron-rich states for HER and electrondeficient states for OER,significantly boosting Pt's electrochemical activity.Furthermore,the simple milling technology for controlling Pt loading offers a promising approach for scaling up the production of electrocatalysts.
文摘A new numerical approach, called the “subdomain Chebyshev spectral method” is presented for calculation of the spatial derivatives in a curved coordinate system, which may be employed for numerical solutions of partial differential equations defined in a 2D or 3D geological model. The new approach refers to a “strong version” against the “weak version” of the subspace spectral method based on the variational principle or Galerkin’s weighting scheme. We incorporate local nonlinear transformations and global spline interpolations in a curved coordinate system and make the discrete grid exactly matches geometry of the model so that it is achieved to convert the global domain into subdomains and apply Chebyshev points to locally sampling physical quantities and globally computing the spatial derivatives. This new approach not only remains exponential convergence of the standard spectral method in subdomains, but also yields a sparse assembled matrix when applied for the global domain simulations. We conducted 2D and 3D synthetic experiments and compared accuracies of the numerical differentiations with traditional finite difference approaches. The results show that as the points of differentiation vector are larger than five, the subdomain Chebyshev spectral method significantly improve the accuracies of the finite difference approaches.
文摘In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.
基金This project was sponsored by the National Science Foundation of China (49734150) and the Join Earthquake Science Foundation of China Seismological Burear(198061).
文摘Based on the propagation characteristics of shear wave in the anisotropic layers,thecorrelation among several splitting shear-wave identification methods hasbeen studied.Thispaper puts forward the method estimating splitting shear-wave phases and its reliability byusing of the assumption that variance of noise and useful signal data obey normaldistribution.To check the validity of new method,the identification results and errorestimation corresponding to 95% confidence level by analyzing simulation signals have beengiven.
基金Supported by the National Natural Science Foundaton of China(No.61340034)China Postdoctoral Science Foundation(No.2013M530873)the Research Program of Application Foundation and Advanced Technology of Tianjin(No.13JCYBJC15600)
文摘Computed tomography(CT) blurring caused by point spread function leads to errors in quantification and visualization. In this paper, multichannel blind CT image restoration is proposed to overcome the effect of point spread function. The main advantage from multichannel blind CT image restoration is to exploit the diversity and redundancy of information in different acquisitions. The proposed approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is addressed with the alternating direction method of multipliers and simply implemented in the Fourier domain. Numerical experiments illustrate that our method obtains a higher average gain value of at least 1.21 d B in terms of Q metric than the other methods, and it requires only 7 iterations of alternating minimization to obtain a fast convergence.
基金Project supported by the National Natural Science Foundation of China(Nos.U21A20430 and 12472155)the Natural Science Foundation of Hebei Province of China(No.A2024210002)。
文摘Due to the intrinsic interaction between piezoelectric effects and semiconducting properties,piezoelectric semiconductors(PSs)have great promise for applications in multi-functional electronic devices,requiring a deep understanding of the multi-field coupling behavior.This work investigates the free vibration and buckling characteristics of a PS beam under different mechanical boundary conditions.The coupling fields of a PS beam are modeled by combining the Timoshenko beam theory for mechanical fields with a high-order expansion along the beam thickness for electric fields and carrier distributions.Based on the hypothesis of small perturbation of carrier density,the governing equations and boundary conditions are derived with the principle of virtual work.The differential quadrature method(DQM)is used to solve the boundary-value problem.The analytical solutions for a simply supported-simply supported(SS)PS beam are also obtained for verification.The convergence and correctness of the solutions obtained with the DQM are first evaluated.Subsequently,the effects of initial electron density,boundary conditions,and geometric parameters on the vibration and buckling characteristics are explored through numerical examples,where the finite element simulations are also included.The interaction mechanism of multi-physics fields is revealed.The scale effect on the static and dynamic responses of a PS beam is demonstrated.The derived model and findings are useful for the analysis and design of PS-based devices.
基金National Natural Science Foundation of China, No.41401164, No.41201128
文摘In this study, housing prices data for residential quarters from the period 2001-2012 were used and Global Differentiation Index （GDI） was established to measure the overall differentiation trend in housing prices in Yangzhou City, eastern China. Then the influence of the natural landscape and environment on prices of global housing market and housing submarkets was evaluated by the hedonic price model. The results are shown as follows. （1） There have been increasing gaps among housing prices since 2001. In this period, the differentiation trend has shown an upward fluctuation, which has been coupled with the annual growth rate of housing prices. （2） The spatial distribution of residential quarters of homogenous prices has changed from clustered in 2001 into dispersed in 2012. （3） Natural landscape and environmental externalities clearly influence spatial differentiation of housing prices. （4） In different housing submarkets, the influence of natural landscape and environmental eternalities are varied. Natural landscape characteristics have significant impact on housing prices of ordinary commercial houses and indemnificatory houses, while the impact of environmental characteristics have obvious influence on housing prices of cottages and villas.
文摘In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.
文摘In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.
基金supported by the National Natural Science Foundation of China(Nos.11772182 and90816001)
文摘The quasi-static and dynamic responses of a thermoviscoelastic Timoshenko beam subject to thermal loads are analyzed. First, based on the small geometric deformation assumption and Boltzmann constitutive relation, the governing equations for the beam are presented. Second, an extended differential quadrature method(DQM)in the spatial domain and a differential method in the temporal domain are combined to transform the integro-partial-differential governing equations into the ordinary differential equations. Third, the accuracy of the present discrete method is verified by elastic/viscoelastic examples, and the effects of thermal load parameters, material and geometrical parameters on the quasi-static and dynamic responses of the beam are discussed. Numerical results show that the thermal function parameter has a great effect on quasi-static and dynamic responses of the beam. Compared with the thermal relaxation time, the initial vibrational responses of the beam are more sensitive to the mechanical relaxation time of the thermoviscoelastic material.
基金support given under the "Brain Pool Program of the Korean Federation of Science and Technology Societies" (KOFST), Republic of South Koreasupported by the Human Resources Development Program (No. 20124010203270) of the Korea Institute of Energy Technology EvaluationPlanning (KETEP) grant funded by the Korea Government Ministry of Trade, Industry and Energy
文摘LiMnOand LiNiAlyMnO（x= 0.50;y = 0.05-0.50） powders have been synthesized via facile solgel method using Behenic acid as active cheiating agent.The synthesized samples are subjected to physical characterizations such as thermo gravimetric analysis（TG/DTA）,X-ray diffraction（XRD）,Fourier transform infrared spectroscopy（FT-IR）,field-emission scanning electron microscopy（FESEM）,transmission electron microscopy（TEM） and electrochemical studies viz.,galvanostatic cycling properties,electrochemical impedance spectroscopy（EIS） and differential capacity curves（dQ/dE）.Finger print XRD patterns of LiMnOand LiNiAlMnOfortify the high degree of crystallinity with better phase purity.FESEM images of the undoped pristine spinel illustrate uniform spherical grains surface morphology with an average particle size of 0.5 μm while Ni doped particles depict the spherical grains growth（50nm） with ice-cube surface morphology.TEM images of the spinel LiMnOshows the uniform spherical morphology with particle size of（100 nm） while low level of Al-doping spinel（LiNio.5Alo.05Mn1.45O4） displaying cloudy particles with agglomerated particles of（50nm）.The LiMnOsamples calcined at 850℃ deliver the discharge capacity of 130 mAh/g in the first cycle corresponds to 94%coiumbic efficiency with capacity fade of 1.5 mAh/g/cycle over the investigated 10 cycles.Among all four dopant compositions investigated,LiNiAlMnOdelivers the maximum discharge capacity of 126 mAh/g during the first cycle and shows the stable cycling performance with low capacity fade of 1 mAh/g/cycle（capacity retention of 92%） over the investigated 10 cycles.Electrochemical impedance studies of spinel LiMnOand LiNiAlMnOdepict the high and low real polarization of 1562 and 1100 Ω.
文摘In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface,a nonlinear initial-boundary value problem satisfies by stream function is obtained,existence and uniqueness of its solution are proven.Based this theory we proposal a new method called"dimension split method"to solve 3D NSE.
文摘This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.
文摘This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.
基金supported by the National Natural Science Foundation of China (No.10662003)Educational Commission of Guangxi Province of China (No.200807MS109)
文摘The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.
基金the grants NSFC 11971021National Key R&D Program of China(No.2018YF645B0204404)NSFC 11501399(R.Du)。
文摘Recent years have witnessed growing interests in solving partial differential equations by deep neural networks,especially in the high-dimensional case.Unlike classical numerical methods,such as finite difference method and finite element method,the enforcement of boundary conditions in deep neural networks is highly nontrivial.One general strategy is to use the penalty method.In the work,we conduct a comparison study for elliptic problems with four different boundary conditions,i.e.,Dirichlet,Neumann,Robin,and periodic boundary conditions,using two representative methods:deep Galerkin method and deep Ritz method.In the former,the PDE residual is minimized in the least-squares sense while the corresponding variational problem is minimized in the latter.Therefore,it is reasonably expected that deep Galerkin method works better for smooth solutions while deep Ritz method works better for low-regularity solutions.However,by a number of examples,we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions.Besides,in some cases,when the boundary condition can be implemented in an exact manner,we find that such a strategy not only provides a better approximate solution but also facilitates the training process.
基金This work was supported by China State Major Key Project for Basic Researches.
文摘The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.
文摘The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory （FSDT）. The equations of motion are obtained applying Hamilton＇s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.
基金Partly supported by the State Major Key Project for Basic Researches
文摘In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.
