The gold (Au) nanorods with various aspect ratios are obtained by a seed-media method in low pH growth solution. Transmission electron microscopy (TEM) and UV-visible spectrophotometry are utilized to characterize...The gold (Au) nanorods with various aspect ratios are obtained by a seed-media method in low pH growth solution. Transmission electron microscopy (TEM) and UV-visible spectrophotometry are utilized to characterize the Au nanorods, and the longitudinal absorption peak positions of Au nanorods show different shifting trends of the growth evolutions in various low pH (1~3) solutions. Other influential factors on the shape of Au nanorod are also systematically studied under low pH reaction condition. The positions of longitudinal peak shift between 600 nm and 900 nm, with the aspect ratios of Au nanorods varying from 2 to 5 both in the simulation and experimental results. The simulation results are in agreement with experimental ones.展开更多
In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibi...In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.展开更多
In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is...In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is given. We use the optimal control framework to establish both the existence and necessary condition of the minimizer for the cost func- tional. Furthermore, we prove the stability and the local uniqueness of the minimizer. Some numerical results will be presented and discussed.展开更多
With more applications of seismic exploration in metal ore exploration,forward modelling of seismic wave has become more important in metal ore. Finite difference method and pseudo-spectral method are two important me...With more applications of seismic exploration in metal ore exploration,forward modelling of seismic wave has become more important in metal ore. Finite difference method and pseudo-spectral method are two important methods of wave-field simulation. Results of previous studies show that both methods have distinct advantages and disadvantages: Finite difference method has high precision but its dispersion is serious; pseudospectral method considers both computational efficiency and precision but has less precision than finite-difference. The authors consider the complex structural characteristics of the metal ore,furthermore add random media in order to simulate the complex effects produced by metal ore for wave field. First,the study introduced the theories of random media and two forward modelling methods. Second,it compared the simulation results of two methods on fault model. Then the authors established a complex metal ore model,added random media and compared computational efficiency and precision. As a result,it is found that finite difference method is better than pseudo-spectral method in precision and boundary treatment,but the computational efficiency of pseudospectral method is slightly higher than the finite difference method.展开更多
This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small ...This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small thicknesses. For discussion and comparison, the scattering matrix method is also presented in physics-based form and coherent form. The latter form resembles closely that of hybrid matrix method and helps to highlight their relationship and distinction. For both scattering and hybrid matrix methods, their formulations in terms of eigenwaves solution are provided concisely. Making use of the hybrid matrix, the recursive asymptotic method without eigenwaves solution is described and discussed. The method bypasses the intricacies of eigenvalue-eigenvector approach and requires only elementary matrix operations along with thin- layer asymptotic approximation. It can be used to determine Green’s function matrix readily and facilitates the trade-off between computation efficiency and accuracy.展开更多
The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s ...The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.展开更多
In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the un-derlying problem. Unconditional L2-stability...In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the un-derlying problem. Unconditional L2-stability and error estimate of order O?τr+1+hk+1/2? are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r+1 in temporal variable t.展开更多
The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based...The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.展开更多
The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin...The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.展开更多
Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on e...Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.展开更多
This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field couple...This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.展开更多
This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all so...This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all solutions of the problem are re- duced to finding eigenvalues and eigensolutions, which include zero-eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian matrix and non-zero-eigenvalue solutions. The classical solutions are described by zero-eigen- solutions and non-zero-eigensolutions show localized solutions. Numerical results show some rules of non-zero-eigenvalue and their eigensolutions.展开更多
The study of wave propagation in finite/infinite media has many applications in geotechnical and structural earthquake engineering and has been a focus of research for the past few decades. This paper presents an anal...The study of wave propagation in finite/infinite media has many applications in geotechnical and structural earthquake engineering and has been a focus of research for the past few decades. This paper presents an analysis of 2D anti- plane problems (Love waves) and 2D in-plane problems (Rayleigh waves) in the frequency domain in media consisting of a near-field irregular and a far-field regular part. The near field part may contain structures and its boundaries with the far-field can be of any shape. In this study, the irregular boundaries of the near-field are treated as consistent boundaries, extending the concept of Lysmer's vertical consistent boundaries. The presented technique is called the Condensed Hyperelements Method (CHM). In this method, the irregular boundary is limited to a vertical boundary at each end that is a consistent boundary at the far-field side. Between the two ends, the medium is discretized with hyperelements. Using static condensation, the stiffness matrix of the far-field is derived for the nodes on the irregular boundary. Examples of the application of the CHM illustrate its excellent accuracy and efficiency.展开更多
基金Project supported by the Nippon Sheet Glass Foundation for Materials Science and Engineering(Japan,January 2012)the Natural Science Foundation of Hubei Province of China(Grant No.2011CDB426)
文摘The gold (Au) nanorods with various aspect ratios are obtained by a seed-media method in low pH growth solution. Transmission electron microscopy (TEM) and UV-visible spectrophotometry are utilized to characterize the Au nanorods, and the longitudinal absorption peak positions of Au nanorods show different shifting trends of the growth evolutions in various low pH (1~3) solutions. Other influential factors on the shape of Au nanorod are also systematically studied under low pH reaction condition. The positions of longitudinal peak shift between 600 nm and 900 nm, with the aspect ratios of Au nanorods varying from 2 to 5 both in the simulation and experimental results. The simulation results are in agreement with experimental ones.
基金the National Natural Science Foundation of China(No.40774056)Program of Excellent Team in Harbin Institute of Technology
文摘In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.
基金supported in part by the CNRST Morocco,the Volkswagen Foundation:Grant number I/79315Hydromed project
文摘In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is given. We use the optimal control framework to establish both the existence and necessary condition of the minimizer for the cost func- tional. Furthermore, we prove the stability and the local uniqueness of the minimizer. Some numerical results will be presented and discussed.
基金Supported by the National"863"Project(No.2014AA06A605)
文摘With more applications of seismic exploration in metal ore exploration,forward modelling of seismic wave has become more important in metal ore. Finite difference method and pseudo-spectral method are two important methods of wave-field simulation. Results of previous studies show that both methods have distinct advantages and disadvantages: Finite difference method has high precision but its dispersion is serious; pseudospectral method considers both computational efficiency and precision but has less precision than finite-difference. The authors consider the complex structural characteristics of the metal ore,furthermore add random media in order to simulate the complex effects produced by metal ore for wave field. First,the study introduced the theories of random media and two forward modelling methods. Second,it compared the simulation results of two methods on fault model. Then the authors established a complex metal ore model,added random media and compared computational efficiency and precision. As a result,it is found that finite difference method is better than pseudo-spectral method in precision and boundary treatment,but the computational efficiency of pseudospectral method is slightly higher than the finite difference method.
文摘This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small thicknesses. For discussion and comparison, the scattering matrix method is also presented in physics-based form and coherent form. The latter form resembles closely that of hybrid matrix method and helps to highlight their relationship and distinction. For both scattering and hybrid matrix methods, their formulations in terms of eigenwaves solution are provided concisely. Making use of the hybrid matrix, the recursive asymptotic method without eigenwaves solution is described and discussed. The method bypasses the intricacies of eigenvalue-eigenvector approach and requires only elementary matrix operations along with thin- layer asymptotic approximation. It can be used to determine Green’s function matrix readily and facilitates the trade-off between computation efficiency and accuracy.
文摘The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.
基金supported by NSFC(11341002)NSFC(11171104,10871066)+1 种基金the Construct Program of the Key Discipline in Hunansupported in part by US National Science Foundation under Grant DMS-1115530
文摘In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the un-derlying problem. Unconditional L2-stability and error estimate of order O?τr+1+hk+1/2? are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r+1 in temporal variable t.
基金the Fundamental Research Funds for the Central Universities under Grant No.HEUCFZ1125National Natural Science Foundation of China under Grant No.10972064
文摘The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.
文摘The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.
基金Iranian Offshore Oil Company (IOOC) for financial support of this work
文摘Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.
基金Project (No. 10372088) supported by the National Natural Science Foundation of China
文摘This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.
基金Project (Nos. 19902014 and 10272024) supported by the NationalNatural Science Foundation of China
文摘This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all solutions of the problem are re- duced to finding eigenvalues and eigensolutions, which include zero-eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian matrix and non-zero-eigenvalue solutions. The classical solutions are described by zero-eigen- solutions and non-zero-eigensolutions show localized solutions. Numerical results show some rules of non-zero-eigenvalue and their eigensolutions.
文摘The study of wave propagation in finite/infinite media has many applications in geotechnical and structural earthquake engineering and has been a focus of research for the past few decades. This paper presents an analysis of 2D anti- plane problems (Love waves) and 2D in-plane problems (Rayleigh waves) in the frequency domain in media consisting of a near-field irregular and a far-field regular part. The near field part may contain structures and its boundaries with the far-field can be of any shape. In this study, the irregular boundaries of the near-field are treated as consistent boundaries, extending the concept of Lysmer's vertical consistent boundaries. The presented technique is called the Condensed Hyperelements Method (CHM). In this method, the irregular boundary is limited to a vertical boundary at each end that is a consistent boundary at the far-field side. Between the two ends, the medium is discretized with hyperelements. Using static condensation, the stiffness matrix of the far-field is derived for the nodes on the irregular boundary. Examples of the application of the CHM illustrate its excellent accuracy and efficiency.