We apply the newly proposed double absorbing boundary condition(DABC)(Hagstrom et al., 2014) to solve the boundary reflection problem in seismic finite-difference(FD) modeling. In the DABC scheme, the local high...We apply the newly proposed double absorbing boundary condition(DABC)(Hagstrom et al., 2014) to solve the boundary reflection problem in seismic finite-difference(FD) modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer(PML), the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.展开更多
Temperature characteristics are important for the performance of organic thin film devices. On the basis of the hopping theory of Miller-Abrahams,an analytical model of charge transport for bilayer organic devices und...Temperature characteristics are important for the performance of organic thin film devices. On the basis of the hopping theory of Miller-Abrahams,an analytical model of charge transport for bilayer organic devices under the organicorganic interface limited current conduction is developed. The dependence of current, field,and carrier distribution in bilayer organic devices with the structure of "injection electrode/Layer Ⅰ/Layer Ⅱ/collection electrode" on temperature are numerically analyzed. We conclude that, for a given applied voltage, when temperature is raised, the voltage of LayerⅠ will increase,and the field will be higher. Meanwhile, the voltage of Layer Ⅲ will decrease, the field will become weaker accordingly,and the current of the device will increase.展开更多
Analysis and comparison of Jiaozhou Bay data collected from May 1991 to February 1994 revealed the spatiotemporal variations of the ambient Si(OH) 4∶NO 3 (Si∶N) concentration ratios and the seasonal variations of (S...Analysis and comparison of Jiaozhou Bay data collected from May 1991 to February 1994 revealed the spatiotemporal variations of the ambient Si(OH) 4∶NO 3 (Si∶N) concentration ratios and the seasonal variations of (Si∶N) ratios in Jiaozhou Bay and showed that the Si∶N ratios were < 1 throughout Jiaozhou Bay in spring, autumn, and winter. These results provide further evidence that silicate limits the growth of phytoplankton (i.e. diatoms) in spring, autumn and winter. Moreover, comparison of the spatiotemporal variations of the Si∶N ratio and primary production in Jiaozhou Bay suggested their close relationship. The spatiotemporal pattern of dissolved silicate matched well that of primary production in Jiaozhou Bay. Along with the environmental change of Jiaozhou Bay in the last thirty years, the N and P concentrations tended to rise, whereas Si concentration showed cyclic seasonal variations. With the variation of nutrient Si limiting the primary production in mind, the authors found that the range of values of primary production is divided into three parts: the basic value of Si limited primary production, the extent of Si limited primary production and the critical value of Si limited primary production, which can be calculated for Jiaozhou Bay by Equations (1), (2) and (3), showing that the time of the critical value of Si limitation of phytoplankton growth in Jiaozhou Bay is around November 3 to November 13 in autumn; and that the time of the critical value of Si satisfaction of phytoplankton growth in Jiaozhou Bay is around May 22 to June 7 in spring. Moreover, the calculated critical value of Si satisfactory for phytoplankton growth is 2.15-0.76 μmol/L and the critical value of Si limitation of phytoplankton growth is 1.42-0.36 μmol/L; so that the time period of Si limitation of phytoplankton growth is around November 13 to May 22 in the next year; the time period of Si satisfactory for phytoplankton growth is around June 7 to November 3. This result also explains why critical values of nutrient silicon affect phytoplankton growth in spring and autumn are different in different waters of Jiaozhou Bay and also indicates how the silicate concentration affects the phytoplankton assemblage structure. The dilution of silicate concentration by seawater exchange affects the growth of phytoplankton so that the primary production of phytoplankton declines outside Jiaozhou Bay earlier than inside Jiaozhou Bay by one and half months. This study showed that Jiaozhou Bay phytoplankton badly need silicon and respond very sensitively and rapidly to the variation of silicon.展开更多
Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,ar...Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.展开更多
Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to t...Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.展开更多
Ultrasonic leaky Lamb waves are sensitive to defects and debonding in multilayer media. In this study, we use the finite-difference method to simulate the response of flexural waves in the presence of defects owing to...Ultrasonic leaky Lamb waves are sensitive to defects and debonding in multilayer media. In this study, we use the finite-difference method to simulate the response of flexural waves in the presence of defects owing to casing corrosion and rough fluctuations at the cement-formation interface. The ultrasonic obliquely incidence could effectively stimulate the flexural waves. The defects owing to casing corrosion change the amplitude of the early- arrival flexural wave, which gradually decrease with increasing defect thickness on the exterior walls and is the lowest when the defect length and wavelength were comparable. The scattering at the defects decreases the energy of flexural waves in the casing that leaks directly to fluids. For rough cement-formation interface, the early-arrival flexural waves do not change, whereas the late-arrival flexural waves have reduced amplitude owing to the scattering at rough interface.展开更多
Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary valu...Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary value problem and variational equations, then replaced the complex resistivity of the model with the Cole-Cole model's parameters under ignoring the EM effect. Through solving the last linear equations, electric potentials of all the model's points were obtained. With changing model's parameters, the authors got different curves of the Fs and phases. According to the results of the simulation, the algorithm is proved to be correct and adaptable.展开更多
In this paper,the initial boundary value problems of the nonlinear Sobolev-Galpern equation are studied.The existence,uniqueness of local solution for the problem are obtained by means of a special Green's functio...In this paper,the initial boundary value problems of the nonlinear Sobolev-Galpern equation are studied.The existence,uniqueness of local solution for the problem are obtained by means of a special Green's function and the contraction mapping principle.Finally,the blow-up of solution in finite time under some assumed conditions is proved with the aid of Jensen's inequality.展开更多
We propose a new method for calculating the dressed fermion propagator at finite chemical potential in QED3 under the rainbow approximation of Dyson-Schwinger equation. In the above approximation, we show that the dre...We propose a new method for calculating the dressed fermion propagator at finite chemical potential in QED3 under the rainbow approximation of Dyson-Schwinger equation. In the above approximation, we show that the dressed fermion propagator at finite chemical potential # has the form S(p) = iγ.p^-A(p^-2) + B( p^-2) with p^-μ= (p^-1p3 + iμ). Using this form of fermion propagator at nonzero chemical potential, we investigate the Dyson-Schwinger equation for the dressed fermion propagator at finite chemical potential and study the effects of the chemical potential on the critical number of the fermion flavors.展开更多
This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establi...This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.展开更多
In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume a...In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho's conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.展开更多
Problems of fluid structure interactions are governed by a set of fundamental parameters. This work aims at showing through simple examples the changes in natural vibration frequencies and mode shapes for wall-cavity ...Problems of fluid structure interactions are governed by a set of fundamental parameters. This work aims at showing through simple examples the changes in natural vibration frequencies and mode shapes for wall-cavity systems when the structural rigidity is modified. Numerical results are constructed using ANSYS software with triangular finite elements for both the fluid (2D acoustic elements) and the solid (plane stress) domains. These former results are compared to proposed analytical expressions, showing an alternative benchmark tool for the analyst. Very rigid wall structures imply in frequencies and mode shapes almost identical to those achieved for an acoustic cavity with Neumann boundary condition at the interface. In this case, the wall behaves as rigid and fluid-structure system mode shapes are similar to those achieved for the uncoupled reservoir case.展开更多
We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear ...We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations.Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal,the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.展开更多
It is widely accepted that the singular term plays a leading role in driving domain switching around the crack tip of ferroelectric ceramics.When an applied electric field approaches or even exceeds the coercive one,h...It is widely accepted that the singular term plays a leading role in driving domain switching around the crack tip of ferroelectric ceramics.When an applied electric field approaches or even exceeds the coercive one,however,non-singular terms are no longer negligible and the switching of a large or global scale takes place.To analyze the large scale switching,one has to get a full asymptotic solution to the electric field in the vicinity of the crack tip.Take a double cantilever beam specimen as an example.The derivation of the full electric field is simplified as a mixed boundary value problem of an infinite strip containing a semi-infinite impermeable crack.The boundary value problem is solved by an analytic function and a conformal mapping to yield a full electric field solution in a closed form.Based on the full field solution,the large scale domain switching is examined.The switching zones predicted by the large and small scale switching models are illustrated and compared with each other near the tip of a stationary crack.展开更多
基金supported by the National Nature Science Foundation of China(Grant No.U1262208)the Important National Science & Technology Specific Projects(Grant No.2011ZX05019-008)
文摘We apply the newly proposed double absorbing boundary condition(DABC)(Hagstrom et al., 2014) to solve the boundary reflection problem in seismic finite-difference(FD) modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer(PML), the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.
文摘Temperature characteristics are important for the performance of organic thin film devices. On the basis of the hopping theory of Miller-Abrahams,an analytical model of charge transport for bilayer organic devices under the organicorganic interface limited current conduction is developed. The dependence of current, field,and carrier distribution in bilayer organic devices with the structure of "injection electrode/Layer Ⅰ/Layer Ⅱ/collection electrode" on temperature are numerically analyzed. We conclude that, for a given applied voltage, when temperature is raised, the voltage of LayerⅠ will increase,and the field will be higher. Meanwhile, the voltage of Layer Ⅲ will decrease, the field will become weaker accordingly,and the current of the device will increase.
文摘Analysis and comparison of Jiaozhou Bay data collected from May 1991 to February 1994 revealed the spatiotemporal variations of the ambient Si(OH) 4∶NO 3 (Si∶N) concentration ratios and the seasonal variations of (Si∶N) ratios in Jiaozhou Bay and showed that the Si∶N ratios were < 1 throughout Jiaozhou Bay in spring, autumn, and winter. These results provide further evidence that silicate limits the growth of phytoplankton (i.e. diatoms) in spring, autumn and winter. Moreover, comparison of the spatiotemporal variations of the Si∶N ratio and primary production in Jiaozhou Bay suggested their close relationship. The spatiotemporal pattern of dissolved silicate matched well that of primary production in Jiaozhou Bay. Along with the environmental change of Jiaozhou Bay in the last thirty years, the N and P concentrations tended to rise, whereas Si concentration showed cyclic seasonal variations. With the variation of nutrient Si limiting the primary production in mind, the authors found that the range of values of primary production is divided into three parts: the basic value of Si limited primary production, the extent of Si limited primary production and the critical value of Si limited primary production, which can be calculated for Jiaozhou Bay by Equations (1), (2) and (3), showing that the time of the critical value of Si limitation of phytoplankton growth in Jiaozhou Bay is around November 3 to November 13 in autumn; and that the time of the critical value of Si satisfaction of phytoplankton growth in Jiaozhou Bay is around May 22 to June 7 in spring. Moreover, the calculated critical value of Si satisfactory for phytoplankton growth is 2.15-0.76 μmol/L and the critical value of Si limitation of phytoplankton growth is 1.42-0.36 μmol/L; so that the time period of Si limitation of phytoplankton growth is around November 13 to May 22 in the next year; the time period of Si satisfactory for phytoplankton growth is around June 7 to November 3. This result also explains why critical values of nutrient silicon affect phytoplankton growth in spring and autumn are different in different waters of Jiaozhou Bay and also indicates how the silicate concentration affects the phytoplankton assemblage structure. The dilution of silicate concentration by seawater exchange affects the growth of phytoplankton so that the primary production of phytoplankton declines outside Jiaozhou Bay earlier than inside Jiaozhou Bay by one and half months. This study showed that Jiaozhou Bay phytoplankton badly need silicon and respond very sensitively and rapidly to the variation of silicon.
基金NASI (National Academy of Sciences, India) for providing financial support
文摘Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.
文摘Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.
基金supported by the Research and Development of Key Instruments and Technologies for Deep Resources Prospecting(No.ZDYZ2012-1-07)the National Natural Science Foundation of China(Nos.41204099,11134011,and 11274341)
文摘Ultrasonic leaky Lamb waves are sensitive to defects and debonding in multilayer media. In this study, we use the finite-difference method to simulate the response of flexural waves in the presence of defects owing to casing corrosion and rough fluctuations at the cement-formation interface. The ultrasonic obliquely incidence could effectively stimulate the flexural waves. The defects owing to casing corrosion change the amplitude of the early- arrival flexural wave, which gradually decrease with increasing defect thickness on the exterior walls and is the lowest when the defect length and wavelength were comparable. The scattering at the defects decreases the energy of flexural waves in the casing that leaks directly to fluids. For rough cement-formation interface, the early-arrival flexural waves do not change, whereas the late-arrival flexural waves have reduced amplitude owing to the scattering at rough interface.
基金Project supported by the National Key Technology R &D Program(2006BAB01A07)
文摘Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary value problem and variational equations, then replaced the complex resistivity of the model with the Cole-Cole model's parameters under ignoring the EM effect. Through solving the last linear equations, electric potentials of all the model's points were obtained. With changing model's parameters, the authors got different curves of the Fs and phases. According to the results of the simulation, the algorithm is proved to be correct and adaptable.
文摘In this paper,the initial boundary value problems of the nonlinear Sobolev-Galpern equation are studied.The existence,uniqueness of local solution for the problem are obtained by means of a special Green's function and the contraction mapping principle.Finally,the blow-up of solution in finite time under some assumed conditions is proved with the aid of Jensen's inequality.
基金the National Natural Science Foundation of China under,高等学校博士学科点专项科研项目
文摘We propose a new method for calculating the dressed fermion propagator at finite chemical potential in QED3 under the rainbow approximation of Dyson-Schwinger equation. In the above approximation, we show that the dressed fermion propagator at finite chemical potential # has the form S(p) = iγ.p^-A(p^-2) + B( p^-2) with p^-μ= (p^-1p3 + iμ). Using this form of fermion propagator at nonzero chemical potential, we investigate the Dyson-Schwinger equation for the dressed fermion propagator at finite chemical potential and study the effects of the chemical potential on the critical number of the fermion flavors.
文摘This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.
基金supported by Singapore AcRF RG59/08 (M52110092)Singapore NRF 2007 IDM-IDM002-010.
文摘In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho's conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.
文摘Problems of fluid structure interactions are governed by a set of fundamental parameters. This work aims at showing through simple examples the changes in natural vibration frequencies and mode shapes for wall-cavity systems when the structural rigidity is modified. Numerical results are constructed using ANSYS software with triangular finite elements for both the fluid (2D acoustic elements) and the solid (plane stress) domains. These former results are compared to proposed analytical expressions, showing an alternative benchmark tool for the analyst. Very rigid wall structures imply in frequencies and mode shapes almost identical to those achieved for an acoustic cavity with Neumann boundary condition at the interface. In this case, the wall behaves as rigid and fluid-structure system mode shapes are similar to those achieved for the uncoupled reservoir case.
基金supported by National Natural Science Foundation of China (Grant Nos. 91330202, 11371026, 11201501, 11571389, 11001259 and 11031006)National Basic Research Program of China (Grant No. 2011CB309703)the National Center for Mathematics and Interdisciplinary Science, Chinese Academy of Sciences, the President Foundation of Academy of Mathematics and Systems Science, Chinese Academy of Sciences and the Program for Innovation Research in Central University of Finance and Economics
文摘We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations.Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal,the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.
基金sponsored by the National Natural Science Foundation of China (Grant No.10702071)the China Postdoctoral Science Foundation+1 种基金the Shanghai Postdoctoral Scientific Program (Grant No.10R21415800)the Shanghai Leading Academic Discipline Project (Grant No.B302)
文摘It is widely accepted that the singular term plays a leading role in driving domain switching around the crack tip of ferroelectric ceramics.When an applied electric field approaches or even exceeds the coercive one,however,non-singular terms are no longer negligible and the switching of a large or global scale takes place.To analyze the large scale switching,one has to get a full asymptotic solution to the electric field in the vicinity of the crack tip.Take a double cantilever beam specimen as an example.The derivation of the full electric field is simplified as a mixed boundary value problem of an infinite strip containing a semi-infinite impermeable crack.The boundary value problem is solved by an analytic function and a conformal mapping to yield a full electric field solution in a closed form.Based on the full field solution,the large scale domain switching is examined.The switching zones predicted by the large and small scale switching models are illustrated and compared with each other near the tip of a stationary crack.