A simple characteristic equation solution strategy for deriving the fun- damental analytical solutions of 3D isotropic elasticity is proposed. By calculating the determinant of the differential operator matrix obtaine...A simple characteristic equation solution strategy for deriving the fun- damental analytical solutions of 3D isotropic elasticity is proposed. By calculating the determinant of the differential operator matrix obtained from the governing equations of 3D elasticity, the characteristic equation which the characteristic general solution vectors must satisfy is established. Then, by substitution of the characteristic general solution vectors, which satisfy various reduced characteristic equations, into various reduced ad- joint matrices of the differential operator matrix, the corresponding fundamental analyt- ical solutions for isotropic 3D elasticity, including Boussinesq-Galerkin (B-G) solutions, modified Papkovich-Neuber solutions proposed by Min-zhong WANG (P-N-W), and quasi HU Hai-chang solutions, can be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form are also discussed in detail. These works provide a basis for constructing complete and independent analytical trial func- tions used in numerical methods.展开更多
The setting work of backup protection using steady-state current is tedious,and mismatches occasionally occur due to the increased proportion of distributed generations(DGs)connected to the power grid.Thus,there is a ...The setting work of backup protection using steady-state current is tedious,and mismatches occasionally occur due to the increased proportion of distributed generations(DGs)connected to the power grid.Thus,there is a practical need to study a backup protection technology that does not require step-by-step setting and can be adaptively coordinated.This paper proposes an action sequence adaptive to fault positions that uses only positive sequence fault component(PSFC)voltage.Considering the influence of DGs,the unified time dial setting can be obtained by selecting specific points.The protection performance is improved by using the adjacent upstream and downstream protections to meet the coordination time interval in the case of metallic faults at the near-and far-ends of the line.Finally,the expression and implementation scheme for inverse-time backup protection(ITBP)based on the unified characteristic equation is given.Simulation results show that this scheme can adapt to DG penetration scenarios and can realize the adaptive coordination of multi-level relays.展开更多
Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow pheno...Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.展开更多
A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only res...A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only reserve thermodynamic characteristics in the current fundamental chromatographic formulae, but also introduce one or more kinetic parameter, so it is possible to make the macroscopic-control on the effect of kinetic characteristics on chromatographic system.展开更多
In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method. To measure the complex moduli and three p...In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method. To measure the complex moduli and three parameters of standard linear solid, the forced vibration technique of beam is successfully used for PCL and PMMA specimens. The dynamical characteristics of viscoelastic Timoshenko beams, especially the damping properties, are derived from a considerable number of numerical computations. The analyses show that the viscosity of materials has great influence on dynamical characteristics of structures, especially on damping, and the standard linear solid model is the better one for describing the dynamic behavior of high viscous materials.展开更多
In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and th...In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.展开更多
The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simpl...The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.展开更多
The vortex-induced vibration is a well-known problem in mechanics,In this paper,with the help fixed point principle, we study. this problem and find the existencecondition of the periodic solution as well as the regio...The vortex-induced vibration is a well-known problem in mechanics,In this paper,with the help fixed point principle, we study. this problem and find the existencecondition of the periodic solution as well as the region of parameters.展开更多
For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of c...For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.展开更多
In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
Properties of continuous solutions of a second order polynomial-like iterated functional equation are given by considering its characteristic.A useful method to discuss the general case is described indeed in this pro...Properties of continuous solutions of a second order polynomial-like iterated functional equation are given by considering its characteristic.A useful method to discuss the general case is described indeed in this procedure.展开更多
Seismic reservoir prediction plays an important role in oil exploration and development.With the progress of artificial intelligence,many achievements have been made in machine learning seismic reservoir prediction.Ho...Seismic reservoir prediction plays an important role in oil exploration and development.With the progress of artificial intelligence,many achievements have been made in machine learning seismic reservoir prediction.However,due to the factors such as economic cost,exploration maturity,and technical limitations,it is often difficult to obtain a large number of training samples for machine learning.In this case,the prediction accuracy cannot meet the requirements.To overcome this shortcoming,we develop a new machine learning reservoir prediction method based on virtual sample generation.In this method,the virtual samples,which are generated in a high-dimensional hypersphere space,are more consistent with the original data characteristics.Furthermore,at the stage of model building after virtual sample generation,virtual samples screening and model iterative optimization are used to eliminate noise samples and ensure the rationality of virtual samples.The proposed method has been applied to standard function data and real seismic data.The results show that this method can improve the prediction accuracy of machine learning significantly.展开更多
The fracture behaviors near the mode II interface crack tip for orthotropic bimaterial are studied. The non-oscillatory field, where the stress singularity exponent is a real number, is discussed by the complex functi...The fracture behaviors near the mode II interface crack tip for orthotropic bimaterial are studied. The non-oscillatory field, where the stress singularity exponent is a real number, is discussed by the complex function method and the undetermined coefficient method. From the research fracture problems, the stress functions with ten undetermined coefficients and an unknown singularity exponent are introduced when △1 〉 0 and △2 〉 0. By the existence theorem of non-trival solutions for the system of eight homogeneous linear equations, the characteristic equation, the stress singularity exponent, and the discriminating condition of the non-oscillatory singularity are found. By the uniqueness theorem of the solutions for the system of twelve non-homogeneous linear equations with ten unknowns, the ten undermined coefficients in the stress functions are uniquely determined. The definitions of the stress intensity factors are given with the help of one-sided limit, and their theoretical formulae are deduced. The analytic solutions of the stresses near the mode II interface crack tip are derived. The classical results for orthotropic material are obtained.展开更多
A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of abse...A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is examined. The mechanical model consists of two coupled pendula both oscillating on a moving board attached to a spring. The final result performs selection among the peculiar parameters of the physical process (the length, the ratio of masses, the friction and damping coefficients, and the stiffness of the spring), providing a tendency to synchronization.展开更多
By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution ...By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.展开更多
In this paper, we established a connection between a square matrix “A” of order “n” and a matrix defined through a new approach of the recursion relation . (where is any column matrix with n real ...In this paper, we established a connection between a square matrix “A” of order “n” and a matrix defined through a new approach of the recursion relation . (where is any column matrix with n real elements). Now the new matrix gives us a characteristic equation of matrix A and we can find the exact determination of Eigenvalues and its Eigenvectors of the matrix A. This new approach was invented by using Two eigenvector theorems along with some examples. In the subsequent paper we apply this approach by considering some examples on this invention.展开更多
In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term ...In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.展开更多
Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations wi...Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.展开更多
The equation of wave propagation in a circular chamber with mean flow is obtained. Computational solution based on finite element method is employed to determine the transmission loss of expansive chamber. The effect ...The equation of wave propagation in a circular chamber with mean flow is obtained. Computational solution based on finite element method is employed to determine the transmission loss of expansive chamber. The effect of the mean flow and geometry (length of expansion chamber and expansion ratio)on acoustic attenuation performance is discussed, the predicted values of transmission loss of expansion chamber without and with mean flow are compared with those reported in the literature and they agree well. The accuracy of the prediction of transmission loss implies that finite element approximations are applicable to a lot of practical applications.展开更多
When we use Modified Configuration Interaction method(MCI) to calculate the correlation energy of double electron systems, for obtaining the higher precision, we always need huge calculations. In order to handle this...When we use Modified Configuration Interaction method(MCI) to calculate the correlation energy of double electron systems, for obtaining the higher precision, we always need huge calculations. In order to handle this problem, which will cost much CPU time and memory room if only using a single computer to do it, we now adopt the parallel multisection recurrence algorithm. Thus we can use several CPUs to get the ground state energy of a Helium atom at the same time.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10872108 and10876100)the Program for New Century Excellent Talents in University (No. NCET-07-0477)the National Basic Research Programs of China (Nos. 2010CB731503 and 2010CB832701)
文摘A simple characteristic equation solution strategy for deriving the fun- damental analytical solutions of 3D isotropic elasticity is proposed. By calculating the determinant of the differential operator matrix obtained from the governing equations of 3D elasticity, the characteristic equation which the characteristic general solution vectors must satisfy is established. Then, by substitution of the characteristic general solution vectors, which satisfy various reduced characteristic equations, into various reduced ad- joint matrices of the differential operator matrix, the corresponding fundamental analyt- ical solutions for isotropic 3D elasticity, including Boussinesq-Galerkin (B-G) solutions, modified Papkovich-Neuber solutions proposed by Min-zhong WANG (P-N-W), and quasi HU Hai-chang solutions, can be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form are also discussed in detail. These works provide a basis for constructing complete and independent analytical trial func- tions used in numerical methods.
基金supported in part by the National Natural Science Foundation of China(NSFC-UKRI_EPSRC)(No.52061635105)in part by the Science and Technology Program of SGCC(No.5100-202040327A-0-0-00).
文摘The setting work of backup protection using steady-state current is tedious,and mismatches occasionally occur due to the increased proportion of distributed generations(DGs)connected to the power grid.Thus,there is a practical need to study a backup protection technology that does not require step-by-step setting and can be adaptively coordinated.This paper proposes an action sequence adaptive to fault positions that uses only positive sequence fault component(PSFC)voltage.Considering the influence of DGs,the unified time dial setting can be obtained by selecting specific points.The protection performance is improved by using the adjacent upstream and downstream protections to meet the coordination time interval in the case of metallic faults at the near-and far-ends of the line.Finally,the expression and implementation scheme for inverse-time backup protection(ITBP)based on the unified characteristic equation is given.Simulation results show that this scheme can adapt to DG penetration scenarios and can realize the adaptive coordination of multi-level relays.
基金King Mongkut’s University of Technology North Bangkok (KMUTNB)the Office of the Higher Education Commission (OHEC)the National Metal and Materials Technology Center (MTEC) for supporting this research work
文摘Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.
文摘A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only reserve thermodynamic characteristics in the current fundamental chromatographic formulae, but also introduce one or more kinetic parameter, so it is possible to make the macroscopic-control on the effect of kinetic characteristics on chromatographic system.
文摘In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method. To measure the complex moduli and three parameters of standard linear solid, the forced vibration technique of beam is successfully used for PCL and PMMA specimens. The dynamical characteristics of viscoelastic Timoshenko beams, especially the damping properties, are derived from a considerable number of numerical computations. The analyses show that the viscosity of materials has great influence on dynamical characteristics of structures, especially on damping, and the standard linear solid model is the better one for describing the dynamic behavior of high viscous materials.
基金Foundation item is supported by the NNSF of China(19971064)
文摘In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.
文摘The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.
文摘The vortex-induced vibration is a well-known problem in mechanics,In this paper,with the help fixed point principle, we study. this problem and find the existencecondition of the periodic solution as well as the region of parameters.
基金supported by the Major State Basic Research Program of China(No.19990328)the National Tackling Key Program(No.20050200069)+1 种基金the National Natural Science Foundation of China(Nos.10372052,10771124,11101244,and 11271231)the Doctorate Foundation of the State Education Commission(No.20030422047)
文摘For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
基金Supported by NSF of China,Sichuan Provincial Youth Sci-Tech Foundation and Math.Grant of CAS
文摘Properties of continuous solutions of a second order polynomial-like iterated functional equation are given by considering its characteristic.A useful method to discuss the general case is described indeed in this procedure.
基金supported by National Natural Science Foundation of China under Grants 41874146 and 42030103。
文摘Seismic reservoir prediction plays an important role in oil exploration and development.With the progress of artificial intelligence,many achievements have been made in machine learning seismic reservoir prediction.However,due to the factors such as economic cost,exploration maturity,and technical limitations,it is often difficult to obtain a large number of training samples for machine learning.In this case,the prediction accuracy cannot meet the requirements.To overcome this shortcoming,we develop a new machine learning reservoir prediction method based on virtual sample generation.In this method,the virtual samples,which are generated in a high-dimensional hypersphere space,are more consistent with the original data characteristics.Furthermore,at the stage of model building after virtual sample generation,virtual samples screening and model iterative optimization are used to eliminate noise samples and ensure the rationality of virtual samples.The proposed method has been applied to standard function data and real seismic data.The results show that this method can improve the prediction accuracy of machine learning significantly.
基金Project supported by the Natural Science Foundation of Shanxi Province(No.2014011009-2)
文摘The fracture behaviors near the mode II interface crack tip for orthotropic bimaterial are studied. The non-oscillatory field, where the stress singularity exponent is a real number, is discussed by the complex function method and the undetermined coefficient method. From the research fracture problems, the stress functions with ten undetermined coefficients and an unknown singularity exponent are introduced when △1 〉 0 and △2 〉 0. By the existence theorem of non-trival solutions for the system of eight homogeneous linear equations, the characteristic equation, the stress singularity exponent, and the discriminating condition of the non-oscillatory singularity are found. By the uniqueness theorem of the solutions for the system of twelve non-homogeneous linear equations with ten unknowns, the ten undermined coefficients in the stress functions are uniquely determined. The definitions of the stress intensity factors are given with the help of one-sided limit, and their theoretical formulae are deduced. The analytic solutions of the stresses near the mode II interface crack tip are derived. The classical results for orthotropic material are obtained.
文摘A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is examined. The mechanical model consists of two coupled pendula both oscillating on a moving board attached to a spring. The final result performs selection among the peculiar parameters of the physical process (the length, the ratio of masses, the friction and damping coefficients, and the stiffness of the spring), providing a tendency to synchronization.
基金Supported by the National Natural Science Foundation of Chinathe Doctoral Training of the State Education Commission of China
文摘By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.
文摘In this paper, we established a connection between a square matrix “A” of order “n” and a matrix defined through a new approach of the recursion relation . (where is any column matrix with n real elements). Now the new matrix gives us a characteristic equation of matrix A and we can find the exact determination of Eigenvalues and its Eigenvectors of the matrix A. This new approach was invented by using Two eigenvector theorems along with some examples. In the subsequent paper we apply this approach by considering some examples on this invention.
文摘In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.
文摘The equation of wave propagation in a circular chamber with mean flow is obtained. Computational solution based on finite element method is employed to determine the transmission loss of expansive chamber. The effect of the mean flow and geometry (length of expansion chamber and expansion ratio)on acoustic attenuation performance is discussed, the predicted values of transmission loss of expansion chamber without and with mean flow are compared with those reported in the literature and they agree well. The accuracy of the prediction of transmission loss implies that finite element approximations are applicable to a lot of practical applications.
文摘When we use Modified Configuration Interaction method(MCI) to calculate the correlation energy of double electron systems, for obtaining the higher precision, we always need huge calculations. In order to handle this problem, which will cost much CPU time and memory room if only using a single computer to do it, we now adopt the parallel multisection recurrence algorithm. Thus we can use several CPUs to get the ground state energy of a Helium atom at the same time.