Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination o...Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination of the characterization for the symbol of generalized operators and the classical scattering results. In addition, some properties （Poincare invariance and irreducibility） of the solutions are discussed.展开更多
Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will ...Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.展开更多
Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculati...Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.展开更多
The application of wavelets is explored to solve acoustic radiation and scattering problems. A new wavelet approach is presented for solving two-dimensional and axisymmetric acoustic problems. It is different from the...The application of wavelets is explored to solve acoustic radiation and scattering problems. A new wavelet approach is presented for solving two-dimensional and axisymmetric acoustic problems. It is different from the previous methods in which Galerkin formulation or wavelet matrix transform approach is used. The boundary quantities are expended in terms of a basis of the periodic, orthogonal wavelets on the interval. Using wavelet transform leads a highly sparse matrix system. It can avoid an additional integration in Galerkin formulation, which may be very computationally expensive. The techniques of the singular integrals in two-dimensional and axisymmetric wavelet formulation are proposed. The new method can solve the boundary value problems with Dirichlet, Neumann and mixed conditions and treat axisymmetric bodies with arbitrary boundary conditions. It can be suitable for the solution at large wave numbers. A series of numerical examples are given. The comparisons of the results from new approach with those from boundary element method and analytical solutions demonstrate that the new techique has a fast convergence and high accuracy.展开更多
基金supported by NSFC (10401011,10871153)China Postdoctoral Science Foundation (2005037660)
文摘Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination of the characterization for the symbol of generalized operators and the classical scattering results. In addition, some properties （Poincare invariance and irreducibility） of the solutions are discussed.
基金Supported by the National Natural Science Foundation of China under Grant Nos 51477039 and 51207041the Program of Hefei Normal University under Grant Nos 2014136KJA04 and 2015TD01the Key Project of Provincial Natural Science Research of University of Anhui Province of China under Grant No KJ2015A174
文摘Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.
基金Supported by the National Natural Science Foundation of China under Grant No.11405128Natural Science Basic Research Plan in Shaanxi Province of China under Grant No.15JK2093
文摘Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.
文摘The application of wavelets is explored to solve acoustic radiation and scattering problems. A new wavelet approach is presented for solving two-dimensional and axisymmetric acoustic problems. It is different from the previous methods in which Galerkin formulation or wavelet matrix transform approach is used. The boundary quantities are expended in terms of a basis of the periodic, orthogonal wavelets on the interval. Using wavelet transform leads a highly sparse matrix system. It can avoid an additional integration in Galerkin formulation, which may be very computationally expensive. The techniques of the singular integrals in two-dimensional and axisymmetric wavelet formulation are proposed. The new method can solve the boundary value problems with Dirichlet, Neumann and mixed conditions and treat axisymmetric bodies with arbitrary boundary conditions. It can be suitable for the solution at large wave numbers. A series of numerical examples are given. The comparisons of the results from new approach with those from boundary element method and analytical solutions demonstrate that the new techique has a fast convergence and high accuracy.
