In this paper, we consider electromagnetic scattering problems for two-dimensional overfilled cavities. A half ringy absorbing perfectly matched layer (PML) is introduced to enclose the cavity, and the PML formulati...In this paper, we consider electromagnetic scattering problems for two-dimensional overfilled cavities. A half ringy absorbing perfectly matched layer (PML) is introduced to enclose the cavity, and the PML formulations for both TM and TE polarizations are presented. Existence, uniqueness and convergence of the PML solutions are considered. Numerical experiments demonstrate that the PML method is efficient and accurate for solving cavity scattering problems.展开更多
This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be a...This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.展开更多
The scattering problem for the Klein–Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein–Gordon equation, we prove the existence of the sc...The scattering problem for the Klein–Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein–Gordon equation, we prove the existence of the scattering operator, which improves the known results in some sense.展开更多
Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda &...Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda > 0,\mu \ge 0,E = F^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right)F$ we obtain the existence of scattering operator in ^(A↑^n) := { u ] H1(A↑^n) : |x|u ] L2(A↑^n)}.展开更多
Acoustic scattering cross sections of smart furtive obstacles are studied and discussed.A smart furtive obstacle is an obstacle that,when hit by an incoming field,avoids detection through the use of a pressure current...Acoustic scattering cross sections of smart furtive obstacles are studied and discussed.A smart furtive obstacle is an obstacle that,when hit by an incoming field,avoids detection through the use of a pressure current acting on its boundary.A highly parallelizable algorithm for computing the acoustic scattering cross section of smart obstacles is developed.As a case study,this algorithm is applied to the(acoustic)scattering cross section of a"smart"(furtive)simplified version of the NASA space shuttle when hit by incoming time-harmonic plane waves,the wavelengths of which are small compared to the characteristic dimensions of the shuttle.The solution to this numerically challenging scattering problem requires the solution of systems of linear equations with many unknowns and equations.Due to the sparsity of these systems of equations,they can be stored and solved using affordable computing resources.A cross section analysis of the simplified NASA space shuttle highlights three findings:i)the smart furtive obstacle reduces the magnitude of its cross section compared to the cross section of a corresponding"passive"obstacle;ii)several wave propagation directions fail to satisfactorily respond to the smart strategy of the obstacle;iii)satisfactory furtive effects along all directions may only be obtained by using a pressure current of considerable magnitude.Numerical experiments and virtual reality applications can be found at the website:http://www.ceri.uniroma1.it/ceri/zirilli/w7.展开更多
We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We ...We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.展开更多
文摘In this paper, we consider electromagnetic scattering problems for two-dimensional overfilled cavities. A half ringy absorbing perfectly matched layer (PML) is introduced to enclose the cavity, and the PML formulations for both TM and TE polarizations are presented. Existence, uniqueness and convergence of the PML solutions are considered. Numerical experiments demonstrate that the PML method is efficient and accurate for solving cavity scattering problems.
基金supported by the Explore Foundation of Weapon Development (Grant No 7130620)
文摘This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.
基金Supported by Natural Science Foundation of China(Grant No.10931007)Zhejiang Provincial NaturalScience Foundation of China(Grant No.Y6090158)
文摘The scattering problem for the Klein–Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein–Gordon equation, we prove the existence of the scattering operator, which improves the known results in some sense.
文摘Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda > 0,\mu \ge 0,E = F^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right)F$ we obtain the existence of scattering operator in ^(A↑^n) := { u ] H1(A↑^n) : |x|u ] L2(A↑^n)}.
基金the DEISA Consortium(www.deisa.eu),co-funded through the EU FP6 project RI-031513 and the FP7 project RI-222919,for support within the DEISA Extreme Computing Initiative.
文摘Acoustic scattering cross sections of smart furtive obstacles are studied and discussed.A smart furtive obstacle is an obstacle that,when hit by an incoming field,avoids detection through the use of a pressure current acting on its boundary.A highly parallelizable algorithm for computing the acoustic scattering cross section of smart obstacles is developed.As a case study,this algorithm is applied to the(acoustic)scattering cross section of a"smart"(furtive)simplified version of the NASA space shuttle when hit by incoming time-harmonic plane waves,the wavelengths of which are small compared to the characteristic dimensions of the shuttle.The solution to this numerically challenging scattering problem requires the solution of systems of linear equations with many unknowns and equations.Due to the sparsity of these systems of equations,they can be stored and solved using affordable computing resources.A cross section analysis of the simplified NASA space shuttle highlights three findings:i)the smart furtive obstacle reduces the magnitude of its cross section compared to the cross section of a corresponding"passive"obstacle;ii)several wave propagation directions fail to satisfactorily respond to the smart strategy of the obstacle;iii)satisfactory furtive effects along all directions may only be obtained by using a pressure current of considerable magnitude.Numerical experiments and virtual reality applications can be found at the website:http://www.ceri.uniroma1.it/ceri/zirilli/w7.
文摘We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.