In this paper, the ascent of 2 × 2 infinite dimensional Hamiltonian operators and a class of 4 × 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2 ×...In this paper, the ascent of 2 × 2 infinite dimensional Hamiltonian operators and a class of 4 × 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2 × 2 infinite dimensional Hamiltonian operator is 1 and the ascent of a class of 4 × 4 infinite dimensional Hamiltonian operators that arises in study of elasticity is2 are obtained. Concrete examples are given to illustrate the effectiveness of criterions.展开更多
A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic...A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.展开更多
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite...This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.展开更多
The formal series symmetry approach （FSSA）, a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supe...The formal series symmetry approach （FSSA）, a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the N = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely f（t）. Some interesting special cases of symmetry algebras are commutativity of higher order generalized symmetries. many generalized symmetries with an arbitrary function presented, including a limit case f（t） = 1 related to the展开更多
This study reports on the propagation of elastic waves in 1D and 2D mass spring structures.An analytical and computation model is presented for the 1D and 2D mass spring systems with different examples.An enhancement ...This study reports on the propagation of elastic waves in 1D and 2D mass spring structures.An analytical and computation model is presented for the 1D and 2D mass spring systems with different examples.An enhancement in the band gap values was obtained by modeling the structures to obtain low frequency band gaps at small dimensions.Additionally,the evolution of the band gap as a function of mass value is discussed.Special attention is devoted to the local resonance property in frequency ranges within the gaps in the band structure for the corresponding infinite periodic lattice in the 1D and 2D mass spring system.A linear defect formed of a row of specific masses produces an elastic waveguide that transmits at the narrow pass band frequency.The frequency of the waveguides can be selected by adjusting the mass and stiffness coefficients of the materials constituting the waveguide.Moreover,we pay more attention to analyze the wave multiplexer and DE-multiplexer in the 2D mass spring system.We show that two of these tunable waveguides with alternating materials can be employed to filter and separate specific frequencies from a broad band input signal.The presented simulation data is validated through comparison with the published research,and can be extended in the development of resonators and MEMS verification.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11101200 and 11371185)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2013ZD01)
文摘In this paper, the ascent of 2 × 2 infinite dimensional Hamiltonian operators and a class of 4 × 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2 × 2 infinite dimensional Hamiltonian operator is 1 and the ascent of a class of 4 × 4 infinite dimensional Hamiltonian operators that arises in study of elasticity is2 are obtained. Concrete examples are given to illustrate the effectiveness of criterions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41575026,41275113,and 41475021)
文摘A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.
基金supported by the National Natural Science Foundation of China(Grant No 10562002)the Natural Science Foundation of Inner Mongolia,China(Grants No 200508010103 and 200711020106)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No 20070126002)
文摘This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.
基金supported by the National Natural Science Foundation of China(Grant Nos.11275123,11175092,11475052,and 11435005)the Shanghai Knowledge Service Platform for Trustworthy Internet of Things,China(Grant No.ZF1213)the Talent Fund and K C Wong Magna Fund in Ningbo University,China
文摘The formal series symmetry approach （FSSA）, a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the N = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely f（t）. Some interesting special cases of symmetry algebras are commutativity of higher order generalized symmetries. many generalized symmetries with an arbitrary function presented, including a limit case f（t） = 1 related to the
文摘This study reports on the propagation of elastic waves in 1D and 2D mass spring structures.An analytical and computation model is presented for the 1D and 2D mass spring systems with different examples.An enhancement in the band gap values was obtained by modeling the structures to obtain low frequency band gaps at small dimensions.Additionally,the evolution of the band gap as a function of mass value is discussed.Special attention is devoted to the local resonance property in frequency ranges within the gaps in the band structure for the corresponding infinite periodic lattice in the 1D and 2D mass spring system.A linear defect formed of a row of specific masses produces an elastic waveguide that transmits at the narrow pass band frequency.The frequency of the waveguides can be selected by adjusting the mass and stiffness coefficients of the materials constituting the waveguide.Moreover,we pay more attention to analyze the wave multiplexer and DE-multiplexer in the 2D mass spring system.We show that two of these tunable waveguides with alternating materials can be employed to filter and separate specific frequencies from a broad band input signal.The presented simulation data is validated through comparison with the published research,and can be extended in the development of resonators and MEMS verification.
