Based on the approach of biorthogonal basis, we carry out the quasinormal modes （QNMs） expansions for a class of open systems described by the wave equation with outgoing wave boundary conditions. For such a non-Her...Based on the approach of biorthogonal basis, we carry out the quasinormal modes （QNMs） expansions for a class of open systems described by the wave equation with outgoing wave boundary conditions. For such a non-Hermitian system, the eigenfunction perturbation expansions and Green function method, which are based on the orthogonal eigenvectors of the Hermitian Hamiltonian for the dosed quantum system, can be generalized in terms of the biorthogonal basis, the two sets of eigenfunctions of H and its adjointness H . The time-independent perturbation theory for the complex frequencies can be also developed.展开更多
This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear syst...This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.展开更多
A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of th...A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presen! Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems x~ two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to ve~ the accuracy and validity of the expansion method.展开更多
A full-duplex optical passive access scheme is proposed and verified by simulation, in which hybrid 64/16/4-quadrature amplitude modulation(64/16/4QAM) orthogonal frequency division multiplexing(OFDM) optical signal i...A full-duplex optical passive access scheme is proposed and verified by simulation, in which hybrid 64/16/4-quadrature amplitude modulation(64/16/4QAM) orthogonal frequency division multiplexing(OFDM) optical signal is for downstream transmission and non-return-to-zero(NRZ) optical signal is for upstream transmission. In view of the transmitting and receiving process for downlink optical signal, in-phase/quadrature-phase(I/Q) modulation based on Mach-Zehnder modulator(MZM) and homodyne coherent detection technology are employed, respectively. The simulation results show that the bit error ratio(BER) less than hardware decision forward error correction(HD-FEC) threshold is successfully obtained over transmission path with 20-km-long standard single mode fiber(SSMF) for hybrid downlink modulation OFDM optical signal. In addition, by dividing the system bandwidth into several subchannels consisting of some continuous subcarriers, it is convenient for users to select different channels depending on requirements of communication.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos. 10647108, 10547101, and 10604002the National Fundamental Research Program of China under Grant No. 2006CB921200
文摘Based on the approach of biorthogonal basis, we carry out the quasinormal modes （QNMs） expansions for a class of open systems described by the wave equation with outgoing wave boundary conditions. For such a non-Hermitian system, the eigenfunction perturbation expansions and Green function method, which are based on the orthogonal eigenvectors of the Hermitian Hamiltonian for the dosed quantum system, can be generalized in terms of the biorthogonal basis, the two sets of eigenfunctions of H and its adjointness H . The time-independent perturbation theory for the complex frequencies can be also developed.
基金supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Research on model order reduction methods based on the discrete orthogonal polynomials”(2023D01C163)The Tianchi Talent Introduction Plan Project of Xinjiang Uygur Autonomous Region of China“Research on orthogonal decomposition model order reduction methods for discrete control systems”.
文摘This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.
基金supported by the National Natural Science Foundation of China (Grant No. 10962004)the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2012MS0105)
文摘A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presen! Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems x~ two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to ve~ the accuracy and validity of the expansion method.
基金supported by the National Natural Science Foundation of China(No.61107064)the Chongqing University Innovation Team Founding(No.KJTD201320)the Chongqing Science and Technology Commission Foundation(No.cstc2016jcyjA 1233)
文摘A full-duplex optical passive access scheme is proposed and verified by simulation, in which hybrid 64/16/4-quadrature amplitude modulation(64/16/4QAM) orthogonal frequency division multiplexing(OFDM) optical signal is for downstream transmission and non-return-to-zero(NRZ) optical signal is for upstream transmission. In view of the transmitting and receiving process for downlink optical signal, in-phase/quadrature-phase(I/Q) modulation based on Mach-Zehnder modulator(MZM) and homodyne coherent detection technology are employed, respectively. The simulation results show that the bit error ratio(BER) less than hardware decision forward error correction(HD-FEC) threshold is successfully obtained over transmission path with 20-km-long standard single mode fiber(SSMF) for hybrid downlink modulation OFDM optical signal. In addition, by dividing the system bandwidth into several subchannels consisting of some continuous subcarriers, it is convenient for users to select different channels depending on requirements of communication.
