We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian i...We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by （bi-） modules over Frobenius algebras.展开更多
With a special gauge transformation,the Lax pair of the derivative nonlinear Shcrdinger (DNLS) equation turns to depend on the squared parameter λ = k2instead of the usual spec-tral parameter k. By introducing a new ...With a special gauge transformation,the Lax pair of the derivative nonlinear Shcrdinger (DNLS) equation turns to depend on the squared parameter λ = k2instead of the usual spec-tral parameter k. By introducing a new direct product of Jost solu-tions,the complete Hamiltonian theory of the DNLS equation is constructed on the basis of the squared spectral parameter,which shows that the integrability completeness is still preserved. This result will be beneficial to the further study of the DNLS equation,such as the direct perturbation method.展开更多
We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain...We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.展开更多
Based on Hamiltonian energy theory, this paper proposes a robust nonlinear controller for the wind turbine with doubly fed induction generator （DFIG）, such that the closed-loop system can achieve its stability. Furt...Based on Hamiltonian energy theory, this paper proposes a robust nonlinear controller for the wind turbine with doubly fed induction generator （DFIG）, such that the closed-loop system can achieve its stability. Furthermore, in the presence of disturbances, the closed-loop system is finite-gain L2 stable by the Hamiltonian controller. The Hamiltonian energy approach provides us a physical insight and gives a new way to the controller design. The simulation results illustrate that the proposed method is effective and has its advantage.展开更多
文摘We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by （bi-） modules over Frobenius algebras.
基金Supported by the National Natural Science Foundation of China (10705022)
文摘With a special gauge transformation,the Lax pair of the derivative nonlinear Shcrdinger (DNLS) equation turns to depend on the squared parameter λ = k2instead of the usual spec-tral parameter k. By introducing a new direct product of Jost solu-tions,the complete Hamiltonian theory of the DNLS equation is constructed on the basis of the squared spectral parameter,which shows that the integrability completeness is still preserved. This result will be beneficial to the further study of the DNLS equation,such as the direct perturbation method.
文摘We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.
基金supported by the National Natural Science Foundation of China(No.51007019)the Priority Academic Program Development of Jiangsu Higher Education Institutions(Coastal Development Conservancy)
文摘Based on Hamiltonian energy theory, this paper proposes a robust nonlinear controller for the wind turbine with doubly fed induction generator （DFIG）, such that the closed-loop system can achieve its stability. Furthermore, in the presence of disturbances, the closed-loop system is finite-gain L2 stable by the Hamiltonian controller. The Hamiltonian energy approach provides us a physical insight and gives a new way to the controller design. The simulation results illustrate that the proposed method is effective and has its advantage.
