Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations that continues today...Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations that continues today. Much progress has been made in the utilization of solid-state NMR to illuminate molecular structure and dynamics in systems not controllable by any other way. NMR deals with time-dependent perturbations of nuclear spin systems and solving the time-dependent Schrodinger equation is a central problem in quantum physics in general and solid-state NMR in particular. This theoretical perspective outlines the methods used to treat theoretical problems in solid-state NMR as well as the recent theoretical development of spin dynamics in NMR and physics. The purpose of this review is to unravel the versatility of theories in solid-state NMR and to present the recent theoretical developments of spin dynamics.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
Solving a time-dependent linear differential equation towards obtaining evolution operators is a central problem in solid-state nuclear magnetic resonance. To this end, average Hamiltonian theory and Floquet theory ha...Solving a time-dependent linear differential equation towards obtaining evolution operators is a central problem in solid-state nuclear magnetic resonance. To this end, average Hamiltonian theory and Floquet theory have been the two commonly used theoretically methods in spin dynamics of NMR. We recently introduced the Floquet-Magnus expansion approach and here, we present the methodology of potentials future theoretical approaches such as the Fer expansion, Chebyshev expansion and Cayley transformation that could be useful tools for numerical integrators and simulations of spin dynamics in NMR.展开更多
针对多机电力系统中,发电机励磁和静止同步串联补偿器(static synchronous series compensator,SSSC)的协调控制问题,引入广义Hamilton系统理论,进行非线性协调控制器设计。SSSC采用考虑内部动态的三阶模型,并将SSSC与各台发电机的相互...针对多机电力系统中,发电机励磁和静止同步串联补偿器(static synchronous series compensator,SSSC)的协调控制问题,引入广义Hamilton系统理论,进行非线性协调控制器设计。SSSC采用考虑内部动态的三阶模型,并将SSSC与各台发电机的相互作用用附加电磁功率表示。将包含发电机励磁和SSSC的多机电力系统描述成广义耗散Hamilton系统形式,利用边界函数法和L2干扰抑制控制方法设计了发电机励磁和SSSC的协调控制器。四机两区域系统的仿真结果表明:与传统的分散控制器相比,所提的非线性协调控制器能够有效地提高系统的暂态稳定性和电压调节性能。展开更多
文摘Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations that continues today. Much progress has been made in the utilization of solid-state NMR to illuminate molecular structure and dynamics in systems not controllable by any other way. NMR deals with time-dependent perturbations of nuclear spin systems and solving the time-dependent Schrodinger equation is a central problem in quantum physics in general and solid-state NMR in particular. This theoretical perspective outlines the methods used to treat theoretical problems in solid-state NMR as well as the recent theoretical development of spin dynamics in NMR and physics. The purpose of this review is to unravel the versatility of theories in solid-state NMR and to present the recent theoretical developments of spin dynamics.
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Solving a time-dependent linear differential equation towards obtaining evolution operators is a central problem in solid-state nuclear magnetic resonance. To this end, average Hamiltonian theory and Floquet theory have been the two commonly used theoretically methods in spin dynamics of NMR. We recently introduced the Floquet-Magnus expansion approach and here, we present the methodology of potentials future theoretical approaches such as the Fer expansion, Chebyshev expansion and Cayley transformation that could be useful tools for numerical integrators and simulations of spin dynamics in NMR.
文摘针对多机电力系统中,发电机励磁和静止同步串联补偿器(static synchronous series compensator,SSSC)的协调控制问题,引入广义Hamilton系统理论,进行非线性协调控制器设计。SSSC采用考虑内部动态的三阶模型,并将SSSC与各台发电机的相互作用用附加电磁功率表示。将包含发电机励磁和SSSC的多机电力系统描述成广义耗散Hamilton系统形式,利用边界函数法和L2干扰抑制控制方法设计了发电机励磁和SSSC的协调控制器。四机两区域系统的仿真结果表明:与传统的分散控制器相比,所提的非线性协调控制器能够有效地提高系统的暂态稳定性和电压调节性能。
