We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on ex...We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge–Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om extended phase space symplectic-like methods with the midpoint permutation.展开更多
We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized plasmas.The adaptive scheme is applied to the Gauss...We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized plasmas.The adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving algorithms.These new adaptive algorithms are second order,and their algebraic order is carefully studied.Numerical results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.展开更多
A high-sensitivity temperature sensor based on the harmonic Vernier effect is proposed and verified by experiments.The main component of the sensor is a Sagnac interferometer consisting of two sections of polarization...A high-sensitivity temperature sensor based on the harmonic Vernier effect is proposed and verified by experiments.The main component of the sensor is a Sagnac interferometer consisting of two sections of polarization maintaining fibers(PMFs)spliced with an intersection angle of 45o between their fast axes.The harmonic Vernier effect is achieved by setting the length of one of the PMFs an integral multiple(i-times)of the length of the other plus a detuning factor.Compared with the Sagnac interferometer based on the fundamental Vernier effect,the temperature sensitivity of the harmonic Vernier effect is higher,reaching i+1 times of that of the fundamental Vernier effect(i is the order of the harmonic).展开更多
We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system.The numerical sim...We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system.The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation.Furthermore,they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.展开更多
A broadband instantaneous multi-frequency measurement system based on chirped pulse compression,which potentially has a sub-megahertz(MHz)accuracy and a hundred-gigahertz(GHz)measurement range,is demonstrated.A signal...A broadband instantaneous multi-frequency measurement system based on chirped pulse compression,which potentially has a sub-megahertz(MHz)accuracy and a hundred-gigahertz(GHz)measurement range,is demonstrated.A signalunder-test(SUT)is converted into a carrier-suppressed double-sideband(CS-DSB)signal,which is then combined with an optical linearly frequency-modulated signal having the sweeping range covering the+1 st-order sideband of the CSDSB signal.With photodetection,low-pass filtering,and pulse compression,accurate frequencies of the SUT are obtained via locating the correlation peaks.In the experiment,single-and multi-frequency measurements with a measurement range from 3 to 18 GHz and a measurement accuracy of<±100 MHz are achieved.展开更多
We propose Poisson integrators for the numerical integration of separable Poisson systems.We analyze three situations in which Poisson systems are separated in threeways and Poisson integrators can be constructed by u...We propose Poisson integrators for the numerical integration of separable Poisson systems.We analyze three situations in which Poisson systems are separated in threeways and Poisson integrators can be constructed by using the splittingmethod.Numerical results show that the Poisson integrators outperform the higher order non-Poisson integrators in terms of long-termenergy conservation and computational cost.The Poisson integrators are also shown to be more efficient than the canonicalized sympletic methods of the same order.展开更多
In this paper,symplectic schemes and symmetric schemes are presented to simulate Nonlinear Schrodinger Equation(NLSE)in case of dark soliton motion.Firstly,by Ablowitz–Ladik model(A–L model),the NLSE is discretized...In this paper,symplectic schemes and symmetric schemes are presented to simulate Nonlinear Schrodinger Equation(NLSE)in case of dark soliton motion.Firstly,by Ablowitz–Ladik model(A–L model),the NLSE is discretized into a non-canonical Hamiltonian system.Then,different kinds of coordinate transformations can be used to standardize the non-canonical Hamiltonian system.Therefore,the symplectic schemes and symmetric schemes can be employed to simulate the solitons motion and test the preservation of the invariants of the A–L model and the conserved quantities approximations of the original NLSE.The numerical experiments show that symplectic schemes and symmetric schemes have similar simulation effect,and own significant superiority over non-symplectic and non-symmetric schemes in long-term tracking the motion of solitons,preserving the invariants and the approximations of conserved quantities.Moreover,it is obvious that coordinate transformations with more symmetry have a better simulation effect.展开更多
Emerging Xenes,mostly group IVA and VA elemental two-dimensional(2D)materials,have small and tunable band gaps between graphene and transition metal dichalcogenides,giving versatile electrical properties.While their m...Emerging Xenes,mostly group IVA and VA elemental two-dimensional(2D)materials,have small and tunable band gaps between graphene and transition metal dichalcogenides,giving versatile electrical properties.While their microelectronic or optoelectronic properties are being extensively explored,there remains a lack of study on Xenes'uniquely advantageous thermoelectric performance.This review highlights state-of-the-art experimental and theoretical progress in the thermoelectric effect and devices of IVA and VA Xenes.Vertically displaced,a.k.a.“buckled”or“puckered,”atomic arrays result in exotic and tunable electrical or thermal transport behaviors.Different from chemical doping strategies usually employed in bulk thermoelectric materials,2D Xenes can be tuned by physical means,such as atomic layer control and quantum confinement effects.A precise and compatible platform for 2D thermoelectric effect and devices study is available via the engagement between micro/nanofabrication of 2D Xene transistors and thermal property measurement techniques.This review also reveals potential thermoelectric applications of Xenes and their compounds(Bi2Te3,Bi2Se3,etc.),such as accurate stretchable temperature sensors,fast terahertz photodetectors,and so on.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11901564 and 12171466)。
文摘We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge–Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om extended phase space symplectic-like methods with the midpoint permutation.
基金supported by National Natural Science Foundation of China(Nos.11901564,11775222 and 12171466)Geo-Algorithmic Plasma Simulator(GAPS)Project。
文摘We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized plasmas.The adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving algorithms.These new adaptive algorithms are second order,and their algebraic order is carefully studied.Numerical results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.
基金supports from the National Natural Science Foundation of China(Grant No.62175116)1311 Talent Plan of Nanjing University of Posts and Telecommunications.
文摘A high-sensitivity temperature sensor based on the harmonic Vernier effect is proposed and verified by experiments.The main component of the sensor is a Sagnac interferometer consisting of two sections of polarization maintaining fibers(PMFs)spliced with an intersection angle of 45o between their fast axes.The harmonic Vernier effect is achieved by setting the length of one of the PMFs an integral multiple(i-times)of the length of the other plus a detuning factor.Compared with the Sagnac interferometer based on the fundamental Vernier effect,the temperature sensitivity of the harmonic Vernier effect is higher,reaching i+1 times of that of the fundamental Vernier effect(i is the order of the harmonic).
基金supported by the ITER-China Program(Grant No.2014GB124005)the National Natural Science Foundation of China(Grant Nos.11371357 and 11505186).
文摘We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system.The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation.Furthermore,they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.
基金supported in part by the Postgraduate Research and Practice Innovation Program of Jiangsu Province(No.KYLX16_0367)the National Natural Science Foundation of China(Nos.62071226 and 61971372)+1 种基金the Hong Kong Scholar Program(No.G-YZ2S)HK RGC GRF(No.15200718)。
文摘A broadband instantaneous multi-frequency measurement system based on chirped pulse compression,which potentially has a sub-megahertz(MHz)accuracy and a hundred-gigahertz(GHz)measurement range,is demonstrated.A signalunder-test(SUT)is converted into a carrier-suppressed double-sideband(CS-DSB)signal,which is then combined with an optical linearly frequency-modulated signal having the sweeping range covering the+1 st-order sideband of the CSDSB signal.With photodetection,low-pass filtering,and pulse compression,accurate frequencies of the SUT are obtained via locating the correlation peaks.In the experiment,single-and multi-frequency measurements with a measurement range from 3 to 18 GHz and a measurement accuracy of<±100 MHz are achieved.
基金supported by the National Natural Science Foundation of China(Grant Nos.11901564 and 12171466).
文摘We propose Poisson integrators for the numerical integration of separable Poisson systems.We analyze three situations in which Poisson systems are separated in threeways and Poisson integrators can be constructed by using the splittingmethod.Numerical results show that the Poisson integrators outperform the higher order non-Poisson integrators in terms of long-termenergy conservation and computational cost.The Poisson integrators are also shown to be more efficient than the canonicalized sympletic methods of the same order.
基金This work was supported by the Fundamental Research Funds for the Central Universities(Nos.2018ZY14,2019ZY20 and 2015ZCQ-LY-01)Beijing Higher Education Young Elite Teacher Project(YETP0769)the National Natural Science Foundation of China(Grant Nos.61571002,61179034 and 61370193).
文摘In this paper,symplectic schemes and symmetric schemes are presented to simulate Nonlinear Schrodinger Equation(NLSE)in case of dark soliton motion.Firstly,by Ablowitz–Ladik model(A–L model),the NLSE is discretized into a non-canonical Hamiltonian system.Then,different kinds of coordinate transformations can be used to standardize the non-canonical Hamiltonian system.Therefore,the symplectic schemes and symmetric schemes can be employed to simulate the solitons motion and test the preservation of the invariants of the A–L model and the conserved quantities approximations of the original NLSE.The numerical experiments show that symplectic schemes and symmetric schemes have similar simulation effect,and own significant superiority over non-symplectic and non-symmetric schemes in long-term tracking the motion of solitons,preserving the invariants and the approximations of conserved quantities.Moreover,it is obvious that coordinate transformations with more symmetry have a better simulation effect.
基金from the Fundamental Research Funds for the Central Universities(Grant No.2242020K40008).L.T.acknowledges the support from National Natural Science Foundation of China(51602051)Jiangsu Province Innovation Talent Program,Jiangsu Province Six-Category Talent Program(DZXX-011).D.A.acknowledges the support from US National Science Foundation(NSF)the Presidential Early Career Award for Scientists and Engineers(PECASE).
文摘Emerging Xenes,mostly group IVA and VA elemental two-dimensional(2D)materials,have small and tunable band gaps between graphene and transition metal dichalcogenides,giving versatile electrical properties.While their microelectronic or optoelectronic properties are being extensively explored,there remains a lack of study on Xenes'uniquely advantageous thermoelectric performance.This review highlights state-of-the-art experimental and theoretical progress in the thermoelectric effect and devices of IVA and VA Xenes.Vertically displaced,a.k.a.“buckled”or“puckered,”atomic arrays result in exotic and tunable electrical or thermal transport behaviors.Different from chemical doping strategies usually employed in bulk thermoelectric materials,2D Xenes can be tuned by physical means,such as atomic layer control and quantum confinement effects.A precise and compatible platform for 2D thermoelectric effect and devices study is available via the engagement between micro/nanofabrication of 2D Xene transistors and thermal property measurement techniques.This review also reveals potential thermoelectric applications of Xenes and their compounds(Bi2Te3,Bi2Se3,etc.),such as accurate stretchable temperature sensors,fast terahertz photodetectors,and so on.
