In this letter, a distributed protocol for sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays is proposed, and a brief procedure of convergence analysis for s...In this letter, a distributed protocol for sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays is proposed, and a brief procedure of convergence analysis for such algorithm over undirected connected graphs is provided. Furthermore, a simple yet generic criterion is also presented to guarantee synchronized oscillatory motions in coupled harmonic oscillators. Subsequently, the simulation results are worked out to demonstrate the efficiency and feasibility of the theoretical results.展开更多
Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determi...Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).展开更多
The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condi...The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain(OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears.展开更多
Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic pa...Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized secondharmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.展开更多
The main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle. The nonlinear coupling relation among various harmonics can be found by balance theorem of freque...The main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle. The nonlinear coupling relation among various harmonics can be found by balance theorem of frequency domain. The superhet receiver circuits which are described by nonlinear differential equation of comprising even degree terms include three main harmonic components: the difference frequency and two signal frequencies. Based on the nonlinear coupling relation, taking superhet circuit as an example, this paper demonstrates that the every one of three main harmonics in networks must individually observe conservation of complex power. The power of difference frequency is from variable-frequency device. And total dissipative power of each harmonic is equal to zero. These conclusions can also be verified by the traditional harmonic analysis. The oscillation solutions which consist of the mixture of three main harmonics possess very long oscillation period, the spectral distribution are very tight, similar to evolution from doubling period leading to chaos. It can be illustrated that the chaos is sufficient or infinite extension of the oscillation period. In fact, the oscillation solutions plotted by numerical simulation all are certainly a periodic function of discrete spectrum. When phase portrait plotted hasn’t finished one cycle, it is shown as aperiodic chaos.展开更多
The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and c...The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and collective Hamiltonians leads to the description of the mechanism for energy dissipation in physical systems.展开更多
The second-harmonic generation （SHG） circular dichroism in the light of reflection from chiral films of tripod-like chiral molecules is investigated. The expressions of the second-harmonic generation circular dichro...The second-harmonic generation （SHG） circular dichroism in the light of reflection from chiral films of tripod-like chiral molecules is investigated. The expressions of the second-harmonic generation circular dichroism are derived from our presented three-coupled-oscillator model for the tripod-like chiral molecules. Spectral dependence of the circular dichroism of SHG from film surface composed of tripod-like chiral molecules is simulated numerically and analysed. Influence of ehiral parameters on the second-harmonic generation circular dichroism spectrum in chiral films is studied. The result shows that the second-harmonic generation circular dichroism is a sensitive method of detecting chirality compared with the ordinary circular dichroism in linear optics. All of our work indicates that the classical molecular models are very effective to explain the second-harmonic generation circular dichroism of chiral molecular system. The classical molecular model theory can give us a clear physical picture and brings us very instructive information about the link between the molecular configuration and the nonlinear processes.展开更多
The factorization of the radial Schrodinger equation of n-dimensional (n≥2) hydrogen atoms and isotropic harmonic oscillators was investigated and four kinds of raising and lowering operators were derived.The relatio...The factorization of the radial Schrodinger equation of n-dimensional (n≥2) hydrogen atoms and isotropic harmonic oscillators was investigated and four kinds of raising and lowering operators were derived.The relation between n -dimensional (n≥2) and one-dimensional hydrogen atoms and harmonic oscillators was discussed.展开更多
In the study of electromechanical coupling vibration of mill main drive system, the influence of electrical system on the mechanical transmission is considered generally, however the research for the mechanism of elec...In the study of electromechanical coupling vibration of mill main drive system, the influence of electrical system on the mechanical transmission is considered generally, however the research for the mechanism of electromechanical interaction is lacked. In order to research the electromechanical coupling resonance of main drive system on the F3 mill in a plant, the cycloconverter and synchronous motor are modeled and simulated by the MTLAB/SIMUL1NK firstly, simulation result show that the current harmonic of the cycloconverter can lead to the pulsating torque of motor output. Then the natural characteristics of the mechanical drive system are calculated by ANSYS, the result show that the modal frequency contains the component which is close to the coupling vibration frequency of 42Hz. According to the simulation result of the mechanical and electrical system, the closed loop feedback model including the two systems are built, and the mechanism analysis of electromechanical coupling presents that there is the interaction between the current harmonic of electrical system and the speed of the mechanical drive system. At last, by building and computing the equivalent nonlinear dynamics model of the mechanical drive system, the dynamic characteristics of system changing with the stiffness, damping coefficient and the electromagnetic torque are obtained. Such electromechanical interaction process is suggested to consider in research of mill vibration, which can induce strong coupling vibration behavior in the rolling mill drive system.展开更多
基金partially supported by the National Science Foundation of China(11272791,61364003,and 61203006)the Innovation Program of Shanghai Municipal Education Commission(10ZZ61 and 14ZZ151)the Science and Technology Foundation of Guizhou Province(20122316)
文摘In this letter, a distributed protocol for sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays is proposed, and a brief procedure of convergence analysis for such algorithm over undirected connected graphs is provided. Furthermore, a simple yet generic criterion is also presented to guarantee synchronized oscillatory motions in coupled harmonic oscillators. Subsequently, the simulation results are worked out to demonstrate the efficiency and feasibility of the theoretical results.
基金Key Track Follow-Up Service Foundation of the State Education Commission of China，Science Foundation of the Liaoning Education Commission of China
文摘Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).
基金supported by the National Natural Science Foundation of China for the Youth (Grant Nos. 11501385 and 11801385)。
文摘The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain(OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears.
基金Project supported by the Natural Science Foundation of Heilongjiang Province, China （Grant No A200406）.
文摘Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized secondharmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.
文摘The main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle. The nonlinear coupling relation among various harmonics can be found by balance theorem of frequency domain. The superhet receiver circuits which are described by nonlinear differential equation of comprising even degree terms include three main harmonic components: the difference frequency and two signal frequencies. Based on the nonlinear coupling relation, taking superhet circuit as an example, this paper demonstrates that the every one of three main harmonics in networks must individually observe conservation of complex power. The power of difference frequency is from variable-frequency device. And total dissipative power of each harmonic is equal to zero. These conclusions can also be verified by the traditional harmonic analysis. The oscillation solutions which consist of the mixture of three main harmonics possess very long oscillation period, the spectral distribution are very tight, similar to evolution from doubling period leading to chaos. It can be illustrated that the chaos is sufficient or infinite extension of the oscillation period. In fact, the oscillation solutions plotted by numerical simulation all are certainly a periodic function of discrete spectrum. When phase portrait plotted hasn’t finished one cycle, it is shown as aperiodic chaos.
文摘The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and collective Hamiltonians leads to the description of the mechanism for energy dissipation in physical systems.
基金Project supported by the excellent Team in Harbin Institute of Technology,Chinathe Natural Science Foundation of Heilongjiang Province,China (Grant No. A200406)
文摘The second-harmonic generation （SHG） circular dichroism in the light of reflection from chiral films of tripod-like chiral molecules is investigated. The expressions of the second-harmonic generation circular dichroism are derived from our presented three-coupled-oscillator model for the tripod-like chiral molecules. Spectral dependence of the circular dichroism of SHG from film surface composed of tripod-like chiral molecules is simulated numerically and analysed. Influence of ehiral parameters on the second-harmonic generation circular dichroism spectrum in chiral films is studied. The result shows that the second-harmonic generation circular dichroism is a sensitive method of detecting chirality compared with the ordinary circular dichroism in linear optics. All of our work indicates that the classical molecular models are very effective to explain the second-harmonic generation circular dichroism of chiral molecular system. The classical molecular model theory can give us a clear physical picture and brings us very instructive information about the link between the molecular configuration and the nonlinear processes.
文摘The factorization of the radial Schrodinger equation of n-dimensional (n≥2) hydrogen atoms and isotropic harmonic oscillators was investigated and four kinds of raising and lowering operators were derived.The relation between n -dimensional (n≥2) and one-dimensional hydrogen atoms and harmonic oscillators was discussed.
基金Supported by National Science&Technology Pillar Program of China during the 12th Five-Year Plan Period(Product Quality Optimization of Precision Strip and R&D for Key Equipment,Grant No.2015BAF30B01)
文摘In the study of electromechanical coupling vibration of mill main drive system, the influence of electrical system on the mechanical transmission is considered generally, however the research for the mechanism of electromechanical interaction is lacked. In order to research the electromechanical coupling resonance of main drive system on the F3 mill in a plant, the cycloconverter and synchronous motor are modeled and simulated by the MTLAB/SIMUL1NK firstly, simulation result show that the current harmonic of the cycloconverter can lead to the pulsating torque of motor output. Then the natural characteristics of the mechanical drive system are calculated by ANSYS, the result show that the modal frequency contains the component which is close to the coupling vibration frequency of 42Hz. According to the simulation result of the mechanical and electrical system, the closed loop feedback model including the two systems are built, and the mechanism analysis of electromechanical coupling presents that there is the interaction between the current harmonic of electrical system and the speed of the mechanical drive system. At last, by building and computing the equivalent nonlinear dynamics model of the mechanical drive system, the dynamic characteristics of system changing with the stiffness, damping coefficient and the electromagnetic torque are obtained. Such electromechanical interaction process is suggested to consider in research of mill vibration, which can induce strong coupling vibration behavior in the rolling mill drive system.
