Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Investigation of analytical harmonic frequency and potential energy function, vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

Variable Frequency Harmonic Oscillator in an Electromagnetic Field

The invariant, propagator, and wavefunction for a variable frequency harmonic oscillator in an electromagnetic field are obtained by making a specific coordinate transformation and by using the method of phase space path integral method. The probability amplitudes for a dissipative harmonic oscillator in the time varying electric field are obtained.

Estimation of the complex frequency of a harmonic signal based on a linear least squares method

In this study, we propose a simple linear least squares estimation method(LLS) based on a Fourier transform to estimate the complex frequency of a harmonic signal. We first use a synthetically-generated noisy time series to validate the accuracy and effectiveness of LLS by comparing it with the commonly used linear autoregressive method(AR). For an input frequency of 0.5 m Hz, the calculated deviations from the theoretical value were 0.004‰and 0.008‰ for the LLS and AR methods respectively; and for an input 5 10 6attenuation,the calculated deviations for the LLS and AR methods were 2.4% and 1.6%. Though the theory of the AR method is more complex than that of LLS, the results show LLS is a useful alternative method. Finally, we use LLS to estimate the complex frequencies of the five singlets of the0S2 mode of the Earth’s free oscillation. Not only are the results consistent with previous studies, the method has high estimation precisions, which may prove helpful in determining constraints on the Earth’s interior structures.

ESPRIT-Based Feature Extraction of Helicopter Acoustic Signal

Aim To extract harmonic frequencies of helicopter acoustic signal as features for hel icopter identification. Methods Estimation of signal parameters via rotational invariance techniques(ESPRIT) was selected to extract harmonic frequencies from really measured helicopter acoustic signal and an algorithm based on the SVD TLS was used. Results ESPRIT correctly extracted harmonic frequencies of helicopter using the data of limited length under the variousflight conditions. Conclusion ESPRIT is an effective method of extracting harmonic frequencies and using harmonic frequencies of helicopter acoustic signal to recognize helicopter is feasible.

Analytical Potential Energy Function,Spectroscopic Constants and Vibrational Levels for A^1E_u^+ State of Dimer ~7Li_2

The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential energycurves are calculated at numbers of basis sets.All the ab initio calculated points are fitted to the analytic MurrellSorbie function and then employed to compute the spectroscopic constants.By comparison,the spectroscopic constantsreproduced by the potential attained at D95(3df,3pd) are found to be very close to the experiments,a^d the values (T_e,D_e,R_e,ω_e,ω_eχ_e,α_e and B_e) are of 1.732 93 eV,1.161 36 eV,0.313 27 nm,251.95 cm^(-1),1.623 cm^(-1),0.005 35 cm^(-1),and0.490 cm^(-1),respectively.With the potential obtained at D95(3df,3pd),the totally 75 vibrational states are found whenJ=0.The vibrational levels,the classical turning points and the inertial rotation constants of the first 68 vibrationalstates are calculated for the first time and compared with the available measurements.Good agreement is obtained.The centrifugal distortion constants of the first 32 vibrational states are also reported for the first time.The reasonabledissociation limit for ~7Li_2(A^1∑_u^+) is deduced using the calculated results at present.

Multi-frequency focusing of microjets generated by polygonal prisms

We systematically investigate the power distribution characteristics of microjets generated by prismatic scatterers with different shapes at sub-THz region(λ = 8.57 mm). Among these prismatic scatterers, the hexagonal-type one shows better focusing feature than the others. Aiming at the hexagonal-type one, we propose a double-layer scatterer composed of a Teflon hexagonal prism as an outer layer and a semiconductor cuboid as an inner layer. Aiming at the double-layer scatterer, we further study the effects of refractive index, size, and shape of the inner cuboid on microjet’s features. The study allows us to present an optimized double-layer scatterer, which has a side length λ/2(λ) and a refractive index 2.0(1.4) for the inner(outer) layer. We show that the optimized scatterer can produce an ultra-strong, ultra-narrow microjet with a power enhancement of;0 and a full width at half maximum(FWHM) of;0.26λ, and the microjet is just located at the output face. The microjet keeps compact within the distance range of λ from the output face. These features and effects are explained from the viewpoint of ray optics theory. According to the optimized double-layer scatterer, we further study the multi-frequency focusing features of the microjets, and find that the microjet remains good features at harmonic frequencies 2f_(0) and 3f_(0). In addition, we investigate the effect of an Au sphere presence in the center of the microjet on the power distribution. The results show that a spherical dark spot with a size similar to that of the Au sphere emerges in the area where the Au sphere is placed. The feature can be used to measure the size of a metallic particle.

Quasi-Z Source Inverter Control of PV Grid-Connected Based on Fuzzy PCI

The photovoltaic grid-connected inverter is an important interface between the photovoltaic power generation system and power grid.Its high-quality operation is directly related to the output power quality of the power grid.In order to further optimize the control effect of the quasi-Z source grid-connected photovoltaic inverter,a fuzzy proportional complex integral control(PCI)method is proposed for the current internal loop control.This method can eliminate the steady-state error,and has the characteristic of zero steady-state error adjustment for the AC disturbance signal of a specific frequency.The inductance-capacitance-inductance(LCL)filter is adopted in the grid-connected circuit,and the feedback capacitive current is taken as the control variable of the inner loop to form the active damping control method,which can not only effectively suppress the resonance of the LCL circuit,but also significantly inhibit the high-order harmonics in the grid-connected current.Finally,a system simulation model is built in MATLAB/Simulink to verify the superiority and effectiveness of the proposed method.

Experimental investigation of nonlinear process based on cSHG/DFG in PPLN waveguide

Effects of second harmonic generation （SHG） and cascaded second harmonic generation/difference frequency generation（cSHG/DFG） based on the quasi-phase-matching （QPM） condition in periodically poled lithium niobate （PPLN） waveguide were investigated experimentally. SHG conversion efficiency of -13.6dB and QPM bandwidth of 0.45nm were achieved using a 16.1dBm power of fundamental wave at 1550.4nm. Using pulsed all-fiber passive mode locked laser and tunable continuous wave laser, cSHG/DFG effect utilized for optical sampling was observed. Conversion efficiencies were calculated, and 11.88nm-wide QPM bandwidth was achieved through changing the wavelength of input signal. Conversion efficiency of cSHG/DFG effect increased linearly with the total injected power.

Studies on convergence and scaling law of Thomson backscattering spectra in strong fields

With the saddle point analysis method for the Bessel function structure and property, the convergence problem and the scaling laws of Thomson backscattering spectra are solved and studied in both cases that are for the plane wave laser field without and with applied external constant magnetic field. Some unclear points appeared in previous work are clarified. The extension of the method to a general situation for the laser field with an arbitrary polarization is discussed. We also make a simple analysis and discussion about the optimal spectra dependence of field parameters and its implication to practical applications.

Periodic response analysis of a misaligned rotor system by harmonic balance method with alternating frequency/time domain technique

A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.

The dependence of high-order harmonic generation on the laser frequency and inter-nuclear distance from multi-atom molecular ions

High-order harmonic generation from one-dimensional （1D） multi-atom molecular ions ill an ultra-short laser field is theoretically- investigated, The dynamics of the electron in a linearly polarized intense laser field is analyzed in terms of 1D Schroedinger equation with the Crank-Nicolson algorithm, The dependence of high-order harmonics on the laser frequeney and the biter-nuclear distance is discussed, It is found that the optimum range of inter-nuclear distance should be changed to get extended harmonic generation for different laser frequency, and the lower frequency laser pulse is favorable to higher order harmonic generation as the inter-nuclear distance increases.

The frequency estimation of harmonic signals embedded in multiplicative and additive noise

A method to separate a harmonic signal from multiplicative and additive noises is proposed. The method is to square the signal x(t), which consists of a harmonic signal embedded in multiplicative and additive noises, to form another signal y(t) = x2(t)-E[x2(t)]. After y(t) having been gotten, the Fourier transform is imposed on it. Because the information of x(t) (especially about frequency) is included in y(t), the frequency of x(t) can be estimated from the power spectrum of y(t). According to the simulation, under the condition where frequencies divided by resolution dω are integer, the maximum relative error of estimated frequencies is less than 0.4% when the signal-to-noise ratio (SNR) is greater than -23 dB. If frequencies divided by resolution dω are not integer, the maximum relative error will be less than 2.9%. But it is still small in terms of engineering.

Effective generation of optical quadruple frequency millimeter-wave based on fiber laser using injection rational harmonic mode-locked technique

A method to generate the optical quadruple frequency millimeter-wave with high power efficiency is pro- posed and demonstrated based on the combination of the injection 2nd-order rational harmonic mode- locked fiber ring laser technique and the fiber grating notch filter. In this approach, the fiber Bragg grating notch filter is inserted into the laser cavity to prevent the undesired optical carrier, so that the pump power can be converted to 2nd-order harmonic wave more efficiently. In our experiment, the power efficiency of optical quadruple frequency millimeter-wave （40 GHz） generation is ten folds of that of our previous method based only on the rational harmonic mode-locked technique.

Global synchronous discontinuous pulse width modulation method with fast calculation capability for distributed three-phase inverters

When multiple distributed converters are integrated, the high frequency harmonics will randomly accumulate at the point of common coupling(PCC). This paper proposes a new fast global synchronous discontinuous pulse width modulation(GSDPWM) method of threephase inverters to effectively attenuate the high frequency current harmonics at PCC. Firstly, the basic principle and the realization method of GSDPWM for three-phase inverters are explained, which can be employed for different modulation types. Then a fast calculation method,which can equally derive the minimized total harmonic distortion(THD) of total current, is proposed to release the calculation burden. Finally, MATLAB simulations and experimental results are presented to verify the performance of GSDPWM.

On the performance of the open-shell perturbation theory

A few open-shell molecules are taken as examples in order to examine the performance of the open-shell perturbation theory for electron correlation(J Chem Theory Comput,2009,5:931–936).The convergence of the perturbation series is shown to be stable for the doublet state of NH2 at both the equilibrium and stretched geometries.The equilibrium bond lengths,and harmonic and anharmonic vibrational frequencies are calculated for NO(X2),OH(X2),CH(X2)and NH(X2)with different second-order perturbation theories at the cc-pVDZ,cc-pVTZ and cc-pVQZ levels.The ground state energies of BeF(X2+), MgH(X2+)and the HCCl triplet state have also been computed with various perturbation theories and compared with configuration interaction with single and double excitations(CISD)and CISD+Davidson correction.The energy difference between the formaldehyde(H2CO + )and hydroxymethylene(HCOH+)radical cations has been computed.Our perturbation theory predicts correctly that H2CO + is more stable than HCOH+.However,calculations using UMP2,CASPT2,the Z-averaged perturbation theory and restricted Mφller–Plesset theory fail even to produce the correct sign of the energy difference.

On-Line Adaptive Repetitive Controller for Power Factor Correction Systems

When the fundamental frequency is shifting, it is hard for traditional repetitive controller to work at the resonant frequencies. In this paper, a novel adaptive repetitive controller for power factor correction systems is proposed to suppress the current harmonics. Through the controller, the shifting sampling times of the repetitive controller in a fundamental period can be obtained. Mathematical analysis, simulations and physical experiments have validated the effectiveness of the adaptive repetitive controller.