Corrigendum： ＂Extracting Closed Classical Orbits from Quantum Recurrence Spectra of a Non-Hydrogenic Atom in Parallel Electric and Magnetic Fields＂

In a paper published by us,[1] we studied how to extract the closed orbit of the non-hydrogenic atom in parallel electric and magnetic fields. However, there was another paper published in 1996 by Courtney,[2] which studied the initial conditions of closed classical orbits from quantum spectra of hydrogen atom in magnetic field. Although the systems are different, both papers studied a similar problem how to extract tile closed orbits from quantum spectra.

State Feedback Stabilzation for a Class of Time-delay Nonlinear Systems

The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.

RESPONSE OF PARAMETRICALLY EXCITED DUFFING-VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK

The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance, it is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node （SN） or Hopf bifurcation （HB） as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.

Fractal analysis of crack paths in Al_2O_3-TiC-4%Co composites

Al2O3-TiC-4%Co(volume fraction) composites(ATC) with high toughness (7.8±0.8 MPa·m1/2) and strength (782±60 MPa) were fabricated. In comparison with Al2O3-TiC composites(AT), the fracture toughness was significantly improved by 60%. The crack paths, generated by Vickers indentation on the polished surfaces of both composites, were analyzed from a fractal point of view to distinguish the possible toughening mechanisms involved. Quantitative evaluation of indentation cracks indicates that the crack deflection plays a more effective role. Cracks of the ATC composites show higher deflection angles and more deflections along the path. ATC composites present higher fractal dimension (D=1.07) than AT composites (D=1.02), which is directly related to the higher fracture toughness. A significant relationship between crack path and toughness is evident: the more irregular the geometry of the crack, the higher the fracture toughness.

Mechanical Properties of Al_2O_3/Cr_3C_2/(W,Ti)C Ceramic Composites with Y_2O_3 Addition

Ceramic composites Al_2O_3/(W, Ti)C/Cr_3C_2 with different contents of Cr_3C_2 and (W, Ti)C particles, and with the additive Y_2O_3, were fabricated with hot-pressing technique at 1700 ℃ under 28 MPa pressure for 30 min in N_2 atmosphere. The mechanical properties were tested, and the microstructure was investigated by environment scanning electron microscope (ESEM), transmission electron microscope (TEM), energy dispersive analysis using X-ray (EDAX) and optical microscope (OM). Results indicate that the incorporation of Cr_3C_2 and (W,Ti)C particles can suppress the grain growth of the others, and the toughening and strengthening effects mainly originate from nano-particles, dispersion toughening and solidification strengthening. The multiphase composite ceramic material Al_2O_3/10%Cr_3C_2/20%(W,Ti)C shows good mechanical properties, especially the fracture toughness increases from 4.0 MPa·m 1/2 (Monolithic Al_2O_3 ceramic) to 8.92 MPa·m 1/2, the flexural strength from 260～340 MPa (Monolithic Al_2O_3 ceramic) to 496 MPa, due to incorporation of the suitable contents of Cr_3C_2 and (W,Ti)C particles.

ELASTIC-PLASTIC DYNAMIC RESPONSE OF A CANTILEVER BEAM SUBJECTED TO OBLIQUE IMPACT AT ITS TIP

By employing large deformation governing equations expressed in the form of finite difference, the dynamic responses of an elastic, perfectly plastic cantilever subjected to an oblique impact at its tip was numerically studied. Through analyzing the instantaneous distribution of the yield function （φ = ｜M/Mo｜ ＋ （N/No）^2）, bending moment and axial force during the early stage of the response, the elastic-plastic deformation mechanism and the influence of axial component of an oblique impact on the dynamic response of a cantilever beam were discussed. The present analysis shows that the deformation mechanism of an elastic-plastic cantilever subjected to an oblique impact consists of four phases, i.e. ‘the expanding compressed plastic region＇ mode; the ‘generalized traveling plastic hinge＇ and ‘shrinking plastic region＇ mixed mode; the ‘stationary plastic hinge＇ mode and ‘elastic vibration＇ mode. Compared with the two-phase deformation mode obtained by using the rigid, perfectly plastic approach, the mode of shrinking plastic region that occurred instantly after the oblique impact and the mode of stationary hinge were both confirmed. The primary features of the deformation mechanism are captured by both analysis methods. It has also been found that the beam＇s deformation is mainly controlled by the axial component of the oblique impact in the early phase of the dynamic response, the deformation mechanism is obviously different from the case of a transverse impact. With further development of the response, the axial component attenuates rapidly and gives negligible contribution to the yielding of the beam cross-section. At the same time, the bending moments along the cantilever develop gradually and dominate the beam＇s deformation. The numerical results indicate that the mass, impact speed and oblique angle are the important factors that influence the elastic-plastic dynamic response of a cantilever beam.

VIBRATION MEASUREMENT OF DOUBLE-ENDED TUNING FORKS RESONATOR

To enhance the coherence and reliability of the double-ended tuning fork （DETF） resonator, a measurement system of resonator vibration is presented to check its dynamic characteristics. Laser Doppler techniques are utilized and the relation between DETF vibration velocity and output current of photodetector is obtained. Resonator vibration equation is also analyzed and its driving power only depends on the direct current bias voltage and the amplitude of alternative voltage. Furthermore, a special resonator driving control circuit based on measurement is designed. The amplitude and frequency of circuit is controlled by a computer so that highly stable and strong driving signal can be output. Experiments on driving and measuring double-ended tuning fork have been done, The frequency of driving signal is 8 kHz and the peak-to-peak value of driving voltage is 140 V. Experimental results indicate resonator can be drived stably by driving control circuit and dynamic characteristics of DETF may be measured in real time.

Feasibility Analysis of Crane Automation

This paper summarizes the modeling methods, open-loop control and closed-loop control techniques of various forms of cranes, worldwide, and discusses their feasibilities and limitations in engineering. Then the dynamic behaviors of cranes are analyzed. Finally, we propose applied modeling methods and feasible control techniques and demonstrate the feasibilities of crane automation.

Microstructures of metallic film and diamond growth from Fe-Ni-C system

The microstructures of metallic film surrounding diamond have been systemically studied using the transmission electron microscopy (TEM) and the atom force microscopy (AFM). The film can be divided into three layers (inner layer near diamond, external layer near graphite and middle layer). The graphite cannot be directly transformed into diamond in the film at HTHP: there exists a parallelrelationship between (111) of γ-(Fe,Ni) and (110) of Fe3C in the inner layer; the sawtooth-like step morphology found by AFM on the film is similar to that of corresponding diamond surface. A new model for diamond growth at HPHT is proposed from the parallel relationship and sawtooth-like step morphology. It is believed that Fe3C may be a transitional phase in the course of diamond growth, γ-(Fe,Ni) in the inner layer can absorb carbon atom groups with lamella structure from Fe3C, and then the carbon groups stack on growing diamond.

Numerical solutions of Green's integral equation for the diffraction of femtosecond laser pulses through a subwavelength aperture

In this letter, we propose a method for the numerical calculations of the femtosecond laser pulse passed through a subwavelength aperture. The time-dependent laser pulse is decomposed into a series of monochromatic simple harmonic waves. For the light field of the harmonic wave with a single frequency, the numerical calculation is made based on the solution of the Green's integral equation set of the electromagnetic waves. Such numerical solution is iterated for all the waves with different frequencies, and all the numerical solutions are transformed into the light fields in the time domain by inverse Fourier transform. The light intensity distributions transmitted the subwavelength aperture are calculated and the results show the propagation of the light field is along the direction of the medium interface.