Femtosecond electron pulse compression by using the time focusing technique in ultrafast electron diffraction

We present a new model of an electron gun for generating subrelativistic femtosecond （fs） electron pulses. The basic idea is to utilize a dc acceleration stage combined with a time focusing region, the time focusing electrode generates an electron energy chirp for bunching at the target. Without considering the space charge effects, simulations of the electron gun were carried out under the conditions of different dc voltages and various slopes of the voltage added on the time focusing electrode. Tracing and simulating large numbers of photoelectrons through Monte-Carlo and finite difference methods, the electron pulses with 1 ps can be compressed to 55 fs, which will allow significant advances in the field of ultrafast diagnosis.

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.

Triangles Technique for Time and Location Finding of the Lightning Discharge in Spherical Model of the Earth

The spherical model of time and location calculation of the lightning discharge is given. The calculations are made by means of radio signals detection by sensors of the distributed network. The full solution of a problem of lightning discharge cloud-ground type location for three sensors is given. Based on this task the lightning location method for a network of sensors was developed. By means of computational experiments, the analysis of accuracy of the model depending on radio signals detection accuracy at observing stations was done.

Crop Yield Forecasted Model Based on Time Series Techniques

Traditional studies on potential yield mainly referred to attainable yield： the maximum yield which could be reached by a crop in a given environment. The new concept of crop yield under average climate conditions was defined in this paper, which was affected by advancement of science and technology. Based on the new concept of crop yield, the time series techniques relying on past yield data was employed to set up a forecasting model. The model was tested by using average grain yields of Liaoning Province in China from 1949 to 2005. The testing combined dynamic n-choosing and micro tendency rectification, and an average forecasting error was 1.24%. In the trend line of yield change, and then a yield turning point might occur, in which case the inflexion model was used to solve the problem of yield turn point.

Comparison of Mode Quality Factors for Equilateral Triangular, Square and Rhombus Optical Micro-Resonators

The mode frequencies and the quality factors for the equilateral triangular resonator (ETR), the square resonator (SR) and the rhombus resonator (RR) are numerically calculated by the finite difference time domain technique and the Padé approximation. The numerical results show that the resonant modes confined in an equilateral triangular cavity have much higher quality factors than those in the square or the rhombus cavities. The modes in the ETR are totally confined in transverse direction while those in the SR and RR are only partly confined. For the ETR with the side length of 4μm and the refractive index of 3 2, the mode quality factor of about 5 5×10 3 at the wavelength of 1 55μm has been obtained.

Measurement of the echo reduction for underwater acoustic passive materials by using the time reversal technique

A measuring method of the echo reduction of passive materials by using the time reversal（TR） technique is presented. To measure the echo reduction of a sample with this approach, the received signals are firstly focused according to the TR theory. Then, the sample is removed and the TR processing is again employed to realize the focus of the received signal.Finally, the echo reduction of the sample is evaluated with these focusing signals. Besides, to calibrate the measured echo reduction via the TR technique, a standard sample is employed to measure a constant coefficient that only depends on the measurement environment. An aluminum plate sample and a steel plate sample with the same size of 1.1 mxl.O m x0.005 m axe tested in a wave guide tank. The experimental results show that the calibrated values are well consistent with theoretical results under the free field at the measured frequency range of0.5-20 kHz. The relative errors of all the measured values are less than 10% and the values of the expanded uncertainty are less than 1.5 dB. The TR processing focuses the energy in spatial domain and temporal domain, so it can be used to measure the echo reduction of passive materials in the environments with reflections induced by boundaries and low frequency sources.

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.

Measurement of insertion loss for underwater acoustic passive materials with the time reversal technique

A method using the time reversal（TR） technique to measure the insertion loss（IL） of passive materials is presented.Firstly the received signals are focused according to the TR theory when there is not a sample between the source and the received array.Then,the sample is placed near the received array and the TR processing is again employed to realize the focus of the received signal.Finally,the IL of the sample is evaluated from these focusing signals.Because the TR processing can focus the energy in spatial domain and time domain,the method can be used to measure acoustic properties of passive materials in a waveguide tank with reflections induced by boundaries or with low source frequencies.Two samples with the same size of 1.1 m×1.0 m×5 mm are tested in the waveguide tank.The method is demonstrated by the comparison of the theoretical and the experimental results in the measured frequency range of 1-20 kHz.

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.

A modified averaging scheme with application to the secondary Hopf bifurcation of a delayed van der Pol oscillator

In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.

Experimental study on slope sliding and debris flow evolution with and without barrier

A constitutive model on the evolution of debris flow with and without a barrier was established based on the theory of the Bingham model. A certain area of the Laoshan Mountain in Nanjing, Jiangsu Province, in China was chosen for experimental study, and the slope sliding and debris flow detection system was utilized. The change curve of the soil moisture content was attained, demonstrating that the moisture content of the shallow soil layer increases faster than that of the deep soil layer, and that the growth rate of the soil moisture content of the steep slope is large under the first weak rainfall, and that of the gentle slope is significantly affected by the second heavy rainfall. For the steep slope, slope sliding first occurs on the upper slope surface under heavy rainfall and further develops along the top platform and lower slope surface, while under weak rainfall the soil moisture content at the lower part of the slope first increases because of the high runoff velocity, meaning that failure occurring there is more serious. When a barrier was placed at a high position on a slope, debris flow was separated and distributed early and had less ability to carry solids, and the variation of the greatest depth of erosion pits on soil slopes was not significant.

THE SYMMETRIC POSITIVE SOLUTIONS OF 2n-ORDER BOUNDARY VALUE PROBLEMS ON TIME SCALES

In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.