Design of a grating by a joint optimization method for a phase-shifting point diffraction interferometer

A grating is an important element of a phase-shifting point diffraction interferometer, and the grating constant and duty cycle have a great impact on the interferometer, so the design of a grating becomes significant. In order to measure the projection objective with a numerical aperture of 0.2, we present a joint optimization method of a pinhole and grating based on scalar diffraction and the finite difference time domain method. The grating constant and the film thickness are selected, and the duty cycle of the grating is optimized. The results show that in the grating processing the material chromium is adopted, the thickness is 200 nm, and the grating constant is 15 μm. When the duty cycle is 55%, the interference fringe contrast is the greatest. The feasibility of the design result is further verified by experiment.     

Efficiency and stability enhancement of a virtual cathode oscillator

A virtual cathode oscillator(VCO) with a resonant cavity is presented and investigated numerically and theoretically,and its efficiency and stability are enhanced. An equivalent circuit method is introduced to analyze the resonant cavity composed of anode foil and feedback annulus, and a theoretical expression for the fundamental mode frequency of the resonant cavity is given. The VCO is investigated in detail with a particle-in-cell method. We obtain the microwave frequencies from simulation, theoretical expression, and relative references, and draw three important conclusions. First, the microwave frequency is a constant when the diode voltage is changed from 588 kV to 717 kV. Second, the fluctuation of the microwave frequency is very small when the AK gap is changed from 1.2 cm to 1.6 cm. Third, the microwave frequency agrees with the theoretical result. The relative error, which is calculated according to the theoretical and simulation frequencies, is only1.7%.     

Three-order form invariance and conserved quantity

In this paper, the definition of three-order form invariance is given. Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition of Lie symmetry, which comes from the three-order form invariance, is obtained. Finally a three-order Hojman conserved quantity is studied and an example is given to illustrate the application of the obtained results.     

Contact mode and force transferring model of cylindrical ultrasonic motor with bending vibration mode

Cylindrical Ultrasonic Motor （CUSM） can be widely used in many fields such as zoom and focus system of cameras, electric curtain and micro-driver of MEMS. This work concentrates on the single-point and the double-point contact modes between the stator and the rotor, which are proved by theory and experiment. There is a critical point of the pre-pressure. When the pre-pressure is below the critical point, the single-point model is suitable; otherwise the double-point model is appropriate. Then the force transferring model is analyzed, and expressions of mechanical characteristics and efficiency of the motor are put forward. Simulation results are confirmed by experimental ones, which shows that the model is well suited to guide design of the motor. Finally a Ф14 mm prototype was fabricated. Its maximum torque is 0.11 Nm, and the no-load speed is about 300 r/min.     

Global Solutions of Einstein—Dirac Equation on the Conformal Space

The difference between the Riemann and Lorentz spinor manifolds of four dimensions is that the Dirac operator of the former is elliptic and that of the latter is hyperbolic.Moreover the spinor group of the former is a compact group and that of the latter is a noncompact group,which is isomorphic to SL(2,C).Hence the results and their interpretation coming from the two theories would be different.In this short note we study only the Lorentz spinor manifold and,especially,the solutions of Einstein-Dirac equations on the conformal space,which is closely related to the AdS/CFT correspondence.     

High sensitivity fiber Bragg grating pressure difference sensor

Based on the effect of fiber Bragg grating (FBG) pressure difference sensitivity enhancement by encapsulating the FBG with uniform strength beam and metal bellows, a FBG pressure difference sensor is proposed, and its mechanism is also discussed. The relationship between Bragg wavelength and the pressure difference is derived, and the expression of the pressure difference sensitivity coefficient is also given. It is indicated that there is good linear relation between the Bragg wavelength shift and the pressure difference of the sensor. The theoretical and experimental pressure difference sensitivity coefficients are 38.67 and 37.6 nm/MPa, which are 12890 and 12533 times of that of the bare FBG, respectively. The pressure difference sensitivity and dynamic range can be easily changed by changing the size, Young's modulus, and Poisson's ratio of the beam and the bellows.     

A New Quantum Key Distribution Scheme Based on Frequency and Time Coding

A new scheme of quantum key distribution （QKD） using frequency and time coding is proposed, in which the security is based on the frequency-time uncertainty relation. In this scheme, the binary information sequence is encoded randomly on either the centrM frequency or the time delay of the optical pulse at the sender. The central frequency of the single photon pulse is set as w1 for bit 0 and set as w2 for bit 1 when frequency coding is selected. However, the single photon pulse is not delayed for bit 0 and is delayed in τ for 1 when time coding is selected. At the receiver, either the frequency or the time delay of the pulse is measured randomly, and the final key is obtained after basis comparison, data reconciliation and privacy amplification. With the proposed method, the effect of the noise in the fiber channel and environment on the QKD system can be reduced effectively.     

Dynamic investigation of the finite dissolution of silicon particles in aluminum melt with a lower dissolution limit

The finite dissolution model of silicon particles in the aluminum melt is built and calculated by the finite difference method, and the lower dissolution limit of silicon particles in the aluminum melt is proposed and verified by experiments, which could be the origin of microinhomogeneity in aluminum-silicon melts. When the effects of curvature and interface reaction on dissolution are not considered; the dissolution rate first decreases and later increases with time. When the effects of curvature and interface reaction on dissolution are considered, the dissolution rate first decreases and later increases when the interface reaction coefficient （k） is larger than 10 1, and the dissolution rate first decreases and later tends to be constant when k is smaller than 10-3. The dissolution is controlled by both diffusion and interface reaction when k is larger than 10-3, while the dissolution is controlled only by the interface reaction when k is smaller than 10-4.     

Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation

The nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film(GMF)-shaped memory alloy(SMA) composite plate subjected to in-plane stochastic excitation are studied. GMF is prepared based on an SMA plate, and combined into a GMF–SMA composite plate. The Van der Pol item is improved to explain the hysteretic phenomena of GMF and SMA, and the nonlinear dynamics model of a GMF–SMA composite cantilever plate subjected to in-plane stochastic excitation is developed. The stochastic stability of the system is analyzed, and the steady-state probability density function of the dynamic response of the system is obtained. The condition of stochastic Hopf bifurcation is discussed, the reliability function of the system is provided, and then the probability density of the first-passage time is given. Finally, the stochastic optimal control strategy is proposed by the stochastic dynamic programming method.Numerical simulation shows that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the system’s reliability is improved through stochastic optimal control, and the firstpassage time is delayed. A GMF–SMA composite plate combines the advantages of GMF and SMA, and can reduce vibration through passive control and active control effectively. The results are helpful for the engineering applications of GMF–SMA composite plates.     

The theory of interaction between wave and basic flow

This paper investigates the interaction between transient wave and non-stationary and non-conservative basic flow. An interaction equation is derived from the zonally symmetric and non-hydrostatic primitive equations in Cartesian coordinates by using the Momentum-Casimir method. In the derivation, it is assumed that the transient disturbances satisfy the linear perturbation equations and the basic states are non-conservative and slowly vary in time and space. The diabatic heating composed of basic-state heating and perturbation heating is also introduced. Since the theory of wave-flow interaction is constructed in non-hydrostatic and ageostrophic dynamical framework, it is applicable to diagnosing the interaction between the meso-scale convective system in front and the background flow.
It follows from the local interaction equation that the local tendency of pseudomomentum wave-activity density depends on the combination of the perturbation flux divergence second-order in disturbance amplitude, the local change of basic-state pseudomomentum density, the basic-state flux divergence and the forcing effect of diabatic heating. Furthermore, the tendency of pseudomomentum wave-activity density is opposite to that of basic-state pseudomomentum density. The globally integrated basic-state pseudomomentum equation and wave-activity equation reveal that the global development of basic-state pseudomomentum is only dominated by the basic-state diabatic heating while it is the forcing effect of total diabatic heating from which the global evolution of pseudomomentum wave activity results. Therefore, the interaction between the transient wave and the non-stationary and non-conservative basic flow is realized in virtue of the basic-state diabatic heating.     

Negative Temperature of Inner Horizon and Planck Absolute Entropy of a Kerr-Newman Black Hole

Considering the contribution of both the outer and inner horizons, the Hamilton-Jacobi method is applied to a Kerr-Newman black hole and a negative temperature of the inner horizon is obtained. Under the negative temperature inside the black hole, the thermodynamics of the two horizons is studied, and the new Bekenstein-Smarr formula is given. The entropies of the inner and outer horizons are all positive. The new entropy expression of the black hole satisfies the Nernst Theorem and can be regarded as the Planck absolute entropy.     

Speckle noise reduction in digital holography with spatial light modulator and nonlocal means algorithm

An integrated method based on optical and digital image processing is presented to suppress speckle in digital holography. A spatial light modulator is adopted to introduce random phases to the illuminating beam. Multiple holograms are reconstructed and superimposed, and the intensity is averaged to smooth the noise. The adaptive algorithm based on the nonlocal means is designed to further suppress the speckle. The presented method is compared with other methods reduction is improved, and the proposed method is effective The experimental results show that speckle and feasible.     

Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems

In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.     

Evolution and Generation of Dynamics of Two-Mode Squeezed States of Time-Dependent Coupled Boson System

The system of the Hamiltonian involving a driving part, a single mode part, and a two-mode squeezed one and a two-mode coupled one is discussed using the Lewis-Riesenfeld invariant theory. The time evolution operator is obtained. When the initial state is a coherent state, the quantum fluctuation of the system is calculated, and it is dependent on the squeezed part and the two-mode coupled part, but not dependent on the driving one.     

Simultaneous temperature and refractive index measurement of liquid using a local micro-structured fiber Bragg grating

An alternative solution for the simultaneous measurement of temperature and refractive index is presented. A local micro-structured fiber Bragg grating（LMSFBG）is formed as the sensing head,in which a standard grating is etched by HF.According to the phase shift theory,the main spectral change of the LMSFBG is the formation of a narrow allowed band,which is strongly dependent on the etching features and the surrounding refractive index.As such,the temperature and refractive index measurements can be achieved by the shifts of the double peaks and narrow allowed band,and their fitting linearity coefficients are 0.996 and 0.994,respectively.Thus,the reflection and transmission peaks of the LMSFBG have a good linear relationship with temperature and refractive index.     

Design and Fabrication of Polarization-Independent Micro-Ring Resonators

Origin of polarization sensitivity of photonic wire waveguides （PWWs） is analysed and the effective refractive indices of two different polarization states are calculated by the three-dimensional full-vector beam propagation method. We find that PWWs are polarization insensitive if the distribution of its refractive index is uniform and the cross section is square. An MRR based on such a polarization-insensitive PWW is fabricated on an 8-inch silicon-on-insulator wafer using 248-nm deep ultraviolet lithography and reactive ion etching. The quasi-TE mode is resonant at 1542.25nm and 1558.90nm, and the quasi-TM mode is resonant at 1542.12nm and 1558.94nm. The corresponding polarization shift is 0. 13 nm at the shorter wavelength and 0.04 nm at the longer wavelength. Thus the fabricated device is polarization independent. The extinction ratio is larger than 10dB. The 3dB bandwidth is about 2.Snm and the Qvalue is about 620 at 1558.90nm.     

Simulation of ball motion and energy transfer in a planetary ball mill

A kinetic model is proposed for simulating the trajectory of a single milling ball in a planetary ball mill, and a model is also proposed for simulating the local energy transfer during the ball milling process under no-slip conditions. Based on the kinematics of ball motion, the collision frequency and power are described, and the normal impact forces and effective power are derived from analyses of collision geometry. The Hertzian impact theory is applied to formulate these models after having established some relationships among the geometric, dynamic, and thermophysical parameters. Simulation is carried out based on two models, and the effects of the rotation velocity of the planetary disk and the vial-to-disk speed ratio ω/Ω on other kinetic parameters is investigated. As a result, the optimal ratio ω/Ω to obtain high impact energy in the standard operating condition at = 800 rpm is estimated, and is equal to 1.15.     

Directivity calculation with experimental verification for a conformal array of underwater acoustic transducers

The radiation directivity of a complicated conformal array of underwater acoustic transducers is presented based on the boundary ＂element method. It includes the element directivity of each transducer, the natural beam pattern and the controlled beam pattern of the transducer array. At first, the boundary element model of the conformal array is built up, and then the boundary condition is exerted on the model according to the design and environment in which the transducer array is used, and the radiation directivity of the conformal array is calculated. An experiment has been done to measure the directivity in an anechoic water tank. The calculated and the experimental results are compared and analyzed. They are consistent to each other. It is shown that the boundary element method together with the detailed calculations is successful to simulate and predict the radiation directivity of an underwater acoustic transducer array.     

Experimental study on supersonic film cooling on the surface of a blunt body in hypersonic flow

The experimental study focuses on the heat flux on a double cone blunt body in the presence of tangential-slot super- sonic injection into hypersonic flow. The tests are conducted in a contoured axisymmetric nozzle with Mach numbers of 7.3 and 8.1, and the total temperature is about 900 K. The injection Mach number is 3.2, and total temperature is 300 K. A constant voltage circuit is developed to supply the temperature detectors instead of the normally used constant current circuit. The schlieren photographs are presented additionally to visualize the flow and help analyze the pressure relationship between the cooling flow and the main flow. The dependence of the film-cooling effectiveness on flow parameters, i.e. the blow ratio, the convective Mach number, and the attack angle, is determined. A semi-empirical formula is tested by the present data, and is improved for a better correlation.     

The influence of divergence angle on the deposition of neutral chromium atoms using a laser standing wave

The characteristics of neutral chromium atoms in the standing wave field are discussed.Based on a semi-classical model,the motion equation of neutral atoms in the laser standing wave field is analyzed,and the trajectories of the atoms are obtained by simulations with the different divergence angles of the atomic beam.The simulation results show that the full width at half maximum(FWHM) of the stripe is 2.75 nm and the contrast is 38.5:1 when the divergence angle equals 0 mrad,the FWHM is 24.1 nm and the contrast is 6.8:1 when the divergence angle equals 0.2 mrad and the FWHMs are 58.6 and 137.8 nm,and the contrasts are 3.3:1 and 1.6:1 when the divergence angles equal 0.5 and 1.0 mrad,respectively.