Symmetry of Lagrangians of nonholonomic systems of non-Chetaev’s type

This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.     

Measurement of Eccentricity of the Centre of Mass from the Geometric Centre of a Sphere

The eccentricity of the centre of mass from the geometric centre of a spherical attracting mass in determining the Newtonian gravitational constant G is tested by means of an electronic balance. The experimental result shows that the eccentricity of the sample is about 0.31 μm with uncertainty of 0.05μm. Two density distribution models are discussed to estimate the uncertainty to G by the eccentricities of the attracting masses.     

Instability of Taylor-Couette Flow of Electrorheological Fluid

A linearized instability analysis of Taylor-Couette flow between two rotating concentric cylinders of an electrorheological (ER) fluid is carried out. The ER fluid exhibits a yield stress in addition to the plastic viscosity when an extra electric-field is applied. It can be found that the yield stress plays a dual role in the flow instability The possibility of the yield surface falling between the cylinders is analysed. Although small waves appeared on the yielded surface is considered, the yielded surface, which has been treated as a free surface, has little effect on the flow instability. The effects of axisymmetric perturbation on the flow instability are presented due to the axisymmetric of the basic flow. The parameterβ in the yield stress formula of the ER fluid is shown to have distinct effects on the flow instability characteristics.     

Improvement of Synchronizability of Scale-Free Networks

We investigate the factors that affect synchronizability of coupled oscillators on scale-free networks. Using the memory Tabu search （MTS） algorithm, we improve the eigen-ratio Q of a coupling matrix by edge intercrossing. The numerical results show that the synchronizatlon-improved scale-free networks should have distinctive both small average distance and larger clustering coefficient, which are consistent with some real-world networks. Moreover, the synchronizability-improved networks demonstrate the disassortative coefficient.     

Effects of Magnetic Coupling of Temperature Profile of Black—Hole Accretion Disc

We propose a model of the magnetic coupling (MC) of a retating black hole(BH) with the surrounding accretion disc in order to study the radial temperature profile in the inner region of the disc,in which a linear map from the angular coordinate on the BH horizon to the radial coordinate on the thin disc is given by closed magnetic field lines.The MC power and torque are derived using a modified equivalent circuit.It is shown that the MC effects on the temperature profile are related intimately to the BH spin,resulting in the variation of the value and the position of the peak temperature.It turns out that the value range of the colour temperature of the disc is extended by the MC effects.     

Analysis of sound radiation characteristics of complex double shells

The double stiffened shell connected by annular plates is systematically studied.The shell motion is obtained using the classical Fliigge operator, the effects of stiffeners are induced into the vibration equation by treating them as reverse included in forces and moments on the shell, and the fluid field between the inner shell and outer shell is solved by applying Helmholtz equation and the continuity conditions of the displacement on the surface of fluidstructure. At last the vibration equation coupled by the sound-fluid-structure are constituted and solved. The effects of the double shell parameters and linked types between the double shells on the sound radiation are discussed in detail. The following conclusions can be gotten:The smaller the space between the inner shell and outer shell, the stronger the coupling of the inner shell and outer shell, the higher the radiated power and radial quadratic velocity, and the more indistinct the shield of the outer shell. The changes of the thickness of the inner shell and outer shell influenced the radial quadratic velocity greatly, and influenced the radiated power indistinctly. The thicker the thickness, the lower the radial quadratic velocity.     

Investigation and Modification of Coupling of Photonic Crystal Defects

We investigate the coupling of photonic crystal (PC) defects by using coupled-mode theory. The PC molecules formed by the coupling of two identical PC atoms are the focus of our study. It is revealed that the flatness of the transmission spectra of the PC molecules is determined uniquely by the phase shift of the travelling wave between the two coupled PC atoms. By properly adjusting the distance between the two constitutional PC atoms, we are able to modify the transmission spectrum of the resulting PC molecule. Theoretical analyses based on the coupled-mode theory are in good agreement with the simulation results obtained by the transfer matrix method and the finite-difference time-domain technique.     

Effects of cosmological constant on motion of UHECR particles

Recent astronomical observations manifest that about two-thirds of the whole energy in the Universe is contributed by a small positive cosmological constant A (> 0). Then, an asymptotically de Sitter spacetime is premised naturally. However, physics in the de Sitter spacetime is very different from that in the Minkowski spacetime. As the first step, a covariant formalism of the kinematics in the de Sitter spacetime is presented here. By solving exactly the equations of motion for a field, we obtain the dispersion relation of a free particle. It is noticed that the dispersion relation is dependent on the degree of freedom of angular momentum of the particle. We show the threshold anomaly of the ultra high energy cosmic ray disappears naturally in the framework of the de Sitter kinematics.     

Excitation of Elastic Wave of an Arbitrary Plane Source on Surface of a Multilayered Medium

We investigate the elastic waves excited by an arbitrary plane piezoelectric source on the surface of a multilayered medium. Based on the previous studies, the 2D elastic wavefield in the multilayered medium is extended to 3D space. The propagator matrix for the 3D wavefield is investigated and the displacement-stress response for the boundary conditions is obtained. The excitation and propagation of the Rayleigh and Love waves are analysed further. It is found that the propagation velocity of the Rayleigh and Love waves does not depend on the propagation azimuth θ in the plane parallel to the free surface of the multilayered medium while the displacement is strongly dependent on the azimuth θ.     

Rediscussion of the Stability Problem of the Schwarzschild Black Hole

We use the Kruskal time coordinate T to define the initial time. By this way, the stability study naturally becomes the one connected with the two regions, i.e. the white-hole-connected region and the black-hole-connected region. The union of the two regions covers the Schwarzschild space-time （r ≥ 2m）. We also obtain the very reasonable conclusion： the white-hole-connected region is unstable and the black-hole-connected region is stable. If we take the instability with caution and seriousness, it is not unreasonable to regard that the Schwarzschild black hole might be unstable to some extent.     

Comparison of Two Kinds of Atmospheric Vorticity Equations

Comparison of two kinds of atmospheric vorticity equations, i.e. the traditional vorticity equation and the complete-form vorticity equation, is performed. The result shows that the two kinds of the vorticity equations can transform from each other and they are consistent in physical essence, while the complete vorticity equation has more advantages in diagnosis. Finally, the application of the complete form vorticity equation is analysed briefly with real data.     

Influence of purity of HfO_2 on reflectance of ultraviolet multilayer

The impurities in two kinds of HfO_2 materials and in their corresponding single layer thin films were determined through glow discharge mass spectrum technology and secondary ion mass spectrometry(SIMS) equipment respectively.It was found that ZrO_2 was the main impurity in the two kinds of HfO_2 either in the original HfO_2 materials or in the electron beam deposited films.In addition,the difference of Zr content in the two kinds of HfO_2 single layer films was much larger than that of the other impurities such as Ti and Fe,which showed that it was just ZrO_2 that made the difference between the optical performance of the film products including the two kinds of HfO_2.With these two kinds of HfO_2 and the same kind of SiO_2,we deposited HfO_2/SiO_2 multilayer reflective coatings at the wavelength of 266 nm.Experimental results showed that the reflectances of these two mirrors were about 99.85% and 99.15% respectively, which agreed well with the designed results what were based on the optical constants obtained from the corresponding single layer thin films.     

Substrate Dependence of Properties of Sputtered ITO Films

High-quality indium-tin-oxide (ITO) films are deposited on p-type Czochralski silicon and 7059 Coming glass by direct-current magnetron sputtering at various temperatures. The structural, electrical and optical properties of the ITO films are investigated as functions of the substrate temperature. A comparison between the characteristics of the ITO films on silicon and Coming glass is presented. The results show that for the ITO film on silicon,the nucleation begins from room temperature; the resistivity reaches a maximum value at 75℃; the reflectivity increases with increasing temperature; when temperature is above 125℃, the ITO grows in a three-dimensional manner and forms a granular structure. However, for the ITO film on glass, it is still in an amorphous state at 75℃. Moreover, both the resistivity and the reflectivity decrease with increasing temperature. Above 125℃, the ITO grows in a two-dimensional manner and forms a domain structure.     

Influence of Wall Charges on Discharge Characteristics of Surface Discharge

The discharge current and the inception voltage in a surface discharge device have been measured to investigate the influence of wall charges on the discharge characteristics in argon. The results show that the inception voltage decreases as the amplitude of the applied voltage Up increases. However, the sum of the inception voltage and the applied voltage almost keeps constant when Up is changed, due to the fact that the wall charges are generated in the discharge process. This phenomenon suggests that net electric field between the electrodes almost keeps constant when the amplitude of the applied voltage is changed. The electron temperature calculated by the intensity ratio of emitted spectral lines has been estimated to be less than 0.3eV and almost keeps constant under different amplitudes of the applied voltage. The result is consistent with nearly constant net field. The duty ratio of the discharge current increases as the amplitude of the applied voltage increases.     

Inverse problem of the scattering of a finite-length cylinder

Dealing with the direct problem of target scattering,the geomet-rical theory of diffraction and resonance scattering theory are used tostudy the scattering of an elastic cylinder,the results of which are appliedto solve the inverse problem.Using the geometrical theory of diffraction,the relations between the geometrical parameters of cylinder and thediffracted signals have been found,meanwhile the connexions between thephysical parameters of cylinder(i.e.the longitudinal velocity,transverse velocity and density of the material consisting of the cylinder)and the internal resonances of the cylinder have been shown by means ofthe resonance scattering theory.Therefore in the present artical an availa-ble method for solving the inverse scattering of cylinder is provided.     

First-Principle-Based Calculations of the Hugoniot of Cu

The equation of state of face-centred-cubic (fcc) copper crystals at pressures up to 500 GPa and relative volume to 0.55 have been evaluated by using the full-potential linear muffin-tin orbital (FPLMTO) total-energy method combining with a mean-field model of the vibrational partition function. The mean-field is constructed from the sum of all the pair potentials between the reference atom and the others of the system. The calculated properties are in good agreement with the available shock-wave experimental measurements.     

Stability of Random Networks under Evolution of Attack and Repair

With a simple model, we study the stability of random networks under the evolution of attack and repair. We introduce a new quantity, i.e. invulnerability I（s）, to describe the stability of the system. It is found that the network can evolve to a stationary state. The stationary value Ic has a power-law dependence on the initial average degree （κ）, with the slope about -1.5. In the stationary state, the degree distribution is a normal distribution, rather than a typical Poisson distribution for general random graphs. The clustering coefficient in the stationary state is much larger than that in the initial state. The stability of the network depends only on the initial average degree （κ）, which increases rapidly with the decrease of （κ）.     

Monte Carlo Simulation of Magnetization Behaviour of Co Nanowires

Based on the Monte Carlo method, we simulate the magnetization curves with various magnetic field orientations for various single Co nanowires at room temperature. The simulated switching field as a function of angle between the field and the wire axis is consistent well with the experimental data. Correspondingly, the coercivity as a function of angle θ is presented, which together with the switching field plays an important role on explaining the magnetic reversal mechanism. It is found that the angular dependence of coercivity depends on the diameter of nanowires, and the coercivity and switching field versus θ deviate markedly from the prediction from the classical uniform rotation mode in the chain-of-sphere model. Furthermore, the magnetic reversal configurations display that magnetization reversal in the wires with small diameters is a nucleation-propagation process, and it is similar to the curling spread process in the larger wires.     

Normalized entropy of rank distribution： a novel measure of heterogeneity of complex networks

Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are important and desirable to the research of the properties and functions of complex networks. In this paper, the rank distribution is proposed as a new statistic feature of complex networks. Based on the rank distribution, a novel measure of the heterogeneity called a normalized entropy of rank distribution (NERD) is proposed. The NERD accords with the normal meaning of heterogeneity within the context of complex networks compared with conventional measures. The heterogeneity of scale-free networks is studied using the NERD. It is shown that scale-free networks become more heterogeneous as the scaling exponent decreases and the NERD of scale-free networks is independent of the number of vertices, which indicates that the NERD is a suitable and effective measure of heterogeneity for networks with different sizes.