We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems. Firstly, we give the definition of integrating factors for the differential equations of motion of a mechanical system. Next, the necessary conditions for the existence of the conserved quantities are studied in detail. Then, we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system. Finally, an example is given to illustrate the application of the result.

Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system, Maple, using the direct algebraic method proposed recently. We explicitly obtain several new solutions of physical interest in addition to rederiving all the known solutions.

Experiments have been conducted to investigate nitrogen gas flow characteristics through four trapezoidal silicon microchannels with different hydraulic diameters. The volume flow rate and pressure ratio are measured in the experiments. It is found that the friction coefficient is no longer a constant, which is different from the conventional theory. The characteristics are first explained by the theoretical analysis. A simplified rectangular model (rectangular straight channel model) is then proposed. The experimental results are compared with the theoretical predictions based on the simplified rectangular model and the two-dimensional flow between the parallel-plate model which was usually used. The difference between the experimental data and the theoretical predictions is found in the high-pressure ratio cases. The influence of the gas compressibility effect based on the Boltzmann gas kinetic analysis method is studied to interpret the discrepancy. We discuss two important factors affecting the application extent of different prediction models.

We propose a scheme for generating bipartite and multipartite entangled squeezed states via the Jaynes－Cummings model with large detuning. Bipartite entanglement of these entangled states is quantified by the concurrence. We also use the N-tangle to compute multipartite entanglement of these multipartite entangled squeezed states. Finally we discuss two limiting cases which arise from r→∞ and r→0, in which the multipartite entangled squeezed state reduces correspondingly into an N-qubit Greenberger－Horne－Zeilinger state and an N-qubit W state.

We show how a CNOT gate and single-qubit rotation can be implemented non-locally. We also report on the quantitative relations between these quantum actions, entanglement and classical communication resources required in the implementation.

The one-loop vacuum polarization is calculated for scalar electrodynamics in a flat space－time with the topology S^{1}×R^{3}. The effect of vacuum polarization upon photon propagation is considered. It is found that photon propagation becomes anisotropic with some photon modes acquiring a positive topological mass and thus travelling at a subluminal speed.

Using the improved brick-wall model, we have calculated the first quantum correction to the entropy of non-static black holes, Vaidya－Bonner black holes, due to the gravitational, electro-magnetic and neutrino fields. The result shows that both bosonic entropy and fermionic entropy are exactly proportional to the area of the event horizon. Thus, the entropy-area law still holds in such a non-static case.

We investigate chaotic synchronization in the generalized sense in unidirectionally coupled erbium-doped fibre dual-ring lasers. Numerical simulation shows that no matter whether the two different erbium-doped fibre dual-ring lasers are chaotic or not before coupling, they show generalized synchronization with a suitable unidirectional coupling coefficient under which the maximum condition Lyapunov exponent is negative. We also use the auxiliary system approach to detect the generalized synchronization.

An open plus nonlinear closed loop control law is presented for chaotic oscillations described by a set of non-autonomous second-order ordinary differential equations. It is proven that the basins of entrainment are global when the right-hand sides of the equations are given by arbitrary polynomial functions. The forced Duffing oscillator and the forced van der Pol oscillator are treated as numerical examples to demonstrate the applications of the method.

Hyperfine structure spectra of singly ionized lanthanum and praseodymium have been measured by collinear fast-ion-beam laser spectroscopy. All the spectral lines were resolved and the magnetic dipole and electric quadruple coupling constants of the metastable levels and excited levels were determined. Our results are in agreement with the published data within the experimental uncertainty. For praseodymium ions, the accuracy of the magnetic dipole coupling constants are improved by one order of magnitude compared with other published data, and the electric quadruple coupling constants are reported for the first time.

In this paper, we present the uniform interaction potentials for helium atoms and halogen hydride molecules (HF, HCl and HBr). The differential cross sections are calculated using the above interaction potentials for the He－HF, HCl and HBr systems, respectively, and the results of the calculations are found to be in agreement with the existing theoretical results and experimental data.

The triple differential cross sections of the 2p electron of argon in a coplanar highly asymmetric geometry have been calculated with the modified distorted wave Born approximation (DWBA) and the target Hartree－Fock approximation methods. The damping polarization of the semi-classical short-range potentials and the M_{ee} factor are included in the distorting potentials of the modified DWBA. Theoretical results are compared with a recent experiment. The dynamic mechanism of inner shell ionization in a coplanar highly asymmetric geometry (e, 2e) reaction are also discussed.

We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopes of two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification are derived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-mode equations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due to the optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears when the frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands.

We study the dynamical behaviour of the ionic inversion in a trapped ion system in running-wave lasers, and we discuss the properties of entanglement between the ion and phonons and the statistics of the vibrational phonon field. It is shown that the appearance of the super-revivals of the ion inversion is dependent on the initial parameters of the vibrational phonon field. The Schr?dinger cat and sub-Poissonian statistics of the phonon field can be also exhibited in this system for suitable initial values.

With the rapid development of CD/DVD (compact disc/digital versatile disc) technology, the disc rotation speed and the information density have increased greatly to fulfil the demand of high information bit rate transfer. As one of the most important elements in a DVD pickup head, objective lens actuators are required to provide a more precise means to accurately follow the disc deviation. The design of the lens actuator becomes all the more important and critical. In order to give complete suggestion to the design of the lens actuator, we put forward the movement differential equations as a new theoretical means to analyse the characteristics of the lens actuator reliably and rigorously. Based on the theoretical analyses, many important and effective methods are proposed. A typical experiment verifies that the performance of our lens actuator head, which adopts these methods, can satisfy the high speed and high density requirement of DVD systems.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

We deduce new expressions for g-factors of the 3d^{9} ions with a compressional tetragonal symmetry, in which we consider not only the contribution from the spin-orbit coupling of the central transition metal ion but also that of the ligand orbits as well as the admixture of ^{2}B_{1g} into ^{2}A_{1g} (ground state). By using the new formulae, the electron paramagnetic resonance g-factors for NaCl:Ni^{+}(I) are studied. Thus, the puzzle that the g_{‖}-shift is positive is reasonably explained.

Sandwiched structures (a-SiN_{x}/a-Si/a-SiN_{x}) have been fabricated by the plasma enhanced chemical vapour deposition technique. A Si nanocrystal (nc-Si) layer was formed by crystallization of an a-Si layer according to the constrained crystallization principle after quasi-static thermal annealing at 1100℃ for 30 min. Transmission electron microscopy (TEM) and Raman scattering spectroscopy clearly demonstrated that nc-Si grains were formed in the as-deposited a-Si layer after annealing. The density of nc-Si grains is about 10^{11}cm^{-2} as shown by TEM photographs. Using capacitance－voltage (C－V) measurements we investigated the electrical characteristics of the sandwiched structures. The charge storage phenomenon of the nc-Si layer was observed from the shift of flat-band voltage (V_{FB}) in C－V curves at a high frequency (1 MHz). We estimated the density of nc-Si grains to be about 10^{11}cm^{-2} from the shift value of V_{FB}, which is in agreement with the result of TEM photographs. At the same time, we found that the shift of V_{FB} increased with the increase of the applied constant dc voltage or the thickness of the nc-Si layer.

One-dimensional Ising systems in random fields (RFs) are studied taking into account the nearest-neighbour and next-nearest-neighbour interactions. We investigate two distributions of RFs: binary and Gaussian distributions. We consider four cases of the exchange couplings: ferro－ferromagnetic (F－F), ferro－antiferromagnetic (F－AF), antiferro－ferromagnetic (AF－F) and antiferro－antiferromagnetic (AF－AF). The energy minima of chains of no more than 30 spins with periodic boundary conditions are analysed exactly. We found that the average number of energy minima grows exponentially with the number of spins in both cases of RFs. The energy distributions across the corresponding energy minima are shown. The effects of RFs on both the average and density of metastable states are explained. For a weak RF, the energy distributions display a multipartitioned structure. We also discuss the frustration effect due to RFs and exchange fields. Finally, the distributions of magnetization are calculated. The absolute value of magnetization averaged over all metastable states decreases logarithmically with the number of spins.

Effects of Ga substitution for Sn on the structure and magnetic properties of TbMn_{6}Sn_{6-x}Ga_{x} (x=0.0－1.2) compounds have been investigated by means of x-ray diffraction, magnetization measurement and ^{119}Sn M?ssbauer spectroscopy. The substitution of Ga for Sn results in a decrease in lattice constants and unit-cell volumes. The magnetic ordering temperature decreases monotonically with increasing Ga content from 423 K for x=0.0 to 390 K for x=1.2. At room temperature, the easy magnetization direction changes from the c-axis to the ab-plane. This variation implies that the substitution of Ga for Sn leads to a decrease in the c-axis anisotropy of the Tb sublattice. An increase in the non-magnetic Ga concentration results in a monotonic decrease of the spontaneous magnetization M_{s} at room temperature. Since there are three non-equivalent Sn sites, 2c (0.33, 0.67,0), 2d (0.33, 0.67,0.5) and 2e (0,0,0.34) in the TbMn_{6}Sn_{6-x}Ga_{x} compounds, the ^{119}Sn M?ssbauer spectra of the TbMn_{6}Sn_{6} and TbMn_{6}Sn_{5.4}Ga_{0.6} compounds can be fitted by three sextets. The hyperfine fields (HFs) decrease in the order of HF(2d)>HF(2e)>HF(2c), which is in agreement with the magnetic structure.

The structure of Au/Si/SiO_{2}/p-Si has been fabricated using the magnetron sputtering technique. It has a very good rectifying behaviour. Visible electroluminescence (EL) has been observed from the Au/Si/SiO_{2}/p-Si structure at a forward bias of 5V or larger. A broad band with one peak around 650－660 nm appears in all the EL spectra of the structure. The effects of the thickness of the Si layer in the Si/SiO_{2} films and of the input electrical power on EL spectra are studied systematically.

A cathodic arc plasma source equipped with a curved magnetic duct to filter macro-particles was used to study plasma diffusion and transport in the duct. We determine the optimal duct bias, at which the magnetic duct produces the maximum plasma output, for titanium cathodic arc plasma at 50, 100 and 150 A arc current, and we investigate the parametric effects of the arc current and guiding magnetic field on the optimal duct bias. The optimal bias decreases as the guiding magnetic field increases from 0.01 to 0.04T and is almost independent of the guiding magnetic field when the magnetic field strength ranges from 0.04 to 0.06T, the upper limit for our equipment. The optimal duct bias at 0.04T guiding magnetic field decreases with increasing arc current.

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