纳米晶体线的晶格动力学格林函数及晶格振动

通过求解差分方程,推导了纳米晶体线的晶格动力学格林函数,分析了其晶格振动,并推导了声子数表象中的原子位移及晶格振动哈密顿公式.研究结果表明,纳米晶体线的晶格振动能带分裂为一系列的子带,格波只能沿纳米晶体线的纵向传播,沿纳米晶体线的横截面只存在驻波.     

单波驱动的过渡粒子效应

本文讨论单波在环等离子体中引起的过渡粒子及其有关效应。 关键词：     

Frequency-division multiplexing of optical-fibre sensors using a frequency-modulated source

Three basic configurations, namely, (i) parallel with a common reference, (ii) parallel with separate references and (iii) series, are studied for a multiplexed system of optical-fibre sensors. With a frequency-modulated laser source, each sensor of a different predetermined path imbalance results in a different beat frequency at the detector and signals are multiplexed in the frequency domain. The cross-term problem arising from undesired interference associated with more than one sensor is described. A series configuration has more cross terms than a parallel configuration if there are four sensors or more and, consequently, suffers more signal power reduction if there are seven sensors or more. Several schemes are presented, which ensures the separation of cross terms from desired signals. In a parallel system with a common reference, signals and cross terms are allocated in the lower and in the higher region, respectively, or to every other line in the frequency domain. In a parallel system with separate references, sensors are made incoherent to each other to produce no cross terms. In a series system, more elaborate schemes are necessary. The estimated maximum number of sensors indicates that a parallel configuration should be used if there are 10 sensors or more to be multiplexed.     

A completely integrable case in three-particle problems with homogeneous potentials

Trajectory equations are considered for classical three-particle problems on a straight line with potentials that are homogeneous coordinate functions. It is proposed to consider the case of a zero total energy as a completely integrable one in a generalized sense, since in it the order of the differential trajectory equation is lowered to the first one, the variables in the Hamiltonian-Jacobi equation are separated, there are additional first integral and invariant tori, in spite of the fact that the system cannot be integrable by the Liouville-Arnold theorem. The solutions are constructed (i) in a parametric form, (ii) in the form of a convergent perturbative series of a new type, and (iii) as a convergent Fourier series.     

Thermodynamics of electrons in the graphene bilayer

Some problems of the thermodynamics of electrons in a doped graphene bilayer are considered. Analytical expressions are derived for chemical potential and specific heat in the limiting cases of low and high temperatures. The Seebeck and Thomson coefficients are estimated. Landau levels are studied using a semi-classical approach. An expression for thermodynamic potential is obtained and the de Haas-van Alphen oscillations are studied. The oscillations of magnetic entropy and electron temperature in a magnetic field, i.e., the oscillating magnetocaloric effect, are investigated. For all parameters, the cases of graphene bilayer and monolayer are compared.     

Transport of polarized neutrons through magnetic noncoplanar layered systems

The transport of neutrons through noncoplanar systems is shown to have a partly unidirectional character. To this end, the transmission of a three-layer magnetic film with a noncoplanar magnetization in the absence of applied magnetic field and the transmission of a two-layer magnetic film with a noncollinear magnetization in the presence of a magnetic field are calculated. The calculations demonstrate that, if the losses in the films are neglected, the transmissions in two opposite directions differ only for processes with and without spin flip. If these losses are taken into account, the total transmissions of a nonpolarized neutron beam in two opposite directions are also different. The consequences of these specific features of noncoplanar systems are discussed.     

Characterisation of valves as sound sources: Structure-borne sound

Taps and other valves are major sound sources in piping systems and can cause unacceptable noise levels in buildings. The noise results from the fluid-, structure- and air-borne sound emission. At present the acoustic emission of water appliances is tested according to a European standard, the shortcomings of which are apparent as a result of a round robin test of different European laboratories. As a result, there are currently neither acceptable measurement methods for water appliances available nor input data for prediction models. This paper considers methods of characterizing water appliances as sources of structure-borne sound. The concepts of mobility and free velocity are employed for a source characterisation based on power. Taps are considered alone and also in combination with a basin, where again the mobility and free velocity are used. A reception plate method is assessed as an alternative. The two methods each provide an independent characterisation of a structure-borne sound source as a single value. The values are on a power basis and provide input data suitable for prediction of the installed structure-borne power and thence the resultant sound pressure in adjacent rooms. Measured and predicted values of sound pressure level, caused by a wash-basin installed in an adjacent room, are compared.     

Radial motion of a solid spherical body in a magnetic field

The object of the present paper is to investigate the radial motion of a solid spherical body, assumed to be homogeneous, isotropic and elastic, in presence of a magnetic field in the azimuthal direction. The body is assumed to be in a state of initial stress which is hydrostatic in nature. This theory of radial motion of a solid spherical body in a magnetic field has been utilised to find the small radial motion of a solid Earth assumed to be homogeneous isotropic elastic sphere in presence of a magnetic field in the azimuthal direction. Considering the effect of gravity and the initial stress produced by slow process of creep due to extra masses over the surface of the Earth, the fundamental equations of motion are derived which are non-linear in character and are solved. The times of a desired radial displacement are calculated in presence of a magnetic field only and in presence of the same magnetic field, initial stress and gravitational field, which are compared and exhibited numerically.     

Inelastic processes in the interaction of an atom with an ultrashort electromagnetic pulse

Electron transitions occurring during the interaction of a heavy relativistic atom with a spatially inhomogeneous ultrashort electromagnetic pulse are considered by solving the Dirac equation. The corresponding transition probabilities are expressed in terms of known inelastic atomic form factors, which are widely used in the theory of relativistic collisions between charged particles and atoms. By way of example, the inelastic processes accompanying the interaction of ultrashort pulses with hydrogen-like atoms are considered. The probabilities of ionization and production of a bound-free electron-positron pair on a bare nucleus, which are accompanied by the formation of a hydrogen-like atom in the final state and a positron in the continuum, are calculated. The developed technique makes it possible to take into account exactly not only the spatial inhomogeneity of an ultrashort electromagnetic pulse, but also the magnetic interaction.     

VIBRATION ANALYSIS OF NON-CIRCULAR CURVED PANELS BY THE DIFFERENTIAL QUADRATURE METHOD

Free-vibration characteristics of cantilever non-circular curved panels are analyzed by using the differential quadrature method (DQM) in this paper. The equations of motion of a curved panel are based on the Love's hypothesis and are expressed in an orthogonal curvilinear co-ordinate system. By applying the differential quadrature formulation and the proposed modified relationships for specified boundary conditions, the free-vibration equations of motion of the curved panel are transformed to a set of algebraic equations. Natural frequencies of a cantilever flat plate and a circular curved panel are obtained for verifying the applicability of the present approach. Good convergent trend and accuracy are observed. Effects of shallowness, thickness and aspect ratios on the natural frequencies of a cantilever curved panel are also investigated. Furthermore, natural frequencies of parabolic curved panels are obtained. In all cases studied, the efficiency and convenience of the DQM are illustrated.     

The Conceptual Design of a 20 Tesla Pulsed Solenoid for a Laser Solenoid Fusion Reactor

Design considerations are described for a strip wound solenoid which is pulsed to 20 tesla while immersed in a 20 tesla bias field so as to achieve within the bore of the pulsed solenoid a net field sequence starting at 20 tesla and going first down to zero, then up to 40 tesla, and finally back to 20 tesla in a period of about 5 × 10-3 seconds. The important parameters of the solenoid, e. g. aperture, build, turns, stored and dissipated energy, field intensity and powering circuit, are given. A numerical example for a specific design is presented. Mechanical stresses in the solenoid and the subsequent choice of materials for coil construction are discussed. Although several possible design difficulties are not discussed in this preliminary report of a conceptual magnet design, such as uniformity of field, long-term stability of insulation under neutron bombardment and choice of structural materials of appropriate tensile strength and elasticity to withstand magnetic forces developed, these questions are addressed in detail in the complete design report and in part in reference one. Furthermore, the authors feel that the problems encountered in this conceptual design are surmountable and are not a hindrance to the construction of such a magnet system.     

A review of commonly used analytical and empirical formulae for predicting sound diffracted by a thin screen

This paper reviews some useful analytical and empirical formulae that are used for the calculation of sound diffracted by a barrier. A brief historic overview of the study of spherical waves diffracted by a rigid half plane is presented also. The physical principles of sound diffraction by a thin plane are explained. The mathematical expressions are cast in a convenient form for ease of numerical implementation. Accurate analytical solutions are expressed in terms of standard mathematical functions that can be computed readily. Among the approximate solutions quoted, quite a few empirical formulations are adequate for most engineering purposes. The information presented in this paper should also be helpful for those who are interested in the study of sound diffracted by a barrier in a room or in a long industrial space.     

Remarks on stratifying interactions in five dimensions

A geometric model is proposed in which the interaction types, namely the strong, weak, electromagnetic, and gravitational interactions, are stratified in a five-dimensional manifold. The strong and electromagnetic interactions are confined to disjoint four-spaces and the weak and gravitational interactions are proposed unified in a five-manifold bounded topologically by the strong and electromagnetic four-spaces. Further, some advantages of the five-dimensional approach to current-current interactions are discussed, and a five-dimensional approach to PCAC is presented. The model is presented in hopes of reconciling some contradictory lines of theoretical thought, and new fields for investigation are stressed.     

In-plane free vibration analysis of combined ring-beam structural systems by wave propagation

This paper presents a systematic, wave propagation approach for the free vibration analysis of networks consisting of slender, straight and curved beam elements and complete rings. The analysis is based on a ray tracing method and a procedure to predict the natural frequencies and mode shapes of complex ring/beam networks is demonstrated. In the wave approach, the elements are coupled using reflection and transmission coefficients, and these are derived for discontinuities encountered in a MEMS rate sensor consisting of a ring supported on an array of folded beams. These are combined, taking into account wave propagation and decay, to provide a concise and efficient method for studying the free vibration problem. A simplification of the analysis that exploits cyclic symmetry in the structure is also presented. The effects of decaying near-field wave components are included in the formulation, ensuring that the solutions are exact. To illustrate the effectiveness of the approach, several numerical examples are presented. The predictions made using the proposed approach are shown to be in excellent agreement with a conventional FE analysis.     

Propagation of a decentered astigmatic partially coherent beam in a turbulent atmosphere

Propagation properties of a decentered general astigmatic partially coherent beam (i.e., decentered twisted anisotropic Gaussian Schell-model beam) in a turbulent atmosphere are investigated. Analytical formulas for the cross-spectral density and decentered parameter of a decentered astigmatic partially coherent beam propagating in a turbulent atmosphere are derived. Irradiance properties of a decentered astigmatic partially coherent beam in a turbulent atmosphere are studied graphically, and are found to be quite different from its properties in free space.     

基于Riemann解的二维流体力学Lagrange有限点无网格方法

在高维流体力学计算中,对于多介质大变形等一类问题,采用有网格方法常遇到较大的困难.针对二维问题,研究了一种无网格方法——Lagrange有限点方法:在求解区域上设置适当的离散点集,视其中每一点为流体力学Lagrange点;对于点集的任一点,确定邻点集合,并基于该点同邻点集合的联系,应用Godunov方法将流体力学Lagrange方程进行离散;考虑到算法的稳健性,方法中可设置较多邻点并采用最小二乘法.将该方法应用于典型的数值算例,取得了良好效果.     

Feasibility of controlling speed-dependent low-frequency brake vibration amplification by modulating actuation pressure

In this article, a feasibility study of controlling the low frequency torque response of a disc brake system with modulated actuation pressure (in the open loop mode) is conducted. First, a quasi-linear model of the torsional system is introduced, and analytical solutions are proposed to incorporate the modulation effect. Tractable expressions for three different modulation schemes are obtained, and conditions that would lead to a reduction in the oscillatory amplitudes are identified. Second, these conditions are evaluated with a numerical model of the torsional system with clearance nonlinearity, and analytical solutions are verified in terms of the trends observed. Finally, a laboratory experiment with a solenoid valve is built to modulate actuation pressure with a constant duty cycle, and time–frequency domain data are acquired. Measurements are utilized to assess analytical observations, and all methods show that the speed-dependent brake torque amplitudes can be altered with an appropriate modulation of actuation pressure.     

Propagation and scattering of light in stratified media

The propagation and scattering of light in stratified media are considered. Based on the Maxwell equations, the present approaches to the solution of these problems are formulated in a unified way. The particular features of the wave propagation in stratified media are discussed. Scalar and vector fields are considered. Media with small-and large-scale regular inhomogeneities are examined. The construction of the Green’s function of the wave equation in a spatially homogeneous medium is discussed. Stratified isotropic and anisotropic media are analyzed. The scattering of light in a stratified medium is studied with emphasis on the Kirchhoff method, as this makes it possible to obtain calculation formulas in a form convenient for comparing the theory with the experiment. The propagation of waves in photonic crystals and the formation of forbidden zones in such objects are briefly considered.