Phase conjugator with two coherent beams in a BaTiO3:Ce crystal

A phase conjugator which includes two coherent beams that are incident upon one of afaces of a BaTiO₃: Ce crystal without internal reflection is performed experimentally. Based on the fourwave mixing, the mechanism of this conjugator is investigated numerically. In comparison with the corresponding self-pumped phase conjugator, the phase-conjugate behavior of this conjugator is established much more quickly, its phase conjugate reflectivity is greater in some cases and the intensity threshold is lower by over two orders of magnitude. The configuration of this conjugator is easy to perform because the output response exists over a wide range of angular and lateral positions of the two incident beams on the crystal.     

Photo-production of pion pairs by polarised nucleons

The problems of production of pion pairs by polarised photon beams on polarised nucleons is examined. It is found that the angular distribution of pion pairs is sensitive to the state of polarisation of the incident photon beam.     

Computation of paraxial wave fields using transparent boundary conditions

The parabolic wave equation is solved numerically by applying transparent conditions used to confine the computational domain. A numerical implementation of the boundary conditions is proposed based on representing the incident wave as a superposition of Gaussian beams. A modification of the transparent conditions in the case of dielectric objects extending beyond the computational domain is described. Numerical examples are presented.     

Theory of photorefractive dynamic grating formulation

The photorefractive holographic recording and two-beam coupling are both dynamic grating formulation process. The interference light intensity of the two coherent beams induces a phase grating though photo-induced refractive index variation and the phase grating changing the intensities of the two beams through beam-coupling take place at the same time. By solving simultaneously the band transport equations and wave-coupled equations, and using the light intensity modulation as the main variable, the analytic solution is obtained, which is valid for any light intensity modulation and constant light excitation efficiency. Here all the mechanics of drift, diffusion and photovoltaic effect are considered. The result shows that the modulation of the dynamic grating varies more slowly compared with that of the linear modulation approximation.     

Harmonic generation and selection rules in nonlinear optics

A simple procedure, based on the transformation properties of the nonlinear susceptibility tensors of different ranks referred to appropriate coordinate systems, is given for studying the selection rules and polarization characters in regard to all orders of harmonics. By this procedure, results covering both linearly and circularly polarized incident light for all the 32 crystal classes with some simplifying restrictions are obtained and listed in the paper. Attention is drawn to special features in each case. There is complete agreement with what has been reported earlier by Tang and Herbert Rabin for circularly polarized incident light.     

具有两个驰豫时间的热弹性立方晶体材料中平面波的传播

研究具有两个驰豫时间的、两个不同弹性和热性质的、广义传热立方晶体固体半空间的有缺陷结合面上,热弹性平面波的反射和折射问题.具有两个驰豫时间的广义热弹性理论,是1972年由Green和Lindsay提出并应用于问题的研究.对有缺陷边界,给出了反射系数和折射系数(即反射波和折射波振幅与入射波振幅之比)的表达式,并推演了法向刚性边界、横向刚性边界、接触传热边界、滑动边界和结合面边界时的表达式.给出了在不同边界条件及出射角时,不同的反射波和折射波的振幅比,在不同的入射波时的变化图.发现反射波和折射波振幅比受到介质刚性和热性质的影响.     

Transverse vibration of viscoelastic sandwich beam with time-dependent axial tension and axially varying moving velocity

Nonlinearly parametric resonances of axially accelerating moving viscoelastic sandwich beams with time-dependent tension are investigated in this paper. Based on the Kelvin differential constitutive equation, the controlling equation of the transverse vibration of a beam with large deflection is established. The system has been subjected to a time varying velocity and a harmonic axial tension. Here the governing equation of motion contains linear parametric terms and two frequencies, one is the frequency of axially moving velocity and the other one is the frequency of varying tension. The method of multiple scales is applied directly to the governing equation to obtain the complex eigenfunctions and natural frequencies of the system. The elimination of secular terms leads to the steady-state response and amplitude of vibrations. The influence of various parameters such as initial tension on natural frequencies and the amplitude of axial fluctuation, the phase angle between the two frequencies on response curves has been investigated for two different resonance conditions. With the help of numerical results, it has been shown that by using suitable initial tension, the amplitude of axial fluctuation, the phase angle, the vibration of the sandwich beam can be significantly controlled.     

On over-reflection of acoustic-gravity waves incident upon a magnetic shear layer in a compressible fluid

A study is made of over-reflection of acoustic-gravity waves incident upon a magnetic shear layer in an isothermal compressible electrically conducting fluid in the presence of an external magnetic field. The reflection and transmission coefficients of hydromagnetic acoustic-gravity waves incident upon magnetic shear layer are calculated. The invariance of wave-action flux is used to investigate the properties of reflection, transmission and absorption of the waves incident upon the shear layer, and then to discuss how these properties depend on the wavelength, length scale of the shear layers, and the ratio of the flow speed and phase speed of the waves. Special attention is given to the relationship between the wave-amplification and critical-level behaviour. It is shown that there exists a critical level within the shear layer and the wave incident upon the shear layer is over-reflected, that is, more energy is reflected back towards the source than was originally emitted. The mechanism of the over-reflection (or wave amplification) is due to the fact that the excess reflected energy is extracted by the wave from the external magnetic field. It is also found that the absence of critical level within the shear layer leads to non-amplification of waves. For the case of very large vertical wavelength of waves, the coefficients of incident, reflected and transmitted energy are calculated. In this limiting situation, the wave is neither amplified nor absorbed by the shear layer. Finally, it is shown that resonance occurs at a particular value of the phase velocity of the wave.     

Chaotic nonlinear dynamics of cantilever beams under the action of signs-variables loads

In this study we investigate the nonlinear chaotic dynamics of structures, consisting of three contacting isotropic Euler-Bernoulli beams under alternating transverse load. The beams are connected to each other via weak contact conditions. Geometric as well as physical nonlinearity and contact interaction between the beams are taken into account. A new method was proposed for the analysis of chaotic phase synchronization for the multilayered construction consisting of three titanium beams by using Morlet wavelets. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and boundary stabilization of a multiple beam system

In this paper we consider two mathematical models for a multiple beam system (MBS) which is composed of two rigidly and angularly connected Euler-Bernoulli beams The cantilevered structure is clamped at one end, and has point controls for forces and bending moments imposed at the other end and at the connection between the two beams The first model incorporates not only transverse deformations of both beams, but also axial compression/extension of the beams. The second model involves only transverse deformations of the beam. By imposing point controls, an unbounded input operator is obtained A variational formulation of the models is used to show well-posedness. Uniform exponential stabilizability of the second model through boundary feedback is established via energy arguments     

A complementary theory of light scattering by homogeneous spheres

A theory of the scattering of electromagnetic waves by homogeneous spheres, the so-called Mie theory, is presented in a unique and coherent manner in this paper. We begin with Maxwell's equations, from which the vector wave equations are derived and solved by means of the two orthogonal solutions to the scalar wave equation. The transverse incident electric field is mapped in spherical coordinates and expanded in known mathematical functions satisfying the scalar wave equation. Determination of the unknown coefficients in the scattered and internal fields is achieved by matching the electromagnetic boundary conditions on the surface of a sphere. Far-field solutions for the electric field are then given in terms of the scattering functions. Transformation of the electric field to the reference plane containing incident and scattered waves is carried out. Extinction parameters and the phase matrix are derived from the electric field perpendicular and parallel to the reference plane. On the basis of the independent-scattering assumption, the theory is extended to cases involving a sample of homogeneous spheres.     

Second-harmonic generation in ferroelectric thin films on metal substrates for isotropic and cubic symmetries

The Landau–Ginzburg phenomenological theory of ferroelectrics and Landau–Khalatnikov equations of motion are used to model the interaction of electromagnetic radiation and a ferroelectric thin film on a metal substrate. The analysis starts with the minimization of a Gibb’s free energy functional that accounts for the free energy cost of the boundaries of the thin film through a gradient term that is non-zero when the polarization in the film varies. The minimization procedure leads to an Euler–Lagrange equation that can be solved to find the equilibrium polarization in the film. Next the nonlinear dynamical equations that describe the response to an incident electromagnetic field are solved by a perturbation expansion about the equilibrium polarization. The second-harmonic generation term from the expansion is selected. We then go on to calculate a reflection coefficient for the harmonic generation term and investigate how the finite thickness of the film influences the reflection coefficient. In Landau theory the symmetry of the crystal making up the film in the paraelectric phase is reflected in the free energy expression. The analysis here is done for an isotropic symmetry that is often used as an approximation to the actual crystal symmetry and which is mathematically easier to handle. However it is also indicated how the free energy expression can be changed so that it is appropriate for cubic symmetry, and a discussion of how the second harmonic term can be calculated for this case is given. The theory presented is relevant to experimental studies using far-infrared or terahertz reflection measurements because the ferroelectric film is resonant in the far infrared and terahertz ranges.     

The modeling and dynamic analysis of two jointed beams with clearance

The dynamic behaviors of two beams connected by a joint with clearance are investigated. A new equivalent joint model using the transverse and torsion spring systems is developed to describe the dynamics of two jointed beams with clearance. Based on the finite element method (FEM), the equations of motion of the two jointed beams with clearance are established using Hamilton's principle. A modified numerical solution method is presented based on the Newmark integration method to solve the equations with the nonlinearity due to clearance. The contributions of the clearance size and stiffness on the amplitude-frequency response are discussed. The effects of the clearance on the vibration transfer between the two connected beams and the impact force of the joint are investigated.     

各向异性压电介质摩擦接触界面波动特性分析

应用Fourier(傅立叶)分析及奇异积分方程技术研究了弹性波与一般压电介质单侧接触界面的相互作用问题.以界面只产生滑移不分离的情况为例,分析了问题的求解思路和过程,给出了弹性波引起界面滑移或分离的条件.以六角晶系极化碳酸钡陶瓷材料和三角晶系石英材料为例,分析了不同材料摩擦接触界面对弹性波入射的不同反应,给出了不同的入射角及不同的外加压力和电场对界面的影响特性.界面产生滑移和分离时,问题的边界条件具有非线性,导致高频谐波出现,以石英材料为例分析了高频成分随外加条件的变化特性.     

光伏光折变晶体中孤立波的数值模拟

高斯光束在光伏光折变晶体中孤立波的演化满足傍轴方程.傍轴方程可以看作无限维Hamil-tonian系统并可以利用辛几何算法进行计算.数值结果表明外加电场和光伏场的强弱和入射高斯光束的振辐对形成稳定的孤立波有显著的影响.傍轴方程的辛几何差分格式能很好地模拟傍轴方程中孤立波的演化行为.     

Elactic buckling of thin-walled beams with sandwich and double bends flanges

This of the paper are two thin–walled beams with sandwich and double bends flanges. Cross section of these beams is of C type. The beams are simply supported and subjected to a couple of moment – the pure bending. Geometric propeties (warping functions and inertia moments) of two sections with sandwich and double bendsflanges are separately described by dimensionless parameters. Values of critical loads for family of thin–walled beams are numerically determined on the ground of analytical solution. A comparative analysis for selected beams with the use of FEM is performed. Morover the values of critical loads for a family of thin–walled beams are experimentally researched in the Material Strength Laboratoey of the Poznan University of Technology. Finally, the results of the investigation for thin–walled beams are compared in paper. Results of the calculation are presented in tables and figures. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reflection of Shock Fronts in a van der Waals Fluid

In this paper, the reflection phenomenon of a vapor shock front （both sides of the front are in the vapor phase） in a van der Waals fluid is considered. Both the 1-dimensional case and the multidimensional case are investigated. The authors find that under certain conditions, the reflected wave can be a single shock, or a single subsonic phase boundary, or one weak shock together with one subsonic phase boundary, which depends on the strength of the incident shock. This is different from the known result for the reflection of shock fronts in a gas dynamical system due to Chen in 1989.     

Novel energy stable schemes for Swift-Hohenberg model with quadratic-cubic nonlinearity based on the H−1-gradient flow approach

The Swift-Hohenberg model is a very important phase field crystal model which can be described many crystal phenomena. This model with quadratic-cubic nonlinearity based on the H^??1-gradient flow approach is a sixth-order system which satisfies mass conservation and energy dissipation law. The negative energy of this model will bring huge difficulties to energy stability for many existing approaches. In this paper, we consider two linear, second-order and unconditionally energy stable schemes by linear invariant energy quadratization (LIEQ) and modified scalar auxiliary variable (MSAV) approaches. These two schemes will be effective for all negative E₁. Furthermore, we proved that all the semi-discrete schemes are unconditionally energy stable with respect to a modified energy. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.

     

Analysis of weak solutions for the phase-field model for lithium-ion batteries

We study a phase-field model for lithium-ion batteries of olivine LiFePO₄. During electrochemical cycling the fundamental behavior of the crystal is the diffusion of Li which controls the movement of the phase boundary without changing the olivine topology. This model with diffusive phase interfaces consists of two nonlinear parabolic equations of second order. We first prove the existence of global solutions to an initial-boundary value problem of this model. Numerical experiments of the model are then performed to simulate the evolution of lithium concentration and of phase interfaces.     

Longitudinal normals and the existence of acoustic axes in crystals

We obtain three conditions on the phase speeds of the longitudinal and transverse waves propagating along the longitudinal normals in a crystal so that each of these conditions guarantees existence of acoustic axes in this crystal. The result is based on the properties of the rational-valued topological degree and of the index of a singular point for some classes of discontinuous mappings. In addition, we give an upper estimate of the number of acoustic axes in a crystal and show some interrelation between their indices.