Orientation dependent size effects in thermal buckling and post-buckling of nanoplates with cubic anisotropy

In this work, a continuum model is presented for size and orientation dependent thermal buckling and post-buckling of anisotropic nanoplates considering surface and bulk residual stresses. The model with von-Karman nonlinear strains and material cubic anisotropy of single crystals contains two parameters that reflect the orientation effects. Using Ritz method, closed form solutions are given for buckling temperature and post-buckling deflections. Regarding self-instability states of nanoplates and their recovering at higher temperatures, an experiment is discussed based on low pressurized membranes to verify the predictions. For simply supported nanoplates, the size effects are lowest when they are aligned in [100] direction. When the edges get clamped, the orientation dependence is ignorable and the behavior becomes symmetric about [510] axis. The surface residual stress makes drastic increase in buckling temperature of thinner nanoplates for which a minimum thickness is pointed to stay far from material softening at higher temperatures. Deflection of [100]-oriented buckled nanoplates is higher than [110] ones but this reverses at higher temperatures. The results for long nanoplates show that the buckling mode numbers are changed by orientation which is verified by FEM.     

Radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to circumferential magnetic field

Knowledge of the vibrational properties of nanoparticles is of fundamental interest since it is a signature of their morphology, and it can be utilized to characterize their physical properties. In addition, the vibration characteristics of the nanoparticles coupled with surrounding media and subjected to magnetic field are of recent interest. This paper develops an analytical approach to study the radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to magnetic field. Based on Maxwell's equations, the nonlocal differential equation of radial motion is derived in terms of radial displacement and Lorentz's force. Bessel functions are used to obtain a frequency equation. The model is justified by a good agreement between the results given by the present model and available experimental and atomic simulation data. Furthermore, the model is used to elucidate the effect of nanoparticle size, the magnetic field and the stiffness of the elastic medium on the radial breathing-mode frequencies of several nanoparticles. Our results reveal that the effects of the magnetic field and the elastic medium are significant for nanoparticle with small size.     

腔光子-自旋波量子耦合系统中各向异性奇异点的实验研究

通过耦合三维微波腔中光子和腔内钇铁石榴石单晶小球中的自旋波量子形成腔-自旋波量子的耦合系统,并通过精确调节系统参数在该实验系统中观测到各向异性奇异点.奇异点对应于非厄米系统中一种特殊状态,在奇异点处,耦合系统的本征值和本征矢均简并,并且往往伴随着非平庸的物理性质.以往大量研究主要集中在各向同性奇异点的范畴,它的特征是在系统参数空间中沿着不同参数坐标趋近该奇异点时具有相同的函数关系.在这篇文章中,主要介绍实验上在腔光子-自旋波量子耦合系统中通过调节系统的耦合强度和腔的耗散衰减系数两条趋近奇异点的路径而实现了各向异性奇异点,具体分别对应于在趋近奇异点时,本征值的虚部的变化与耦合强度和腔的衰减系数的变化会有线性和平方根不同的行为.各向异性奇异点的实现有助于基于腔光子-自旋波量子耦合系统的量子信息处理和精密探测器件的进一步研究.     

Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: generalized reflection function

Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large.     

马歇尔-勒纳条件的实证研究

本文从人民币实际汇率变动是否会对我国贸易收支产生影响出发，基于马歇尔．勒纳条件，对计算贸易弹性常用的OLS回归模型进行了改进，建立了向量自回归误差修正模型来估算我国的国际贸易弹性。实证研究表明：我国进出口需求的价格弹性之和大于1。因此人民币贬值可改善贸易收支；反之升值将使贸易收支恶化。     

A WKB analysis of the buckling condition for a cylindrical shell of arbitrary thickness subjected to an external pressure

We consider the plane-strain buckling of a cylindrical shellof arbitrary thickness which is made of a Varga material andis subjected to an external hydrostatic pressure on its outersurface. The WKB method is used to solve the eigenvalue problemthat results from the linear bifurcation analysis. We show thatthe circular cross-section buckles into a non-circular shapeat a value of µ₁ which depends on A₁/A₂ and a mode number,where A₁ and A₂ are the undeformed inner and outer radii, andµ₁ is the ratio of the deformed inner radius to A₁. Inthe large mode number limit, we find that the dependence ofµ₁ on A₁/A₂ has a boundary layer structure: it is constantover almost the entire region of 0 < A₁/A₂ < 1 and decreasessharply from this constant value to unity as A₁/A₂ tends tounity. Our asymptotic results for A₁ – 1 = O(1) and A₁– 1 = O(1/n) are shown to agree with the numerical resultsobtained by using the compound matrix method.     

Development of the mechanics of underground and special structures in Kazakhstan over the last 40 years

Some results on underground structures obtained by Kazakh mechanicians are reviewed. The review covers a period of the last forty years. Also results on the mechanics of special objects are discussed.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 3–36, October 2004.     

Anisotropic and isotropic phases of polymer melts

The melting mechanism of polymer crystals is proposed. It is assumed that the melting happens due to forming supervacancies. This mechanism leads the appearance of anisotropic phase of a melt. It is shown that two phases—anisotropic and isotropic—can exist in polymer melts.     

AGSM光束在自由空间中的传输

 用矩阵方法研究了有扭曲的各向异性高斯-尔模型（AGSM）光束通过自由空间的传输。给出了光束参数的解析传输公式和详细数值计算结果，说明AGSM光束的传输特性以及扭曲因子和空间相关长度的影响。