在热腔中产生多原子GHZ态的方法

我们提出了一个在热腔中产生多原子GHZ态的方法来检验量子非定域性。在这个方法中,三个原子被同时送入一个热腔中,它们初始时处于相同的态。这个方法既对腔的衰减不敏感又对热场不敏感,这为检验量子力学的基本方面提供了新的前景。     

向列相液晶中强非局域空间光孤子的实验观察

通过实验对向列相液晶中的非局域空间光孤子的传输进行了研究。理论上基于非线性的液晶孤子传输方程,采用高斯形式的试探解,得到了孤子传输的解析解,以及对液晶中的非局域孤子和Snyder等提出的强非局域孤子模型的结果进行了比较。实验上,观察了空间光孤子在向列相液晶中的传输,找到了不同束宽下空间光孤子的临界功率。比如束宽为2μm时临界功率为2.0mW。观察了向列相液晶中空间光孤子的弛豫过程,并注意到液晶分子的响应时间长达几秒钟,液晶中的孤子形成速度较慢。     

ON THE NONLOCAL SYMMETRIES OF THE μ-CAMASSA–HOLM EQUATION

The μ-Camassa–Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa–Holm and the Hunter–Saxton equations. This equation admits quadratic pseudo-potentials which allow us to compute some first-order nonlocal symmetries. The found symmetries preserve the mean of solutions. Finally, we discuss also the associated μCH equation.     

Recovery of An Unknown Flux in Parabolic Problems with Nonstandard Boundary Conditions: Error Estimates

In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain ^N, with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant (t), accompanied with a nonlocal (integral) Dirichlet side condition.We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution u and also of the unknown function .     

Application of MCD spectroscopy and TD-DFT to nonplanar core-modified tetrabenzoporphyrins: effect of reduced symmetry on nonplanar porphyrinoids

The optical spectra of a series of core-modified tetrabenzoporphyrins were analyzed to determine the effects of core modification, ligand folding, and partial benzo substitution at the ligand periphery on the electronic structure by using magnetic circular dichroism (MCD) and NMR spectroscopy, X-ray crystallography, cyclic and differential pulse voltammetry, and TD-DFT calculations. Planar 21-carba-, 21-thia-, 21,23-dithia-, and 21-oxa-23-thiatetrabenzo[b,g,l,q]porphyrins reported previously were studied together with the previously unreported 21-oxa- and 21-carba-23-thiatetrabenzo[b,g,l,q]porphyrins. The optical properties of these compounds are compared to those of tetrabenzo[b,g,l,q]-, 5,10,15,20-tetraphenyl-, 5,10,15,20-tetraphenyltetrabenzo[b,g,l,q]-21-thia-, 5,10,15,20-tetraphenyltetrabenzodithia-, 5,10,15,20-tetraphenyldibenzo[g,q]-21,23-dithia-, 5,10,15,20-tetraphenyldibenzo[b,l]-21,23-dithia-, 5,10,15,20-tetraphenyltribenzo[g,q,l]-21-thia-, and 5,10,15,20-tetraphenylbenzo[b]-21-thiaporphyrins. Michl's perimeter model and Gouterman's four-orbital model are used to conceptualize the results and to account for red shifts commonly observed in the spectral bands of nonplanar porphyrinoids.     

Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory

Abstract

This article contains the nonlocal elasticity theory to capture size effects in functionally graded (FG) nano-rod under magnetic field supported by a torsional foundation. Torque effect of an axial magnetic field on an FG nano-rod has been defined using Maxwell’s relation. The material properties were assumed to vary according to the power law in radial direction. The Navier equation and boundary conditions of the size-dependent FG nano-rod were derived by the Hamilton’s principle. These equations were solved by employing the generalized differential quadrature method (GDQM). Presented model has the ability to turn into the classical model if the material length scale parameter is taken to be zero. The effects of some parameters, such as inhomogeneity constant, magnetic field and small-scale parameter, were studied. As an important result of this study can be stated that an FG nano-rod model based on the nonlocal elasticity theory behaves softer and has smaller natural frequency.     

基于能量等效原理的应变局部化分析:Ⅰ.一维解析解

基于热力学第一定律和非局部塑性理论,提出了一种求解应变局部化问题的非局部方法.对材料的每一点定义了局部和非局部两种状态空间,局部状态空间的内变量通过非局部权函数映射到非局部空间,成为非局部内变量.在应变软化过程中,局部状态空间中的塑性变形服从正交流动法则,材料的软化律在非局部状态空间中被引入.通过两个状态空间的塑性应变能耗散率的等效,得到了应变软化过程中明确定义的局部化区域以及其中的塑性应变分布.应用本方法导出了一维应变局部化问题的解析解.解析解表明,应变局部化区域的尺寸只与材料内尺度有关;对于高斯型非局部权函数,局部化区域的尺寸大约是材料内尺度的6倍.一维算例表明,局部化区域的塑性应变分布以及载荷-位移曲线仅与材料参数和结构几何尺寸有关,变形局部化区域的尺寸随着材料内尺度的减小而减小,同时塑性应变也随着材料内尺度的减小变得更加集中.当内尺度趋近于零时,应用本文方法得到的解与采用传统的局部塑性理论得到的解相同.     

TRANSVERSE VIBRATION OF A HANGING NONUNIFORM NANOSCALE TUBE BASED ON NONLOCAL ELASTICITY THEORY WITH SURFACE EFFECTS

The aim of this paper is to study the free transverse vibration of a hanging nonuni- form nanoscale tube. The analysis procedure is based on nonlocal elasticity theory with surface effects. The nonlocal elasticity theory states that the stress at a point is a function of strains at all points in the continuum. This theory becomes significant for small-length scale objects such as micro- and nanostructures. The effects of nonlocality, surface energy and axial force on the natural frequencies of the nanotube are investigated. In this study, analytical solutions are formulated for a clamped-free Euler-Bernoulli beam to study the free vibration of nanoscale tubes.