On the non-uniform motion of dislocations: the retarded elastic fields,the retarded dislocation tensor potentials and the Liénard–Wiechert tensor potentials

The topic of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key formulae for the dynamics of dislocations are derived (Jefimenko type and Heaviside–Feynman type equations of dislocations). In addition, exact closed-form solutions of the elastic fields produced by a dislocation loop are calculated as retarded line integral expressions for subsonic motion. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocation loop are given explicitly in terms of the so-called three-dimensional elastodynamic Liénard–Wiechert tensor potentials. The two-dimensional elastodynamic Liénard–Wiechert tensor potentials and the near-field approximation of the elastic fields for straight dislocations are calculated. The singularities of the near-fields of accelerating screw and edge dislocations are determined.     

用于投影显示的匀光杆照明系统设计

基于DMD和LCoS空间光调制器的投影显示对照明系统提出了更高的要求,有必要对原有的匀光杆照明系统进行分析和改进。着重于建立一个精确的匀光杆照明系统模型,对各个参数进行了细致的分析和总体的优化。同时提出了一种高效率的组合反射镜模型,通过LightTools软件模拟仿真,实现了ANSI照明均匀性为( 4．2％,-4．6％),光能利用率为82％的照明输出。能够满足投影显示对照明系统的指标要求。     

On the Self-Normalized Cramér-type Large Deviation

For the self-normalized sum, , it is shown that converges to 1, uniformly in a region, under the optimal assumption that the sampled distribution is in the domain of attraction of the normal law. Bounds for this convergence are given and their applications to exponential non-uniform Berry–Esseen bound are also discussed.     

QUASI-INTERPOLATING OPERATORS AND THEIR APPLICATIONS IN HYPERSINGULAR INTEGRALS

1.IntroductionSinceP.ZwartobtainedanexpressionofbivariateB--spline[2],R.--HWangandC.K.Chuihavedevelopedaseriesofresults,especially,thequasi--interpolatingoperatorsofSI(AL.)onuniformtype-2triangulationanditsapproximationproperties[']whichhavewidespreadapplicationsinMechanicsandEngineering.Furthermore,R-HWangandC.K.ChuialsoobtainedthefunctionwithminimumsupportinSI(A:)onnon-uniformtype-2triangulationandthebasisofSI(a:)[#].Inthispaperweintroducesomequasi-interpolatingoperatorsofSa(~Z~)o…     

用蒙特卡罗方法计算棒状放大器内的泵浦能量分布

建立了用蒙特卡罗和光线跟踪法计算高功率固体激光系统棒状放大器能量沉积分布的模拟程序。在本文的模型中正确考虑了光线在反射器激光棒上的多次反射，氙灯的辐射光谱以及钕玻璃的吸收光谱。计算结果与作者用阈值法测量的增益均匀性以及用哈特曼网格法测量的氙灯泵浦对激光波面畸变的影响是一致的。     

Liquid crystalline main chain polymers with a poly(p-phenyleneterephthalate) backbone. 2. Fiber spinning and mechanical properties of polyesters with alkoxy side chains

Fiber spinning and mechanical properties of four rigid polyesters with alkoxy substituents of different length and placement were evaluated. Properties of oriented fibers from the polymer with dodecyloxy substituents on the terephthalate moiety, PTA12HQ, were significantly affected by the crystal modification. At room temperature the following properties (tensile modulus E, tensile strength σ_b, and strain at break ε_b) could be obtained: E = 9.5 GPa, σ_b = 85 MPa and ε_b = 1.1% for phase L_f (the “frozen in layered mesophase”); E = 10.4 GPa, σ_b = 59 MPa and ε_b = 0.6% for modification A; E = 17.3 GPa, σ_b = 158 MPa and ε_b = 1.2% for modification B. Because of the higher amount of main chains per cross sectional area the polymer with hexyloxy side chains, PTA6HQ, showed better properties at a comparable degree of molecular orientation: E = 24 GPa, σ_b = 270 MPa, ε_b = 1.4%. Fibers obtained from the polyester with dodecyloxy substituents on the hydroquinone moiety, PTAHQ12, were too brittle to handle. The polyester with dodecyloxy substituents on both moieties, PTA12HQ12, was spun from the isotropic melt. Because of the obtained low degree of orientation, properties (E = 1 GPa, σ_b = 40 MPa, and ε_b = 6.3%) were governed by interactions between the chains (the main chains are not load-bearing). © 1993 John Wiley & Sons, Inc.     

光斑位置对靶丸辐照不均匀度时间行为的影响

 从数值模拟和定性分析两个方面研究了腔靶内光斑位置对靶丸辐照不均匀度随时间变化规律的影响。结果表明，光斑相对于靶丸的极点和赤道点的几何因子随其位置的变化规律不同。根据它们大小的比较，靶丸辐照不均匀度随时间变化的趋势可分为三种类型，分别对应于光斑处于三个不同区域。定性分析与数值模拟给出一致的结果。     

The Fourth Order Difference Equation for the Laguerre-Hahn Polynomials Orthogonal on Special Non-uniform Lattices

We firstly establish the fourth order difference equation satisfied by the Laguerre-Hahn polynomials orthogonal on special non-uniform lattices in general case, secondly give it explicitly for the cases of polynomials r-associated to the classical polynomials orthogonal on linear, q-linear and q-nonlinear (Askey-Wilson) lattices, and thirdly give it semi-explicitly for the class one Laguerre-Hahn polynomials orthogonal on linear lattice.     

RANS simulations for transition and turbulent flow regimes in wire-wrapped rod bundles

Internal flows through rod assemblies are commonly found in heat exchangers, steam generators, and nuclear reactors. One of the fuel assembly designs considered for liquid metal-cooled reactors utilizes wires helically wrapped around each fuel rod as spacers. The wires keep the fuel pins separated, enhancing the turbulent mixing, and heat transfer, but also affecting the pressure drop. It is of interest the understanding of the fluid flow phenomena in the sodium-cooled fast reactor as it is one of the Generation IV advanced reactor designs and it has been a motivating topic of research for the last decade. A wire-wrapped fuel assembly replica with 61-pins has been in operation at the Thermal-Hydraulic Research Laboratory of Texas A&M University. This facility produced high-fidelity velocity and pressure drop data for validation of computational fluid dynamics codes. This study investigates the effects of geometrical features and operating conditions on the flow behavior of the 61-pin wire wrapped bundle using Reynolds-Averaged Navier-Stokes (RANS) models to predict the axial and transverse pressure drops for a range of Reynolds numbers from 1,270 to 100,000. The friction factor predictions were in satisfactory agreement with the experimental data and the Upgraded Chen and Todreas correlation. The internal subchannel velocity results were compared with experimental data and Large Eddy Simulations (LES) and found in reasonable agreement. This study demonstrates that RANS is a suitable approach in predicting velocity and pressure fields in wire-wrapped rod bundles, with a relatively low computational effort.     

Sharp estimate of electric field from a conductive rod and application

We are concerned with the quantitative study of the electric field perturbation due to the presence of an inhomogeneous conductive rod embedded in a homogenous conductivity. We sharply quantify the dependence of the perturbed electric field on the geometry of the conductive rod. In particular, we accurately characterize the localization of the gradient field (i.e., the electric current) near the boundary of the rod where the curvature is sufficiently large. We develop layer‐potential techniques in deriving the quantitative estimates and the major difficulty comes from the anisotropic geometry of the rod. The result complements and sharpens several existing studies in the literature. It also generates an interesting application in EIT (electrical impedance tomography) in determining the conductive rod by a single measurement, which is also known as the Calderón's inverse inclusion problem in the literature.