Some theoretical aspects of elastic wave modeling with a recently developed spectral element method

A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.     

Phase transition in CeSe, EuSe and LaSe under high pressure

The high pressure phase transition and elastic behavior of rare earth monoselenides (CeSe, EuSe and LaSe) which crystallize in a NaCl-structure have been investigated using the three body interaction potential (TBIP) approach. These interactions arise due to the electronshell deformation of the overlapping ions in crystals. The TBP model consists of a long range Coulomb, three body interactions and the short range overlap repulsive forces operative up to the second neighboring ions. The authors of this paper estimated the values of the phase transition pressure and the associated volume collapse to be closer than other calculations. Thus, the TBIP approach also promises to predict the phase transition pressure and pressure variations of elastic constants of lanthanide compounds.      

Neutron cross-sections above 20 MeV for design and modeling of accelerator driven systems

One of the outstanding new developments in the field of partitioning and transmutation (P&T) concerns accelerator-driven systems (ADS) which consist of a combination of a high-power, high-energy accelerator, a spallation target for neutron production and a sub-critical reactor core. The development of the commercial critical reactors of today motivated a large effort on nuclear data up to about 20 MeV, and presently several million data points can be found in various data libraries. At higher energies, data are scarce or even non-existent. With the development of nuclear techniques based on neutrons at higher energies, nowadays there is a need also for higher-energy nuclear data. To provide alternative to this lack of data, a wide program on neutron-induced data related to ADS for P&T is running at the 20–180 MeV neutron beam facility at ‘The Svedberg Laboratory’ (TSL), Uppsala. The programme encompasses studies of elastic scattering, inelastic neutron production, i.e., (n, xn′) reactions, light-ion production, fission and production of heavy residues. Recent results are presented and future program of development is outlined.      

利用光杠杆法测量金属丝的弹性滞后环

利用大学物理实验中的光杠杆法测定金属丝弹性模量的原理和设备,对具有超弹性的NiTi丝的弹性滞后环进行了测定结果表明,此种方法可以很好地测定NiTi丝的弹性滞后环,而且操作简单使用方便,是一种非常有效的测定金属细丝弹性滞后环的方法.     

Quantitative interpretation of the low-loss electron signal

Low-loss electron spectra from clean elemental standards of C, Si, Cr, Fe, Cu, Ag, and Au are presented and theoretically interpreted with the aid of two basic theories. One of these assumes a simple elastic scattering and Bethe loss regime in which the low-loss signal arises from primary electrons that have undergone a single large-angle scattering event and whose energy loss is described by the continuous slowing down approximation. However, better qualitative agreement with experiment is obtained when multiple elastic scattering is considered via the transport approximation for electron deflection. The simple low-loss electron detector used to obtain the data is also described.     

4 ,4′-二巯基二苯醚分子的电子输运性质研究

利用从头算方法和弹性散射格林函数理论,研究了4 ,4′-二巯基二苯醚分子的电输运性质.计算表明,当外加偏压少于0 .9 V时,该分子器件不导电.当外加偏压进一步增加时,该分子器件的电导呈现出平台特征.由于中间氧原子的存在,相对于4 ,4′-二巯基联苯分子来说,该分子的导电特性较差.     

Molten polystyrene structures above the glass transition,T > Tg

The old controversial idea of structures in molten amorphous polymers is being accepted with theoretical and experimental evidence. Wool's twinkling fractal theory of the glass transition and recent atomic force micrographs are convincing proof of the dynamic, solid aggregate presence below and above T_g. This article offers detailed analysis of the experimental data from high‐pressure dilatometry, as well as from the oscillatory shear tests in the glassy and the molten state of polystyrenes. The results indicate the presence of a transient structure at T > T_g; transient as it depends on the structure of the vitreous polymer and the rate of heating it across T_g. Thus, molten polymer is not always at the thermodynamic equilibrium. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1369–1380, 2011     

Mathematical analogy of a beam on elastic supports as a beam on elastic foundation

This paper presents the mathematical hypothesis that a beam on equidistant elastic supports (BOES) can be considered as a beam on an elastic foundation (BOEF) in static and free vibration problems. This modeling of BOES as BOEF is presumed to be applicable to a limited range of support stiffness, spacing and flexural rigidity of the beam. The authors investigate the applicability of the modeling of BOEF from the property of characteristic solutions obtained from governing equations of both BOES and BOEF. In this study, the formulation of BOES leads to governing difference equations, and the motions of BOEF are expressed by differential equations. This is because exact solutions must be employed in order to verify their analogy accurately. The characteristic solutions obtained from these two governing equations are compared to each other in order to investigate the relationship between them.     

Anisotropy of the angle resolved electron attenuation at crystal surfaces

Photoemission multiple scattering theory is used to describe the electron transport in the surface region of a crystal. Intensities of photoemission from core levels of atoms situated in subsurface atomic layers are calculated as a function of the emitter distance from the surface. The electron angle resolved attenuation length (ARAL) is extracted from the exponential fitting of the intensity decays of photoemission into different directions. Substantial anisotropy of the electron ARAL is found for the Cu(1 1 1) surface in Mg Kα photoexcitation of Cu 2p_3/2 levels and correlated with the orientation of highly packed atomic rows. Enhanced photoemission contributions from specific subsurface layers, caused by electron forward focusing effects, are reported.     

基于弹性波散射对二维障碍物边界的识别

给出了二维障碍物弹性波散射场的一种近似积分形式 ,基于 Fourier变换法建立了均匀障碍物特征函数与其远场散射振幅中形状因子的关系式 ,最后就基体为锌 ,对圆形和椭圆形截面铁夹杂进行了计算机模拟 ,结果表明该反演方法对定量无损检测技术具有应用价值。