Assessment of some iterative methods for non-symmetric linear systems arising in computational fluid dynamics

Various tests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme.     

Anomalous electric-field effect and glassy behaviour in granular aluminium thin films: electron glass?

We present a study of non-equilibrium phenomena observed in the electrical conductance of insulating granular aluminium thin films. An anomalous field effect and its slow relaxation are studied in some detail. The phenomenology is very similar to the one already observed in indium oxide. The origin of the phenomena is discussed. In granular systems, the present experiments can naturally be interpreted along two different lines. One relies on a slow polarisation in the dielectric surrounding the metallic islands. The other one relies on a purely electronic mechanism: the formation of an electron Coulomb glass in the granular metal. More selective experiments and/or quantitative predictions about the Coulomb glass properties are still needed to definitely distinguish between the two scenarios.     

Electron-confined LO-phonon scattering in GaAs-Al0.45Ga0.55As superlattice

We develop a theoretical model to the scattering time due to the electron-confined LO-phonon in GaAs-Al_xGa_1-xAs superlattice taking into account the sub-band parabolicity. Using the new analytic wave function of electron miniband conduction of superlattice and a reformulation slab model for the confined LO-phonon modes, an expression for the electron-confined LO-phonon scattering time is obtained. In solving numerically a partial differential equation for the phonon generation rate, our results show that forx = 0.45, the LO-phonon in superlattice changes from a bulk-like propagating mode to a confined mode. The dispersion of the relaxation time due to the emission of confined LO-phonons depends strongly on the total energy.     

A Relaxation Scheme for Solving the Boltzmann Equation Based on the Chapman-Enskog Expansion

Abstract In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jinand Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weaklyparabolic, has a linearly hyperbolic convection part, and is endowed with a generalized eotropy inequality. Itagrees with the solution of the Boltzmann equation up to the Burnett order via the Chapman-Enskog expansion. We develop a one-dimensional non-oscillatory numerical scheme based on the relaxed Burnett system forthe Boltzmann equation. We compare numerical results for stationary shocks based on this relaxation scheme,and those obtained by the DSMC (Direct Simulation Monte Carlo), by the Navier-Stokes equations and bythe extended thermodynamics with thirteen moments (the Grad equations). Our numerical experiments showthat the relaxed Burnett gives more accurate approximations to the shock profiles of the Boltzmann equationobtained by the DSMC, for a range of Mach numbers for hypersonic flows, th     

利用微悬臂梁表面应力研究聚N-异丙基丙烯酰胺分子的构象转变

提出了一种基于微悬臂梁传感技术研究大分子折叠/构象转变的新方法.通过分子自组装的方法将热敏性的聚N-异丙基丙烯酰胺(PNIPAM)分子链修饰到微悬臂梁的单侧表面，用光杠杆技术检测温度在20—40℃之间变化时由于微悬臂梁上的PNIPAM分子在水中的构象转变所引起的微悬臂梁变形.实验结果显示：在升温过程中，微悬臂梁的表面应力发生了变化并且导致微悬臂梁产生了弯曲变形，这个过程对应着微悬臂梁上的PNIPAM分子从无规线团构象到塌缩小球构象的构象转变.在降温过程中，微悬臂梁发生了反方向的弯曲变形，这对应着PNIPA 关键词： 构象转变 聚N-异丙基丙烯酰胺分子链 表面应力 微悬臂梁     

Converged properties of clean metal surfaces by all-electron first-principles calculations

All-electron full-potential linearized augmented plane-wave calculations of the surface energy, work function, and interlayer spacings of close-packed metal surfaces are presented, in particular, for the free-electron-like metal surfaces, Mg(0 0 0 1) and Al(1 1 1), and for the transition metal surfaces, Ti(0 0 0 1), Cu(1 1 1), Pd(1 1 1), and Pt(1 1 1). We investigate the convergence of the surface energy as a function of the number of layers in the slab, using the Cu(1 1 1) surface as an example. The results show that the surface energy, as obtained using total energies of the slab and bulk from separate calculations, converges well with respect to the number of layers in the slab. Obviously, it is necessary that bulk and surface calculations are performed with the same high accuracy. Furthermore, we discuss the performance of the local-density and generalized gradient approximations for the exchange-correlation functional in describing the various surface properties.     

Lagrangean heuristics combined with reoptimization for the 0-1 bidimensional knapsack problem

First, this paper deals with lagrangean heuristics for the 0-1 bidimensional knapsack problem. A projected subgradient algorithm is performed for solving a lagrangean dual of the problem, to improve the convergence of the classical subgradient algorithm. Secondly, a local search is introduced to improve the lower bound on the value of the biknapsack produced by lagrangean heuristics. Thirdly, a variable fixing phase is embedded in the process. Finally, the sequence of 0-1 one-dimensional knapsack instances obtained from the algorithm are solved by using reoptimization techniques in order to reduce the total computational time effort. Computational results are presented.     

The Casimir effect of Reissner-NordstrSm black hole

The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.     

On a nonlinear multigrid algorithm with primal relaxation for the image total variation minimisation

Digital image restoration has drawn much attention in the recent years and a lot of research has been done on effective variational partial differential equation models and their theoretical studies. However there remains an urgent need to develop fast and robust iterative solvers, as the underlying problem sizes are large. This paper proposes a fast multigrid method using primal relaxations. The basic primal relaxation is known to get stuck at a ‘local’ non-stationary minimum of the solution, which is usually believed to be ‘non-smooth’. Our idea is to utilize coarse level corrections, overcoming the deadlock of a basic primal relaxation scheme. A further refinement is to allow non-regular coarse levels to correct the solution, which helps to improve the multilevel method. Numerical experiments on both 1D and 2D images are presented.     

用干涉方法测量薄膜应力

基于基片弯曲法和牛顿环的基本原理,使用He-Ne激光器、扩束镜、凸透镜和带分光镜的移测显微镜,搭建了薄膜应力测量装置.采用直流溅射法制备了厚度为30~144 nm的银薄膜,衬底采用厚度为0.15 mm、直径为18 mm的圆形玻璃片.实验发现,薄膜厚度对银薄膜的内应力有显著的影响,在薄膜厚度很小时,随着薄膜厚度的增加,应力迅速增大,达到最大值后,随着厚度的继续增加,薄膜应力下降较快并趋于稳定值.