Comparison of Several Spatial Discretizations for the Navier–Stokes Equations

Grid convergence studies for subsonic and transonic flows over airfoils are presented in order to compare the accuracy of several spatial discretizations for the compressible Navier–Stokes equations. The discretizations include the following schemes for the inviscid fluxes: (1) second-order-accurate centered differences with third-order matrix numerical dissipation, (2) the second-order convective upstream split pressure scheme (CUSP), (3) third-order upwind-biased differencing with Roe's flux-difference splitting, and (4) fourth-order centered differences with third-order matrix numerical dissipation. The first three are combined with second-order differencing for the grid metrics and viscous terms. The fourth discretization uses fourth-order differencing for the grid metrics and viscous terms, as well as higher-order approximations near boundaries and for the numerical integration used to calculate forces and moments. The results indicate that the discretization using higher-order approximations for all terms is substantially more accurate than the others, producing less than two percent numerical error in lift and drag components on grids with less than 13,000 nodes for subsonic cases and less than 18,000 nodes for transonic cases. Since the cost per grid node of all of the discretizations studied is comparable, the higher-order discretization produces solutions of a given accuracy much more efficiently than the others.     

Lie-optics, geometrical phase and nonlinear dynamics of self-focusing and soliton evolution in a plasma

It is useful to state propagation laws for a self-focusing laser beam or a soliton in group-theoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index profile than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.     

基于AHP权重和灰色服务器负载预测的云计算On-line迁移策略

为了克服云计算环境下由于实时用户任务的不确定性到来和服务器性能差异而导致的云计算环境的负载不均衡问题,提出了一种AHP权重获取和灰度算法预测服务器负载的云计算on-line虚拟机迁移策略。首先,设计了基于AHP和灰色服务器预测的虚拟机on-line迁移模型,提出了采用AHP获取虚拟机各资源需求权重,然后,采用灰色模型预测下一时刻的服务器负载,采用此权值向量与各无需迁移的服务器的空闲资源向量进行加权得到加权和,将具有最小加权和的物理服务器作为迁移的目标宿主机。最后,定义了基于AHP权重和灰色服务器负载预测的云计算on-line迁移算法。在CloudSim环境下进行实验,结果表明文中的迁移策略使得云计算在响应用户任务时,具有任务失败次数少、SLA违约率低和迁移成功率高的优点,同时与其它方法相比,具有负载均衡程度高的优点,具有较强的可行性。     

基于云环境的分布式软件接口自动化测试

软件测试是保证软件质量,提供可靠服务的重要技术手段。目前基于Web Service的分布式软件越来越多,其测试技术手段也越来越受到关注。Web Service的分布性和多样性使手工测试变得非常低效,因而需要不断提高Web Service测试的自动化程度。另外,云计算因其计算成本低、可伸缩性强的特点为自动化测试提供了新的支持环境。本文结合Web Service的测试需求,首次提出了基于云环境的Web Service接口自动化测试的技术框架,分析了框架内原子Web Service、组合Web Service测试的关键技术,并研发了基于CloudStack云平台的自动化测试的原型系统。实验结果表明,本文所提出的基于云平台的WebService自动化测试方案可行且提高了测试效率。     

Inverse statistical problems: from the inverse Ising problem to data science

Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.     

Migration of seismic data

Prospecting for oil and gas resources poses the problem of determining the geological structure of the earth's crust from indirect measurements. Seismic migration is an acoustic image reconstruction technique based on the inversion of the scalar wave equation. Extensive computation is necessary before reliable information can be extracted from large sets of recorded data. In this paper a collection of industrial migration techniques, each giving rise to a data parallel algorithm, is outlined. Computer simulations on synthetic seismic data illustrate the problem and the approach.     

Generalized Brownian motion and elasticity

We introduce a family of stochastic processes which are a natural extension of Brownian motion to a tensor form. This allows us to solve a Dirichlet problem of linear elasticity obeying Lamé's equation, [1–(d– 1)]²V(x)+ [·V(x)]=0.     

Potential-induced structure transitions in self-assembled monolayers: ethanethiol on Au(1 0 0)

We have characterized the structural behaviour of ethanethiol self-assembled monolayers (SAMs) on Au(1 0 0) in 0.1 M H₂SO₄ as a function of electrode potential, using in-situ scanning tunneling microscopy (STM). After modification of the Au(1 0 0) electrode in an ethanolic solution of ethanethiol, STM images in air reveal a disordered thiol adlayer and a surface that is covered by 25% of monoatomic high gold islands, which originate from lifting of the (hex) reconstruction during thiol adsorption. In contrast to alkanethiol SAMs on Au(1 1 1), no vacancy islands are seen on the Au(1 0 0) surface. After contact of the SAM-covered Au(1 0 0) electrode with 0.1 M H₂SO₄ under potential control, two different structures are observed, depending on the potential range positive or negative of +0.3 V vs. SCE. In both cases the emerging ordered structures are quadratic, their unit cells being rotated by 45° with respect to the main crystallographic axes of the substrate. However, the ordered structure at negative potentials is more densely packed than the one at positive potentials, and in addition the surface reveals an almost 50% coverage of monoatomic high gold islands. The structure of the SAM changes reversibly with the electrode potential, the long range order gradually decreasing with each transition. Concomittant with this structure transition monoatomic deep holes are created when the potential is stepped from the cathodic to the anodic region. The experimental observations are rationalized by a high mobility of the gold thiolate moiety, causing the surface density of the SAM-covered gold to change drastically with potential.     

A cluster Monte Carlo algorithm for 2-dimensional spin glasses

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100² down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e ^2βJ) and not as a power law as T↦T _c = 0. Received 10 January 2001 and Received in final form 29 May 2001     

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

The one-body and two-body density matrices in coordinate space and their Fourier transforms in momentum space are studied for a nucleus (a nonrelativistic, self-bound finite system). Unlike the usual procedure, suitable for infinite or externally bound systems, they are determined as expectation values of appropriate intrinsic operators, dependent on the relative coordinates and momenta (Jacobi variables) and acting on intrinsic wave functions of nuclear states. Thus, translational invariance (TI) is respected. When handling such intrinsic quantities, we use an algebraic technique based upon the Cartesian representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators and for oscillator quanta. Each of the relevant multiplicative operators can then be reduced to the form: one exponential of the set { } times another exponential of the set { }. In the course of such a normal-ordering procedure we offer a fresh look at the appearance of “Tassie-Barker” factors, and point out other model-independent results. The intrinsic wave function of the nucleus in its ground state is constructed from a nontranslationally-invariant (nTI) one via existing projection techniques. As an illustration, the one-body and two-body momentum distributions (MDs) for the ⁴He nucleus are calculated with the Slater determinant of the harmonic-oscillator model as the trial, nTI wave function. We find that the TI introduces quite important effects in the MDs.