A boundary value problem for the KdV equation: Comparison of finite-difference and Chebyshev methods

Solutions of a boundary value problem for the Korteweg–de Vries equation are approximated numerically using a finite-difference method, and a collocation method based on Chebyshev polynomials. The performance of the two methods is compared using exact solutions that are exponentially small at the boundaries. The Chebyshev method is found to be more efficient.     

Engineering Analysis and Design with ALE-VMS and Space–Time Methods

Flow problems with moving boundaries and interfaces include fluid–structure interaction (FSI) and a number of other classes of problems, have an important place in engineering analysis and design, and offer some formidable computational challenges. Bringing solution and analysis to them motivated the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method and also the variational multiscale version of the Arbitrary Lagrangian–Eulerian method (ALE-VMS). Since their inception, these two methods and their improved versions have been applied to a diverse set of challenging problems with a common core computational technology need. The classes of problems solved include free-surface and two-fluid flows, fluid–object and fluid–particle interaction, FSI, and flows with solid surfaces in fast, linear or rotational relative motion. Some of the most challenging FSI problems, including parachute FSI, wind-turbine FSI and arterial FSI, are being solved and analyzed with the DSD/SST and ALE-VMS methods as core technologies. Better accuracy and improved turbulence modeling were brought with the recently-introduced VMS version of the DSD/SST method, which is called DSD/SST-VMST (also ST-VMS). In specific classes of problems, such as parachute FSI, arterial FSI, ship hydrodynamics, fluid–object interaction, aerodynamics of flapping wings, and wind-turbine aerodynamics and FSI, the scope and accuracy of the FSI modeling were increased with the special ALE-VMS and ST FSI techniques targeting each of those classes of problems. This article provides an overview of the core ALE-VMS and ST FSI techniques, their recent versions, and the special ALE-VMS and ST FSI techniques. It also provides examples of challenging problems solved and analyzed in parachute FSI, arterial FSI, ship hydrodynamics, aerodynamics of flapping wings, wind-turbine aerodynamics, and bridge-deck aerodynamics and vortex-induced vibrations.     

Optical Properties of Doped Antiferromagnets

We investigate the consequences of an incommensurate magnetic order in doped La_2–x Sr _x CuO₄ using dynamical mean-field theory for the effective single-band model. The high-energy optical transitions are due to high-energy excitations across large Mott–Hubbard gap, while low-energy excitations involve a pseudogap induced by the local spin order. The latter lead to a strong drop in the scattering rate at low , in qualitative agreement with the experimental data.     

Oscillation limits for weighted residual methods applied to convective diffusion equations

Convection–diffusion equations are difficult to solve when the convection term dominates because most solution methods give solutions which oscillate in space. Previous criteria based on the one-dimensional convection–diffusion equation have shown that finite difference and Galerkin (linear or quadratic basis functions) will not give oscillatory solutions provided the Peclet number times the mesh size (Pe Δx) is below a critical value. These criteria are based on the solution at the nodes, and ensure that the nodal values are monotone. Similar criteria are developed here for other methods: quadratic Galerkin with upwind weighting, cubic Galerkin, orthogonal collocation on finite elements with quadratic, cubic or quartic polynomials using Lagrangian interpolation, cubic or quartic polynominals using Hermite interpolation, and the method of moments. The nodal values do not oscillate for collocation or moments methods with Hermite cubic polynomials regardless of the value of Pe Δx. A new criterion is developed for all methods based on the monotonicity of the solutions throughout the domain. This criterion is more restrictive than one based only on the nodal values. All methods that are second order (Δx²) or better in truncation error give oscillatory solutions (based on the entire domain) unless Pe Δx is below a critical value. This value ranges from 2 for finite difference methods to 4·6 for Hermite, quartic, collocation methods.     

A new spd tight-binding model of magnetism in transition metals

We present the extension of an efficient spd tight-binding model to the case of spin polarized materials by including electron–electron interactions, in an extended Hubbard–Hartree–Fock formalism. It is applied with success to rhodium and palladium clusters and slabs.     

Perceived Air Quality,Sick Building Syndrome (SBS) Symptoms and Productivity in an Office with Two Different Pollution Loads

Abstract Perceived air quality, Sick Building Syndrome (SBS) symptoms and productivity were studied in an existing office in which the air pollution level could be modified by introducing or removing a pollution source. This reversible intervention allowed the space to be classified as either non-low-polluting or low-polluting, as specified in the new European design criteria for the indoor environment CEN CR 1752 (1998). The pollution source was a 20-year-old used carpet which was introduced on a rack behind a screen so that it was invisible to the occupants. Five groups of six female subjects each were exposed to the conditions in the office twice, once with the pollution source present and once with the pollution source absent, each exposure being 265 min in the afternoon, one group at a time. They assessed the perceived air quality and SBS symptoms while performing simulated office work. The subject-rated acceptability of the perceived air quality in the office corresponded to 22% dissatisfied when the pollution source was present, and to 15% dissatisfied when the pollution source was absent. In the former condition there was a significantly increased prevalence of headaches (P= 0.04) and significantly lower levels of reported effort (P=0.02) during the text typing and calculation tasks, both of which required a sustained level of concentration. In the text typing task, subjects worked significantly more slowly when the pollution source was present in the office (P=0.003), typing 6.5% less text than when the pollution source was absent from the office. Reducing the pollution load on indoor air proved to be an effective means of improving the comfort, health and productivity of building occupants.     

Consequences of Orbital Degeneracy in Insulating and Doped Manganites

We derive a spin-orbital model for manganites which includes the complete e _g and t _2g superexchange of S=2 spins at Mn³⁺ ions and predicts that the same type of antiferromagnetic and orbital ordering is stabilized in insulating La₃Mn₂O₇ as in LaMnO₃ by a purely electronic mechanism dominated by the e _g-superexchange. At finite doping we consider a model of t–J variety which describes a metal–insulator transition due to a competition between lattice polarons and kinetic energy in the metallic ferromagnetic ground state.     

丹麦区域供热水处理标准简介

在丹麦,许多区域供热系统都曾经有过由于有垢形成或由于腐蚀而造成的管道破坏及能源损失,这是由于水处理不充分或缺乏水处理造成的。当原有的区域供热系统被更新的时候,在某些部位需要修理之前将水处理水平提高通常是非常重要的。因为只有水质符合要求我们才能使系统能使用更长时间。１９８８年,ＤａｎｓｋｅＦｊｅｒｖａｒｍｅｖｅｒｋｅｒｓＦｏｒｅｎ－ｉｎｇ（丹麦区域供热协会）为适应发展需要提供了如今丹麦区域供热系统应用的给水和循环水的建议。这些标准应用的温度范围为３５℃至１８０℃,而且必须强调的是系统中不能有铝材存…     

Acoustic beam position monitor for microanalysis of particles in the 10 nm range in a TEM-SCAN system

This paper describes the principle and use of a simple equipment which makes it possible to keep the electron beam in the centre of a small particle analysed by X-ray microanalysis in a STEM system. A deviation from the correct beam position introduced by drift or other deficiencies is monitored by an audible change in a sound frequency and corrected for by a convenient manual operation.