Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier–Stokes equations

We present an iterative semi-implicit scheme for the incompressible Navier–Stokes equations, which is stable at CFL numbers well above the nominal limit. We have implemented this scheme in conjunction with spectral discretizations, which suffer from serious time step limitations at very high resolution. However, the approach we present is general and can be adopted with finite element and finite difference discretizations as well. Specifically, at each time level, the nonlinear convective term and the pressure boundary condition – both of which are treated explicitly in time – are updated using fixed-point iteration and Aitken relaxation. Eigenvalue analysis shows that this scheme is unconditionally stable for Stokes flows while numerical results suggest that the same is true for steady Navier–Stokes flows as well. This finding is also supported by error analysis that leads to the proper value of the relaxation parameter as a function of the flow parameters. In unsteady flows, second- and third-order temporal accuracy is obtained for the velocity field at CFL number 5–14 using analytical solutions. Systematic accuracy, stability, and cost comparisons are presented against the standard semi-implicit method and a recently proposed fully-implicit scheme that does not require Newton’s iterations. In addition to its enhanced accuracy and stability, the proposed method requires the solution of symmetric only linear systems for which very effective preconditioners exist unlike the fully-implicit schemes.     

On the Number of Even Parts in All Partitions of $$\varvec{n}$$n into Distinct Parts

Annals of Combinatorics - A famous theorem of Euler asserts that there are as many partitions of n into distinct parts as there are partitions into odd parts. The even parts in partitions of n into...     

Comparative extreme ultraviolet emission measurements for lithium and tin laser plasmas

Detailed spectroscopic studies on extreme UV emission from laser plasmas using tin and lithium planar solid targets were completed. At 13.5 nm, the best conversion efficiency (CE) for lithium was found to be 2.2% at intensities near 7 x 10(10) W/cm(2). The highest CE measured for tin was near 5.0% at an intensity close to 1 x 10(11) W/cm(2).     

Tailoring the structure of water at a metal surface: a structural analysis of the water bilayer formed on an alloy template

Recent studies show that structures based on the traditional "icelike" water bilayer are not stable on flat transition metal surfaces and, instead, more complex wetting layers are formed. Here we show that an ordered bilayer can be formed on a SnPt(111) alloy template and determine the structure of the water layer by low energy electron diffraction. Close agreement is found between experiment and the structure calculated by density functional theory. Corrugation of the alloy surface allows only alternate water molecules to chemisorb, stabilizing the H-down water bilayer by reducing the metal-hydrogen repulsion compared to a flat surface.     

Quantitative combination of volumetric MR imaging and MR spectroscopy data for the discrimination of meningiomas from metastatic brain tumors by means of pattern recognition

The analysis of information derived from magnetic resonance imaging (MRI) and spectroscopy (MRS) has been identified as an important indicator for discriminating among different brain pathologies. The purpose of this study was to investigate the efficiency of the combination of textural MRI features and MRS metabolite ratios by means of a pattern recognition system in the task of discriminating between meningiomas and metastatic brain tumors. The data set consisted of 40 brain MR image series and their corresponding spectral data obtained from patients with verified tumors. The pattern recognition system was designed employing the support vector machines classifier with radial basis function kernel; the system was evaluated using an external cross validation process to render results indicative of the generalization performance to “unknown” cases. The combination of MR textural and spectroscopic features resulted in 92.15% overall accuracy in discriminating meningiomas from metastatic brain tumors. The fusion of the information derived from MRI and MRS data might be helpful in providing clinicians a useful second opinion tool for accurate characterization of brain tumors.     

Equity portfolio construction and selection using multiobjective mathematical programming

A multi-objective mixed integer programming model for equity portfolio construction and selection is developed in this study, in order to generate the Pareto optimal portfolios, using a novel version of the well known ε-constraint method. Subsequently, an interactive filtering process is also proposed to assist the decision maker in making his/her final choice among the Pareto solutions. The proposed methodology is tested through an application in the Athens Stock Exchange.     

Dielectric properties of beryllia ceramics in the near-millimeter wavelength range

We report the refractive indices and absorption coefficients for four beryllia (BeO) ceramic samples. These dielectric properties have been measured over the range from 4 to 18 cm^–1 by use of a Michelson interferometer. The index n, follows the linear relationship n=0.6517 cm³/g×+0.7130 with density, , over the range 2.8<<3.0 g/cm³.     

Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.     

Bichromatic and Equichromatic Lines in ℂ2 and ℝ2

Let G and R each be a finite set of green and red points, respectively, such that |G|=n, |R|=n−k, G∩R=∅, and the points of G∪R are not all collinear. Let t be the total number of lines determined by G∪R. The number of equichromatic lines (a subset of bichromatic) is at least (t+2n+3−k(k+1))/4. A slightly weaker lower bound exists for bichromatic lines determined by points in ℂ². For sufficiently large point sets, a proof of a conjecture by Kleitman and Pinchasi is provided. A lower bound of (2t+14n−k(3k+7))/14 is demonstrated for bichromatic lines passing through at most six points. Lower bounds are also established for equichromatic lines passing through at most four, five, or six points.