Numerical Analysis of Thermally Coupled Flow Problems with Interfaces and Phase-change Effects

In this work a fixed mesh finite element approach is presented to solve thermally coupled flow problems including moving interfaces between immiscible fluids and phase-change effects. The weak form of the full incompressible Navier-Stokes equations is obtained using a generalized streamline operator (GSO) technique that enables the use of equal order interpolation of the primitive variables of the problem: velocity, pressure and temperature. The interfaces are defined with a mesh of marker points whose motion is obtained applying a Lagrangian scheme. Moreover, a temperature-based formulation is considered to describe the phase-change phenomena. The proposed methodology is used in the analysis of a filling of a step mould and a gravity-driven flow of an aluminium alloy in an obstructed vertical channel.     

On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Anomalous curie response of impurities in quantum-critical spin-1/2 Heisenberg antiferromagnets

We consider a magnetic impurity in two different S=1/2 Heisenberg bilayer antiferromagnets at their respective critical interlayer couplings separating Néel and disordered ground states. We calculate the impurity susceptibility using a quantum Monte Carlo method. With intralayer couplings in only one of the layers (Kondo lattice), we observe an anomalous Curie constant C*, as predicted on the basis of field-theoretical work [S. Sachdev, Science 286, 2479 (1999)10.1126/science.286.5449.2479]. The value C* = 0.262 +/- 0.002 is larger than the normal Curie constant C=S(S+1)/3. Our low-temperature results for a symmetric bilayer are consistent with a universal C*.     

A production-transportation problem with stochastic demand and concave production costs

Well known extensions of the classical transportation problem are obtained by including fixed costs for the production of goods at the supply points (facility location) and/or by introducing stochastic demand, modeled by convex nonlinear costs, at the demand points (the stochastic transportation problem, [STP]). However, the simultaneous use of concave and convex costs is not very well treated in the literature. Economies of scale often yield concave cost functions other than fixed charges, so in this paper we consider a problem with general concave costs at the supply points, as well as convex costs at the demand points. The objective function can then be represented as the difference of two convex functions, and is therefore called a d.c. function. We propose a solution method which reduces the problem to a d.c. optimization problem in a much smaller space, then solves the latter by a branch and bound procedure in which bounding is based on solving subproblems of the form of [STP]. We prove convergence of the method and report computational tests that indicate that quite large problems can be solved efficiently. Problems up to the size of 100 supply points and 500 demand points are solved. Received October 11, 1993 / Revised version received July 31, 1995 Published online November 24, 1998     

Measurements in Situ and Spectral Analysis of Wind Flow Effects on Overhead Transmission Lines

In the paper an important issue of vibrations of the transmission line in real conditions was analyzed. Such research was carried out by the authors of this paper taking into account the cross-section of the cable being in use on thetransmission line. Analysis was performed for the modern ACSR high voltage transmission line with span of 213.0 m. The purpose of the investigation was to analyze the vibrations of the power transmission line in the natural environmentand compare with the results obtained in the numerical simulations. Analysis was performed for natural and wind excited vibrations. The numerical model was made using the Spectral Element Method. In the spectral model, for variousparameters of stiffness, damping and tension force, the system response was checked and compared with the results of the accelerations obtained in the situ measurements. A frequency response functions (FRF) were calculated. Thecredibility of the model was assessed through a validation process carried out by comparing graphical plots of FRF functions and numerical values expressing differences in acceleration amplitude (MSG), phase angle differences (PSG) and differences in acceleration and phase angle total (CSG) values. Particular attention was paid to the hysteretic damping analysis. Sensitivity of the wave number was performed for changing of the tension force and section area of thecable. The next aspect constituting the purpose of this paper was to present the wide possibilities of modelling and simulation of slender conductors using the Spectral Element Method. The obtained results show very good accuracy in the range of both experimental measurements as well as simulation analysis. The paper emphasizes the ease with which the sensitivity of the conductor and its response to changes in density of spectral mesh division, cable cross-section,tensile strength or material damping can be studied.     

Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the “magic field” of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr–Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the “accelerating magic field” represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born’s solution for two uniformly accelerated monopole charges.     

Highly oriented crystalline Er:YAG and Er:YAP layers prepared by PLD and annealing

High quality, thick, highly oriented crystalline thin films of Yttrium Aluminum Garnet (Y₃Al₅O₁₂) and Yttrium Aluminum Perovskite (YAlO₃) doped with Erbium were prepared by pulsed laser deposition. Samples were created in vacuum or oxygen environment. Depositions were arranged at room temperature, or at high substrate temperatures ranging from 800 to 1100 °C. Amorphous layers were annealed by laser, or in oven (argon flow, temperatures in range from 1200 to 1400 °C). Fused silica and sapphire (0 0 0 1) were used as substrates. Properties of films were characterized by X-ray diffraction, atomic force microscopy, and by photoluminescence measurement. Size of crystalline grains was in the range 116-773 nm. Thickness of layers was up to 17 μm.