Mathieu and Heun Solutions to the Wheeler–De Witt Equation for Hyperbolic Universes

For the spatially open Friedmann–Robertson–Walker (FRW) Universe with stiff matter and radiation as non-interacting matter sources, the scale function coming from the integration of the Friedmann equation is expressed in terms of elliptic integrals. For a negative cosmological constant, we identify the allowed ranges for the model’s parameters. Within the quantum analysis, the Wheeler–De Witt (WDW) equation turns into a modified Morse equation whose solutions are Mathieu and Heun functions.     

Emergence of regular meandered step structure in simulated growth of GaN(0001) surface

Step meandering during the growth of gallium nitride crystal is studied on using kinetic Monte Carlo method. Cause of instability is identified to be the particle advection caused by the step flow. Growth process is conducted in N-rich conditions and GaN(0001) surface kinetics is modeled by setting jump probabilities for Ga atoms adsorbed at the surface. We show that at low enough temperatures and relatively high external particle fluxes periodic regular pattern of meanders is created with its wavelength inversely proportional to the particle flux. An increase of the meander amplitude saturates after some period and further crystal grow is stationary, creating “finger-like” structure. For medium fluxes regular structure of meanders builds up for low or zero value of Schwoebel barrier. For higher fluxes wavelengths of meanders become shorter than the terrace width and they start to grow independently and finally transfer the surface to a rough structure. For very low fluxes or at relatively high temperatures steps move steadily remaining their initial shapes of straight, parallel lines.     

Corrosion protection performance of ceria‐copolymer bilayer coating on low nickel stainless steel in 0.5 M H2SO4 medium

In this paper, we have reported the anti‐corrosion performance of ceria / poly (indole‐co‐pyrrole) (Ce/(poly(In‐co‐Py)) bilayer coating on low nickel stainless steel (LN SS). Electrochemical polymerization of (poly (In‐co‐Py)) was achieved on ceria‐coated LN SS (CeO₂/LN SS) in acetonitrile medium containing LiClO₄ (ACN‐LiClO₄) by cyclic voltammetric technique. The coatings were characterized by analytical techniques like Fourier transform infrared spectroscopy, scanning electron microscopy with energy dispersive analysis of X‐ray, respectively. The mechanical behavior of the coatings was studied using peel test, hardness and wear resistance tests. The corrosion defensive performance of this bilayer coating on LN SS was investigated using electrochemical techniques such as potentiodynamic polarization and electrochemical impedance spectroscopy in 0.5 M H₂SO₄. These results show that the bilayer coating on LN SS lowered the permeability of corrosive ions present in the acidic medium and thus acts as a barrier against the attack of corrosive environment. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability analysis of thermodynamic lubrication problems in journal bearings

A new numerical scheme (which combines FEM, FVM and BEM methods) for solving thermohydrodynamic lubrication transient problems with cavitation is described. The algorithm is then applied to study the stability of a journal-bearing system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gradient Formula for Linearly Self-Interacting Branes

 The computation of long range linear self-interaction forces in string and higher dimensional brane models requires the evaluation of the gradients of regularised values of divergent self-interaction potentials. It is shown that the appropriately regularised gradient in directions orthogonal to the brane surface will always be obtainable simply by multiplying the regularised potential components by just half the trace of the second fundamental tensor, except in the hypermembrane case for which the method fails. Whatever the dimension of the background this result is valid provided the codimension is two (the hyperstring case) or more, so it can be used for investigating brane-world scenarios with more than one extra space dimension. Received: 15 April 2002 / Accepted: 23 October 2002 Published online: 25 February 2003 Communicated by H. Nicolai     

Extrapolation techniques for ill-conditioned linear systems

Summary. In this paper, the regularized solutions of an ill–conditioned system of linear equations are computed for several values of the regularization parameter . Then, these solutions are extrapolated at by various vector rational extrapolations techniques built for that purpose. These techniques are justified by an analysis of the regularized solutions based on the singular value decomposition and the generalized singular value decomposition. Numerical results illustrate the effectiveness of the procedures. Received June 23, 1997 / Revised version received October 24, 1997     

Von klassischen Flächen zum Computer-Aided Geometric Design

Zusammenfassung. Der vorliegende Artikel beschreibt anhand einfacher Beispiele ein Verfahren, vorgegebene Zylinder oder Kegel durch ein weiteres Fl?chenstück (Teil einer sog.Dupinschen Zyklide) glatt zu verbinden (Blending). Zur L?sung werden Laguerregeometrie und Bézierdarstellung von Kurven verwendet. Ziel des Artikels ist es, grundlegende Ideen aus aktueller Forschung und Anwendung klassischer Geometrie darzustellen. Eingegangen am 07.01.1998 / Angenommen am 22.05.1998     

On GMW Designs and Cyclic Hadamard Designs

We generalise results of Jackson concerning cyclic Hadamard designs admitting SL(2,2ⁿ) as a point transitive automorphism group. The generalisation concerns the designs of Gordon, Mills and Welch and we characterise these as designs admitting GM(m,qⁿ) acting in a certain way. We also generalise a construction given by Maschietti, using hyperovals, of cyclic Hadamard designs, and characterise these amongst the designs of Gordon, Mills and Welch.     

Thermodynamic model and high-temperature Raman spectra of 25Na2O·75B2O3 glassforming melts

Journal of Thermal Analysis and Calorimetry - The temperature dependence of Raman spectra of 25Na2O·75B2O3 melts recorded in the temperature range 321–1142 °C was studied...