Time-marching numerical schemes for the electric field integral equation on a straight thin wire

We derive and analyse four algorithms for computing the current induced on a thin straight wire by a transient electric field. They all involve solving the thin wire electric field integral equations (EFIEs) and consist of a very accurate differential equations solver together with various schemes to approximate the vector potential integral equation. We carry out a rigorous numerical stability analysis of each of these methods. This has not previously been done for solution schemes for the thin wire EFIEs. Each scheme is shown to be stable and convergent provided the radius of the wire is small enough for the thin wire equations to be a valid model.     

The many facets of linear programming

We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex, ellipsoid, interior-point, and other methods. Received: June 22, 2000 / Accepted: April 4, 2001?Published online October 2, 2001     

The Investigation of Bulk and Surface Polariton Modes in Ga1?xNxAs by Using Infrared Magneto Spectroscopy

We present and discuss infrared magnetoplasma reflectivity and surface polariton modes in Ga_1–xN_xAs. It assumed that the sample is characterized by a magnetoplasma dielectric tensor. Surface polariton dispersion for two component magnetoplasma was calculated from reflectivity spectra data. We detect transverse optic phonon of GaN sublattice in 470 cm^-1. The origin of sharp feature in p-polarization reflectivity about 300 cm^–1 as well as LO phonon frequency of GaAs sublattice is due to Brewster mode. An interesting feature of surface modes in Voigt geometry is nonreciprocalicity, which means that the frequency changes when the direction of propagation is reversed. Also, the infrared magnetoplasma reflectivity of GaNAs should be providing determination of the electrons and heavy holes effective mass and carrier's concentration.     

Metastability of a circular o-ring due to intrinsic curvature

An o-ring takes spontaneously the shape of a chair when strong enough torsion is applied in its tangent plane. This state is metastable, since work has to be done on the o-ring to return to the circular shape. We show that this metastable state exists in a Hamiltonian where curvature and torsion are coupled via an intrinsic curvature term. If the o-ring is constrained to be planar (2d case), this metastable state displays a kink-anti-kink pair. This state is metastable if the ratio is less than , where C and A are the torsion and the bending elastic constants [#!landau!#]. In three dimensions, our variational approach shows that . This model can be generalized to the case where the bend is induced by a concentration field which follows the variations of the curvature. Received: 27 August 1997 / Revised: 23 October 1997 / Accepted: 12 November 1997     

Magnetism in electron-doped copper oxides

We report muon spin relaxation/rotation measurements on sintered powder samples of Nd_2−x Ce _x CuO_4−y and a large single crystal of Nd₂CuO_4−y . We find an electronic phase diagram which is quite similar to that of hole-doped superconductors such as La_2−x Sr _x CuO_4−y , although the doping of electrons into the system is less efficient in destroying the static moments on the copper spins. Static magnetic order in Nd₂CuO_4−y appears below about 250 K, and two spin reorientations are seen atT=75 K andT=35 K. Measurements of the magnetic field penetration depth have been unsuccessful due to the rare-earth paramagnetism of these materials.     

The use of radioanalytical techniques to study intermediate energy,relativistic, and ultra-relativistic nuclear collisions

The use of radioanalytical techniques to study heavy ion induced nuclear reactions offers some distinct advantages over conventional physical techniques. Among these are (a) unit Z and A resultion in detecting the reaction products (b) high sensitivity for low probability events (c) lack of low energy thresholds or cutoffs in measuring reactcion product energy spectcra (d) economical use of accelerator time and (e) simple, portable experimental apparatus allowing broad survey measurements of reaction mechanisms at a variety of nuclear particle accelerators. We describe examples of these advantages from our research in nuclear chemistry.     

Collision Avoidance in Bi-Directional AGV Systems

The use of a bi-directional, as opposed to a one-way, transportation system, can increase the operational efficiency of automated guided vehicles in both manufacturing and warehousing environments. However, the full potential will only be realized if the routeing algorithms pay particular attention to the problem of collision avoidance. This paper is concerned with the development of such an algorithm. The method is based on the use of delays and deviations to avoid collisions that could arise when using the shortest routes for each vehicle, and is applicable to any transportation system which can be represented as a network with known travel times.     

The liquid-crystalline behaviour of amphiphilic ethane-1,2-diol derivatives incorporating a six membered ring in their principal structure

Novel 3-phenyloxy substituted propane-1,2-diol derivatives, 4-(4-n-hexyloxyphenyl)-butane-1,2-diol and 4-(trans-4-n-pyropylcyclohexyl)-butane-1,2-diol have been synthesized and their thermal behaviour has been studied. These compounds exhibit thermotropic and, after addition of water, also lyotropic liquid-crystalline behaviour. The clearing temperatures of the smectic mesophases were found to be strongly dependent on the alkyl chain length and on the structural units that link the aromatic ring to the alkyl chain and to the diol unit. The behaviour of the aromatic compounds is compared with that of the cyclohexane derivative. Thereby it has been realized that the mesophase stability of the amphiphilic diols incorporating a rigid unit is largely determined by both, the molecular geometry (molecular shape and intramolecular flexibility) and the amphiphilic structural pattern.     

Riccati-based preconditioner for computing invariant subspaces of large matrices

Summary. This paper introduces and analyzes the convergence properties of a method that computes an approximation to the invariant subspace associated with a group of eigenvalues of a large not necessarily diagonalizable matrix. The method belongs to the family of projection type methods. At each step, it refines the approximate invariant subspace using a linearized Riccati's equation which turns out to be the block analogue of the correction used in the Jacobi-Davidson method. The analysis conducted in this paper shows that the method converges at a rate quasi-quadratic provided that the approximate invariant subspace is close to the exact one. The implementation of the method based on multigrid techniques is also discussed and numerical experiments are reported. Received June 15, 2000 / Revised version received January 22, 2001 / Published online October 17, 2001