5786909
The QR algorithm and Hyman’s method on vector computers
The implementation on vector computers of the QR algorithm and of iterative schemes based on obtaining the determinant and its derivatives by Hyman's method are presented. It is shown that iterative schemes based on Hyman's method will probably be more efficient than the QR algorithm on vector computers for large matrices. A theoretical comparison of the Laguerre iterative scheme with the QR algorithm is presented using the latest available CDC STAR-100 instruction execution times. In addition, the results of several test cases run on the Laguerre-Hyman algorithm on a serial computer are reported.
120013608
Computing the singular value decompostion of a product of two matrices
An algorithm is developed for computing the singular value decomposition of a product of two general matrices without explicitly forming the product. The algorithm is based on an earlier Jacobi-like method due to Kogbetliantz and uses plane rotations applied to the two matrices separately. A triangular variant of the basic algorithm is developed that reduces the amount of work required.
57087721
EZVIDEO, FORTRAN graphics routines for the IBM AT
A set of IBM PC-based FORTRAN plotting routines called EZVIDEO is described in this report. These routines are written in FORTRAN and can be called from FORTRAN programs. EZVIDEO simulates a subset of the well-known DISSPLA graphics calls and makes plots directly on the IBM AT display screen. Screen dumps can also be made to an attached LaserJet or Epson printer to make hard copy without using terminal emulators. More than forty DISSPLA calls are simulated by the EZVIDEO routines. Typical screen plots require about 10 seconds (s), and good hard copy of the screen image on a laser printer requires less than 2 minutes (min). This higher-resolution hard copy is adequate for most purposes because of the enhanced resolution of the screen in the EGA and VGA modes. These EZVIDEO routines give the IB, AT user a stand-alone capability to make useful scientific or engineering plots directly on the AT, using data generated in FORTRAN programs. The routines will also work on the IBM PC or XT in CGA mode, but they require more time and yield less resolution. 7 refs., 4 figs.
121961363
Two Yang-Mills-Higgs monopoles close together
Abstract A procedure for constructing a seven-parameter family of Yang-Mills-Higgs multipopole e solutions is presented. Each solution represents a separated 2-monopole configuration. The distance between the monopoles is restricted to be less than a certain positive number, in the sense that the solutions are not known to be smooth for greater distances.
120625279
Measurement of the Velocity of Sound in Crystals by Pulsed Neutron Diffraction
The diffraction method of observing elementary excitations in crystals has been applied to the study of one-phonon thermal diffuse scattering from pyrolitic graphite on a high-resolution pulsed neutron diffractometer. The variation of the phase velocity of sound as a function of direction in the crystal has been determined for the out-of-plane modes. This is a quick and efficient method of determining sound velocities in crystals under extreme conditions.
119858441
Classical solutions of the chiral model, unitons, and holomorphic vector bundles
This paper deals with classical solutions of theSU(2) chiral model on ℝ2, and of a generalized chiral model on ℝ2+1. Such solutions are shown to correspond to certain holomorphic vector bundles over minitwistor space. With an appropriate boundary condition, the solutions (called 1-unitons in [9]) correspond to bundles over a compact 2-dimensional complex manifold, and the problem becomes one of algebraic geometry.
119185655
Skyrmion multi-walls
Skyrmion walls are topologically nontrivial solutions of the Skyrme system which are periodic in two spatial directions. We report numerical investigations which show that solutions representing parallel multi-walls exist. The most stable configuration is that of the square N-wall, which in the N → ∞ limit becomes the cubically symmetric Skyrme crystal. There is also a solution resembling parallel hexagonal walls, but this is less stable.
117789490
Curved twistor spaces
﻿ This thesis is concerned with the problem of "coding" the information of various zero-rest-mass fields into the complex structure of "curved twistor spaces". Chapter 2 is devoted to various preliminaries: a brief outline of twistor theory; an introduction to vector bundles and sheaf cohomology and some of their applications in twistor theory; and a discussion of potentials for electromagnetic fields. Chapter 3 deals with left-handed (i.e. anti-self-dual) electromagnetic fields and describes in some detail the associated curved twistor spaces. It is shown how holomorphic functions on the curved spaces give rise to "charged" zero-rest-mass fields on space-time. The first section of Chapter 4 gives the corresponding results for left-handed gravitational fields, using Penrose's "nonlinear graviton" construction. The rest of Chapter 4 is devoted to the concept of twistors relative to a hypersurface in a general curved space-time. In §4.2 the hypersurface is taken to be spacelike; the hypersurface twistors are described and the problem of using holomorphic hypersurface twistor functions to generate fields on the hypersurface and in space-time is discussed. Next the hypersurface is taken to be null. The structure of the associated hypersurface twistor space and and#x210b;-space are described in some detail. The twistor space has a natural inner product and, if the hypersurface is shear-free, then it has a "fibred" structure as well. In §4.4 the hypersurface twistor language is used to show that the propagation of twistors through an analytic pp-wave is given by the unfolding of a canonical transformation. Chapter 5 extends the "electromagnetic" construction of Chapter 3 to non-Abelian gauge theories; left-handed gauge fields are described in terms of complex vector bundles over protective twistor space.