121522591
Self-dual metrics with self-dual Killing vectors
Twistor methods are used to derive a class of solutions to Einstein’s vacuum equations, with anti-self-dual Weyl tensor. In particular, all metrics with a Killing vector whose derivative is anti-self-dual and which admit a real positive-definite section are exhibited and shown to coincide with the metrics of Hawking (Phys. Lett. A 60, 81 (1977)).
123186755
Deformations of the embedding of the SU(2) monopole solution in SU (3)
This paper is concerned with static Yang-Mills-Higgs fields, in the Prasad-Sommerfield limit of no Higgs self-interaction. One can obtain SU (3) multipole solutions from SU(2) solutions by embedding, in several different ways. In some of these cases, the embedding belongs to a family of SU(3) solutions that are not all embeddings; in other words, some embeddings can be deformed into non-embeddings. The simplest case, an embedding of the SU(2) spherically symmetric monopole, is studied with the aid of the twistor construction procedure. The family of axially symmetric SU(3) solutions to which it belongs is described.
115690938
Twistor techniques in gauge theories
120434886
Generalized Nahm equations and classical Yang-Baxter equations
Abstract The Nahm equations for the three matrices T j (t), namely T j = 1 2 ϵ jkl [T k , T l ] , are generalized to set of equations involving more than three matrices. This generalization is closely linked to the classical Yang-Baxter equations. It seems to be “completely integrable” in the same sense that Nahm's equations are.
6860273
Periodic Monopoles
This paper deals with static BPS monopoles in three dimensions which are periodic either in one direction (monopole chains) or two directions (monopole sheets). The Nahm construction of the simplest monopole chain is implemented numerically, and the resulting family of solutions described. For monopole sheets, the Nahm transform in the U(1) case is computed explicitly, and this leads to a description of the SU(2) monopole sheet which arises as a deformation of the embedded U(1) solution. PACS 11.27.+d, 11.10.Lm, 11.15.-q ∗email: richard.ward@durham.ac.uk
8637389
Stability of sigma-model strings and textures
In flat spacetime, sigma-model strings and textures are both unstable: they tend to collapse (and subsequently decay). With sufficient cosmological expansion, however, they are stable in a generalized sense: a small perturbation will cause them to change their shape, but they do not decay. The current rate of expansion is sufficient to stabilize strings, but not textures.
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.
122864423
Numerical Computation of the Matrix Exponential with Accuracy Estimate
This paper presents and analyzes an algorithm for computing the exponential of an arbitrary $n \times n$ matrix. Diagonal Pade table approximations are used in conjunction with several techniques for reducing the norm of the matrix. An important feature of the algorithm is that an estimate for the minimum number of digits accurate in the norm of the computed exponential matrix is returned to the user. In obtaining this estimate, several interesting results concerning rounding errors and Pade approximations are presented.
120828253
Balancing the Generalized Eigenvalue Problem
An algorithm is presented for balancing the A and B matrices prior to computing the eigensystem of the generalized eigenvalue problem $Ax = \lambda Bx$. The three-step algorithm is specifically designed to precede the $QZ$-type algorithms, but improved performance is expected from most eigensystem solvers. Permutations and two-sided diagonal transformations are applied to A and B to produce matrices with certain desirable properties. Test cases are presented to illustrate the improved accuracy of the computed eigenvalues.
119056020
Solving quadratic lambda-matrix problems without factorization
An algorithm is presented for computing the eigenvalues of smallest magnitude and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ + C lambda + K. M, C, and K are assumed to be symmetric matrices with K positive definite and M negative definite. The algorithm is based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence to the smallest positive and negative eigenvalue is proved. Test examples are presented.
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.