119422845
Hopf solitons from instanton holonomy
The holonomy of an SU(2) N-instanton in the x4-direction gives a map from 3 into SU(2), which provides a good model of an N-Skyrmion. Combining this map with the standard Hopf map from SU(2)S3 to S2 gives a configuration for a Hopf soliton of charge N. In this way, one may define a collective-coordinate manifold for Hopf solitons. This paper deals with instanton approximations to Hopf solitons in the Skyrme-Faddeev model, focusing in particular on the N = 1 and 2 sectors, and the two-soliton interaction.
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.
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.
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
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.
120593178
A time-of-flight neutron reflectometer for surface and interfacial studies
A time-of-flight neutron reflectometer constructed for surface and interfacial studies, and installed at the ISIS pulsed neutron source, is described. One of its important design features is its inclined incident beam, since this allows both liquid- and solid-surface phenomena to be investigated. Measurements are presented to show the performance of the instrument, and new representative results, which include studies of liquid surfaces, Langmuir-Blodgett films, and thin-film multilayers, are included as illustrations of the scientific potential of the method.
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.
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.
118452505
Nuclear Astrophysics Away from Stability
Explosive astrophysical environments invariably lead to the production of nuclei away from stability. An understanding of the dynamics and nucleosynthesis in such environments is inextricably coupled to an understanding of the properties of the synthesized nuclei. In this talk a review is presented of the basic explosive nucleosynthesis mechanisms (s-process, r-process, n-process, p-process, and rp-process). Specific stellar model calculations are discussed and a summary of the pertinent nuclear data is presented. Possible experiments and nuclear-model calculations are suggested that could facilitate a better understanding of the astrophysical scenarios. 39 refs., 4 figs.