123489527
Skyrmions and monopoles — isolated and arrayed
There are two basic types of three-dimensional topological soliton, namely skyrmions and monopoles. This article reviews some of the features of such solitons, concentrating on static multi-skyrmions and multi-monopoles with structure group SU(2), and focusing in particular on periodic arrays. An isolated multi-skyrmion typically has a regular, for example polyhedral, structure; and there are multi-monopoles which look very similar. However, when it comes to infinite arrays of solitons — chains, walls or crystals — then the skyrmion and monopole systems behave rather differently.
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
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.
115690938
Twistor techniques in gauge theories
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.
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.
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.
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.
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.
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.