119091321
Skyrmions and Faddeev-Hopf solitons
This paper describes a natural one-parameter family of generalized Skyrme systems, which includes the usual SU(2) Skyrme model and the Skyrme-Faddeev system. Ordinary Skyrmions resemble polyhedral shells, whereas the Hopf-type solutions of the Skyrme-Faddeev model look like closed loops, possibly linked or knotted. By looking at the minimal-energy solutions in various topological classes, and for various values of the parameter, we see how the polyhedral Skyrmions deform into looplike Hopf Skyrmions.
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
119377966
Hopf solitons on S**3 and R**3
The Skyrme-Faddeev system, a modified O(3) sigma model in three space dimensions, admits topological solitons with nonzero Hopf number. One may learn something about these solitons by considering the system on the 3-sphere of radius R. In particular, the Hopf map is a solution which is unstable if .
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.
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.
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.
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.
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.
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.