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.
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.
122197255
Integrable Yang–Mills–Higgs equations in three-dimensional de Sitter space–time
This paper describes an integrable Yang–Mills–Higgs system on (2+1)-dimensional de Sitter space–time. It is the curved-space–time analog of the Bogomolnyi equations for monopoles on R3. A number of solutions, of various types, are constructed.
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.
7691760
Symmetric Calorons
Calorons (periodic instantons) interpolate between monopoles and instantons, and their holonomy gives approximate Skyrmion configurations. We show that, for each caloron charge N ≤ 4, there exists a one-parameter family of calorons which are symmetric under subgroups of the three-dimensional rotation group. In each family, the corresponding symmetric monopoles and symmetric instantons occur as limiting cases. Symmetric calorons therefore provide a connection between symmetric monopoles, symmetric instantons and Skyrmions. PACS 11.27.+d, 11.10.Lm, 11.15.-q ∗email: richard.ward@durham.ac.uk
121880030
Instantons and algebraic geometry
Minimum action solutions for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via the Penrose twistor transform, to algebraic bundles on the complex projective 3-space. These bundles in turn correspond to algebraic curves. The implication of these results for the Yang-Mills fields is described. In particular all solutions are rational and can be constructed from a series of AnsätzeAl forl≧1.
120294348
Stationary axisymmetric space-times: A new approach
This essay describes a new approach to the problem of understanding stationary axisymmetric solutions of Einstein's vacuum equations, different from the “Bäcklund transformation” approach which has recently been extensively developed. It translates the problem into one of complex geometry, using the machinery of twistor theory. This, in turn, leads to a procedure which, in principle, generates all solutions. Some explicit examples are presented.