Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure

EFFECT OF THE DOMAIN GEOMETRY ON THE EXISTENCE OF MULTIPEAK SOLUTIONS FOR AN ELLIPTIC PROBLEM

Abstract. In this paper, we construct multipeak solutions for a singularly perturbed Dirichlet problem. Under the conditions that the distance function d(x, ∂Ω) has k isolated compact connected critical sets T1,..., Tk satisfying d(x, ∂Ω) = cj = const., for all x ∈ Tj, mini̸=j d(Ti, Tj)> 2 max1≤j≤k d(Tj, ∂Ω), and the critical group of each critical set Ti is nontrivial, we construct a solution which has exactly one local maximum point in a small neighbourhood of Ti, i = 1,..., k. (1.1

Properties of non-BPS SU(3) monopoles

This paper is concerned with magnetic monopole solutions of SU(3) Yang-Mills-Higgs system beyond the Bogomol'nyi-Prasad-Sommerfield limit. The different SU(2) embeddings, which correspond to the fundamental monopoles, as well the embedding along composite root are studied. The interaction of two different fundamental monopoles is considered. Dissolution of a single fundamental non-BPS SU(3) monopole in the limit of the minimal symmetry breaking is analysed.Comment: 19 pages, 7 figures. Typos corrected, reference added. Final version published in Physica Script

SU(3) monopoles and their fields

Some aspects of the fields of charge two SU(3) monopoles with minimal symmetry breaking are discussed. A certain class of solutions look like SU(2) monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding the monopoles. For large cloud size the relative moduli space metric splits as a direct product AH\times R^4 where AH is the Atiyah-Hitchin metric for SU(2) monopoles and R^4 has the flat metric. Thus the cloud is parametrised by R^4 which corresponds to its radius and SO(3) orientation. We solve for the long-range fields in this region, and examine the energy density and rotational moments of inertia. The moduli space metric for these monopoles, given by Dancer, is also expressed in a more explicit form.Comment: 17 pages, 3 figures, latex, version appearing in Phys. Rev.

Characterisation of damage mechanisms in oxide ceramics indented at dynamic and quasi-static strain rates

Ceramic materials are known to display rate dependent behaviour under impact. Tests to establish the strain-rate dependent variations in damage mechanisms have been carried out on debased alumina, an alumina-zirconia composite, and 3Y-TZP. Materials were indented dynamically and quasi-statically using identical sharp hardened steel projectiles while recording the load profile. Characteristics typical of both sharp and blunt indentation types were observed using scanning electron microscopy and piezospectroscopic mapping. At dynamic strain rates both the depth of the indentation and the residual stress in the material were lower than for quasi-static tests. This was attributed to temperature-induced softening of the projectile. Unusual behaviour was observed in the 3Y-TZP samples due to the reversible transformation from tetragonal to monoclinic crystal structures during mechanical loading. These effects and the observed superior mechanical strength against impact suggest that zirconia or zirconia-composite materials may have advantages over debased alumina for application as ceramic armour materials

Measuring the effect of enhanced cleaning in a UK hospital : a prospective cross-over study

Increasing hospital-acquired infections have generated much attention over the last decade. There is evidence that hygienic cleaning has a role in the control of hospital-acquired infections. This study aimed to evaluate the potential impact of one additional cleaner by using microbiological standards based on aerobic colony counts and the presence of Staphylococcus aureus including meticillin-resistant S. aureus. We introduced an additional cleaner into two matched wards from Monday to Friday, with each ward receiving enhanced cleaning for six months in a cross-over design. Ten hand-touch sites on both wards were screened weekly using standardised methods and patients were monitored for meticillin-resistant S. aureus infection throughout the year-long study. Patient and environmental meticillin-resistant S. aureus isolates were characterised using molecular methods in order to investigate temporal and clonal relationships. Enhanced cleaning was associated with a 32.5% reduction in levels of microbial contamination at handtouch sites when wards received enhanced cleaning (P < 0.0001: 95% CI 20.2%, 42.9%). Near-patient sites (lockers, overbed tables and beds) were more frequently contaminated with meticillin-resistant S. aureus/S. aureus than sites further from the patient (P = 0.065). Genotyping identified indistinguishable strains from both handtouch sites and patients. There was a 26.6% reduction in new meticillin-resistant S. aureus infections on the wards receiving extra cleaning, despite higher meticillin-resistant S. aureus patient-days and bed occupancy rates during enhanced cleaning periods (P = 0.032: 95% CI 7.7%, 92.3%). Adjusting for meticillin-resistant S. aureus patient-days and based upon nine new meticillin-resistant S. aureus infections seen during routine cleaning, we expected 13 new infections during enhanced cleaning periods rather than the four that actually occurred. Clusters of new meticillin-resistant S. aureus infections were identified 2 to 4 weeks after the cleaner left both wards. Enhanced cleaning saved the hospital £30,000 to £70,000.Introducing one extra cleaner produced a measurable effect on the clinical environment, with apparent benefit to patients regarding meticillin-resistant S. aureus infection. Molecular epidemiological methods supported the possibility that patients acquired meticillin-resistant S. aureus from environmental sources. These findings suggest that additional research is warranted to further clarify the environmental, clinical and economic impact of enhanced hygienic cleaning as a component in the control of hospital-acquired infection