Formation of extended topological defects during symmetry breaking phase transitions in O(2) and O(3) models

The density of extended topological defects created during symmetry-breaking phase transitions depends on the ratio between the correlation length in the symmetric phase near $T_c$ and the winding length of the defects as determined by the momentaneous effective action after a typical relaxation time. Conservation of winding number in numerical simulations requires a suitable embedding of the field variables and the appropriate geometrical implementation of the winding density on the discrete lattice. We define a modified Kibble limit for the square lattice and obtain defect densities as functions of winding lengths in O(2) and O(3) models. The latter allows to observe formation of disoriented aligned domains within the easy plane. Their extent is severely limited by the momentaneous defect density during the course of the quench.Comment: 16 pages, 9 figure

Gravitating monopoles in SU(3) gauge theory

We consider the Einstein-Yang-Mills-Higgs equations for an SU(3) gauge group in a spherically symmetric ansatz. Several properties of the gravitating monopole solutions are obtained an compared with their SU(2) counterpart.Comment: 7 pages, Latex, 3 figure

The field theory of Skyrme lattices in quantum Hall ferromagnets

We report the application of the nonlinear $\sigma$ model to study the multi-skyrmion problem in the quantum Hall ferromagnet system. We show that the ground state of the system can be described by a ferromagnet triangular Skyrme lattice near $\nu=1$ where skyrmions are extremely dilute. We find a transition into antiferromagnet square lattice by increasing the skyrmion density and therefore $|\nu-1|$. We investigate the possibility that the square Skyrme lattice deforms to a single skyrmion with the same topological charge when the Zeeman energy is extremely smaller than the Coulomb energy. We explicitly show that the energy of a skyrmion with charge two is less than the energy of two skyrmions each with charge one when $g \leq g_c$. By taking the quantum fluctuations into account, we also argue the possibility of the existence of a non-zero temperature Kosterlitz-Thouless and a superconductor-insulator phase transition.Comment: 17 page

Simulated Annealing for Topological Solitons

The search for solutions of field theories allowing for topological solitons requires that we find the field configuration with the lowest energy in a given sector of topological charge. The standard approach is based on the numerical solution of the static Euler-Lagrange differential equation following from the field energy. As an alternative, we propose to use a simulated annealing algorithm to minimize the energy functional directly. We have applied simulated annealing to several nonlinear classical field theories: the sine-Gordon model in one dimension, the baby Skyrme model in two dimensions and the nuclear Skyrme model in three dimensions. We describe in detail the implementation of the simulated annealing algorithm, present our results and get independent confirmation of the studies which have used standard minimization techniques.Comment: 31 pages, LaTeX, better quality pics at http://www.phy.umist.ac.uk/~weidig/Simulated_Annealing/, updated for publicatio

Development and validation of the predicted heat strain model

Abstract Eight laboratories participated in a concerted research project on the assessment of hot working conditions. The objectives were, among others, to co-ordinate the work of the main European research teams in the field of thermal factors and to improve the methods available to assess the risks of heat disorders at the workplace, and in particular the "Required Sweat Rate" model as presented in International Standard ISO 7933 Standard (1989). The scientific bases of this standard were thoroughly reviewed and a revised model, called "Predicted Heat Strain" (PHS), was developed. This model was then used to predict the minute by minute sweat rates and rectal temperatures during 909 laboratory and field experiments collected from the partners. The Pearson correlation coefficients between observed and predicted values were equal to 0.76 and 0.66 for laboratory experiments and 0.74 and 0.59 for field experiments, respectively, for the sweat rates and the rectal temperatures. The change in sweat rate with time was predicted more accurately by the PHS model than by the required sweat rate model. This suggests that the PHS model would provide an improved basis upon which to determine allowable exposure times from the predicted heat strain in terms of dehydration and increased core temperature

Static solitons with non-zero Hopf number

We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We explicitly compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons.Comment: 13 pages, RevTeX, 7 Postscript figures, minor changes have been made, a reference has been corrected and a figure replace

Variation in Estimated Medicare Prescription Drug Plan Costs and Affordability for Beneficiaries Living in Different States

BACKGROUND: Medicare Part D prescription drug plans (PDPs) implemented in January 2006 are designed to improve beneficiaries’ access to pharmaceuticals and use market competition to yield affordable drug costs. Variations in estimated PDP costs for beneficiaries living in different states have not previously been characterized. OBJECTIVE: To describe variations in the estimated costs of PDPs (plan premium, copays, and coinsurance) within and across states. DESIGN: To estimate PDP costs based on 4 actual patient cases that exemplify common conditions and prescription drug combinations for Medicare beneficiaries, we used the online tool provided by the Centers for Medicare and Medicaid Services. MEASUREMENTS: Principal study outcomes included (a) variation across states in the estimated annual cost of the lowest-cost PDP for each case and (b) variation in the estimated affordability of the lowest-cost PDPs across states, based on cost-of-living-adjusted median income for zero-earner households. RESULTS: For all 4 patient cases, we found substantive within-state and between-state differences in the estimated costs of Medicare PDPs incurred by beneficiaries. The estimated annual costs to beneficiaries of the lowest-cost PDPs varied across states by as much as $320 for medications in the least expensive scenario, and by as much as$13,000 for the most expensive scenario. On average across states, a beneficiary with cost-of-living-adjusted median income would expect to spend 3%–28% of annual income to pay for medications in the lowest-cost PDPs in the 4 patient cases. The affordability of the lowest-cost plans varied across states, and for 2 of the 4 cases the lowest-cost PDP estimates were negatively correlated with cost-of-living-adjusted median income. CONCLUSIONS: Substantive differences in estimated PDP costs are evident across states for patients with common Medicare conditions. Importantly, the lowest-cost plans were not proportionally affordable with respect to state-specific cost-of-living-adjusted median income. Refinement of the Medicare drug program may be needed to improve national balance in PDP affordability for beneficiaries living in different states. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material is available for this article at http://dx.doi.org/10.1007/s11606-006-0018-y and is accessible for authorized users

New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.Comment: 23 page