Electric field formulation for thin film magnetization problems

We derive a variational formulation for thin film magnetization problems in type-II superconductors written in terms of two variables, the electric field and the magnetization function. A numerical method, based on this formulation, makes it possible to accurately compute all variables of interest, including the electric field, for any value of the power in the power law current-voltage relation characterizing the superconducting material. For high power values we obtain a good approximation to the critical state model solution. Numerical simulation results are presented for simply and multiply connected films, and also for an inhomogeneous film.Comment: 15 p., submitte

Asymptotics of Relativistic Spin Networks

The stationary phase technique is used to calculate asymptotic formulae for SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the Spin Network evaluation. Finally we discuss the asymptotics of the SO(3,1) 10j-symbol.Comment: 31 pages, latex. v3: minor clarification

The Quantum Tetrahedron in 3 and 4 Dimensions

Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use geometric quantization to obtain a Hilbert space of states. This Hilbert space has a basis of states labeled by the areas of the faces of the tetrahedron together with one more quantum number, e.g. the area of one of the parallelograms formed by midpoints of the tetrahedron's edges. Repeating the procedure for the tetrahedron in R^4, we obtain a Hilbert space with a basis labelled solely by the areas of the tetrahedron's faces. An analysis of this result yields a geometrical explanation of the otherwise puzzling fact that the quantum tetrahedron has more degrees of freedom in 3 dimensions than in 4 dimensions

Building Blocks in the Economics of Mandates

The paper constructs an asymmetric information model to investigate the efficiency and equity cases for government mandated benefits. A mandate can improve workers' insurance, and may also redistribute in favour of more "deserving" workers. The risk is that it may also reduce output. The more diverse are free market contracts – separating the various worker types – the more likely it is that such output effects will on balance serve to reduce welfare. It is shown that adverse effects can be reduced by restricting mandates to larger firms. An alternative to a mandate is direct government provision. We demonstrate that direct government provision has the advantage over mandates of preserving separations.asymmetric information, labour mandates, compensation packages

A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres

Published versio

Asymptotics of 10j symbols

The Riemannian 10j symbols are spin networks that assign an amplitude to each 4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This amplitude is a function of the areas of the 10 faces of the 4-simplex, and Barrett and Williams have shown that one contribution to its asymptotics comes from the Regge action for all non-degenerate 4-simplices with the specified face areas. However, we show numerically that the dominant contribution comes from degenerate 4-simplices. As a consequence, one can compute the asymptotics of the Riemannian 10j symbols by evaluating a `degenerate spin network', where the rotation group SO(4) is replaced by the Euclidean group of isometries of R^3. We conjecture formulas for the asymptotics of a large class of Riemannian and Lorentzian spin networks in terms of these degenerate spin networks, and check these formulas in some special cases. Among other things, this conjecture implies that the Lorentzian 10j symbols are asymptotic to 1/16 times the Riemannian ones.Comment: 25 pages LaTeX with 8 encapsulated Postscript figures. v2 has various clarifications and better page breaks. v3 is the final version, to appear in Classical and Quantum Gravity, and has a few minor corrections and additional reference

Identifying Priority Species and Conservation Opportunities Under Future Climate Scenarios: Amphibians in a Biodiversity Hotspot

Climate change is driving shifts in the distribution of plants and animals, and prioritizing management actions for such shifts is a necessary but technically difficult challenge. We worked with state agencies in the southeastern United States to identify high-priority amphibian species, to model the vulnerabilities of those species to regional climate change, and to identify long-term climatic refugia within the context of existing conservation lands. Directly interfacing with state natural resource experts ensured that 1) species prioritization schemes extend beyond political boundaries and 2) our models resulted in conservation-relevant applications. We used a correlative model to project midcentury distributions of suitable climate for priority species and to evaluate each species\u27 vulnerability to climate change. Using spatially explicit projected climate distributions, we ranked existing protected areas relative to their ability to provide climatic refugia for priority species in 2050. We identified 21 species as regional high-priority species. Fifteen of the 21 species are forecast to lose more than 85% of their climatically suitable habitat. Regions in the Appalachian Mountains, the Florida Panhandle, and the north-central region of Alabama are projected to lose the most climatic habitat for priority amphibian species. We identified many existing protected areas as midcentury climatic refugia in the Appalachians; however, our projections indicated refugia in the Southeast Coastal Plain to be exceedingly scarce. Although the topographic relief present in the Appalachians appears to provide future conservation opportunities via climatic refugia, the Coastal Plain affords fewer such opportunities and conservation of amphibians in that region is likely to be more challenging. The approach outlined here could be applied across a broad range of taxa and regions

Fuel injection assembly for gas turbine engine combustor

A fuel injection assembly for a gas turbine engine combustor, including at least one fuel stem, a plurality of concentrically disposed tubes positioned within each fuel stem, wherein a cooling supply flow passage, a cooling return flow passage, and a tip fuel flow passage are defined thereby, and at least one fuel tip assembly connected to each fuel stem so as to be in flow communication with the flow passages, wherein an active cooling circuit for each fuel stem and fuel tip assembly is maintained by providing all active fuel through the cooling supply flow passage and the cooling return flow passage during each stage of combustor operation. The fuel flowing through the active cooling circuit is then collected so that a predetermined portion thereof is provided to the tip fuel flow passage for injection by the fuel tip assembly

An Interview on Leadership with Al Carey, CEO, PepsiCo Beverages

Paul T. Barrett, PhD, CPA, is dean and professor of business for the College of Business and Economics, Longwood University, Farmville, VA 23909. James C. Haug, DBA, is associate professor of management, Longwood University, College of Business and Economics, Farmville, VA 23909. John N. Gaskins, PhD, currently serves as associate professor of marketing and retailing, Longwood University, College of Business and Economics, Farmville, VA 23909