Heat flow for the Yang-Mills-Higgs field and the Hermitian Yang-Mills-Higgs metric

For a parameter lambda > 0, we study a type of vortex equations, which generalize the well-known Hermitian-Einstein equation, for a connection A and a section phi of a holomorphic vector bundle E over a Kahler manifold X. We establish a global existence of smooth solutions to heat flow for a self-dual Yang-Mills-Higgs field on E. Assuming the lambda -stability of (E, phi), we prove the existence of the Hermitian Yang-Mills-Higgs metric on the holomorphic bundle E by studying the limiting behaviour of the gauge flow.

The aesthetic turn in international political theory

This essay explores the nature and significance of aesthetic approaches to international political theory. More specifically, it contrasts aesthetic with mimetic forms of representation. The latter, which have dominated the study of international relations, seek to represent politics as realistically and authentically as possible, aiming at capturing world politics as it really is. An aesthetic approach, by contrast, assumes that there is always a gap between a form of representation and what is represented therewith. Rather than ignoring or seeking to narrow this gap, as mimetic approaches do, aesthetic insight recognises that the inevitable difference between the represented and its representation is the very location of politics. The essay, thus, argues for the need to reclaim the political value of the aesthetic; not to replace social science or technological reason, but to broaden our abilities to comprehend and deal with the key dilemmas of world politics. The ensuing model of thought facilitates productive interactions across different faculties, including sensibility, imagination and reason, without any of them annihilating the unique position and insight of the other.

Production under uncertainty and choice under uncertainty in the emergence of generalized expected utility theory

This paper presents a personal view of the interaction between the analysis of choice under uncertainty and the analysis of production under uncertainty. Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under uncertainty. This interest led to the development of generalized models including rank-dependent expected utility theory. In turn, the development of generalized expected utility models raised the question of whether such models could be used in the analysis of applied problems such as those involving production under uncertainty. Finally, the revival of the state-contingent approach led to the recognition of a fundamental duality between choice problems and production problems.

A director theory for visco-elastic folding instabilities in multilayered rock

A model for finely layered visco-elastic rock proposed by us in previous papers is revisited and generalized to include couple stresses. We begin with an outline of the governing equations for the standard continuum case and apply a computational simulation scheme suitable for problems involving very large deformations. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. The standard continuum solution becomes unstable for extreme values of the shear/normal viscosity ratio. The instability is a consequence of the neglect of the bending stiffness/viscosity in the standard continuum model. We suggest considering these effects within the framework of a couple stress theory. Couple stress theories involve second order spatial derivatives of the velocities/displacements in the virtual work principle. To avoid C-1 continuity in the finite element formulation we introduce the spin of the cross sections of the individual layers as an independent variable and enforce equality to the spin of the unit normal vector to the layers (-the director of the layer system-) by means of a penalty method. We illustrate the convergence of the penalty method by means of numerical solutions of simple shears of an infinite layer for increasing values of the penalty parameter. For the shear problem we present solutions assuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. For high values of the ratio of the normal-to the shear viscosity the deformation concentrates in thin bands around to the layer surfaces. The effect of couple stresses on the evolution of folds in layered structures is also investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.

Halo formation in directional solidification

A new model of halo formation in directional solidification is presented. The model describes halo formation in terms of competitive growth between the halo phase and coupled eutectic in liquid with a nominal composition that follows the primary phase liquidus extension with decreasing temperature. The model distinguishes between the effects of constitutional, capillarity and (where applicable) kinetic undercooling and avoids a number of theoretical inconsistencies associated with previous models. The critical growth rate for halo formation in directionally solidified hypereutectic Al-Si alloys is calculated using the model in conjunction with models of primary phase and coupled eutectic growth from the literature. The calculated result agrees reasonably well with the experimental result of Yilmaz and Elliott (Met. Sci. 18 (1984) 362), given the use of a relatively simple isolated dendrite tip model to calculate the growth undercooling of the halo tip. (C) 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

On the theory of mixing-frequency electron spin-echo envelope modulation spectroscopy

It has recently been stated that the parametrization of the time variables in the one-dimensional (I-D) mixing-frequency electron spin-echo envelope modulation (MIF-ESEEM) experiment is incorrect and hence the wrong frequencies for correlated nuclear transitions are predicted. This paper is a direct response to such a claim, its purpose being to show that the parametrization in land 2-D MIF-ESEEM experiments possesses the same form as that used in other 4-pulse incrementation schemes and predicts the same correlation frequencies. We show that the parametrization represents a shearing transformation of the 2-D time-domain and relate the resulting frequency domain spectrum to the HYSCORE spectrum in terms of a skew-projection. It is emphasized that the parametrization of the time-domain variables may be chosen arbitrarily and affects neither the computation of the correct nuclear frequencies nor the resulting resolution. The usefulness or otherwise of the MIF parameters \gamma\ > 1 is addressed, together with the validity of the original claims of the authors with respect to resolution enhancement in cases of purely homogeneous and inhomogeneous broadening. Numerical simulations are provided to illustrate the main points.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Anisotropic convection model for the earth's mantle

The paper presents a theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including the folding and kinking of multi-layered visco-elastic rock (Muhlhaus et al. [1,2]). The orientation of slip planes in the context of crystallographic slip is determined by the normal vector - the director - of these surfaces. The model is applied to simulate anisotropic mantle convection. We compare the evolution of flow patterns, Nusselt number and director orientations for isotropic and anisotropic rheologies. In the simulations we utilize two different finite element methodologies: The Lagrangian Integration Point Method Moresi et al [8] and an Eulerian formulation, which we implemented into the finite element based pde solver Fastflo (www.cmis.csiro.au/Fastflo/). The reason for utilizing two different finite element codes was firstly to study the influence of an anisotropic power law rheology which currently is not implemented into the Lagrangian Integration point scheme [8] and secondly to study the numerical performance of Eulerian (Fastflo)- and Lagrangian integration schemes [8]. It turned out that whereas in the Lagrangian method the Nusselt number vs time plot reached only a quasi steady state where the Nusselt number oscillates around a steady state value the Eulerian scheme reaches exact steady states and produces a high degree of alignment (director orientation locally orthogonal to velocity vector almost everywhere in the computational domain). In the simulations emergent anisotropy was strongest in terms of modulus contrast in the up and down-welling plumes. Mechanisms for anisotropic material behavior in the mantle dynamics context are discussed by Christensen [3]. The dominant mineral phases in the mantle generally do not exhibit strong elastic anisotropy but they still may be oriented by the convective flow. Thus viscous anisotropy (the main focus of this paper) may or may not correlate with elastic or seismic anisotropy.

Spatial and temporal variation in distribution of mangroves in Moreton Bay, subtropical Australia: a comparison of pattern metrics and change detection analyses based on aerial photographs

An assessment of the changes in the distribution and extent of mangroves within Moreton Bay, southeast Queensland, Australia, was carried out. Two assessment methods were evaluated: spatial and temporal pattern metrics analysis, and change detection analysis. Currently, about 15,000 ha of mangroves are present in Moreton Bay. These mangroves are important ecosystems, but are subject to disturbance from a number of sources. Over the past 25 years, there has been a loss of more than 3800 ha, as a result of natural losses and mangrove clearing (e.g. for urban and industrial development, agriculture and aquaculture). However, areas of new mangroves have become established over the same time period, offsetting these losses to create a net loss of about 200 ha. These new mangroves have mainly appeared in the southern bay region and the bay islands, particularly on the landward edge of existing mangroves. In addition, spatial patterns and species composition of mangrove patches have changed. The pattern metrics analysis provided an overview of mangrove distribution and change in the form of single metric values, while the change detection analysis gave a more detailed and spatially explicit description of change. An analysis of the effects of spatial scales on the pattern metrics indicated that they were relatively insensitive to scale at spatial resolutions less than 50 m, but that most metrics became sensitive at coarser resolutions, a finding which has implications for mapping of mangroves based on remotely sensed data. (C) 2003 Elsevier Science B.V. All rights reserved.

Background risk in generalized expected utility theory

In this paper, it is shown that, for a wide range of risk-averse generalized expected utility preferences, independent risks are complementary, contrary to the results for expected utility preferences satisfying conditions such as proper and standard risk aversion.

Social class and cultural mobility - Reconfiguring the cultural omnivore thesis

This article explores the idea of 'cultural mobility' both as a way of thinking about the polarizing logic of class relations and practices in contemporary society and as a means by which the debate over the cultural omnivore might be advanced. The concept of cultural mobility refers to the differential capacity to engage with or consume cultural goods and services across the entire spectrum of cultural life, an ability which is itself premised upon an unequal, class-related distribution in cultural competence. Cultural mobility, then, is the ability to move at will between cultural realms, a freedom to choose where one is positioned in the cultural landscape. I argue that the concept provides fertile ground for exploring possible interconnections between a number of divergent strands in current social theory which have largely developed independently of each other. At the same time much of this theoretical effort remains divorced from concrete research agendas. Using data collected as part of a major study of Australian cultural consumption, the article provides a case study of cultural mobility and its class moorings which serves to clarify some of the existing confusions concerning the cultural omnivore.