Convergence of the Generalized Volume Averaging Method on a Convection-Diffusion Problem: A Spectral Perspective

A mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization

Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories

We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.Comment: 12 pages, no figures; REVTeX; uses multicol,fancyheadings,eqsecnum; to appear in Phys. Rev.

Evolutionary Laws, Initial Conditions, and Gauge Fixing in Constrained Systems

We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and the determination of inequivalent initial data. The Lagrangian discussion is novel, and a proof is given that the final number of degrees of freedom in the two formulations agrees. We give applications to reparameterization invariant theories, where we prove that one of the constraints must be explicitly time dependent. We illustrate our procedure with the examples of trajectories in spacetime and with spatially homogeneous cosmological models. Finally, we comment briefly on Dirac's extended Hamiltonian technique.Comment: 23 pages; plain TeX. To appear: Classical & Quantum Gravit

Gravity Waves Signatures from Anisotropic pre-Inflation

We show that expanding or contracting Kasner universes are unstable due to the amplification of gravitational waves (GW). As an application of this general relativity effect, we consider a pre-inflationary anisotropic geometry characterized by a Kasner-like expansion, which is driven dynamically towards inflation by a scalar field. We investigate the evolution of linear metric fluctuations around this background, and calculate the amplification of the long-wavelength GW of a certain polarization during the anisotropic expansion (this effect is absent for another GW polarization, and for scalar fluctuations). These GW are superimposed to the usual tensor modes of quantum origin from inflation, and are potentially observable if the total number of inflationary e-folds exceeds the minimum required to homogenize the observable universe only by a small margin. Their contribution to the temperature anisotropy angular power spectrum decreases with the multipole l as l^(-p), where p depends on the slope of the initial GW power-spectrum. Constraints on the long-wavelength GW can be translated into limits on the total duration of inflation and the initial GW amplitude. The instability of classical GW (and zero-vacuum fluctuations of gravitons) during Kasner-like expansion (or contraction) may have other interesting applications. In particular, if GW become non-linear, they can significantly alter the geometry before the onset of inflation

Exploring what lies behind public preferences for avoiding health losses caused by lapses in healthcare safety and patient lifestyle choices

© 2013 Singh et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This article has been made available through the Brunel Open Access Publishing Fund.Background: Although many studies have identified public preferences for prioritising health care interventions based on characteristics of recipient or care, very few of them have examined the reasons for the stated preferences. We conducted an on-line person trade-off (PTO) study (N=1030) to investigate whether the public attach a premium to the avoidance of ill health associated with alternative types of responsibilities: lapses in healthcare safety, those caused by individual action or lifestyle choice; or genetic conditions. We found that the public gave higher priority to prevention of harm in a hospital setting such as preventing hospital associated infections than genetic disorder but drug administration errors were valued similar to genetic disorders. Prevention of staff injuries, lifestyle diseases and sports injuries, were given lower priority. In this paper we aim to understand the reasoning behind the responses by analysing comments provided by respondents to the PTO questions. Method: A majority of the respondents who participated in the survey provided brief comments explaining preferences in free text responses following PTO questions. This qualitative data was transformed into explicit codes conveying similar meanings. An overall coding framework was developed and a reliability test was carried out. Recurrent patterns were identified in each preference group. Comments which challenged the assumptions of hypothetical scenarios were also investigated. Results: NHS causation of illness and a duty of care were the most cited reasons to prioritise lapses in healthcare safety. Personal responsibility dominated responses for lifestyle related contexts, and many respondents mentioned that health loss was the result of the individual’s choice to engage in risky behaviour. A small proportion of responses questioned the assumptions underlying the PTO questions. However excluding these from the main analysis did not affect the conclusions. Conclusion: Although some responses indicated misunderstanding or rejection of assumptions we put forward, the results were still robust. The reasons put forward for responses differed between comparisons but responsibility was the most frequently cited. Most preference elicitation studies only focus on eliciting numerical valuations but allowing for qualitative data can augment understanding of preferences as well as verifying results.EPSRC through the MATCH programme(EP/F063822/1 and EP/G012393/1) and HERG within Brunel University

A Connection Approach to Numerical Relativity

We discuss a general formalism for numerically evolving initial data in general relativity in which the (complex) Ashtekar connection and the Newman-Penrose scalars are taken as the dynamical variables. In the generic case three gauge constraints and twelve reality conditions must be solved. The analysis is applied to a Petrov type \{1111\} planar spacetime where we find a spatially constant volume element to be an appropriate coordinate gauge choice.Comment: 17 pages, LaTe

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.Comment: 19 pages; a reference adde