Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary

The mathematical formalism necessary for the diagramatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of quantum corrections to the effective action past one-loop necessitates diagramatic techniques. Diagramatic evaluations and higher loop-order renormalisation can be best accomplished on a Riemannian manifold of constant curvature accommodating a boundary of constant extrinsic curvature. In such a context the stated evaluations can be accomplished through a consistent interpretation of the Feynman rules within the spherical formulation of the theory for which the method of images allows. To this effect, the mathematical consequences of such an interpretation are analyzed and the spherical formulation of the Feynman rules on the bounded manifold is, as a result, developed.Comment: 12 pages, references added. To appear in Classical and Quantum Gravit

Electrical Treeing in Silicone Rubber

Electrical treeing has been widely studied in a range of polymeric materials. In these investigations, the morphology and PD patterns associated with the growth of electrical trees in a model transparent silicone rubber were investigated using a new system recently developed at Southampton. With increasing voltage the trees became more complex in appearance but nevertheless grow more rapidly. As the tree evolves the PD pattern becomes more intense which may provide a method of monitoring the extent of treeing in opaque samples. Raman studies indicate that treeing and breakdown channels are hollow, carbonaceous entities, a finding consistent with other studies

Cosmological Constraints on Dissipative Models of Inflation

(Abridged) We study dissipative inflation in the regime where the dissipative term takes a specific form, \Gamma=\Gamma(\phi), analyzing two models in the weak and strong dissipative regimes with a SUSY breaking potential. After developing intuition about the predictions from these models through analytic approximations, we compute the predicted cosmological observables through full numerical evolution of the equations of motion, relating the mass scale and scale of dissipation to the characteristic amplitude and shape of the primordial power spectrum. We then use Markov Chain Monte Carlo techniques to constrain a subset of the models with cosmological data from the cosmic microwave background (WMAP three-year data) and large scale structure (SDSS Luminous Red Galaxy power spectrum). We find that the posterior distributions of the dissipative parameters are highly non-Gaussian and their allowed ranges agree well with the expectations obtained using analytic approximations. In the weak regime, only the mass scale is tightly constrained; conversely, in the strong regime, only the dissipative coefficient is tightly constrained. A lower limit is seen on the inflation scale: a sub-Planckian inflaton is disfavoured by the data. In both weak and strong regimes, we reconstruct the limits on the primordial power spectrum and show that these models prefer a {\it red} spectrum, with no significant running of the index. We calculate the reheat temperature and show that the gravitino problem can be overcome with large dissipation, which in turn leads to large levels of non-Gaussianity: if dissipative inflation is to evade the gravitino problem, the predicted level of non-Gaussianity might be seen by the Planck satellite.Comment: 14 pages, 9 figures, Accepted by JCAP without text changes, References adde

Effective Actions for Heterotic M-Theory

We discuss the moduli space approximation for heterotic M-theory, both for the minimal case of two boundary branes only, and when a bulk brane is included. The resulting effective actions may be used to describe the cosmological dynamics in the regime where the branes are moving slowly, away from singularities. We make use of the recently derived colliding branes solution to determine the global structure of moduli space, finding a boundary at which the trajectories undergo a hard wall reflection. This has important consequences for the allowed moduli space trajectories, and for the behaviour of cosmological perturbations in the model.Comment: 21 pages, 4 figures. References added and some discussions clarifie

Radiative Contributions to the Effective Action of Self-Interacting Scalar Field on a Manifold with Boundary

The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the boundary of which is characterised by constant extrinsic curvature. An extension of the spherical formulation in the presence of a boundary is attained through use of the method of images. Contrary to the consolidated vanishing effect in maximally symmetric space-times the contribution of the massless "tadpole" diagram no longer vanishes in dimensional regularisation. As a result, conformal invariance is broken due to boundary-related vacuum contributions. The evaluation of one-loop contributions to the two-point function suggests an extension, in the presence of matter couplings, of the simultaneous volume and boundary renormalisation in the effective action.Comment: 14 pages, 1 figure. Additional references and minor elucidating remarks added. To appear in Classical and Quantum Gravit

Preliminary design of a Primary Loop Pump Assembly (PLPA), using electromagnetic pumps

A preliminary design study of flight-type dc conduction-permanent magnetic, ac helical induction, and ac linear induction pumps for circulating 883 K (1130 F) NaK at 9.1 kg/sec (20 lb/sec) is described. Various electromagnetic pump geometrics are evaluated against hydraulic performance, and the effects of multiple windings and numbers of pumps per assembly on overall reliability were determined. The methods used in the electrical-hydraulic, stress, and thermal analysis are discussed, and the high temperature electrical materials selected for the application are listed

On the consistency of warm inflation

Conditions are obtained for the existence of a warm inflationary attractor in the system of equations describing an inflaton coupled to radiation. These conditions restrict the temperature dependence of the dissipative terms and the size of thermal corrections to the inflaton potential, as well as the gradient of the inflaton potential. When these conditions are met, the evolution approaches a slow-roll limit and only curvature fluctuations survive on super-horizon scales. Formulae are given for the spectral indices of the density perturbations and the tensor/scalar density perturbation amplitude ratio in warm inflation.Comment: 7 pages, ReVTeX. New refs in v

Numerical investigation of friction in inflaton equations of motion

The equation of motion for the expectation value of a scalar quantum field does not have the local form that is commonly assumed in studies of inflationary cosmology. We have recently argued that the true, temporally non-local equation of motion does not possess a time-derivative expansion and that the conversion of inflaton energy into particles is not, in principle, described by the friction term estimated from linear response theory. Here, we use numerical methods to investigate whether this obstacle to deriving a local equation of motion is purely formal, or of some quantitative importance. Using a simple scalar-field model, we find that, although the non-equilibrium evolution can exhibit significant damping, this damping is not well described by the local equation of motion obtained from linear response theory. It is possible that linear response theory does not apply to the situation we study only because thermalization turns out to be slow, but we argue that that the large discrepancies we observe indicate a failure of the local approximation at a more fundamental level.Comment: 13 pages, 7 figure