Differential temperature transducer Patent

Differential thermopile for measuring cooling water temperature ris

Effect of Size on Electrical Performance

This paper was presented at IEEE International Symposium on Electrical Insulation, June 2006. ©2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Digital Object Identifier: 10.1109/ELINSL.2006.1665249The electrical breakdown performance, either unaged or after ageing (laboratory or service), is often used as the basis for qualification of a device, design or material. Many of the features that affect these performance levels have been discussed in other documents; contaminants, propensity for water treeing, insulating and semiconducting materials. However the size of cable tested is rarely discussed. This is somewhat surprising as it has been long recognized that electrical failure is an extreme value (the Weibull distribution is a member of this family) or weakest link process. In extreme value processes the performance of the whole device is determined by the single "weakest link". Thus when more "weak links" are present the chance of failure is consequently higher: the measured performance depends on weak link concentration or size of the device. Additionally at some dimensions the thickness of the dielectric can influence the breakdown mechanism itself; especially if the thermal influences are present. This paper will attempt to discuss a number of these size related issues for both AC & impulse conditions; these will include: 1) the effect of the dielectric volume actual mechanism of failure, 2) prediction of performance on service length cables from short length laboratory tests. This has practical relevance on the selection of appropriate qualification levels which will have direct relevance to service performance, 3) the requirements for cable quality when increasing the size (thickness or length) installed

Light-sheets and Bekenstein's bound

From the covariant bound on the entropy of partial light-sheets, we derive a version of Bekenstein's bound: S/M \leq pi x/hbar, where S, M, and x are the entropy, total mass, and width of any isolated, weakly gravitating system. Because x can be measured along any spatial direction, the bound becomes unexpectedly tight in thin systems. Our result completes the identification of older entropy bounds as special cases of the covariant bound. Thus, light-sheets exhibit a connection between information and geometry far more general, but in no respect weaker, than that initially revealed by black hole thermodynamics.Comment: 5 pages, 1 figure; v2: published version, improved discussion of weak gravity condition, final paragraph adde

A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories

We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the gauge and solving the linearized gravitational field equations to eliminate the metric perturbation variable in terms of the matter variables. In a wide class of cases--which include f(R) gravity, the Einstein-aether theory of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining perturbation equations for the matter fields are second order in time. We show how the symplectic current arising from the original Lagrangian gives rise to a symmetric bilinear form on the variables of the reduced theory. If this bilinear form is positive definite, it provides an inner product that puts the equations of motion of the reduced theory into a self-adjoint form. A variational principle can then be written down immediately, from which stability can be tested readily. We illustrate our method in the case of Einstein's equation with perfect fluid matter, thereby re-deriving, in a systematic manner, Chandrasekhar's variational principle for radial oscillations of spherically symmetric stars. In a subsequent paper, we will apply our analysis to f(R) gravity, the Einstein-aether theory, and Bekenstein's TeVeS theory.Comment: 13 pages; submitted to Phys. Rev. D. v2: changed formatting, added conclusion, corrected sign convention

New Proof of the Generalized Second Law

The generalized second law of black hole thermodynamics was proved by Frolov and Page for a quasi-stationary eternal black hole. However, realistic black holes arise from a gravitational collapse, and in this case their proof does not hold. In this paper we prove the generalized second law for a quasi-stationary black hole which arises from a gravitational collapse.Comment: 13 pages, Late

On leading order gravitational backreactions in de Sitter spacetime

Backreactions are considered in a de Sitter spacetime whose cosmological constant is generated by the potential of scalar field. The leading order gravitational effect of nonlinear matter fluctuations is analyzed and it is found that the initial value problem for the perturbed Einstein equations possesses linearization instabilities. We show that these linearization instabilities can be avoided by assuming strict de Sitter invariance of the quantum states of the linearized fluctuations. We furthermore show that quantum anomalies do not block the invariance requirement. This invariance constraint applies to the entire spectrum of states, from the vacuum to the excited states (should they exist), and is in that sense much stronger than the usual Poincare invariance requirement of the Minkowski vacuum alone. Thus to leading order in their effect on the gravitational field, the quantum states of the matter and metric fluctuations must be de Sitter invariant.Comment: 12 pages, no figures, typos corrected and some clarifying comments added, version accepted by Phys. Rev.

Global Properties of Locally Spatially Homogeneous Cosmological Models with Matter

The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matter.Comment: 18 pages, MPA-AR-94-

Control of black hole evaporation?

Contradiction between Hawking's semi-classical arguments and string theory on the evaporation of black hole has been one of the most intriguing problems in fundamental physics. A final-state boundary condition inside the black hole was proposed by Horowitz and Maldacena to resolve this contradiction. We point out that original Hawking effect can be also regarded as a separate boundary condition at the event horizon for this scenario. Here, we found that the change of Hawking boundary condition may affect the information transfer from the initial collapsing matter to the outgoing Hawking radiation during evaporation process and as a result the evaporation process itself, significantly.Comment: Journal of High Energy Physics, to be publishe

Perturbations of Matter Fields in the Second-order Gauge-invariant Cosmological Perturbation Theory

Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K.Nakamura, Prog.Theor.Phys., 117 (2007), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.Comment: (v1) 76 pages, no figure; (v2) minor revision, typos are corrected, references are added; (v3) Title is changed, Compactified into 55 pages, Comment on the comparison with the other work is added; (v4)typos are correcte

How red is a quantum black hole?

Radiating black holes pose a number of puzzles for semiclassical and quantum gravity. These include the transplanckian problem -- the nearly infinite energies of Hawking particles created near the horizon, and the final state of evaporation. A definitive resolution of these questions likely requires robust inputs from quantum gravity. We argue that one such input is a quantum bound on curvature. We show how this leads to an upper limit on the redshift of a Hawking emitted particle, to a maximum temperature for a black hole, and to the prediction of a Planck scale remnant.Comment: 3 pages, essay for the Gravity Research Foundatio