The Creation and Propagation of Radiation: Fields Inside and Outside of Sources

We present a new algorithm for computing the electromagnetic fields of currents inside and outside of finite current sources, for arbitrary time variations in the currents. Unexpectedly, we find that our solutions for these fields are free of the concepts of differential calculus, in that our solutions only involve the currents and their time integrals, and do not involve the time derivatives of the currents. As examples, we give the solutions for two configurations of current: a planar solenoid and a rotating spherical shell carrying a uniform charge density. For slow time variations in the currents, we show that our general solutions reduce to the standard expressions for the fields in classic magnetic dipole radiation. In the limit of extremely fast turn-on of the currents, we show that for our general solutions the amount of energy radiated is exactly equal to the magnetic energy stored in the static fields a long time after current creation. We give three associated problem statements which can be used in courses at the undergraduate level, and one problem statement suitable for courses at the graduate level. These problems are of physical interest because: (1) they show that current systems of finite extent can radiate even during time intervals when the currents are constant; (2) they explicitly display transit time delays across a source associated with its finite dimensions; and (3) they allow students to see directly the origin of the reaction forces for time-varying systemsComment: 25 pages, 5 figure

Mifepristone reduces insulin resistance in patient volunteers with adrenal incidentalomas that secrete low levels of cortisol : a pilot study

Background: Incidental adrenal masses are commonly detected during imaging for other pathologies. 10% of the elderly population has an ‘adrenal incidentaloma’, up to 20% of these show low-grade autonomous cortisol secretion and 60% of patients with autonomous cortisol secretion have insulin resistance. Cortisol excess is known to cause insulin resistance, an independent cardiovascular risk marker, however in patients with adrenal incidentalomas it is unknown whether their insulin resistance is secondary to the excess cortisol and therefore potentially reversible. In a proof of concept study we examined the short-term effects of glucocorticoid receptor (GR) antagonism in patients with an adrenal incidentaloma to determine whether their insulin resistance was reversible. Methodology/Principal Findings: In a prospective open-label pilot study, six individuals with adrenal incidentalomas and autonomous cortisol secretion were treated with mifepristone (a GR antagonist) 200 mg twice daily and studied for 4 weeks on a Clinical Research Facility. Insulin resistance at four weeks was assessed by insulin resistance indices, lnHOMA-IR and lnMatsuda, and AUC insulin during a 2-hour glucose tolerance test. Biochemical evidence of GR blockade was shown in all individuals and across the group there was a significant reduction in insulin resistance: lnHOMA-IR (1.0vs0.6; p = 0.03), lnHOMA-%beta (4.8vs4.3; p = 0.03) and lnMatsuda (1.2vs1.6; p = 0.03). Five out of six individuals showed a reduction in insulin AUC .7237 pmol/l.min, and in two patients this showed a clinically significant cardiovascular benefit (as defined by the Helsinki heart study). Conclusions: Short-term GR antagonism is sufficient to reduce insulin resistance in some individuals with adrenal incidentalomas and mild cortisol excess. Further assessment is required to assess if the responses may be used to stratify therapy as adrenal incidentalomas may be a common remediable cause of increased cardiovascular risk

Nonexistence of conformally flat slices of the Kerr spacetime

Initial data for black hole collisions are commonly generated using the Bowen-York approach based on conformally flat 3-geometries. The standard (constant Boyer-Lindquist time) spatial slices of the Kerr spacetime are not conformally flat, so that use of the Bowen-York approach is limited in dealing with rotating holes. We investigate here whether there exist foliations of the Kerr spacetime that are conformally flat. We limit our considerations to foliations that are axisymmetric and that smoothly reduce in the Schwarzschild limit to slices of constant Schwarzschild time. With these restrictions, we show that no conformally flat slices can exist.Comment: 5 LaTeX pages; no figures; to be submitted to Phys. Rev.

Examining the Effect of Pore Size Distribution and Shape on Flow through Unsaturated Peat using Computer Tomography

The hydraulic conductivity of unsaturated peat soil is controlled by the air-filled porosity, pore size and geometric distribution as well as other physical properties of peat materials. This study investigates how the size and shape of pores affects the flow of water through peat soils. In this study we used X-ray Computed Tomography (CT), at 45μm resolution under 5 specific soil-water pressure head levels to provide 3-D, high-resolution images that were used to detect the inner pore structure of peat samples under a changing water regime. Pore structure and configuration were found to be irregular, which affected the rate of water transmission through peat soils. The 3-D analysis suggested that pore distribution is dominated by a single large pore-space. At low pressure head, this single large air-filled pore imparted a more effective flowpath compared to smaller pores. Smaller pores were disconnected and the flowpath was more tortuous than in the single large air-filled pore, and their contribution to flow was negligible when the single large pore was active. We quantify the pore structure of peat soil that affects the hydraulic conductivity in the unsaturated condition, and demonstrate the validity of our estimation of peat unsaturated hydraulic conductivity by making a comparison with a standard permeameter-based method. Estimates of unsaturated hydraulic conductivities were made for the purpose of testing the sensitivity of pore shape and geometry parameters on the hydraulic properties of peats and how to evaluate the structure of the peat and its affects on parameterization. We also studied the ability to quantify these factors for different soil moisture contents in order to define how the factors controlling the shape coefficient vary with changes in soil water pressure head. The relation between measured and estimated unsaturated hydraulic conductivity at various heads shows that rapid initial drainage, that changes the air-filled pore properties, creates a sharp decline in hydraulic conductivity. This is because the large pores readily lose water, the peat rapidly becomes less conductive and the flow path among pores, more tortuous

Late-time tails in the Kerr spacetime

Outside a black hole, perturbation fields die off in time as 1/t n. For spherical holes n = 2ℓ + 3 where ℓ is the multipole index. In the nonspherical Kerr spacetime there is no coordinate-independent meaning of \u27multipole\u27, and a common sense viewpoint is to set ℓ to the lowest radiatiable index, although theoretical studies have led to very different claims. Numerical results, to date, have been controversial. Here we show that expansion for small Kerr spin parameter a leads to very definite numerical results confirming previous theoretical predictions. © 2008 IOP Publishing Ltd

Pulsar timing as a probe of non-einsteinlan polarizations of gravitational waves

Einstein\u27s theory of gravity predicts waves of the distortion of spacetime with two degrees of polarization; alternative theories predict more polarizations, up to a maximum of six. Although laser interferometric gravity wave detectors can be used to search for at least some of the non-Einsteinian polarizations, their configuration is not optimal for the task. By contrast, the angular distribution of pulsars in the sky makes pulsar timing a flexible tool for detecting all polarizations. We give here an analysis of the sensitivity of pulsar timing to an isotropic stochastic gravitational wave background of waves with non-Einsteinian polarizations and conclude that their detection may be feasible in the near future. In particular, we compute the number of pulsars necessary to detect a stochastic background made up of one type of polarization and to distinguish non-Einsteinian from standard polarizations. We conclude that for biweekly observations made for five years with rms timing accuracy of 100 ns, detecting non-Einsteinian modes will require: 60 pulsars in the case of the longitudinal mode; 60 for the two spin-1 \ shear\ modes; and 40 for the spin-0 \ breathing\ mode. These are targets that should be easily achievable with the proposed Square Kilometer Array project. To discriminate non-Einsteinian modes from Einsteinian modes, we need 40 pulsars for the breathing mode, 100 pulsars for the longitudinal mode, and 500 pulsars for the shear mode. We confirm the previous estimate that 40 pulsars are needed to detect the spin-2 \ transverse\ (Einsteinian) polarizations. Better focused statistical tests may allow improvements in sensitivity for some of these polarizations. © 2008. The American Astronomical Society. All rights reserved

Adam Smith and the theory of punishment

A distinctive theory of punishment plays a central role in Smith's moral and legal theory. According to this theory, we regard the punishment of a crime as deserved only to the extent that an impartial spectator would go along with the actual or supposed resentment of the victim. The first part of this paper argues that Smith's theory deserves serious consideration and relates it to other theories such as utilitarianism and more orthodox forms of retributivism. The second part considers the objection that, because Smith's theory implies that punishment is justified only when there is some person or persons who is the victim of the crime, it cannot explain the many cases where punishment is imposed purely for the public good. It is argued that Smith's theory could be extended to cover such cases. The third part defends Smith's theory against the objection that, because it relies on our natural feelings, it cannot provide an adequate moral justification of punishment