Characterisation and representation of non-dissipative electromagnetic medium with a double light cone

We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable (2,2)-tensor on the 4-manifold N. Moreover, in each cotangent space on N, the medium defines a Fresnel surface. Essentially, the Fresnel surface is a tensorial analogue of the dispersion equation that describes the response of the medium for signals in the geometric optics limit. For example, in isotropic medium the Fresnel surface is at each point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L. Bergamin introduced a condition that constrains the polarisation for plane waves. In this paper we show (under suitable assumptions) that a slight strengthening of this condition gives a pointwise characterisation of all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. This is for example the behaviour of uniaxial medium like calcite. Moreover, using the representation formulas from Lindell et al. we obtain a closed form representation formula that pointwise parameterises all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. Both the characterisation and the representation formula are tensorial and do not depend on local coordinates

Form Geometry and the 'tHooft-Plebanski Action

Riemannian geometry in four dimensions, including Einstein's equations, can be described by means of a connection that annihilates a triad of two-forms (rather than a tetrad of vector fields). Our treatment of the conformal factor of the metric differs from the original presentation of this result, due to 'tHooft. In the action the conformal factor now appears as a field to be varied.Comment: 12pp, LaTe

Neighbours of Einstein's Equations: Connections and Curvatures

Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers.Comment: 16 pages, LaTe

Geochemistry of lavas from Mohns Ridge, Norwegian-Greenland Sea: implications for melting conditions and magma sources near Jan Mayen

Mohns Ridge lavas between 71 and 72°30′N (∼360 km) have heterogeneous compositions varying between alkali basalts and incompatible-element-depleted tholeiites. On a large scale there is a continuity of incompatible element and isotopic compositions between the alkali basalts from the island Jan Mayen and Mohns Ridge tholeiites. The variation in isotopes suggests a heterogeneous mantle which appears to be tapped preferentially by low degree melts (∼5%) close to Jan Mayen but also shows its signature much further north on Mohns Ridge. Three lava types with different incompatible element compositions [e.g. chondrite-normalized (La/Sm)N2] occur in the area at 72°N and were generated from this heterogeneous mantle. The relatively depleted tholeiitic melts were mixed with a small degree melt from an enriched source. The elements Ba, Rb and K of the enriched melt were probably buffered in the mantle by residual amphibole or phlogopite. That such a residual phase is stable in this region of oceanic mantle suggests both high water contents and low mantle temperatures, at odds with a hotspot origin for Jan Mayen. Instead we suggest that the melting may be induced by the lowered solidus temperature of a “wet” mantle. Mohns MORB (mid ocean ridge basalt) and Jan Mayen area alkali basalts have high contents of Ba and Rb compared to other incompatible elements (e.g. Ba/La >10). These ratios reflect the signature of the mantle source. Ratios of Ce/Pb and Rb/Cs are normal MORB mantle ratios of 25 and 80, respectively, thus the enrichments of Ba and Rb are not indicative of a sedimentary component added to the mantle source but were probably generated by the influence of a metasomatizing fluid, as supported by the presence of hydrous phases during the petrogenesis of the alkali basalts. Geophysical and petrological models suggest that Jan Mayen is not the product of hotspot activity above a mantle plume, and suggest instead that it owes its existence to the unique juxtaposition of a continental fragment, a fracture zone and a spreading axis in this part of the North Atlantic

Geochemical and Isotopic Evolution of Late Oligocene Magmatism in Quchan, NE Iran

Magmatic activity that accompanied the collision between Arabia and Eurasia at ∼27 Ma, provides unique opportunities for understanding the triggers and magma reservoirs for collisional magmatism and its different styles in magmatic fronts and back-arcs. We present new ages and geochemical-isotopic results for magmatic rocks that formed during the collision between Arabia and Eurasia in NE Iran, which was a back-arc region to the main magmatic arcs of Iran. Our new zircon U-Pb ages indicate that collisional magmatism began at ∼24 Ma in the NE Iran back-arc, although magmatism in this area started in the Late Cretaceous time and continued until the Pleistocene. The collisional igneous rocks are characteristically bimodal, and basaltic-andesitic and dacitic-rhyolitic components show significant isotopic differences; εNd(t) = +4.4 to +7.4 and εHf(t) = +5.4 to +9.5 for mafic rocks and εNd(t) = +0.2 to +8.4 and εHf(t) = +3.4 to +12.3 for silicic rocks. The isotopic values and modeling suggest that fractional crystallization and assimilation-fractional crystallization played important roles in the genesis of felsic rocks in the NE Iran collisional zone. Trace element and isotopic modeling further emphasize that the main triggers of the magmatism in NE Iran comprise a depleted to the enriched mantle and the Cadomian continental crust of Iran. Our results also emphasize the temporal magmatic variations in the NE Iran back-arc from Late Cretaceous to Pleistocene. © 2021. The Authors

Radiation dose of chaperones during common pediatric computed tomography examinations

Background One main challenge in pediatric imaging is to reduce motion artifacts by calming young patients. To that end, the Radiological Society of North America (RSNA) as early as 1997 stated the necessity of adults accompanying their child during the child’s examination. Nonetheless, current research lacks data regarding radiation dose to these chaperones. Objective The aim of this study was to measure the radiation dose of accompanying adults during state-of-the-art pediatric CT protocols. Materials and methods In addition to a 100-kV non-contrast-enhanced chest CT (Protocol 1), we performed a 70-kV contrast-enhanced chest protocol (Protocol 2) using a third-generation dual-source CT. We acquired data on the radiation dose around the scanner using digital dosimetry placed right at the gantry, 1 m away, as well as beside the gantry. We acquired the CT-surrounding radiation dose during scanning of a pediatric phantom as well as 12 pediatric patients. Results After conducting 10 consecutive phantom scans using Protocol 1, we found the location with the highest cumulative dose acquired was right next to the gantry opening, at 3 μSv. Protocol 2 showed highest cumulative dose of 2 μSv at the same location. For Protocol 1, the location with the highest radiation doses during pediatric scans was right next to the gantry opening, with doses of 0.75±0.70 μSv. For Protocol 2, the highest radiation was measured 1 m away at 0.50±0.60 μSv. No radiation dose was measured at any time beside the gantry. Conclusion Our results provide proof that chaperones receive low radiation doses during state-of-the-art CT examinations. Given knowledge of these values as well as the optimal spots with the lowest radiation doses, parents as well as patients might be more relaxed during the examination

Determination of electromagnetic medium from the Fresnel surface

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is described by an antisymmetric $2\choose 2$-tensor $\kappa$. In this setting, the Tamm-Rubilar tensor density determines a polynomial surface of fourth order in each cotangent space. This surface is called the Fresnel surface and acts as a generalisation of the light-cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speed as a function of direction. Favaro and Bergamin have recently proven that if $\kappa$ has only a principal part and if the Fresnel surface of $\kappa$ coincides with the light cone for a Lorentz metric $g$, then $\kappa$ is proportional to the Hodge star operator of $g$. That is, under additional assumptions, the Fresnel surface of $\kappa$ determines the conformal class of $\kappa$. The purpose of this paper is twofold. First, we provide a new proof of this result using Gr\"obner bases. Second, we describe a number of cases where the Fresnel surface does not determine the conformal class of the original $2\choose 2$-tensor $\kappa$. For example, if $\kappa$ is invertible we show that $\kappa$ and $\kappa^{-1}$ have the same Fresnel surfaces.Comment: 23 pages, 1 figur

Wave propagation in linear electrodynamics

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a sufficient condition for the reduction of the fourth order surface to the familiar second order light cone structure. We finally study whether this condition is also necessary.Comment: 13 pages. Phys. Rev. D, to appea