Radiogenic power and geoneutrino luminosity of the Earth and other terrestrial bodies through time

We report the Earth's rate of radiogenic heat production and (anti)neutrino luminosity from geologically relevant short-lived radionuclides (SLR) and long-lived radionuclides (LLR) using decay constants from the geological community, updated nuclear physics parameters, and calculations of the $\beta$ spectra. We track the time evolution of the radiogenic power and luminosity of the Earth over the last 4.57 billion years, assuming an absolute abundance for the refractory elements in the silicate Earth and key volatile/refractory element ratios (e.g., Fe/Al, K/U, and Rb/Sr) to set the abundance levels for the moderately volatile elements. The relevant decays for the present-day heat production in the Earth ($19.9\pm3.0$ TW) are from $^{40}$K, $^{87}$Rb, $^{147}$Sm, $^{232}$Th, $^{235}$U, and $^{238}$U. Given element concentrations in kg-element/kg-rock and density $\rho$ in kg/m$^3$, a simplified equation to calculate the present day heat production in a rock is: $$h \, [\mu \text{W m}^{-3}] = \rho \left( 3.387 \times 10^{-3}\,\text{K} + 0.01139 \,\text{Rb} + 0.04595\,\text{Sm} + 26.18\,\text{Th} + 98.29\,\text{U} \right)$$ The radiogenic heating rate of Earth-like material at Solar System formation was some 10$^3$ to 10$^4$ times greater than present-day values, largely due to decay of $^{26}$Al in the silicate fraction, which was the dominant radiogenic heat source for the first $\sim10$ Ma. Assuming instantaneous Earth formation, the upper bound on radiogenic energy supplied by the most powerful short-lived radionuclide $^{26}$Al ($t_{1/2}$ = 0.7 Ma) is 5.5$\;\times\;$10$^{31}$ J, which is comparable (within a factor of a few) to the planet's gravitational binding energy.Comment: 28 pages, 6 figures, 5 table

NASTRAN general purpose interface requirements document

This NASTRAN (NASA STRuctural ANalysis) General Purpose Interface Requirements Document (IRD) defines standards for deliverables required of New Capability Contractors (NCCs) and relates these deliverables to the software development cycle. It also defines standards to be followed by NCCs for adding to and modifying the code in the NASTRAN software system and for adding to and modifying the four official NASTRAN manuals: The NASTRAN Theoretical Manual, the NASTRAN User's Manual, The NASTRAN Programmer's Manual, and The NASTRAN Demonstration Problem Manual. It is intended that this General Purpose IRD shall be incorporated by reference in all contracts for a new NASTRAN capability

Poisson transition rates from time-domain measurements with finite bandwidth

In time-domain measurements of a Poisson two-level system, the observed transition rates are always smaller than those of the actual system, a general consequence of finite measurement bandwidth in an experiment. This underestimation of the rates is significant even when the measurement and detection apparatus is ten times faster than the process under study. We derive here a quantitative form for this correction using a straightforward state-transition model that includes the detection apparatus, and provide a method for determining a system's actual transition rates from bandwidth-limited measurements. We support our results with computer simulations and experimental data from time-domain measurements of quasiparticle tunneling in a single-Cooper-pair transistor.Comment: 4 pages, 5 figure

Teleology and Realism in Leibniz's Philosophy of Science

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz

Re-187-Os-187, Pt-190-Os-186 Isotopic and Highly Siderophile Element Systematics of Group IVA Irons

We have recently completed Re-187-Os-187 and Pt-190-Os-186 isotopic and elemental studies of the two largest magmatic iron meteorite groups, IIAB and IIIAB [1]. These studies revealed closed-system behavior of both isotopic systems, but complex trace element behavior for Re, Pt and Os in group IIIAB. Here we examine isotopic and trace elemental systematics of group IVA irons. The IVA irons are not as extensively fractionated as IIAB and IIIAB and their apparently less complex crystallization history may make for more robust interpretation of the relative partitioning behavior of Re, Pt and Os, as well as the other highly siderophile elements (HSE) measured here; Pd, Ru and Ir [e.g. 2]. An additional goal of our continuing research plan for iron meteorites is to assess the possibility of relating certain ungrouped irons with major groups via trace element modeling. Here, the isotopic and trace element systematics of the ungrouped irons Nedagolla and EET 83230 are compared with the IVA irons

Imaging the Earth's Interior: the Angular Distribution of Terrestrial Neutrinos

Decays of radionuclides throughout the Earth's interior produce geothermal heat, but also are a source of antineutrinos. The (angle-integrated) geoneutrino flux places an integral constraint on the terrestrial radionuclide distribution. In this paper, we calculate the angular distribution of geoneutrinos, which opens a window on the differential radionuclide distribution. We develop the general formalism for the neutrino angular distribution, and we present the inverse transformation which recovers the terrestrial radioisotope distribution given a measurement of the neutrino angular distribution. Thus, geoneutrinos not only allow a means to image the Earth's interior, but offering a direct measure of the radioactive Earth, both (1) revealing the Earth's inner structure as probed by radionuclides, and (2) allowing for a complete determination of the radioactive heat generation as a function of radius. We present the geoneutrino angular distribution for the favored Earth model which has been used to calculate geoneutrino flux. In this model the neutrino generation is dominated by decays in the Earth's mantle and crust; this leads to a very ``peripheral'' angular distribution, in which 2/3 of the neutrinos come from angles > 60 degrees away from the downward vertical. We note the possibility of that the Earth's core contains potassium; different geophysical predictions lead to strongly varying, and hence distinguishable, central intensities (< 30 degrees from the downward vertical). Other uncertainties in the models, and prospects for observation of the geoneutrino angular distribution, are briefly discussed. We conclude by urging the development and construction of antineutrino experiments with angular sensitivity. (Abstract abridged.)Comment: 25 pages, RevTeX, 7 figures. Comments welcom

Mutation analysis of HIF prolyl hydroxylases (PHD/EGLN) in individuals with features of phaeochromocytoma and renal cell carcinoma susceptibility

Germline mutations in the von Hippel–Lindau disease (VHL) and succinate dehydrogenase subunit B (SDHB) genes can cause inherited phaeochromocytoma and/or renal cell carcinoma(RCC). Dysregulation of the hypoxia-inducible factor (HIF) transcription factors has been linked to VHL and SDHB-related RCC; both HIF dysregulation and disordered function of a prolyl hydroxylase domain isoform 3 (PHD3/EGLN3)-related pathway of neuronal apoptosis have been linked to the development of phaeochromocytoma. The 2-oxoglutarate-dependent prolyl hydroxylase enzymes PHD1 (EGLN2), PHD2 (EGLN1) and PHD3 (EGLN3) have a key role in regulating the stability of HIF-a subunits (and hence expression of the HIF-a transcription factors). A germline PHD2 mutation has been reported in association with congenital erythrocytosis and recurrent extra-adrenal phaeochromocytoma. We undertook mutation analysis of PHD1, PHD2 and PHD3 in two cohorts of patients with features of inherited phaeochromocytoma (nZ82) and inherited RCC (nZ64) and no evidence of germline mutations in known susceptibility genes. No confirmed pathogenic mutations were detected suggesting that mutations in these genes are not a frequent cause of inherited phaeochromocytoma or RCC