Numerical versus analytical accuracy of the formulas for light propagation

Numerical integration of the differential equations of light propagation in the Schwarzschild metric shows that in some situations relevant for practical observations the well-known post-Newtonian solution for light propagation has an error up to 16 microarcsecond. The aim of this work is to demonstrate this fact, identify the reason for this error and to derive an analytical formula accurate at the level of 1 microarcsecond as needed for high-accuracy astrometric projects (e.g., Gaia). An analytical post-post-Newtonian solution for the light propagation for both Cauchy and boundary problems is given for the Schwarzschild metric augmented by the PPN and post-linear parameters $\beta$, $\gamma$ and $\epsilon$. Using analytical upper estimates of each term we investigate which post-post-Newtonian terms may play a role for an observer in the solar system at the level of 1 microarcsecond and conclude that only one post-post-Newtonian term remains important for this numerical accuracy. In this way, an analytical solution for the boundary problem for light propagation is derived. That solution contains terms of both post-Newtonian and post-post-Newtonian order, but is valid for the given numerical level of 1 microarcsecond. The derived analytical solution has been verified using the results of a high-accuracy numerical integration of differential equations of light propagation and found to be correct at the level well below 1 microarcsecond for arbitrary observer situated within the solar system. Furthermore, the origin of the post-post-Newtonian terms relevant for the microarcsecond accuracy is elucidated. We demonstrate that these terms result from an inadequate choice of the impact parameter in the standard post-Newtonian formulas

The cost and risk impacts of rerouting railroad shipments of hazardous materials

Cataloged from PDF version of article.Rail shipments of hazardous materials expose the population near the routes to the possibility of an accident resulting in a spill. Rail routes are determined by economic concerns such as route length and the revenue generated for the originating carrier. In this paper we consider an alternate routing strategy that takes accident risks into account. We employ a model to quantify rail transport risk and then use a weighted combination of cost and risk and generate alternate routes. In some cases the alternate routes achieve significantly lower risk values than the practical routes at a small incremental cost. While there are generally fewer rerouting alternatives for rail than for road transport, considering the possible consequences of a train derailment we argue that risk should be taken into account when selecting rail routes and that the cost–risk tradeoffs should be evaluated. © 2007 Elsevier Ltd. All rights reserved

An International Classification of Inherited Metabolic Disorders (ICIMD)

Several initiatives at establishing a classification of inherited metabolic disorders have been published previously, some focusing on pathomechanisms, others on clinical manifestations, while yet another attempted a simplified approach of a comprehensive nosology. Some of these classifications suffered from shortcomings, such as lack of a mechanism for continuous update in light of a rapidly‐evolving field, or lack of widespread input from the metabolic community at large. Our classification – the International Classification of Inherited Metabolic Disorders, or ICIMD – includes 1,450 disorders, and differs from prior approaches in that it benefited from input by a large number of experts in the field, and was endorsed by major metabolic societies around the globe. Several criteria such as pathway involvement and pathomechanisms were considered. The main purpose of the hierarchical, group‐based approach of the ICIMD is an improved understanding of the interconnections between many individual conditions that may share functional, clinical and diagnostic features. The ICIMD aims to include any primary genetic condition in which alteration of a biochemical pathway is intrinsic to specific biochemical, clinical and/or pathophysiological features. As new disorders are discovered, we will seek the opinion of experts in the advisory board prior to inclusion in the appropriate group of the ICIMD, thus guaranteeing the continuing relevance of this classification via regular curation and expert advice

Impact of Nucleon Mass Shift on the Freeze Out Process

The freeze out of a massive nucleon gas through a finite layer with time-like normal is studied. The impact of in-medium nucleon mass shift on the freeze out process is investigated. A considerable modification of the thermodynamical variables temperature, flow-velocity, energy density and particle density has been found. Due to the nucleon mass shift the freeze out particle distribution functions are changed noticeably in comparison with evaluations, which use vacuum nucleon mass.Comment: submitted to Physical Review

Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation

A procedure avoiding any integration of the null geodesic equations is used to derive the direction of light propagation in a three-parameter family of static, spherically symmetric spacetimes within the post-post-Minkowskian approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries of spacetime are systematically used. It is found that the expression of the angle formed by two light rays as measured by a static observer staying at a given point is remarkably simple in these coordinates. The attention is mainly focused on the null geodesic paths that we call the "quasi-Minkowskian light rays". The vector-like functions characterizing the direction of propagation of such light rays at their points of emission and reception are firstly obtained in the generic case where these points are both located at a finite distance from the centre of symmetry. The direction of propagation of the quasi-Minkowskian light rays emitted at infinity is then straightforwardly deduced. An intrinsic definition of the gravitational deflection angle relative to a static observer located at a finite distance is proposed for these rays. The expression inferred from this definition extends the formula currently used in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction; corrected typos; published in Class. Quantum Gra

ost in promiscuity? An evolutionary and biochemical evaluation of HSD10 function in cardiolipin metabolism

Multifunctional proteins are challenging as it can be difficult to confirm pathomechanisms associated with disease-causing genetic variants. The human 17β-hydroxysteroid dehydrogenase 10 (HSD10) is a moonlighting enzyme with at least two structurally and catalytically unrelated functions. HSD10 disease was originally described as a disorder of isoleucine metabolism, but the clinical manifestations were subsequently shown to be linked to impaired mtDNA transcript processing due to deficient function of HSD10 in the mtRNase P complex. A surprisingly large number of other, mostly enzymatic and potentially clinically relevant functions have been attributed to HSD10. Recently, HSD10 was reported to exhibit phospholipase C-like activity towards cardiolipins (CL), important mitochondrial phospholipids. To assess the physiological role of the proposed CL-cleaving function, we studied CL architectures in living cells and patient fibroblasts in different genetic backgrounds and lipid environments using our well-established LC–MS/MS cardiolipidomic pipeline. These experiments revealed no measurable effect on CLs, indicating that HSD10 does not have a physiologically relevant function towards CL metabolism. Evolutionary constraints could explain the broad range of reported substrates for HSD10 in vitro. The combination of an essential structural with a non-essential enzymatic function in the same protein could direct the evolutionary trajectory towards improvement of the former, thereby increasing the flexibility of the binding pocket, which is consistent with the results presented here

Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields

The equivalence of the covariant renormalization and the partial-wave renormaliz ation (PWR) approach is proven explicitly for the one-loop self-energy correction (SE) of a bound electron state in the presence of external perturbation potentials. No spurious correctio n terms to the noncovariant PWR scheme are generated for Coulomb-type screening potentia ls and for external magnetic fields. It is shown that in numerical calculations of the SE with Coulombic perturbation potential spurious terms result from an improper treatment of the unphysical high-energy contribution. A method for performing the PWR utilizing the relativistic B-spline approach for the construction of the Dirac spectrum in external magnetic fields is proposed. This method is applied for calculating QED corrections to the bound-electron $g$-factor in H-like ions. Within the level of accuracy of about 0.1% no spurious terms are generated in numerical calculations of the SE in magnetic fields.Comment: 22 pages, LaTeX, 1 figur

Rho - Omega Splitting and Mixing in Nuclear Matter

We investigate the splitting and mixing of $\rho$ and $\omega$ mesons in nuclear matter. The calculations were performed on the basis of QCD sum rules and include all operators up to mass dimension-6 twist-4 and up to first order in the coupling constants. Special attention is devoted to the impact of the scalar 4-quark condensates on both effects. In nuclear matter the Landau damping governs the $\rho - \omega$ mass splitting while the scalar 4-quark condensates govern the strenght of individual mass shifts. A strong in-medium mass splitting causes the disappearance of the $\rho - \omega$ mixing.Comment: 28 pages, 8 figures, Phys. Rev. C 70 (2004) 03520