The hyperfine structure in the rotational spectrum of CF+

Context. CF+ has recently been detected in the Horsehead and Orion Bar photo-dissociation regions. The J=1-0 line in the Horsehead is double-peaked in contrast to other millimeter lines. The origin of this double-peak profile may be kinematic or spectroscopic. Aims. We investigate the effect of hyperfine interactions due to the fluorine nucleus in CF+ on the rotational transitions. Methods. We compute the fluorine spin rotation constant of CF+ using high-level quantum chemical methods and determine the relative positions and intensities of each hyperfine component. This information is used to fit the theoretical hyperfine components to the observed CF+ line profiles, thereby employing the hyperfine fitting method in GILDAS. Results. The fluorine spin rotation constant of CF+ is 229.2 kHz. This way, the double-peaked CF+ line profiles are well fitted by the hyperfine components predicted by the calculations. The unusually large hyperfine splitting of the CF+ line therefore explains the shape of the lines detected in the Horsehead nebula, without invoking intricate kinematics in the UV-illuminated gas.Comment: 2 pages, 1 figure, Accepted for publication in A&

Analytic evaluation of the dipole Hessian matrix in coupled-cluster theory

The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections to dipole moments. The superior accuracy of the analytic evaluation of third energy derivatives as compared to numerical differentiation schemes is demonstrated in some pilot calculations

Direct radiative effect of aerosols emitted by transport from road, shipping and aviation

Aerosols and their precursors are emitted abundantly by transport activities. Transportation constitutes one of the fastest growing activities and its growth is predicted to increase significantly in the future. Previous studies have estimated the aerosol direct radiative forcing from one transport sub-sector, but only one study to our knowledge estimated the range of radiative forcing from the main aerosol components (sulphate, black carbon (BC) and organic carbon) for the whole transportation sector. In this study, we compare results from two different chemical transport models and three radiation codes under different hypothesis of mixing: internal and external mixing using emission inventories for the year 2000. The main results from this study consist of a positive direct radiative forcing for aerosols emitted by road traffic of +20±11 mW m−2 for an externally mixed aerosol, and of +32±13 mW m−2 when BC is internally mixed. These direct radiative forcings are much higher than the previously published estimate of +3±11 mW m−2. For transport activities from shipping, the net direct aerosol radiative forcing is negative. This forcing is dominated by the contribution of the sulphate. For both an external and an internal mixture, the radiative forcing from shipping is estimated at −26±4 mW m−2. These estimates are in very good agreement with the range of a previously published one (from −46 to −13 mW m−2) but with a much narrower range. By contrast, the direct aerosol forcing from aviation is estimated to be small, and in the range −0.9 to +0.3 mW m−2

Active Mass Under Pressure

After a historical introduction to Poisson's equation for Newtonian gravity, its analog for static gravitational fields in Einstein's theory is reviewed. It appears that the pressure contribution to the active mass density in Einstein's theory might also be noticeable at the Newtonian level. A form of its surprising appearance, first noticed by Richard Chase Tolman, was discussed half a century ago in the Hamburg Relativity Seminar and is resolved here.Comment: 28 pages, 4 figure

Proposal of a population wide genome-based testing for Covid-19

Our lives (and deaths) have by now been dominated for two years by COVID-19, a pandemic that has caused hundreds of millions of disease cases, millions of deaths, trillions in economic costs, and major restrictions on our freedom. Here we suggest a novel tool for controlling the COVID-19 pandemic. The key element is a method for a population-scale PCR-based testing, applied on a systematic and repeated basis. For this we have developed a low cost, highly sensitive virus-genome-based test. Using Germany as an example, we demonstrate by using a mathematical model, how useful this strategy could have been in controlling the pandemic. We show using real-world examples how this might be implemented on a mass scale and discuss the feasibility of this approach

Basic Understanding of Condensed Phases of Matter via Packing Models

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298

Multi-model simulations of the impact of international shipping on Atmospheric Chemistry and Climate in 2000 and 2030

The global impact of shipping on atmospheric chemistry and radiative forcing, as well as the associated uncertainties, have been quantified using an ensemble of ten state-of-the-art atmospheric chemistry models and a predefined set of emission data. The analysis is performed for present-day conditions ( year 2000) and for two future ship emission scenarios. In one scenario ship emissions stabilize at 2000 levels; in the other ship emissions increase with a constant annual growth rate of 2.2% up to 2030 ( termed the "Constant Growth Scenario" (CGS)). Most other anthropogenic emissions follow the IPCC ( Intergovernmental Panel on Climate Change) SRES ( Special Report on Emission Scenarios) A2 scenario, while biomass burning and natural emissions remain at year 2000 levels. An intercomparison of the model results with observations over the Northern Hemisphere (25 degrees - 60 degrees N) oceanic regions in the lower troposphere showed that the models are capable to reproduce ozone (O-3) and nitrogen oxides (NOx= NO+ NO2) reasonably well, whereas sulphur dioxide (SO2) in the marine boundary layer is significantly underestimated. The most pronounced changes in annual mean tropospheric NO2 and sulphate columns are simulated over the Baltic and North Seas. Other significant changes occur over the North Atlantic, the Gulf of Mexico and along the main shipping lane from Europe to Asia, across the Red and Arabian Seas. Maximum contributions from shipping to annual mean near-surface O-3 are found over the North Atlantic ( 5 - 6 ppbv in 2000; up to 8 ppbv in 2030). Ship contributions to tropospheric O3 columns over the North Atlantic and Indian Oceans reach 1 DU in 2000 and up to 1.8 DU in 2030. Tropospheric O-3 forcings due to shipping are 9.8 +/- 2.0 mW/m(2) in 2000 and 13.6 +/- 2.3 mW/m(2) in 2030. Whilst increasing O-3, ship NOx simultaneously enhances hydroxyl radicals over the remote ocean, reducing the global methane lifetime by 0.13 yr in 2000, and by up to 0.17 yr in 2030, introducing a negative radiative forcing. The models show future increases in NOx and O-3 burden which scale almost linearly with increases in NOx emission totals. Increasing emissions from shipping would significantly counteract the benefits derived from reducing SO2 emissions from all other anthropogenic sources under the A2 scenario over the continents, for example in Europe. Globally, shipping contributes 3% to increases in O-3 burden between 2000 and 2030, and 4.5% to increases in sulphate under A2/CGS. However, if future ground based emissions follow a more stringent scenario, the relative importance of ship emissions will increase. Inter-model differences in the simulated O-3 contributions from ships are significantly smaller than estimated uncertainties stemming from the ship emission inventory, mainly the ship emission totals, the distribution of the emissions over the globe, and the neglect of ship plume dispersion

TRADEOFFs in climate effects through aircraft routing: forcing due to radiatively active gases

We have estimated impacts of alternative aviation routings on the radiative forcing. Changes in ozone and OH have been estimated in four Chemistry Transport Models (CTMs) participating in the TRADEOFF project. Radiative forcings due to ozone and methane have been calculated accordingly. In addition radiative forcing due to CO2 is estimated based on fuel consumption. Three alternative routing cases are investigated; one scenario assuming additional polar routes and two scenarios assuming aircraft cruising at higher (+2000 ft) and lower (−6000 ft) altitudes. Results from the base case in year 2000 are included as a reference. Taking first a steady state backward looking approach, adding the changes in the forcing from ozone, CO2 and CH4, the ranges of the models used in this work are −0.8 to −1.8 and 0.3 to 0.6 m Wm−2 in the lower (−6000 ft) and higher (+2000 ft) cruise levels, respectively. In relative terms, flying 6000ft lower reduces the forcing by 5–10% compared to the current flight pattern, whereas flying higher, while saving fuel and presumably flying time, increases the forcing by about 2–3%. Taking next a forward looking approach we have estimated the integrated forcing (m Wm−2 yr) over 20 and 100 years time horizons. The relative contributions from each of the three climate gases are somewhat different from the backward looking approach. The differences are moderate adopting 100 year time horizon, whereas under the 20 year horizon CO2 naturally becomes less important relatively. Thus the forcing agents impact climate differently on various time scales. Also, we have found significant differences between the models for ozone and methane. We conclude that we are not yet at a point where we can include non-CO2 effects of aviation in emission trading schemes. Nevertheless, the rerouting cases that have been studied here yield relatively small changes in the radiative forcing due to the radiatively active gases

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017