Distance Geometry in Quasihypermetric Spaces. III

Let $(X, d)$ be a compact metric space and let $\mathcal{M}(X)$ denote the space of all finite signed Borel measures on $X$. Define $I \colon \mathcal{M}(X) \to \R$ by $$I(\mu) = \int_X \int_X d(x,y) d\mu(x) d\mu(y),$$ and set $M(X) = \sup I(\mu)$, where $\mu$ ranges over the collection of signed measures in $\mathcal{M}(X)$ of total mass 1. This paper, with two earlier papers [Peter Nickolas and Reinhard Wolf, Distance geometry in quasihypermetric spaces. I and II], investigates the geometric constant $M(X)$ and its relationship to the metric properties of $X$ and the functional-analytic properties of a certain subspace of $\mathcal{M}(X)$ when equipped with a natural semi-inner product. Specifically, this paper explores links between the properties of $M(X)$ and metric embeddings of $X$, and the properties of $M(X)$ when $X$ is a finite metric space.Comment: 20 pages. References [10] and [11] are arXiv:0809.0740v1 [math.MG] and arXiv:0809.0744v1 [math.MG

Analysis of Sun/Moon Gravitational Redshift tests with the STE-QUEST Space Mission

The STE-QUEST space mission will perform tests of the gravitational redshift in the field of the Sun and the Moon to high precision by frequency comparisons of clocks attached to the ground and separated by intercontinental distances. In the absence of Einstein equivalence principle (EP) violation, the redshift is zero up to small tidal corrections as the Earth is freely falling in the field of the Sun and Moon. Such tests are thus null tests, allowing to bound possible violations of the EP. Here we analyze the Sun/Moon redshift tests using a generic EP violating theoretical framework, with clocks minimally modelled as two-level atoms. We present a complete derivation of the redshift (including both GR and non-GR terms) in a realistic experiment such as the one envisaged for STE-QUEST. We point out and correct an error in previous formalisms linked to the atom's recoil not being properly taken into account.Comment: 17 pages, 3 figure

An optical clock with neutral atoms confined in a shallow trap

We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunnelling leads to a residual sensitivity to the atom dynamics hence requiring large depths (50 to $100 E\_r$ for Sr) to avoid any frequency shift or line broadening of the atomic transition at the $10^{-17}-10^{-18}$ level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g. higher order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunnelling. We show that using the Earth's gravity, much shallower traps (down to $5 E\_r$ for Sr) can be used for the same accuracy goal

Frequency and duration of low-wind-power events in Germany

In the transition to a renewable energy system, the occurrence of low-wind-power events receives increasing attention. We analyze the frequency and duration of such events for onshore wind power in Germany, based on 40 years of reanalysis data and open software. We find that low-wind-power events are less frequent in winter than in summer, but the maximum duration is distributed more evenly between months. While short events are frequent, very long events are much rarer. Every year, a period of around five consecutive days with an average wind capacity factor below 10% occurs, and every ten years a respective period of nearly eight days. These durations decrease if only winter months are considered. The longest event in the data lasts nearly ten days. We conclude that public concerns about low-wind-power events in winter may be overrated, but recommend that modeling studies consider multiple weather years to properly account for such events.Comment: This is an update version after peer revie

Existence of the critical endpoint in the vector meson extended linear sigma model

The chiral phase transition of the strongly interacting matter is investigated at nonzero temperature and baryon chemical potential mu_B within an extended (2+1) flavor Polyakov constituent quark-meson model which incorporates the effect of the vector and axial vector mesons. The effect of the fermionic vacuum and thermal fluctuations computed from the grand potential of the model is taken into account in the curvature masses of the scalar and pseudoscalar mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values in a chi^2-minimization procedure which selects between various possible assignments of scalar nonet states to physical particles. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates and the chiral partners' masses and of the mixing angles for the pseudoscalar eta-eta' and the corresponding scalar complex. We calculate the pressure and various thermodynamical observables derived from it and compare them to the continuum extrapolated lattice results of the Wuppertal-Budapest collaboration. We study the T-mu_B phase diagram of the model and find that a critical end point exists for parameters of the model, which give acceptable values of chi^2.Comment: 21 pages, 8 color eps figures, published versio

Power from the Desert: Not a Mirage

Energy policy is confronted by two major challenges. First, fossil fuels will become ever more scarce and expensive in coming years, a trend which will intensify conflicts for the control of natural resources. Second, the burning of fossil fuels-particularly coal-is leading to an increase in harmful greenhouse gas emissions. To address these challenges, the share of renewable energy in total energy consumption must be considerably increased. In sharp contrast to fossil fuels, which are becoming ever more depleted, renewable energy sources are essentially inexhaustible. Furthermore, renewable energy produces hardly any greenhouse gases. The large-scale exploitation of solar energy for power generation offers enormous potential. In theory, solar-thermal collectors installed in North Africa over an area roughly the size of New Jersey could meet all of Europe's electricity needs. The construction of high-voltage direct current (HVDC) lines would be necessary to import power from the Mediterranean region without excessive transmission losses. An expansion of European electricity networks could also yield supplementary benefits, including enhanced integration of domestic renewable energy (such as wind power), and improved competition in electricity markets.Electricity trade, Solar energy, DESERTEC

Mitigation of Methane Emissions: A Rapid and Cost-Effective Response to Climate Change

Methane is a major anthropogenic greenhouse gas, second only to carbon dioxide (CO2) in its impact on climate change. Methane (CH4) has a high global warming potential that is 25 times as large as the one of CO2 on a 100 year time horizon according to the latest IPCC report. Thus, CH4 contributes significantly to anthropogenic radiative forcing, although it has a relatively short atmospheric perturbation lifetime of 12 years. CH4 has a variety of sources that can be small, geographically dispersed, and not related to energy sectors. In this report, we analyze methane emission abatement options in five different sectors and identify economic mitigation potentials for different CO2 prices. While mitigation potentials are generally large, there are substantial potentials at low marginal abatement costs. Drawing on different assumptions on the social costs of carbon, we calculate benefit/cost ratios for different sectors and mitigation levels. We recommend an economically efficient global methane mitigation portfolio for the year 2020 that includes the sectors of livestock and manure, rice management, solid waste, coal mine methane and natural gas. Depending on assumptions of social costs of carbon, this portfolio leads to global CH4 mitigation levels of 1.5 or 1.9 GtCO2-eq at overall costs of around $14 billion or$30 billion and benefit/cost ratios of 1.4 and 3.0, respectively. We also develop an economically less efficient alternative portfolio that excludes cost-effective agricultural mitigation options. It leads to comparable abatement levels, but has higher costs and lower benefit/cost ratios. If the global community wanted to spend an even larger amount of money - say, $250 billion - on methane mitigation, much larger mitigation potentials could be realized, even such with very high marginal abatement costs. Nonetheless, this approach would be economically inefficient. If the global community wanted to spend such an amount, we recommend spreading the effort cost-effectively over different greenhouse gases. While methane mitigation alone will not suffice to solve the climate problem, it is a vital part of a cost-effective climate policy. Due to the short atmospheric lifetime, CH4 emission reductions have a rapid effect. Methane mitigation is indispensable for realizing ambitious emission scenarios like IPCC's "B1", which leads to a global temperature increase of less than 2°C by the year 2100. Policy makers should put more emphasis on methane mitigation and aim for realizing low-cost methane mitigation potentials by providing information to all relevant actors and by developing appropriate regulatory and market frameworks. We also recommend including methane in emissions trading schemes.Methane, mitigation, climate change, cost-benefit analysis

Methane: A Neglected Greenhouse Gas

Methane is a greenhouse gas that gets far less public attention than carbon dioxide. This is entirely unwarranted. Being 25 times more potent than carbon dioxide in trapping heat in the atmosphere, methane accounts for about one-sixth of all anthropogenic (i.e. human-induced) greenhouse gas emissions. Methane is also overlooked when it comes to taking concrete measures for climate protection, despite the fact that reducing methane emissions is potentially cheap. Major sources of methane emissions are livestock farming, the natural gas sector, landfills, wetland rice cultivation and coal mining. In many cases, it is possible to mitigate substantial amounts of methane in a cost-effective way. Moreover, captured methane can be used for generating heat and power. In other words, abating one ton of methane emissions is sometimes cheaper than abating an equivalent amount of carbon dioxide. The challenge is to effectively incorporate cutbacks of methane gas emissions into climate policy strategies.Methane, Mitigation, Climate policy