The electron density is smooth away from the nuclei

We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.Comment: 16 page

Comparing Criteria for Circular Orbits in General Relativity

We study a simple analytic solution to Einstein's field equations describing a thin spherical shell consisting of collisionless particles in circular orbit. We then apply two independent criteria for the identification of circular orbits, which have recently been used in the numerical construction of binary black hole solutions, and find that both yield equivalent results. Our calculation illustrates these two criteria in a particularly transparent framework and provides further evidence that the deviations found in those numerical binary black hole solutions are not caused by the different criteria for circular orbits.Comment: 4 pages; to appear in PRD as a Brief Report; added and corrected reference

Computing and Counting Longest Paths on Circular-Arc Graphs in Polynomial Time

The longest path problem asks for a path with the largest number of vertices in a given graph. The first polynomial time algorithm (with running time O(n4)) has been recently developed for interval graphs. Even though interval and circular-arc graphs look superficially similar, they differ substantially, as circular-arc graphs are not perfect. In this paper, we prove that for every path P of a circular-arc graph G, we can appropriately “cut” the circle, such that the obtained (not induced) interval subgraph G′ of G admits a path P′ on the same vertices as P. This non-trivial result is of independent interest, as it suggests a generic reduction of a number of path problems on circular-arc graphs to the case of interval graphs with a multiplicative linear time overhead of O(n). As an application of this reduction, we present the first polynomial algorithm for the longest path problem on circular-arc graphs, which turns out to have the same running time O(n4) with the one on interval graphs, as we manage to get rid of the linear overhead of the reduction. This algorithm computes in the same time an n-approximation of the number of different vertex sets that provide a longest path; in the case where G is an interval graph, we compute the exact number. Moreover, our algorithm can be directly extended with the same running time to the case where every vertex has an arbitrary positive weight

Life cycle modelling of environmental impacts of application of processed organic municipal solid waste on agricultural land (EASEWASTE)

A model capable of quantifying the potential environmental impacts of agricultural application of composted or anaerobically digested source-separated organic municipal solid waste (MSW) is presented. In addition to the direct impacts, the model accounts for savings by avoiding the production and use of commercial fertilizers. The model is part of a larger model, Environmental Assessment of Solid Waste Systems and Technology (EASEWASTE), developed as a decisionsupport model, focusing on assessment of alternative waste management options. The environmental impacts of the land application of processed organic waste are quantified by emission coefficients referring to the composition of the processed waste and related to specific crop rotation as well as soil type. The model contains several default parameters based on literature data, field experiments and modelling by the agro-ecosystem model, Daisy. All data can be modified by the user allowing application of the model to other situations. A case study including four scenarios was performed to illustrate the use of the model. One tonne of nitrogen in composted and anaerobically digested MSW was applied as fertilizer to loamy and sandy soil at a plant farm in western Denmark. Application of the processed organic waste mainly affected the environmental impact categories global warming (0.4–0.7 PE), acidification (–0.06 (saving)–1.6 PE), nutrient enrichment (–1.0 (saving)–3.1 PE), and toxicity. The main contributors to these categories were nitrous oxide formation (global warming), ammonia volatilization (acidification and nutrient enrichment), nitrate losses (nutrient enrichment and groundwater contamination), and heavy metal input to soil (toxicity potentials). The local agricultural conditions as well as the composition of the processed MSW showed large influence on the environmental impacts. A range of benefits, mainly related to improved soil quality from long-term application of the processed organic waste, could not be generally quantified with respect to the chosen life cycle assessment impact categories and were therefore not included in the model. These effects should be considered in conjunction with the results of the life cycle assessment

Supersymmetric Gauge Theories in Twistor Space

We construct a twistor space action for N=4 super Yang-Mills theory and show that it is equivalent to its four dimensional spacetime counterpart at the level of perturbation theory. We compare our partition function to the original twistor-string proposal, showing that although our theory is closely related to string theory, it is free from conformal supergravity. We also provide twistor actions for gauge theories with N<4 supersymmetry, and show how matter multiplets may be coupled to the gauge sector.Comment: 23 pages, no figure

A master equation for a two-sided optical cavity.

Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same notion of photons as in linear optics scattering theory and consider a continuum of travelling-wave cavity photon modes. Our model predicts the same stationary state photon emission rates for the different sides of a laser-driven optical cavity as classical theories. Moreover, it predicts the same time evolution of the total cavity photon number as the standard standing-wave description in experiments with resonant and near-resonant laser driving. The proposed resonator Hamiltonian can be used, for example, to analyse coherent cavity-fiber networks [E. Kyoseva et al., New J. Phys. 14, 023023 (2012

Using domain-independent problems for introducing formal methods

The key to the integration of formal methods into engineering practice is education. In teaching, domain-independent problems i.e., not requiring prior engineering background-offer many advantages. Such problems are widely available, but this paper adds two dimensions that are lacking in typical solutions yet are crucial to formal methods: (i) the translation of informal statements into formal expressions; (ii) the role of formal calculation (including proofs) in exposing risks or misunderstandings and in discovering pathways to solutions. A few example problems illustrate this: (a) a small logical one showing the importance of fully capturing informal statements; (b) a combinatorial one showing how, in going from "real-world" formulations to mathematical ones, formal methods can cover more aspects than classical mathematics, and a half-page formal program semantics suitable for beginners is presented as a support; (c) a larger one showing how a single problem can contain enough elements to serve as a Leitmotiv for all notational and reasoning issues in a complete introductory course. An important final observation is that, in teaching formal methods, no approach can be a substitute for an open mind, as extreme mathphobia appears resistant to any motivation

Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry

Being neither commutative nor associative, Einstein velocity addition of relativistically admissible velocities gives rise to gyrations. Gyrations, in turn, measure the extent to which Einstein addition deviates from commutativity and from associativity. Gyrations are geometric automorphisms abstracted from the relativistic mechanical effect known as Thomas precession

Moment of Inertia and Quadrupole Response Function of a Trapped Superfluid

We derive an explicit relationship between the moment of inertia and the quadrupole response function of an interacting gas confined in a harmonic trap. The relationship holds for both Bose and Fermi systems and is well suited to reveal the effects of irrotationality of the superfluid motion. Recent experimental results on the scissors mode are used to extract the value of the moment of inertia of a trapped Bose gas and to point out the deviations from the rigid value due to superfluidity.Comment: 6 page