A key-formula to compute the gravitational potential of inhomogeneous discs in cylindrical coordinates

We have established the exact expression for the gravitational potential of a homogeneous polar cell - an elementary pattern used in hydrodynamical simulations of gravitating discs. This formula, which is a closed-form, works for any opening angle and radial extension of the cell. It is valid at any point in space, i.e. in the plane of the distribution (inside and outside) as well as off-plane, thereby generalizing the results reported by Durand (1953) for the circular disc. The three components of the gravitational acceleration are given. The mathematical demonstration proceeds from the "incomplete version of Durand's formula" for the potential (based on complete elliptic integrals). We determine first the potential due to the circular sector (i.e. a pie-slice sheet), and then deduce that of the polar cell (from convenient radial scaling and subtraction). As a by-product, we generate an integral theorem stating that "the angular average of the potential of any circular sector along its tangent circle is 2/PI times the value at the corner". A few examples are presented. For numerical resolutions and cell shapes commonly used in disc simulations, we quantify the importance of curvature effects by performing a direct comparison between the potential of the polar cell and that of the Cartesian (i.e. rectangular) cell having the same mass. Edge values are found to deviate roughly like 2E-3 x N/256 in relative (N is the number of grid points in the radial direction), while the agreement is typically four orders of magnitude better for values at the cell's center. We also produce a reliable approximation for the potential, valid in the cell's plane, inside and close to the cell. Its remarkable accuracy, about 5E-4 x N/256 in relative, is sufficient to estimate the cell's self-acceleration.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

The clock paradox in a static homogeneous gravitational field

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars.Comment: Revision: Posted with the caption included with the figure

Sharp transition towards shared vocabularies in multi-agent systems

What processes can explain how very large populations are able to converge on the use of a particular word or grammatical construction without global coordination? Answering this question helps to understand why new language constructs usually propagate along an S-shaped curve with a rather sudden transition towards global agreement. It also helps to analyze and design new technologies that support or orchestrate self-organizing communication systems, such as recent social tagging systems for the web. The article introduces and studies a microscopic model of communicating autonomous agents performing language games without any central control. We show that the system undergoes a disorder/order transition, going trough a sharp symmetry breaking process to reach a shared set of conventions. Before the transition, the system builds up non-trivial scale-invariant correlations, for instance in the distribution of competing synonyms, which display a Zipf-like law. These correlations make the system ready for the transition towards shared conventions, which, observed on the time-scale of collective behaviors, becomes sharper and sharper with system size. This surprising result not only explains why human language can scale up to very large populations but also suggests ways to optimize artificial semiotic dynamics.Comment: 12 pages, 4 figure

Model Order Reduction for Rotating Electrical Machines

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that contain non-symmetric components. These are usually introduced during the mass production process and are modeled by small perturbations in the geometry (e.g., eccentricity) or the material parameters. While model order reduction for symmetric machines is clear and does not need special treatment, the non-symmetric setting adds additional challenges. An adaptive strategy based on proper orthogonal decomposition is developed to overcome these difficulties. Equipped with an a posteriori error estimator the obtained solution is certified. Numerical examples are presented to demonstrate the effectiveness of the proposed method

The evolutionarily conserved protein CG9186 is associated with lipid droplets, required for their positioning and for fat storage.

Lipid droplets (LDs) are specialized cell organelles for the storage of energy-rich lipids. Although lipid storage is a conserved feature of all cells and organisms, little is known about fundamental aspects of the cell biology of LDs, including their biogenesis, structural assembly and subcellular positioning, and the regulation of organismic energy homeostasis. We identified a novel LD-associated protein family, represented by the Drosophila protein CG9186 and its murine homolog MGI:1916082. In the absence of LDs, both proteins localize at the endoplasmic reticulum (ER). Upon lipid storage induction, they translocate to LDs using an evolutionarily conserved targeting mechanism that acts through a 60-amino-acid targeting motif in the center of the CG9186 protein. Overexpression of CG9186, and MGI: 1916082, causes clustering of LDs in both tissue culture and salivary gland cells, whereas RNAi knockdown of CG9186 results in a reduction of LDs. Organismal RNAi knockdown of CG9186 results in a reduction in lipid storage levels of the fly. The results indicate that we identified the first members of a novel and evolutionarily conserved family of lipid storage regulators, which are also required to properly position LDs within cells

Ralstonia pickettii—innocent bystander or a potential threat?

ABSTRACTRalstonia pickettii can be isolated from water, soil and plants, and can also form part of the commensal flora of the oral cavity and the upper respiratory tract of healthy individuals. R. pickettii is an infrequent pathogen, but can cause infections, mainly of the respiratory tract, in immunocompromised and cystic fibrosis patients. It can be isolated from a variety of clinical specimens, including sputum, blood, wound infections, urine, ear and nose swabs, and cerebrospinal fluid. Resistance can occur to ciprofloxacin, trimethoprim–sulphamethoxazole, piperacillin–tazobactam, imipenem–cilastatin and ceftazidime. Early detection of R. pickettii allows prompt appropriate antimicrobial therapy with a favourable outcome, but removal of infected indwelling devices is mandatory