Lie algebroid structures on a class of affine bundles

We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the theory of Lagrangian systems on Lie algebroids. An extensive discussion is given of a way one can think of forms acting on sections of the affine bundle. It is further shown that the affine Lie algebroid structure gives rise to a coboundary operator on such forms. The concept of admissible curves and dynamical systems whose integral curves are admissible, brings an associated affine bundle into the picture, on which one can define in a natural way a prolongation of the original affine Lie algebroid structure.Comment: 28 page

Homology and modular classes of Lie algebroids

For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evans, J.-H. Lu, and A. Weinstein.Comment: 11 pages, AmSLaTeX, 3 typos correcte

Completely integrable systems: a generalization

We present a slight generalization of the notion of completely integrable systems to get them being integrable by quadratures. We use this generalization to integrate dynamical systems on double Lie groups.Comment: Latex, 15 page

Construction of completely integrable systems by Poisson mappings

Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.Comment: AmsTeX, 9 page

libcloudph++ 0.2: single-moment bulk, double-moment bulk, and particle-based warm-rain microphysics library in C++

This paper introduces a library of algorithms for representing cloud microphysics in numerical models. The library is written in C++, hence the name libcloudph++. In the current release, the library covers three warm-rain schemes: the single- and double-moment bulk schemes, and the particle-based scheme with Monte-Carlo coalescence. The three schemes are intended for modelling frameworks of different dimensionality and complexity ranging from parcel models to multi-dimensional cloud-resolving (e.g. large-eddy) simulations. A two-dimensional prescribed-flow framework is used in example simulations presented in the paper with the aim of highlighting the library features. The libcloudph++ and all its mandatory dependencies are free and open-source software. The Boost.units library is used for zero-overhead dimensional analysis of the code at compile time. The particle-based scheme is implemented using the Thrust library that allows to leverage the power of graphics processing units (GPU), retaining the possibility to compile the unchanged code for execution on single or multiple standard processors (CPUs). The paper includes complete description of the programming interface (API) of the library and a performance analysis including comparison of GPU and CPU setups.Comment: The library description has been updated to the new library API (i.e. v0.1 -> v0.2 update). The key difference is that the model state variables are now mixing ratios as opposed to densities. The particle-based scheme was supplemented with the "particle recycling" process. Numerous editorial corrections were mad

Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions

On a cotangent bundle T\sp*G of a Lie group $G$ one can describe the standard Liouville form $\theta$ and the symplectic form $d \theta$ in terms of the right Maurer Cartan form and the left moment mapping (of the right action of $G$ on itself), and also in terms of the left Maurer-Cartan form and the right moment mapping, and also the Poisson structure can be written in related quantities. This leads to a wide class of exact symplectic stuctures on T\sp*G and to Poisson structures by replacing the canonical momenta of the right or left actions of $G$ on itself by arbitrary ones, followed by reduction (to $G$ cross a Weyl-chamber, e.g.). This method also works on principal bundles

Decision Performance and Safety Performance: A Value-Focused Thinking Study in the Oil Industry

Considerable research has been performed to develop leading indicators of safety performance. We use value-focused thinking to understand the objectives and evaluation measures that frame a particular safety-related decision within an organization. These decisions are part of the safety culture. Our research partners were two oil shipping companies; we surveyed crewmembers on their tankers to evaluate performance in each decision objective on their vessel. We demonstrate that measurements of the achievement of these objectives are related to future safety performance and thus provide leading indicators of safety

Examining the efficacy of a genotyping-by-sequencing technique for population genetic analysis of the mushroom Laccaria bicolor and evaluating whether a reference genome is necessary to assess homology

Given the diversity and ecological importance of Fungi, there is a lack of population genetic research on these organisms. The reason for this can be explained in part by their cryptic nature and difficulty in identifying genets. In addition the difficulty (relative to plants and animals) in developing molecular markers for fungal population genetics contributes to the lack of research in this area. This study examines the ability of restriction-site associated DNA (RAD) sequencing to generate SNPs in Laccaria bicolor. Eighteen samples of morphologically identified L. bicolor from the United States and Europe were selected for this project. The RAD sequencing method produced anywhere from 290 000 to more than 3 000 000 reads. Mapping these reads to the genome of L. bicolor resulted in 84 000-940 000 unique reads from individual samples. Results indicate that incorporation of non-L. bicolor taxa into the analysis resulted in a precipitous drop in shared loci among samples, suggests the potential of these methods to identify cryptic species. F-statistics were easily calculated, although an observable "noise" was detected when using the "All Loci" treatment versus filtering loci to those present in at least 50% of the individuals. The data were analyzed with tests of Hardy-Weinburg equilibrium, population genetic statistics (FIS and FST), and population structure analysis using the program Structure. The results provide encouraging feedback regarding the potential utility of these methods and their data for population genetic analysis. We were unable to draw conclusions of life history of L. bicolor populations from this dataset, given the small sample size. The results of this study indicate the potential of these methods to address population genetics and general life history questions in the Agaricales. Further research is necessary to explore the specific application of these methods in the Agaricales or other fungal groups

On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

Thermal transport of the XXZ chain in a magnetic field

We study the heat conduction of the spin-1/2 XXZ chain in finite magnetic fields where magnetothermal effects arise. Due to the integrability of this model, all transport coefficients diverge, signaled by finite Drude weights. Using exact diagonalization and mean-field theory, we analyze the temperature and field dependence of the thermal Drude weight for various exchange anisotropies under the condition of zero magnetization-current flow. First, we find a strong magnetic field dependence of the Drude weight, including a suppression of its magnitude with increasing field strength and a non-monotonic field-dependence of the peak position. Second, for small exchange anisotropies and magnetic fields in the massless as well as in the fully polarized regime the mean-field approach is in excellent agreement with the exact diagonalization data. Third, at the field-induced quantum critical line between the para- and ferromagnetic region we propose a universal low-temperature behavior of the thermal Drude weight.Comment: 9 pages REVTeX4 including 5 figures, revised version, refs. added, typos correcte