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

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

Drag reduction in pipe flows with polymer additives

Polyethylene Oxides (PEO) with molecular weights of 4 and 6 million and a Polyacrylamide (PAM) with a molecular weight of 15 million, were added to a turbulent pipe flow (15000 \u3c Re \u3c 50000) for drag reduction. The polymer was injected directly into the test section in one scenario, premixed in a tank and then pumped through the test section in the second. The injection addition method was found to be optimal because it subjected the polymer to lower amounts of shear stresses than the premixed addition method. A maximum of 75% reduction in drag was obtained. Even trace concentrations, as low as 2.5 WPPM (weight parts per million) , resulted in as high as 37% reduction in drag. Long thin high molecular weight polymers (PEO) were more effective than coiled high molecular weight polymer (PAM) . For the same molecular structure it was found that the polymer with heavier molecules had better drag reducing characteristics. The polymer with coiled molecules, however, is more resistant to shear stresses which break down the polymer into smaller less effective molecules. It was found that there is a critical concentration for the greatest drag reduction. This concentration is approximately 375 WPPM (.0375% byweight) of PEO for the injection method, and 500 WPPM of PEO for the premixed method. At greater concentrations, the viscosity of the solution increases such that the drag reduction characteristics of the polymer can no longer compensate

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

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

Solutions of the Navier-Stokes equations for vortex breakdown

Steady solutions of the Navier-Stokes equations, in terms of velocity and pressure, for breakdown in an unconfined viscous vortex are obtained numerically using the artificial compressibility technique of Chorin combined with an ADI finite-difference scheme. Axisymmetry is assumed and boundary conditions are carefully applied at the boundaries of a large finite region in an axial plane while resolution near the axis is maintained by a coordinate transformation. The solutions, which are obtained for Reynolds numbers up to 200 based on the free-stream axial velocity and a characteristic core radius, show that breakdown results from the diffusion and convection of vorticity away from the vortex core which, because of the strong coupling between the circumferential and axial velocity fields in strongly swirling flows, can lead to stagnation and reversal of the axial flow near the axis

Limited-are a modelling of stratocumulus over South-Eastern Pacific

This paper presents application of the Weather Research and Forecasting (WRF) model to limited-area modeling of atmospheric processes over the subtropical south-eastern Pacific, with the emphasis on the stratocumulus-topped boundary layer. The simulations cover a domain from the VAMOS (Variability of the American Monsoon Systems) Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS-REx) field project conducted in the subtropical south-eastern Pacific in October and November 2008. We focus on a day where the UK's BAe-146 research aircraft encountered Pockets of Open Cells (POCs) at the very western edge of its flight track, rather than on the entire campaign as investigated in previous limited-area modeling studies. Model results are compared to aircraft observations with the main conclusion that the simulated stratocumulus-topped boundary layer is significantly too shallow. This appears to be a combination of an already too shallow boundary layer in the dataset used to provide initial and lateral boundary conditions, and the inability of the WRF model to increase the boundary-layer height. Several sensitivity simulations, applying different subgrid-scale parameterizations available in the model, a larger computational domain and longer simulations, as well as a different dataset providing initial and lateral boundary conditions were all tried to improve the simulation. These changes appeared to have a rather small effect on the results. The model does simulate the formation of mesoscale cloud-free regions that one might consider similar to Pockets of Open Cells observed in nature. However, formation of these regions does not seem to be related to drizzle-induced transition from open- to closed-cell circulations as simulated by LES models. Instead, the cloud-free regions appear to result from mesoscale variations of the lower-tropspheric vertical velocity. Areas of negative vertical velocity with minima (a few cm s<sup>−1</sup>) near the boundary layer top seem to induce direct evaporation of the cloud layer. It remains to be seen in LES studies whether the mechanism seen in the model is realistic or if it is simply an artifact of interactions between resolved and parameterized processes

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