A study of turbulent flow between parallel plates by a statistical method

Turbulent Couette flow between parallel plates was studied from a statistical mechanics approach utilizing a model equation, similar to the Boltzmann equation of kinetic theory, which was proposed by Lundgren from the velocity distribution of fluid elements. Solutions to this equation are obtained numerically, employing the discrete ordinate method and finite differences. Two types of boundary conditions on the distribution function are considered, and the results of the calculations are compared to available experimental data. The research establishes that Lundgren's equation provides a very good description of turbulence for the flow situation considered and that it offers an analytical tool for further study of more complex turbulent flows. The present work also indicates that modelling of the boundary conditions is an area where further study is required

Regional scale effects of the aerosol cloud interaction simulated with an online coupled comprehensive chemistry model

We have extended the coupled mesoscale atmosphere and chemistry model COSMO-ART to account for the transformation of aerosol particles into cloud condensation nuclei and to quantify their interaction with warm cloud microphysics on the regional scale. The new model system aims to fill the gap between cloud resolving models and global scale models. It represents the very complex microscale aerosol and cloud physics as detailed as possible, whereas the continental domain size and efficient codes will allow for both studying weather and regional climate. The model system is applied in a first extended case study for Europe for a cloudy five day period in August 2005. <br><br> The model results show that the mean cloud droplet number concentration of clouds is correlated with the structure of the terrain, and we present a terrain slope parameter TS to classify this dependency. We propose to use this relationship to parameterize the probability density function, PDF, of subgrid-scale cloud updraft velocity in the activation parameterizations of climate models. <br><br> The simulations show that the presence of cloud condensation nuclei (CCN) and clouds are closely related spatially. We find high aerosol and CCN number concentrations in the vicinity of clouds at high altitudes. The nucleation of secondary particles is enhanced above the clouds. This is caused by an efficient formation of gaseous aerosol precursors above the cloud due to more available radiation, transport of gases in clean air above the cloud, and humid conditions. Therefore the treatment of complex photochemistry is crucial in atmospheric models to simulate the distribution of CCN. <br><br> The mean cloud droplet number concentration and droplet diameter showed a close link to the change in the aerosol. To quantify the net impact of an aerosol change on the precipitation we calculated the precipitation susceptibility <i>β</i> for the whole model domain over a period of two days with an hourly resolution. The distribution function of <i>β</i> is slightly skewed to positive values and has a mean of 0.23. Clouds with a liquid water path LWP of approximately 0.85 kg m<sup>−2</sup> are on average most susceptible to aerosol changes in our simulations with an absolute value of <i>β</i> of 1. The average <i>β</i> for LWP between 0.5 kg m<sup>−2</sup> and 1 kg m<sup>−2</sup> is approximately 0.4

Atomic Configuration of Nitrogen Doped Single-Walled Carbon Nanotubes

Having access to the chemical environment at the atomic level of a dopant in a nanostructure is crucial for the understanding of its properties. We have performed atomically-resolved electron energy-loss spectroscopy to detect individual nitrogen dopants in single-walled carbon nanotubes and compared with first principles calculations. We demonstrate that nitrogen doping occurs as single atoms in different bonding configurations: graphitic-like and pyrrolic-like substitutional nitrogen neighbouring local lattice distortion such as Stone-Thrower-Wales defects. The stability under the electron beam of these nanotubes has been studied in two extreme cases of nitrogen incorporation content and configuration. These findings provide key information for the applications of these nanostructures.Comment: 25 pages, 13 figure

On the number of Mather measures of Lagrangian systems

In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Ma\~n\'e obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able with Gonzalo Contreras to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest