La distribution des zéros des fonctions L

Selon la philosophie de Katz et Sarnak, la distribution des zéros des fonctions $L$ est prédite par le comportement des valeurs propres de matrices aléatoires. En particulier, le comportement des zéros près du point central révèle le type de symétrie de la famille de fonctions $L$. Une fois la symétrie identifiée, la philosophie de Katz et Sarnak conjecture que plusieurs statistiques associées aux zéros seront modélisées par les valeurs propres de matrices aléatoires du groupe correspondant. Ce mémoire étudiera la distribution des zéros près du point central de la famille des courbes elliptiques sur $\mathbb{Q}[i]$. Brumer a effectué ces calculs en 1992 sur la famille de courbes elliptiques sur $\mathbb{Q}$. Les nouvelles problématiques reliées à la généralisation de ses travaux vers un corps de nombres seront mises en évidence

La distribution des zéros des fonctions L

Selon la philosophie de Katz et Sarnak, la distribution des zéros des fonctions $L$ est prédite par le comportement des valeurs propres de matrices aléatoires. En particulier, le comportement des zéros près du point central révèle le type de symétrie de la famille de fonctions $L$. Une fois la symétrie identifiée, la philosophie de Katz et Sarnak conjecture que plusieurs statistiques associées aux zéros seront modélisées par les valeurs propres de matrices aléatoires du groupe correspondant. Ce mémoire étudiera la distribution des zéros près du point central de la famille des courbes elliptiques sur $\mathbb{Q}[i]$. Brumer a effectué ces calculs en 1992 sur la famille de courbes elliptiques sur $\mathbb{Q}$. Les nouvelles problématiques reliées à la généralisation de ses travaux vers un corps de nombres seront mises en évidence

Improved model of an electric calciner for carbon materials

Teknova have 2D steady-state models of the calciner but wish, in the long term, to have a 3D model that can also cover unsteady conditions, and can can model the loss of axisymmetry that someties occurs. Teknova also wish to understand the processes happening around the tip of the upper electrode, in particular the formation of a lip on it and the the shape of the empty region below it. The Study Group proposed potential models for the degree of graphitization, and for the granular flow. Also the Study Group considered the upper electrode in detail. The proposed model for the lip formation is by sublimation of carbon from the hottest parts of the furnace with redeposition in the region around the electrode, which may stick particles onto the electrode surface. In this model the region below the electrode would be a void, roughly a vertex-down conical cavity. The electric field near the lower rim of the electrode will then have a singularity and so the most intense heating of the charge will be around the rim. We conjecture that the reason why the lower electrode lasts so much longer than the upper is that it is not adjacent to a cavity like this, and therefore does not have a singularity in the field.

Scalar turbulent behavior in the roughness sublayer of an Amazonian forest.

An important current problem in micrometeorology is the characterization of turbulence in the roughness sublayer (RSL), where most of the measurements above tall forests are made. There, scalar turbulent fluctuations display significant departures from the predictions of Monin?Obukhov similarity theory (MOST). In this work, we analyze turbulence data of virtual temperature, carbon dioxide, and water vapor in the RSL above an Amazonian forest (with a canopy height of 40 m), measured at 39.4 and 81.6 m above the ground under unstable conditions. We found that dimensionless statistics related to the rate of dissipation of turbulence kinetic energy (TKE) and the scalar variance display significant departures from MOST as expected, whereas the vertical velocity variance follows MOST much more closely. Much better agreement between the dimensionless statistics with the Obukhov similarity variable, however, was found for the subset of measurements made at a low zenith angle Z, in the range 0°  <  |Z|  <  20°. We conjecture that this improvement is due to the relationship between sunlight incidence and the ?activation?deactivation? of scalar sinks and sources vertically distributed in the forest. Finally, we evaluated the relaxation coefficient of relaxed eddy accumulation: it is also affected by zenith angle, with considerable improvement in the range 0°  <  |Z|  <  20°, and its values fall within the range reported in the literature for the unstable surface layer. In general, our results indicate the possibility of better stability-derived flux estimates for low zenith angle ranges.

Scalar turbulent behavior in the roughness sublayer of an Amazonian forest.

An important current problem in micrometeorology is the characterization of turbulence in the roughness sublayer (RSL), where most of the measurements above tall forests are made. There, scalar turbulent fluctuations display significant departures from the predictions of Monin?Obukhov similarity theory (MOST). In this work, we analyze turbulence data of virtual temperature, carbon dioxide, and water vapor in the RSL above an Amazonian forest (with a canopy height of 40?m), measured at 39.4 and 81.6?m above the ground under unstable conditions. We found that dimensionless statistics related to the rate of dissipation of turbulence kinetic energy (TKE) and the scalar variance display significant departures from MOST as expected, whereas the vertical velocity variance follows MOST much more closely. Much better agreement between the dimensionless statistics with the Obukhov similarity variable, however, was found for the subset of measurements made at a low zenith angle Z, in the range 0°??conjecture that this improvement is due to the relationship between sunlight incidence and the ?activation?deactivation? of scalar sinks and sources vertically distributed in the forest. Finally, we evaluated the relaxation coefficient of relaxed eddy accumulation: it is also affected by zenith angle, with considerable improvement in the range 0°??