The meccano method for automatic 3-d triangulation and volume parametrization of complex solids

[EN]In this paper we review the novel meccano method. We summarize the main stages (subdivision, mapping, optimization) of this automatic tetrahedral mesh generation technique and we concentrate the study to complex genus-zero solids. In this case, our procedure only requires a surface triangulation of the solid. A crucial consequence of our method is the volume parametrization of the solid to a cube. We construct volume T-meshes for isogeometric analysis by using this result. The efficiency of the proposed technique is shown with several examples. A comparison between the meccano method and standard mesh generation techniques is introduced.-1…

A forgotten little chapter on isoperimetric inequalities. On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

[EN]Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle

Labile Fe(II) concentrations in the Atlantic sector of the Southern Ocean along a transect from the subtropical domain to the Weddell Sea Gyre

[EN]Labile Fe(II) distributions were investigated in the Sub-Tropical South Atlantic and the Southern Ocean during the BONUS-GoodHope cruise from 34 to 57_ S (February? March 2008). Concentrations ranged from below the detection limit (0.009 nM) to values as high 5 as 0.125 nM. In the surface mixed layer, labile Fe(II) concentrations were always higher than the detection limit, with values higher than 0.060nM south of 47_ S, representing between 39% and 63% of dissolved Fe (DFe). Biological production was evidenced. At intermediate depth, local maxima were observed, with the highest values in the Sub-Tropical domain at around 200 m, and represented more than 70% of DFe. Remineralization processes were likely responsible for those sub-surface maxima. Below 1500 m, concentrations were close to or below the detection limit, except at two stations (at the vicinity of the Agulhas ridge and in the north of the Weddell Sea Gyre) where values remained as high as _0.030?0.050 nM. Hydrothermal or sediment inputs may provide Fe(II) to these deep waters. Fe(II) half life times (t1/2) at 4 _C were measured in the upper and deep waters and ranged from 2.9 to 11.3min, and from 10.0 to 72.3 min, respectively. Measured values compared quite well in the upper waters with theoretical values from two published models, but not in the deep waters. This may be due to the lack of knowledge for some parameters in the models and/or to organic complexation of Fe(II) that impact its oxidation rates. This study helped to considerably increase the Fe(II) data set in the Ocean and to better understand the Fe redox cycle.