Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..

A simple strategy for defining polynomial spline spaces over hierarchical T-meses

[EN]We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision scheme. The proposed technique includes some simple rules for inferring local knot vectors to define C 2 -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0- balanced mesh...

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..

Effect of organic exudates of Phaeodactylum tricornutum on the Fe(II) oxidation rate constant

[EN] Fe(II) oxidation kinetics were studied in seawater and in seawater enriched with exudates excreted by Phaeodactylum tricornutum as an organic ligand model. The exudates produced after 2, 4, and 8 days of culture at 6.21 .. 107, 2.29 .. 108, and 4.98 .. 108 cell L?1 were selected. The effects of pH (7.2?8.2), temperature (5?35 ºC), and salinity (10?36.72) on the Fe(II) oxidation rate were studied. All the data were compared with the results for seawater without exudates (control). The Fe(II) rate constant decreased as a function of culture time and cell concentration in the culture at different pH, temperature, and salinity. All the experimental data obtained in this study were fitted to a polynomial function in order to quantify the fractional contribution of the organic exudates from the diatoms to the Fe(II) oxidation rate in natural seawater. Experimental results showed that the organic exudates excreted by P. tricornutum affect Fe(II) oxidation, increasing the lifetime of Fe(II) in seawater. A kinetic model approach was carried out to account for the speciation of each Fe(II) type together with its contribution to the overall rate.