RESUMEN
The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier-Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical, i.e., there is a 'scaling gap' between what can be established by mathematical analysis and what is needed to rule out a singularity. A recently introduced mathematical framework-based on a suitably defined 'scale of sparseness' of the regions of intense vorticity-brought the first scaling reduction of the NS super-criticality since the 1960s. Here, we put this framework to the first numerical test using a spatially highly resolved computational simulation performed near a 'burst' of the vorticity magnitude. The results confirm that the scale is well suited to detect the onset of dissipation and provide numerical evidence that ongoing mathematical efforts may succeed in closing the scaling gap.
RESUMEN
The bis tetrabutylammonium salt of the solar cell dye, L(2)Ru(NCS)(2), ((Bu(4)N(+))(2) [Ru(dcbpyH)(2)(NCS)(2)](2-)), was oxidized electrochemically in both dimethylformamide and acetonitrile. Four different ruthenium complexes were identified by LC-UV/Vis-MS during the electrochemical oxidation process in dimethylformamide. The formation of the four complexes may be explained by a competition between a solvent-independent route with the formation of the intermediate complex L(2)Ru(NCS)(CN) and the final oxidation product L(2)Ru(CN)(2) and a solvent-dependent route, which proceeds through the intermediate complex L(2)Ru(NCS)(DMF)(+) to the final product L(2)Ru(CN)(DMF)(+). In acetonitrile the solvent-dependent mechanism is dominant and only the oxidation products L(2)Ru(NCS)(ACN)(+) and L(2)Ru(CN)(ACN)(+) were identified.