The atomic orbitals of the topological atom

The effective atomic orbitals have been realized in the framework of Bader’s atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure

Discrete transformation for matrix 3-waves problem in three dimensional space

Discrete transformation for 3- waves problem is constructed in explicit form. Generalization of this system on the matrix case in three dimensional space together with corresponding discrete transformation is presented also.Comment: LaTeX, 16 page

Direct observation of melting in a 2-D superconducting vortex lattice

Topological defects such as dislocations and disclinations are predicted to determine the twodimensional (2-D) melting transition. In 2-D superconducting vortex lattices, macroscopic measurements evidence melting close to the transition to the normal state. However, the direct observation at the scale of individual vortices of the melting sequence has never been performed. Here we provide step by step imaging through scanning tunneling spectroscopy of a 2-D system of vortices up to the melting transition in a focused-ion-beam nanodeposited W-based superconducting thin film. We show directly the transition into an isotropic liquid below the superconducting critical temperature. Before that, we find a hexatic phase, characterized by the appearance of free dislocations, and a smectic-like phase, possibly originated through partial disclination unbinding. These results represent a significant step in the understanding of melting of 2-D systems, with impact across several research fields, such as liquid crystal molecules, or lipids in membranes.Comment: Submitted to Nature Physic

Local solvability and turning for the inhomogeneous Muskat problem

In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R^2 or a bounded strip S=RX(-pi/2,pi/2). The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in [5] for the homogenous Muskat problem with infinite depth

Critical current modulation induced by an electric field in superconducting tungsten-carbon nanowires

The critical current of a superconducting nanostructure can be suppressed by applying an electric field in its vicinity. This phenomenon is investigated throughout the fabrication and electrical characterization of superconducting tungsten-carbon (W-C) nanostructures grown by Ga+ focused ion beam induced deposition (FIBID). In a 45 nm-wide, 2.7 mu m-long W-C nanowire, an increasing side-gate voltage is found to progressively reduce the critical current of the device, down to a full suppression of the superconducting state below its critical temperature. This modulation is accounted for by the squeezing of the superconducting current by the electric field within a theoretical model based on the Ginzburg-Landau theory, in agreement with experimental data. Compared to electron beam lithography or sputtering, the single-step FIBID approach provides with enhanced patterning flexibility and yields nanodevices with figures of merit comparable to those retrieved in other superconducting materials, including Ti, Nb, and Al. Exhibiting a higher critical temperature than most of other superconductors, in which this phenomenon has been observed, as well as a reduced critical value of the gate voltage required to fully suppress superconductivity, W-C deposits are strong candidates for the fabrication of nanodevices based on the electric field-induced superconductivity modulation

Olefin Purification and Selective Hydrogenation of Alkynes with Low Loaded Pd Nanoparticle Catalysts

The catalytic performance of Pd-nanoparticle catalysts for the selective hydrogenation of alkynes at mild conditions (150 kPa and 303 K) was evaluated. A Lindlar commercial catalyst was also tested for comparison. The effects of acidity, amount of active sites and dispersion on the catalytic activity and selectivity were studied. At mild conditions, Pd-nanoparticle catalysts were considerably more active and slightly more selective than the Lindlar catalyst. The best synthesized catalyst for the purification of 1-pentene was Pd/Al2O3-Mg (r0 = 41.1 mol gPd–1 min–1, 94% selectivity). The activity and selectivity of Pd/CaCO3 were similar to those of the Lindlar catalyst. The smallest particle sizes (3–4.5 nm) favored the dissociative adsorption of hydrogen over Pd° active sites and a good catalytic behavior. The weaker acid centers (Lewis) of Pd/Al2O3-Mg and Pd/CaCO3 favored higher selectivities to the desired alkene. Pd/Al2O3 was the most active catalyst but also the least selective. This was due to strong acid sites, remnant Bronsted acid sites, which provide extra hydrogen that favors the alkyne hydrogenation rate and also the undesired overhydrogenation of the alkene and/or the isomerization.The financial support provided by UNL (Grants CAI+D 50420150100074LI and 50420150100028LI), CONICET (Grant PIP 11220130100457CO), and ANPCyT (Grant PICT 2016 1453) are acknowledged