Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions

We consider a system of three surfaces, graphs over a bounded domain in ?², intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to 2π/3.) For the corresponding two-dimensional parabolic free boundary problem we prove short-time existence of classical solutions (in parabolic Hölder spaces), for sufficiently regular initial data satisfying a compatibility condition.     

Mass-Capacity Inequalities for Conformally Flat Manifolds with Boundary

In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, capacity and Aleksandrov-Fenchel inequalities for mean-convex Euclidean domains are obtained. For each inequality, the case of equality is characterized.     

Divergence symmetries of critical Kohn-Laplace equations on Heisenberg groups

We show that every Lie point symmetry of semilinear Kohn-Laplace equations with a power-law nonlinearity on the Heisenberg group H ¹ is a divergence symmetry if and only if the corresponding exponent takes a critical value.     

Stern-Brocot trees in the periodicity of mixed-mode oscillations

We investigate the distribution of mixed-mode oscillations in the control parameter space for two paradigmatic chemical models: a three-variable fourteen-parameter model of the Belousov-Zhabotinsky reaction and a three-variable four-parameter autocatalator. For both systems, several high-resolution phase diagrams show that the number of spikes of their mixed-mode oscillations emerges consistently organized in a surprising and unexpected symmetrical way, forming Stern-Brocot trees. The Stern-Brocot tree is more general and contains the Farey tree as a subtree. We conjecture the Stern-Brocot hierarchical organization to be the archetypal skeleton underlying several systems displaying mixed-mode oscillations.     

Tuning of the excitation wavelength from UV to visible region in Eu(3+)-β-diketonate complexes: comparison of theoretical and experimental photophysical properties

A novel class of efficient visible light sensitized antenna complexes of Eu(3+) based on the use of a series of highly conjugated β-diketonates, namely, 1-(1-phenyl)-3-(2-fluoryl) propanedione, 1-(2-naphthyl)-3-(2-fluoryl)propanedione, 1-(4-biphenyl)-3-(2-fluoryl) propanedione, and 2,2'-bis(di-p-tolylphosphino)-1,1'-binaphthyl oxide as an ancillary ligand has been designed, synthesized, characterized and their photophysical properties investigated. The coordination geometries of the typical Eu(3+) complexes were calculated using the Sparkle/PM3 model. Photophysical properties of europium complexes benefit from adequate protection of the metal by the rigid phosphine oxide ligand against non-radiative deactivation and efficient ligand-to-metal energy transfer exceeding 50% as compared to precursor samples. The replacement of the phenyl group with the naphthyl or biphenyl groups in the 3-position of the fluoryl based β-diketonate ligand remarkably extends the excitation window of the corresponding Eu(3+) complexes towards the visible region (up to 500 nm). The highly conjugated β-diketonate ligands sensitize efficiently the luminescence of Eu(3+) ions with quantum yields ranging from 19 to 43 % in the solid state, which is among the highest reported for a visible sensitized Eu(3+)complex. The theoretical quantum efficiencies from the Sparkle/PM3 structures are in good agreement with the experimental values, clearly attesting to the efficacy of the theoretical models.     

Thermophysical properties of pure and water-saturated tetradecyltrihexylphosphonium-based ionic liquids

In this work, the solubility of water in several tetradecyltrihexylphosphonium-based ionic liquids at 298.15 K, and densities and viscosities of both pure and water-saturated ionic liquids in a broad temperature range were measured. The selected ionic liquids comprise the common tetradecyltrihexylphosphonium cation combined with the following anions: bromide, chloride, bis(trifluoromethylsulfonyl)imide, decanoate, methanesulfonate, dicyanamide and bis(2,4,4-trimethylpentyl)phosphinate. The isobaric thermal expansion coefficients for pure and water-saturated ionic liquids were determined based on the density dependence with temperature. Taking into account that the excess molar volumes of the current hydrophobic water-saturated ionic liquids are negligible, the solubility of water was additionally estimated from the gathered density data and compared with the experimental solubilities obtained. Moreover, the experimental densities were compared with those predicted by the Gardas and Coutinho model while viscosity data were correlated using the Vogel–Tammann–Fulcher method.     

Structural, optoelectronic, infrared and Raman spectra of orthorhombic SrSnO3 from DFT calculations

Orthorhombic SrSnO₃ was investigated using density functional theory (DFT) considering both the local density and generalized gradient approximations, LDA and GGA, respectively. The electronic band structure, density of states, complex dielectric function, optical absorption, and the infrared and Raman spectra were computed. Calculated lattice parameters are close to the experimental measurements, and an indirect band gap (2.27 eV) was obtained within the GGA (LDA) level of calculation. Effective masses for holes and electrons were estimated, being very anisotropic in comparison with similar results for orthorhombic CaSnO₃. The complex dielectric function and the optical absorption of SrSnO₃ were shown to be sensitive to the plane of polarization of the incident light. The infrared spectrum between 100 and 600 cm⁻¹ was obtained, with its main peaks being assigned, and a nice agreement between experimental and theoretical peaks of the Raman spectrum of orthorhombic SrSnO₃ was achieved.     

A DFT quantum mechanical study of 3-hydroxy-4-pyrone and 3-hydroxy-4-pyridinone based oxidovanadium(IV) complexes

Oxidovanadium(IV) complexes have revealed interesting pharmacological properties which make them promising agents in the treatment of diabetes mellitus. A computational study of 17 complexes of oxidovanadium(IV) with 3-hydroxy-4-pyrone- and 3-hydroxy-4-pyridinone-based ligands was carried out at the density functional theory level. The geometry, electronic structure, and vibration modes at the metallic center were predicted, and their dependence on the nature of the ligand was evaluated. Slight distinctions between both classes of compounds were observed, namely the higher value of dipole moments and the smaller HOMO–LUMO energy gap for the 3-hydroxy-4-pyridinone-based complexes. The modes of vibration at the metallic coordination region do not vary significantly throughout the whole series, and a particular corrective scaling factor is proposed for the V=O stretching mode of this type of oxidovanadium(IV) complexes. The results presented here are of particular relevance since it was not yet possible to obtain X-ray diffraction data for the oxidovanadium(IV) complexes of 3-hydroxy-4-pyridinones, and also as the influence of the solvent, in particular the local interaction at the sixth coordination position, was considered.     

Pseudo-molecular approach for the elastic constants of nematic liquid crystals interacting via anisotropic dispersion forces

The bulk and the surface-like elastic constants of a nematic liquid crystal are calculated for an ensemble of particles interacting via anisotropic dispersion forces using the pseudo-molecular method. The geometrical anisotropy of the molecules is also taken into account in the calculations by choosing a molecular volume of ellipsoidal shape. Analytical expressions for the elastic constants are obtained as a function of the eccentricity in the molecular volume shape. The method allows one to explore the dependence on the molecular orientation with respect to the intermolecular vector by analyzing the magnitude and the behaviour of macroscopic elastic parameters defining the nematic phase.