Abstract: We introduce a differential geometry description of the path lines, stream lines and particles contours in hydrodynamics. We present a generalized form of a Korteweg-de Vries type of equation for the exterior of a circle. Nonlinearities from the boundary conditions, surface tension and the Euler equations are taken into account, but the flow is considered inviscid and irrotational. For the circular case we describe the traveling waves shapes, solitons and the particles trajectories.

Abstract: This study presents first-principles results on the electronic functionalization of silicene and germanene monolayers by means of chemisorption of adatom species H, Li, F, Sc, Ti, V. Three general adatom-monolayer configurations are considered, each having its distinct effect on the electronic structure, yielding metallic or semiconducting dispersions depending on the adatom species and configuration. The induced bandgap is a (in)direct F gap ranging from 0.2 to 2.3 eV for both silicene and germanene. In general the alternating configuration was found to be the most energetically stable. The boatlike and chairlike conformers are degenerate with the former having anisotropic effective carrier masses. The top configuration leads to the planar monolayer and predominately to a gapped dispersion. The hollow configuration with V adatoms retains the Dirac cone, but with strong orbital planar hybridization at the Fermi level. We also observe a planar surface state the Fermi level for the latter systems. (C) 2013 Elsevier B.V. All rights reserved.

Abstract: The electronic and vibrational properties of 2D honeycomb structures of molybdenum disulfide (MoS2) subjected to strain have been investigated using first-principles calculations based on density functional theory. We have studied the evolution of the electronic properties of bulk and layered MoS2, going down from a few layers up to a mono-layer, and next investigated the effect of bi-axial strain on their electronic structure and vibrational frequencies. Both for tensile and compressive biaxial strains, the shrinking of the energy band-gap of MoS2 with increasing level of applied strain is observed and a transition limit of the system from semiconducting to metallic is predicted to occur for strains in the range of 8-10%. We also found a progressive downshift (upshift) of both the E-2g(1) and A(1g) Raman active modes with increasing level of applied tensile (compressive) strain. Interestingly, significant changes in the curvature of the conduction and valence band near their extrema upon the application of strain are also predicted, with correlated variations of the electron and hole effective masses. These changes present interesting possibilities for engineering the electronic properties of 2D structures of MoS2. (C) 2012 Elsevier B.V. All rights reserved.

Abstract: Magnetoelectric multiferroics showing coupling between polarization and magnetic order are attracting much attention. For instance, they could be used in memory devices. Metal-transition oxides are provided several examples of inorganic magnetoelectric multiferroics. In the present short review, spinel and delafossite chromites are described. For the former, an electric polarization is evidenced in the ferrimagnetic state for ACr2O4 polycrystalline samples (A=Ni, Fe, Co). The presence of a JahnTeller cation such as Ni2+ at the A site is shown to yield larger polarization values. In the delafossites, substitution by V3+ at the Cr or Fe site in CuCrO2 (CuFeO2) suppresses the complex antiferromagnetic structure at the benefit of a spin glass state. The presence of cation disorder, probed by transmission electron microscopy, favors relaxor-like ferroelectricity. The results on the ferroelectricity of ferrimagnets and insulating spin glasses demonstrate that, in this research field, transition-metal oxides are worth to be studied.