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: ZnO is a wide band-gap (ca. 3.4 eV) semiconductor, piezoelectric, pyroelectric, biocompatible, transparent in the visible spectrum and UV light emitting material. The fabrication in 2001 of the first nanobelts of semiconductor oxide materials lead to a rapid expansion of researches concerning one dimensional nanostructures (nanotubes, nanowires, nanobelts), given their possible application in optics, optoelectronics, piezoelectricity, catalysis. Researches carried on up to date evidenced the possibility to obtain an extraordinary variety of ZnO nanostructures, in function of the experimental parameters and the used growth methods. In this work we present morphostructural results on nanostructured ZnO layers obtained by electrochemical deposition. The films have been grown on gold covered glass plates and Si wafers, in various experimental conditions such as: nature of the wetting agents, electrical polarization of the substrate (continuous, pulsed). The influence of the growth conditions on the crystalline structure and morphology of the films is revealed by scanning and transmission electron microscopy studies. The films show a variety of growth morphologies, from entangled-wires-like to honeycomb-like layers. These large-specific-surface layers will be tested as nanostructured substrates for photovoltaic cells with improved efficiency.