Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

Development of Electrochromic Devices

Electrochromic devices (ECD) are systems of considerable commercial interest due to their controllable transmission, absorption and/or reflectance. For instance, these devices are mainly applied to glare attenuation in automobile rearview mirrors and also in some smart windows that can regulate the solar gains of buildings. Other possible applications of ECDs include solar cells, small-and large-area flat panel displays, frozen food monitoring and document authentication also are of great interest. Over the past 20 years almost 1000 patents and 1500 papers in journals and proceedings have been published with the keyword ""electrochromic windows"". Most of these documents report on materials for electrochromic devices and only some of them about complete systems. This paper describes the first patents and some of the recent ones on ECDs, whose development is possible due to the advances in nanotechnology.

TLC Separation and Identification of the Essential Oil Constituents from Aloysia gratissima

The present work had as objective the isolation of the five compounds by thin-layer Chromatography (TLC) from the essential oil of the Aloysia gratissima. For this, a number of systems of eluents were used for its separation, indicating that through the system acetone/hexane in proportions (v/v) 1:30 it was possible to isolate guaiol, elemol, pinocanphone (trans-3-pinanone), cis-pinocarvyl, and acorenone. The isolation of the compound acorenone from the other compounds was possible with the mixture of solvents hexane/dichloromethane in proportions (v/v) (1:1,3).