An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Variations in Structure Explain the Viscometric Behavior of AOT Microemulsions at Low Water/AOT Molar Ratios

The viscosity of AOT/water/decane water-in-oil microemulsions exhibits a well-known maximum as a function of water/AOT molar ratio, which is usually attributed to increased attractions among nearly spherical droplets. The maximum can be removed by adding salt or by changing the oil to CCl4. Systematic small-angle X-ray scattering (SAXS) measurements have been used to monitor the structure of the microemulsion droplets in the composition regime where the maximum appears. On increasing the droplet concentration, the scattering intensity is found to scale with the inverse of the wavevector, a behavior which is consistent with cylindrical structures. The inverse wavevector scaling is not observed when the molar ratio is changed, moving the system away from the value corresponding to the viscosity maximum. It is also not present in the scattering from systems containing enough added salt to essentially eliminate the viscosity maximum. An asymptotic analysis of the SAXS data, complemented by some quantitative modeling, is consistent with cylindrical growth of droplets as their concentration is increased. Such elongated structures are familiar from related AOT systems in which the sodium counterion has been exchanged for a divalent one. However, the results of this study suggest that the formation of non-spherical aggregates at low molar ratios is an intrinsic property of AOT.

Using AMS combined with mineral shape preferred orientation analysis to understand the emplacement fabrics of the Apiai gabbro-norite (Ribeira Belt, SE Brazil)

The Apiai gabbro-norite is a massive fine-grained Neoproterozoic intrusion emplaced in a core of synformal structure that deforms low-grade marine metasedimentary rocks of the Ribeira Belt of south-eastern Brazil. The lack of visible magmatic layering or any internal fabric has been a major limitation in deciding whether the emplacement occurred before or after the regional folding. To assist in the tectonic interpretations, we combine low-field anisotropy of magnetic susceptibility (AMS) and silicate shape preferred orientation (SPO) to reveal the internal structure of the mafic intrusion. Magnetic data indicate a mean susceptibility of about 10(-2) SI and a mean anisotropy degree (P) of about 1.08, essentially yielded by titanomagnetite. The magnetic and silicate foliations for P >= 1.10 are parallel to each other, while the lineations tend to scatter on the foliation plane, in agreement with the dominant oblate symmetry of the AMS and SPO ellipsoids. For lower P values, the magnetic and silicate fabrics vary from coaxial to oblique, and for P <= 1.05, their shapes and orientations can be quite distinct. The crystal size distribution (CSD) of plagioclase for P > 1.05 is log linear, in agreement with a bulk simple crystallisation history. These results combined show that for a strong SPO, corresponding to a magnetic anisotropy above 1.10, AMS is a reliable indicator of the magmatic fabric. They indicate that the Apiai gabbro-norite consists of sill-like body that was inclined gently to the north by the regional folding.

Figures of equilibrium for tidally deformed non-homogeneous celestial bodies

Abstract (2,250 Maximum Characters): Several theories of tidal evolution, since the theory developed by Darwin in the XIX century, are based on the figure of equilibrium of the tidally deformed body. Frequently the adopted figure is a Jeans prolate spheroid. In some case, however, the rotation is important and Roche ellipsoids are used. The main limitations of these models are (a) they refer to homogeneous bodies; (b) the rotation axis is perpendicular to the plane of the orbit. This communication aims at presenting several results in which these hypotheses are not done. In what concerns the non-homogeneity, the presented results concerns initially bodies formed by N homogeneous layers and we study the non sphericity of each layer and relate them to the density distribution. The result is similar to the Clairaut figure of equilibrium, often used in planetary sciences, but taking into full account the tidal deformation. The case of the rotation axis non perpendicular to the orbital plane is much more complex and the study has been restricted for the moment to the case of homogeneous bodies.