An estimate on the fractal dimension of attractors of gradient-like dynamical systems

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A*) is an attractor-repeller pair for the attractor A of a semigroup {T(t) : t >= 0}, then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A*, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved.

Photoconduction action spectra of regio-regular poly(3-hexylthiopene):TiO2 diodes

The development of polymer-based photovoltaic devices brings the promise of low-cost and lightweight solar energy conversion systems. This technology requires new materials and device architectures with enhanced efficiency and lifetime, which depends on the understanding of charge-transport mechanisms. Organic films combined with electronegative nanoparticles may form systems with efficient dissociation of the photogenerated excitons, thus increasing the number of carriers to be collected by the electrodes. In this paper we investigate the steady-state photoconductive action spectra of devices formed by a bilayer of regio-regular poly(3-hexylthiophene) (RRP3HT) and TiO2 sandwiched between ITO and aluminum electrodes (ITO/TiO2:RRP3HT/Al). Photocurrents were measured for distinct bias voltages with illumination from either side of the device. Heterojunction structures were prepared by spin coating a RRP3HT film on an already deposited TiO2 layer on ITO. Symbatic and antibatic curves were obtained and a model for photocurrent action spectra was able to fit the symbatic responses. The quantum yield increased with the electric field, indicating that exciton dissociation is a field-assisted process as in an Onsager mechanism. Furthermore, the quantum yield was significantly higher when illumination was carried out through the ITO electrode onto which the TiO2 layer was deposited, as the highly electronegative TiO2 nanoparticles were efficient in exciton dissociation.

Stability and dynamics of terrestrial planets in binary star systems: application on Alpha Centauri

Binary stars are frequent in the universe, with about 50% of the known main sequence stars being located at a multiple star system (Abt, 1979). Even though, they are universally thought as second rate sites for the location of exo-planets and the habitable zone, due to the difficulties of detection and high perturbation that could prevent planet formation and long term stability. In this work we show that planets in binary star systems can have regular orbits and remain on the habitable zone. We introduce a stability criterium based on the solution of the restricted three body problem and apply it to describe the short period planar and three-dimentional stability zones of S-type orbits around each star of the Alpha Centauri system. We develop as well a semi-analytical secular model to study the long term dynamics of fictional planets in the habitable zone of those stars and we verify that planets on the habitable zone would be in regular orbits with any eccentricity and with inclination to the binary orbital plane up until 35 degrees. We show as well that the short period oscillations on the semi-major axis is 100 times greater than the Earth's, but at all the time the planet would still be found inside the Habitable zone.