On the continuity of pullback attractors for evolution processes

In this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes. We then revisit results of [D. Li, P.E. Kloeden, Equi-attraction and the continuous dependence of pullback attractors on parameters, Stoch. Dyn. 4 (3) (2004) 373-384] which show that, under certain conditions, continuity is equivalent to uniformity of attraction over a range of parameters (""equi-attraction""): we are able to simplify their proofs and weaken the conditions required for this equivalence to hold. Generalizing a classical autonomous result [A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992] we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting. To apply these results in a more concrete situation we show that a non-autonomous regular perturbation of a gradient-like system produces a family of pullback attractors that are uniformly exponentially attracting: these attractors are therefore continuous, and we can give an explicit bound on the distance between members of this family. (C) 2009 Elsevier Ltd. All rights reserved.

The effects of temperature on the molecular orientation of zinc phthalocyanine films

Phthalocyanine compounds have been widely investigated as candidate materials for technological applications, which is mainly due to their thermal stability and possibility of processing in the form of thin films. In most applications, the controlled growth of thin films with high crystalline quality is essential. In this study, zinc phthalocyanine (ZnPc) thin films were prepared by evaporation on glass and Au-coated glass substrates with subsequent annealing at different temperatures in ambient atmosphere. The morphological and structural features of 80 nm thick zinc phthalocyanine films were investigated, evidencing an alpha -> beta phase transformation after annealing the films at 200 A degrees C, as indicated by UV-Vis spectroscopy and FTIR analyses. A better uniformity of the annealed films was also evidenced via AFM analysis, which may be of importance for applications where film homogeneity and excellent optical quality are required.