Normalization of bundle holomorphic contractions and applications to dynamics

We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic contractions whose differentials d_0 G_n split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of contraction. Our results are actually stated in the framework of bundle maps. Such sequences of holomorphic contractions appear naturally as iterated inverse branches of endomorphisms of CP(k). In this context, our normalization result allows to precisely estimate the distortions of ellipsoids along typical orbits. As an application, we show how the Lyapunov exponents of the equilibrium measure are approximated in terms of the multipliers of the repulsive cycles.Comment: 29 pages, references added, to appear in Ann. Inst. Fourie

Structural Characterisation of Printable Noble Metal/Poly(Vinyl-­Alcohol) Nanocomposites for Optical Applications

This work was conducted under the aegis of the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom (EP/I004173/1). Amin Abdolvand is an EPSRC Career Acceleration Fellow at the University of Dundee.In order to enable exploitation of noble metal/poly(vinyl-alcohol) nanocomposites for device fabrication, solutions of poly(vinyl-alcohol) suitable for piezo-driven inkjet printing techniques are identified and discussed in terms of their material properties. The printable poly(vinyl-alcohol) medium is then exploited as a host material through the formation of silver or gold nanoparticles in order to create nanocomposites that exhibit a surface plasmon resonance behaviour associated with the small metallic inclusions. To mitigate some of the material redistribution effects associated with the drying of printed droplets containing finely divided materials, the metallic nanoparticles are formed after the printing and drying process is completed, by way of an in-situ reduction of an appropriate metal salt by the poly(vinyl-alcohol)-host matrix itself, which takes place at modest temperatures compatible with most substrate materials. An obvious application for such nanocomposites is in optical elements whereby the surface plasmon resonance associated with the metal is the functional aspect of devices such as sensors or active optical elements. High Resolution Transmission Electron Microscopy was used to examine the dimensions, distribution, morphology and crystal structure of the silver and gold nanoparticles in detail allowing discussion of their suitability for these applications and what further optimisation may be necessary to adequately control their formation.Publisher PDFPeer reviewe

Mechanical tuning of the evaporation rate of liquid on crossed fibers

We investigate experimentally the drying of a small volume of perfectly wetting liquid on two crossed fibers. We characterize the drying dynamics for the three liquid morphologies that are encountered in this geometry: drop, column and a mixed morphology, in which a drop and a column coexist. For each morphology, we rationalize our findings with theoretical models that capture the drying kinetics. We find that the evaporation rate depends significantly on the liquid morphology and that the drying of liquid column is faster than the evaporation of the drop and the mixed morphology for a given liquid volume. Finally, we illustrate that shearing a network of fibers reduces the angle between them, changes the morphology towards the column state, and so enhances the drying rate of a volatile liquid deposited on it