Slow escaping points of quasiregular mappings

This article concerns the iteration of quasiregular mappings on Rd and entire functions on C. It is shown that there are always points at which the iterates of a quasiregular map tend to infinity at a controlled rate. Moreover, an asymptotic rate of escape result is proved that is new even for transcendental entire functions. Let f:Rd→Rd be quasiregular of transcendental type. Using novel methods of proof, we generalise results of Rippon and Stallard in complex dynamics to show that the Julia set of f contains points at which the iterates fn tend to infinity arbitrarily slowly. We also prove that, for any large R, there is a point x with modulus approximately R such that the growth of |fn(x)| is asymptotic to the iterated maximum modulus Mn(R,f)

Boundaries of univalent Baker domains

Let $f$ be a transcendental entire function and let $U$ be a univalent Baker domain of $f$. We prove a new result about the boundary behaviour of conformal maps and use this to show that the non-escaping boundary points of $U$ form a set of harmonic measure zero with respect to $U$. This leads to a new sufficient condition for the escaping set of $f$ to be connected, and also a new general result on Eremenko's conjecture

The iterated minimum modulus and conjectures of Baker and Eremenko

In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape at least as fast as iterates of the minimum modulus, and obtain new results related to Eremenko's conjecture and Baker's conjecture, and the rate of escape in Baker domains. To do this we prove a result of wider interest concerning the existence of points that escape to infinity under the iteration of a positive continuous function

Classifying simply connected wandering domains

While the dynamics of transcendental entire functions in periodic Fatou components and in multiply connected wandering domains are well understood, the dynamics in simply connected wandering domains have so far eluded classification. We give a detailed classification of the dynamics in such wandering domains in terms of the hyperbolic distances between iterates and also in terms of the behaviour of orbits in relation to the boundaries of the wandering domains. In establishing these classifications, we obtain new results of wider interest concerning non-autonomous forward dynamical systems of holomorphic self maps of the unit disk. We also develop a new general technique for constructing examples of bounded, simply connected wandering domains with prescribed internal dynamics, and a criterion to ensure that the resulting boundaries are Jordan curves. Using this technique, based on approximation theory, we show that all of the nine possible types of simply connected wandering domain resulting from our classifications are indeed realizable

Effects of atmospheric pressure plasma on dye uptake by the surface of wool

A woven pure wool fabric has been exposed to atmospheric pressure plasma for 30 seconds using a pilot-scale. commercial machine. X-ray photoelectron spectral data revealed large increases in oxygen and nitrogen. and a large reduction in carbon. on the surfaces of the plasma-treated fibres. A CIN ratio of 3.55 for plasma-treated wool was consistent with removal of the covalently-bound fatty acids from the surface of the cuticle cells. resulting in exposure of the proteinaceous epicuticle. Dye staining experiments revealed that the back of the fabric had received the same, uniform level of treatment as the face, despite the fact that only the face had been directly exposed to the plasma. Dyes (1 % oww) were applied to fabric at 50&deg;C (liquor ratio =40: 1) and pH values from 3 to 6. The relatively low temperature of 50&deg;C was selected in order to accentuate the effects of plasma on the rate of dye uptake. Under these conditions, dye was adsOibed onto the fibre surfaces, with very little penetration into the fibres. Effects of the plasma treatment on the rate of dyes adsorption were dyespecific. No significant effects of plasma on the rate of dye uptake were observed with relatively hydrophobic dyes, but hydrophilic dyes were adsorbed more rapidly by the plasmatreated fabric. It would appear that for more hydrophobic dyes, hydrophobic effects are more important for the adsorption of dyes by the plasma-treated fibres, even though these fibres were quite hydrophilic. On the other hand. it is concluded that for more hydrophilic dyes, electrostatic effects are more important for adsorption by the plasma-treated fibre.<br /

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997 4. TKK Engineering\u27s Catchment (Williams)

High water use vegetation systems for salinity control were trialed on a 70 ha catchment located about 15 km north of Williams, Western Australia. The catchment receives about 545 mm annual rainfall and 1870 mm annual evaporation. Development of salinity is characterised by passive discharge upslope from a dolerite dyke. Because recharge exceeds the discharge capacity of current seeps, there is potential for new seeps to develop in the mid to lower slopes

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997 1. Wooldridge/Wright\u27s Catchment (Kojonup)

High water use vegetation systems for salinity control were trialed on a 170 ha catchment located 13 km north of Kojonup, Western Australia. The catchment receives about 470 mm annual rainfall and 1825 mm annual evaporation

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997 5 White/Beattys\u27 Catchment (Dinninup)

High water use vegetation systems for salinity control were trialed on a 250 ha catchment located three km north-west of Dinninup, Western Australia. The catchment receives about 620 mm annual rainfall and 1500 mm annual evaporation. The catchment is characterised by slopes with gradients in excess of 5%, deep weathering (15-25 m to bedrock), active seepage in the valley (piezometric heads 204 m above ground surface) and high recharge (water table fluctuations of 1-4 m)