Droplet shapes on structured substrates and conformal invariance

We consider the finite-size scaling of equilibrium droplet shapes for fluid adsorption (at bulk two-phase co-existence) on heterogeneous substrates and also in wedge geometries in which only a finite domain $\Lambda_{A}$ of the substrate is completely wet. For three-dimensional systems with short-ranged forces we use renormalization group ideas to establish that both the shape of the droplet height and the height-height correlations can be understood from the conformal invariance of an appropriate operator. This allows us to predict the explicit scaling form of the droplet height for a number of different domain shapes. For systems with long-ranged forces, conformal invariance is not obeyed but the droplet shape is still shown to exhibit strong scaling behaviour. We argue that droplet formation in heterogeneous wedge geometries also shows a number of different scaling regimes depending on the range of the forces. The conformal invariance of the wedge droplet shape for short-ranged forces is shown explicitly.Comment: 20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.

Brane Gas Inflation

We consider the brane gas picture of the early universe. At later stages, when there are no winding modes and the background is free to expand, we show that a moving 3-brane, which we identify with our universe, can inflate even though it is radiation-dominated. The crucial ingredients for successful inflation are the coupling to the dilaton and the equation of state of the bulk. If we suppose the brane initially forms in a collision of higher-dimensional branes, then the spectrum of primordial density fluctuations naturally has a thermal origin.Comment: 4 pages, 1 figur

Coupled Fluctuations near Critical Wetting

Recent work on the complete wetting transition has emphasized the role played by the coupling of fluctuations of the order parameter at the wall and at the depinning fluid interface. Extending this approach to the wetting transition itself we predict a novel crossover effect associated with the decoupling of fluctuations as the temperature is lowered towards the transition temperature T_W. Using this we are able to reanalyse recent Monte-Carlo simulation studies and extract a value \omega(T_W)=0.8 at T_W=0.9T_C in very good agreement with long standing theoretical predictions.Comment: 4 pages, LaTex, 1 postscript figur

Interfacial Structural Changes and Singularities in Non-Planar Geometries

We consider phase coexistence and criticality in a thin-film Ising magnet with opposing surface fields and non-planar (corrugated) walls. We show that the loss of translational invariance has a strong and unexpected non-linear influence on the interface structure and phase diagram. We identify 4 non-thermodynamic singularities where there is a qualitative change in the interface shape. In addition, we establish that at the finite-size critical point, the singularity in the interface shape is characterized by two distint critical exponents in contrast to the planar case (which is characterised by one). Similar effects should be observed for prewetting at a corrugated substrate. Analogy is made with the behaviour of a non-linear forced oscillator showing chaotic dynamics.Comment: 13 pages, 3 figure

Conceptual design of a hybrid Ge:Ga detector array

For potential applications in space infrared astronomy missions such as the Space Infrared Telescope Facility and the Large Deployable Reflector, integrated arrays of long-wavelength detectors are desired. The results of a feasibility study which developed a design for applying integrated array techniques to a long-wavelength (gallium-doped germanium) material to achieve spectral coverage between 30 and 200 microns are presented. An approach which builds up a two-dimensional array by stacking linear detector modules is presented. The spectral response of the Ge:Ga detectors is extended to 200 microns by application of uniaxial stress to the stack of modules. The detectors are assembled with 1 mm spacing between the elements. Multiplexed readout of each module is accomplished with integration sampling of a metal-oxide-semiconductor (MOS) switch chip. Aspects of the overall design, including the anticipated level of particle effects on the array in the space environment, a transparent electrode design for 200 microns response, estimates of optical crosstalk, and mechanical stress design calculations are included

SPIRAL Phase A: A Prototype Integral Field Spectrograph for the AAT

We present details of a prototype fiber feed for use on the Anglo-Australian Telescope (AAT) that uses a dedicated fiber-fed medium/high resolution (R > 10000) visible-band spectrograph to give integral field spectroscopy (IFS) of an extended object. A focal reducer couples light from the telescope to the close-packed lenslet array and fiber feed, allowing the spectrograph be used on other telescopes with the change of a single lens. By considering the properties of the fibers in the design of the spectrograph, an efficient design can be realised, and we present the first scientific results of a prototype spectrograph using a fiber feed with 37 spatial elements, namely the detection of Lithium confirming a brown dwarf candidate and IFS of the supernova remnant SN1987A.Comment: 41 pages, 15 figures, 3 tables; accepted by PAS

The structure of uniform discrete defective crystals

In the continuum context, a uniform crystal has dislocation density tensor constant in space. A simple iteration procedure generates an infinite set of points which is associated with uniform defective crystals. When certain necessary conditions are satisfied, there is a minimum (non-zero) separation of points in this set, so the set is discrete. We describe the structure of such sets explicitly, and show in particular that any such set is either a simple lattice or a 4-lattice