The mathematical research of William Parry FRS

In this article we survey the mathematical research of the late William (Bill) Parry, FRS

Correlation function algebra for inhomogeneous fluids

We consider variational (density functional) models of fluids confined in parallel-plate geometries (with walls situated in the planes z=0 and z=L respectively) and focus on the structure of the pair correlation function G(r_1,r_2). We show that for local variational models there exist two non-trivial identities relating both the transverse Fourier transform G(z_\mu, z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2 and z_3. These relations form an algebra which severely restricts the possible form of the function G_0(z_\mu,z_\nu). For the common situations in which the equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an odd or even reflection symmetry in the z=L/2 plane the algebra simplifies considerably and is used to relate the correlation function to the finite-size excess free-energy \gamma(L). We rederive non-trivial scaling expressions for the finite-size contribution to the free-energy at bulk criticality and for systems where large scale interfacial fluctuations are present. Extensions to non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte

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

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

Derivation of a Non-Local Interfacial Hamiltonian for Short-Ranged Wetting II: General Diagrammatic Structure

In our first paper, we showed how a non-local effective Hamiltionian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Green's function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zig-zag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed.Comment: (14 pages, 2 figures) Submitted J. Phys. Condens. Matte

3D wedge filling and 2D random-bond wetting

Fluids adsorbed in 3D wedges are shown to exhibit two types of continuous interfacial unbinding corresponding to critical and tricritical filling respectively. Analytic solution of an effective interfacial model based on the transfer-matrix formalism allows us to obtain the asymptotic probability distribution functions for the interfacial height when criticality and tricriticality are approached. Generalised random walk arguments show that, for systems with short-ranged forces, the critical singularities at these transitions are related to 2D complete and critical wetting with random bond disorder respectively.Comment: 7 pages, 3 figures, accepted for publication in Europhysics Letter

Optimal Extraction of Fibre Optic Spectroscopy

We report an optimal extraction methodology, for the reduction of multi-object fibre spectroscopy data, operating in the regime of tightly packed (and hence significantly overlapping) fibre profiles. The routine minimises crosstalk between adjacent fibres and statistically weights the extraction to reduce noise. As an example of the process we use simulations of the numerous modes of operation of the AAOmega fibre spectrograph and observational data from the SPIRAL Integral Field Unit at the Anglo-Australian Telescope.Comment: Accepted for publication in PAS

Development of uniform and predictable battery materials for nickel cadmium aerospace cells Quarterly report, 8 Aug. - 7 Nov. 1968

Sintering of carbonyl nickel powders for nickel cadmium batteries fabricatio

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