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

Physical education as Olympic education

Introduction In a recent paper (Parry, 1998, p. 64), I argued that the justification of PE activities lies in their capacity to facilitate the development of certain human excellences of a valued kind. Of course, the problem now lies in specifying those ‘human excellences of a valued kind’, and (for anyone) this task leads us into the area of philosophical anthropology. I suggested that the way forward for Physical Education lies in the philosophical anthropology (and the ethical ideals) of Olympism, which provide a specification of a variety of human values and excellences which: •have been attractive to human groups over an impressive span of time and space •have contributed massively to our historically developed conceptions of ourselves •have helped to develop a range of artistic and cultural conceptions that have defined Western culture. •have produced a range of physical activities that have been found universally satisfying and challenging. Although physical activities are widely considered to be pleasurable, their likelihood of gaining wide acceptance lies rather in their intrinsic value, which transcends the simply hedonic or relative good. Their ability to furnish us with pleasurable experiences depends upon our prior recognition in them of opportunities for the development and expression of valued human excellences. They are widely considered to be such opportunities for the expression of valued human excellences because, even when as local instantiations, their object is to challenge our common human propensities and abilities. I claimed that Olympic ideals may be seen not merely as inert ‘ideals’, but living ideas which have the power to remake our notions of sport in education, seeing sport not as mere physical activity but as the cultural and developmental activity of an aspiring, achieving, well-balanced, educated and ethical individual. This paper seeks to make good that claim by trying to develop a case for Physical Education as Olympic Education. I begin by setting out various accounts and conceptions of the Olympic Idea; then I suggest a unifying and organising account of the philosophical anthropology of Olympism; and this is followed by the practical application of that account in two examples of current ethical issues. Finally, I seek to present an account of Physical Education as Olympic Education

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.

Corner wetting in a far-from-equilibrium magnetic growth model

The irreversible growth of magnetic films is studied in three-dimensional confined geometries of size $L\times L\times M$, where $M\gg L$ is the growing direction. Competing surface magnetic fields, applied to opposite corners of the growing system, lead to the observation of a localization-delocalization (weakly rounded) transition of the interface between domains of up and down spins on the planes transverse to the growing direction. This effective transition is the precursor of a true far-from-equilibrium corner wetting transition that takes place in the thermodynamic limit. The phenomenon is characterized quantitatively by drawing a magnetic field-temperature phase diagram, firstly for a confined sample of finite size, and then by extrapolating results, obtained with samples of different size, to the thermodynamic limit. The results of this work are a nonequilibrium realization of analogous phenomena recently investigated in equilibrium systems, such as corner wetting transitions in the Ising model.Comment: 14 pages, 8 figures. EPJ styl

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

Zenithal bistability in a nematic liquid crystal device with a monostable surface condition

The ground-state director configurations in a grating-aligned, zenithally bistable nematic device are calculated in two dimensions using a Q tensor approach. The director profiles generated are well described by a one-dimensional variation of the director across the width of the device, with the distorted region near the grating replaced by an effective surface anchoring energy. This work shows that device bistability can in fact be achieved by using a monostable surface term in the one-dimensional model. This implies that is should be possible to construct a device showing zenithal bistability without the need for a micropatterned surface

A Lightweight Loudspeaker for Aircraft Communications and Active Noise Control

A series of new, lightweight loudspeakers for use on commercial aircraft has been developed. The loudspeakers use NdFeB magnets and aluminum alloy frames to reduce the weight. The NdFeB magnet is virtually encapsulated by steel in the new speaker designs. Active noise reduction using internal loudspeakers was demonstrated to be effective in 1983. A weight, space, and cost efficient method for creating the active sound attenuating fields is to use the existing cabin loudspeakers for both communication and sound attenuation. This will require some additional loudspeaker design considerations

Fluid adsorption near an apex: Covariance between complete and critical wetting

Critical wetting is an elusive phenomenon for solid-fluid interfaces. Using interfacial models we show that the diverging length scales, which characterize complete wetting at an apex, precisely mimic critical wetting with the apex angle behaving as the contact angle. Transfer matrix, renormalization group (RG) and mean field analysis (MF) shows this covariance is obeyed in 2D, 3D and for long and short ranged forces. This connection should be experimentally accesible and provides a means of checking theoretical predictions for critical wetting.Comment: 4 pages, 1 figure, submitted to Physical Review Letter

Local functional models of critical correlations in thin-films

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin-films with symmetric surface fields in arbitrary dimension d. In d=2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths as well as the detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin-film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let