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.

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

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

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

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

Non-locality and short-range wetting phenomena

We propose a non-local interfacial model for 3D short-range wetting at planar and non-planar walls. The model is characterized by a binding potential \emph{functional} depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tube-like fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories, and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong non-perturbative influence of non-locality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. Let

A symmetric polymer blend confined into a film with antisymmetric surfaces: interplay between wetting behavior and phase diagram

We study the phase behavior of a symmetric binary polymer blend which is confined into a thin film. The film surfaces interact with the monomers via short range potentials. We calculate the phase behavior within the self-consistent field theory of Gaussian chains. Over a wide range of parameters we find strong first order wetting transitions for the semi-infinite system, and the interplay between the wetting/prewetting behavior and the phase diagram in confined geometry is investigated. Antisymmetric boundaries, where one surface attracts the A component with the same strength than the opposite surface attracts the B component, are applied. The phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition. For very thin films or weak surface fields one finds a single critical point at $\phi_c=1/2$. For thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions. Only below a triple point there is a single two phase coexistence region. When we increase the film thickness the two coexistence regions become the prewetting lines of the semi-infinite system, while the triple temperature converges towards the wetting transition temperature from above. The behavior close to the tricritical point, which separates phase diagrams with one and two critical points, is studied in the framework of a Ginzburg-Landau ansatz. Two-dimensional profiles of the interface between the laterally coexisting phases are calculated, and the interfacial and line tensions analyzed. The effect of fluctuations and corrections to the self-consistent field theory are discussed.Comment: Phys.Rev.E in prin

Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach

The phase diagram of the 2D Ising model confined between two infinite walls and subject to opposing surface fields and to a bulk "gravitational" field is calculated by means of density matrix renormalization methods. In absence of gravity two phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores the two phase coexistence up to the bulk critical temperature, in agreement with previous mean-field predictions. We calculate the exponents governing the finite size scaling in the temperature and in the gravitational field directions. The former is the exponent which describes the shift of the critical temperature in capillary condensation. The latter agrees, for large surface fields, with a scaling assumption of Van Leeuwen and Sengers. Magnetization profiles in the two phase and in the single phase region are calculated. The profiles in the single phase region, where an interface is present, agree well with magnetization profiles calculated from a simple solid-on-solid interface hamiltonian.Comment: 4 pages, RevTeX and 4 PostScript figures included. Final version as published. To appear in Phys. Rev. Let

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