Abstract:
I review a simple method, recently introduced to convert rheological compliance measurements into frequency-dependent moduli. New experimental data are presented, and the scientific implications of various data conversion methods discussed.

Abstract:
The width of the distribution of species in a polydisperse system is employed in a small-variable expansion, to obtain a well-controlled and compact scheme by which to calculate phase equilibria in multi-phase systems. General and universal relations are derived, which determine the partitioning of the fluid components among the phases. The analysis applies to mixtures of arbitrarily many slightly-polydisperse components. An explicit solution is approximated for hard spheres.

Abstract:
A theoretical study of vesicles of topological genus zero is presented. The bilayer membranes forming the vesicles have various degrees of intrinsic (tangent-plane) orientational order, ranging from smectic to hexatic, frustrated by curvature and topology. The field-theoretical model for these `$n$-atic' surfaces has been studied before in the low temperature (mean-field) limit. Work presented here includes the effects of thermal fluctuations. Using the lowest Landau level approximation, the coupling between order and shape is cast in a simple form, facilitating insights into the behaviour of vesicles. The order parameter contains vortices, whose effective interaction potential is found, and renormalized by membrane fluctuations. The shape of the phase space has a counter-intuitive influence on this potential. A criterion is established whereby a vesicle of finite rigidity may be burst by its own in-plane order, and an analogy is drawn with flux exclusion from a type-I superconductor.

Abstract:
A theoretical study of toroidal membranes with various degrees of intrinsic orientational order is presented at mean-field level. The study uses a simple Ginzburg-Landau style free energy functional, which gives rise to a rich variety of physics and reveals some unusual ordered states. The system is found to exhibit many different phases with continuous and first order phase transitions, and phenomena including spontaneous symmetry breaking, ground states with nodes and the formation of vortex-antivortex quartets. Transitions between toroidal phases with different configurations of the order parameter and different aspect ratios are plotted as functions of the thermodynamic parameters. Regions of the phase diagrams in which spherical vesicles form are also shown.

Abstract:
Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behaviour and, for steady shear, gives rise to stress-mediated long-range interactions.

Abstract:
The conditions of multi-phase equilibrium are solved for generic polydisperse systems. The case of multiple polydispersity is treated, where several properties (e.g. size, charge, shape) simultaneously vary from one particle to another. By developing a perturbative expansion in the width of the distribution of constituent species, it is possible to calculate the effects of polydispersity alone, avoiding difficulties associated with the underlying many-body problem. Explicit formulae are derived in detail, for the partitioning of species at coexistence and for the shift of phase boundaries due to polydispersity. `Convective fractionation' is quantified, whereby one property (e.g. charge) is partitioned between phases due to a driving force on another. To demonstrate the ease of use and versatility of the formulae, they are applied to models of a chemically-polydisperse polymer blend, and of fluid-fluid coexistence in polydisperse colloid-polymer mixtures. In each case, the regime of coexistence is shown to be enlarged by polydispersity.

Abstract:
When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is theoretically well founded. Hypothesising ergodicity constrains the transition rates in driven steady states to respect relations analogous to, but different from the equilibrium principle of detailed balance. The constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables. This prevents over-description of the non-equilibrium reservoir, and implies that not all stochastic equations of motion are equally valid. The resulting recipe for transition rates has many features in common with equilibrium statistical mechanics.

Abstract:
We investigate shock formation in an asymmetric exclusion process with creation and annihilation of particles in the bulk. We show how the continuum mean-field equations can be studied analytically and hence derive the phase diagrams of the model. In the large system-size limit direct simulations of the model show that the stationary state is correctly described by the mean-field equations, thus the predicted mean field phase diagrams are expected to be exact. The emergence of shocks and the structure of the phase diagram are discussed. We also analyse the fluctuations of the shock position by using a phenomenological random walk picture of the shock dynamics. The stationary distribution of shock positions is calculated, by virtue of which the numerically determined finite-size scaling behaviour of the shock width is explained.

Abstract:
We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field, they shed light on the local dynamics of an interface. Exact solutions are given for a particular class of order-parameter potentials, and an expandable integral equation is derived for the general case. As well as revealing some generic properties of interfaces moving under condensation or evaporation, the formalism is used to investigate two distinct modes of interface propagation in systems with a metastable potential well. Given a sufficient transient increase in the flux of material onto a condensation nucleus, the normal motion of the interface can be disrupted by interfacial unbinding, leading to growth of a macroscopic amount of a metastable phase.

Abstract:
We examine the geometry of the spaces between particles in diffusion-limited cluster aggregation, a numerical model of aggregating suspensions. Computing the distribution of distances from each point to the nearest particle, we show that it has a scaled form independent of the concentration phi, for both two- (2D) and three-dimensional (3D) model gels at low phi. The mean remoteness is proportional to the density-density correlation length of the gel, xi, allowing a more precise measurement of xi than by other methods. A simple analytical form for the scaled remoteness distribution is developed, highlighting the geometrical information content of the data. We show that the second moment of the distribution gives a useful estimate of the permeability of porous media.