We survey a collection of statistical-mechanical problems involving systems inhomogeneous (only) in one spatial direction and seldom discussed by way of a unified treatment. We employ a Landau density functional approach and present the analysis with the help of the equivalent nonlinear...

We study the stability of planar, cylindrical and spherical interfaces with respect to shape and width fluctuations for a model amphiphile solution described by a free energy density functional with square-gradient and square-Laplacian terms. That is, we determine the stability matrix when the...

A prominent feature of the phase behavior of aqueous solutions of nonionic amphiphiles is a phase separation into dilute and concentrated micellar liquids above a lower critical solution temperature Tc. Experiment has revealed a strong asymmetry of the coexistence curve, a high sensitivity of...

We report on a study of the free energy of a spherical interface described by a van der Waals density functional with a squared-Laplacian term. We examine the bulk, the surface tension and the bending rigidity terms, and find the position for the dividing surface that satisfies the Laplace...

We analyze the fluctuating dynamics at the golden-mean transition to chaos in the critical circle map and find that trajectories within the critical attractor consist of infinite sets of power laws mixed together. We elucidate this structure assisted by known renormalization group (RG) results....

The density fluctuations about the equilibrium structure of fluids confined by parallel planar walls are analyzed for the cases of identical and symmetrically opposed fields at the walls. We determine the stability matrix (of the second derivatives of the free energy functional with respect to...

We derive explicit expressions for the stress tensor for general inhomogeneities in a one-component simple fluid in terms of density gradients and moments of the direct correlation function. The expressions follow from the change in grand potential ΔΩV that takes place in a selected portion of...

The long wavelength behavior of the Ornstein-Zernike direct correlation function for nonuniform fluids c(r,r′) has provided important results that comprise our current understanding of fluid interfaces. As we know, the surface tension is obtained from the second moment of c(r,r′), and...

We investigate the properties of the line, say the x-axis, at which two or more interfaces meet, and derive an exact expression for its excess free energy in terms of the gradients of the densities ϱa = ϱa(y,z) and the direct correlation function C(2)ab(|x−x'|; y, y'; z, z'). We evaluate the...

The spinodal decomposition of a simple fluid or binary alloy is studied within the Cahn model of conserved order parameter for a slab geometry generated by competing walls. We restrict our calculations to short-range surface forces and consider parameter values that correspond to both nonwet and...