We review the general properties of non-linear systems and show the basic techniques, used universally, to study the symmetry breaking and bifurcation properties. We exemplify these characteristics by using a Turing system that is general enough as to present many of the universal features of...

A comprehensive description of interfaces containing amphiphiles has been developed through the use of a free energy density functional with squared-gradient and squared-Laplacian terms. This elemental model functional contains the basic ingredients for the problem, it is technically tractable...

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...

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 analyze in mean-field approximation the liquid–liquid interfacial properties of a micellar solution model designed to describe amphiphiles in polar solvents. Under specific conditions the amphiphile concentration profiles become non-monotonous and entail enhanced interfacial adsorption. We...

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...

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...

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 derivation from first principles of the elastic curvature free energy, or Helfrich free energy, of a nonplanar interface demands a detailed cross-examination and call in question of the statistical-mechanical basis of the theory of nonplamar interfaces. Here we give an account that (i)...

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...