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...

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)...

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...

Recently, in [Phys. Rev. Lett. 95 (2005) 140601], Grassberger addresses the interesting issue of the applicability of q-statistics to the renowned Feigenbaum attractor. He concludes there is no genuine connection between the dynamics at the critical attractor and the generalized statistics and...

A random-walk formalism is applied to some general Ornstein-Zernike lattice systems to obtain information as to the asymptotic form of the total correlation function. Calculations in terms of the Percus-Yevick approximation are then presented for certain lattice gases with interactions extending...

The random-walk formalism that describes correlation functions in a homogenous system is here extended to cover correlations in ordered phases of a lattice gas. The general method is illustrated by application to certain lattice gases on linear, square and honeycomb lattices, treated under the...

An exact non-equilibrium Ornstein-Zernike (OZ) equation is derived for lattice fluid systems whose time development is given by a generalized master equation. The derivation is based on a generalization of the Montroll-Weiss continuous-time random walk on a lattice, and on their relationship...

As a step towards a random-process formulation for classical fluids which ivolve many-body correlations, a random-walk formulation is presented wherein, for both lattice-gas and continuum models, the Green function and weight function describing the random walk are related to the total...