Landau density functional theory for one-dimensional inhomogeneities

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 dynamical system. The different possible behaviors are visualized in terms of orbits in the corresponding phase portraits. We focus on some exceptional features of inhomogeneous sytems, like the scaling of the order parameter profiles near criticality.