Triangular lattice models for pattern formation by hard-core soft-shell particles at interfaces are introduced and studied in order to determine the effect of the shell thickness and structure. In model I, we consider particles with hard-cores covered by shells of cross-linked polymeric chains. In model II, such inner shell is covered by a much softer outer shell. In both models, the hard cores can occupy sites of the triangular lattice, and nearest-neighbor repulsion following from overlapping shells is assumed. The capillary force is represented by the second or the fifth neighbor attraction in model I or II, respectively. Ground states with fixed chemical potential μ or with fixed fraction of occupied sites c are thoroughly studied. For T > 0, the μ(c) isotherms, compressibility and specific heat are calculated by Monte Carlo simulations. In model II, 6 ordered periodic patterns occur in addition to 4 phases found in model I. These additional phases, however, are stable only at the phase coexistence lines at the (μ, T) diagram, which otherwise looks like the diagram of model I. In the canonical ensemble, these 6 phases and interfaces between them appear in model II for large intervals of c and the number of possible patterns is much larger than in model I. We calculated line tensions for different interfaces, and found that the favorable orientation of the interface corresponds to its smoothest shape in both models.

Charge and spin transport in a junction involving two triplet superconductors and a ferromagnetic barrier are studied. We use Bogoliubov–de Gennes wavefunctions to construct the Green’s function, from which we obtain the Josephson currents in terms of the Andreev reflection coefficients. We focus on the consequences of a finite barrier width for the occurrence of 0–π transitions and for the spin currents, and examine the appropriateness of the common δ-function approximation for the tunneling region.