Abstract: We report on the ordering and dynamics of interacting colloidal particles confined by a parabolic potential. By means of Brownian dynamics simulations, we find that by varying the magnitude of the trap stiffness, it is possible to control the dimension of the system and, thus, explore both the structural transitions and the long-time self-diffusion coefficient as a function of the degree of confinement. We particularly study the structural ordering in the directions perpendicular and parallel to the confinement. Further analysis of the local distribution of the first-neighbors layer allows us to identify the different structural phases induced by the parabolic potential. These results are summarized in a structural state diagram that describes the way in which the colloidal suspension undergoes a structural re-ordering while increasing the confinement. To fully understand the particle dynamics, we take into account hydrodynamic interactions between colloids; the parabolic potential constricts the available space for the colloids, but it does not act on the solvent. Our findings show a non-linear behavior of the long-time self-diffusion coefficient that is associated to the structural transitions induced by the external field. (C) 2015 AIP Publishing LLC.

Abstract: In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the ul-component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.