Relative periodic orbits in point vortex systems

We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is applied to point vortices systems on a sphere and on the plane, but works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method permits also to determine some relative equilibria and heteroclinic cycles connecting these relative equilibria.Comment: 27 pages, 17 figure

Chirplet approximation of band-limited, real signals made easy

In this paper we present algorithms for approximating real band-limited signals by multiple Gaussian Chirps. These algorithms do not rely on matching pursuit ideas. They are hierarchial and, at each stage, the number of terms in a given approximation depends only on the number of positive-valued maxima and negative-valued minima of a signed amplitude function characterizing part of the signal. Like the algorithms used in \cite{gre2} and unlike previous methods, our chirplet approximations require neither a complete dictionary of chirps nor complicated multi-dimensional searches to obtain suitable choices of chirp parameters

Tight-binding molecular-dynamics studies of defects and disorder in covalently-bonded materials

Tight-binding (TB) molecular dynamics (MD) has emerged as a powerful method for investigating the atomic-scale structure of materials --- in particular the interplay between structural and electronic properties --- bridging the gap between empirical methods which, while fast and efficient, lack transferability, and ab initio approaches which, because of excessive computational workload, suffer from limitations in size and run times. In this short review article, we examine several recent applications of TBMD in the area of defects in covalently-bonded semiconductors and the amorphous phases of these materials.Comment: Invited review article for Comput. Mater. Sci. (38 pages incl. 18 fig.

Island morphology and adatom self-diffusion on Pt(111)

The results of a density-functional-theory study of the formation energies of (100)- and (111)-faceted steps on the Pt(111) surface, as well as of the barrier for diffusion of an adatom on the flat surface, are presented. The step formation energies are found to be in a ratio of 0.88 in favour of the (111)-faceted step, in excellent agreement with experiment; the equilibrium shape of islands should therefore clearly be non-hexagonal. The origin of the difference between the two steps is discussed in terms of the release of stress at the surface through relaxation. For the diffusion barrier, we also find relaxation to be important, leading to a 20% decrease of its energy. The value we obtain, 0.33 eV, however remains higher than available experimental data; possible reasons for this discrepancy are discussed. We find the ratio of step formation energies and the diffusion barrier to be the same whether using the local-density approximation or the generalized-gradient approximation for the exchange-and-correlation energy.Comment: Submitted to Physical Review B; 11 postscript pages including 4 figures; this and related publications available from web sites at http://www.centrcn.umontreal.ca/~lewis and http://www.fhi-berlin.mpg.de/th/th.htm