32,184 research outputs found
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
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.
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
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
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