306 research outputs found
Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph
Traffic grooming is a major issue in optical networks. It refers to grouping
low rate signals into higher speed streams, in order to reduce the equipment
cost. In SONET WDM networks, this cost is mostly given by the number of
electronic terminations, namely ADMs. We consider the case when the topology is
a unidirectional ring. In graph-theoretical terms, the traffic grooming problem
in this case consists in partitioning the edges of a request graph into
subgraphs with a maximum number of edges, while minimizing the total number of
vertices of the decomposition. We consider the case when the request graph has
bounded maximum degree , and our aim is to design a network being able
to support any request graph satisfying the degree constraints. The existing
theoretical models in the literature are much more rigid, and do not allow such
adaptability. We formalize the problem, and solve the cases (for all
values of ) and (except the case C=4). We also provide lower
and upper bounds for the general case
Equilibrium crystal shapes in the Potts model
The three-dimensional -state Potts model, forced into coexistence by
fixing the density of one state, is studied for , 3, 4, and 6. As a
function of temperature and number of states, we studied the resulting
equilibrium droplet shapes. A theoretical discussion is given of the interface
properties at large values of . We found a roughening transition for each of
the numbers of states we studied, at temperatures that decrease with increasing
, but increase when measured as a fraction of the melting temperature. We
also found equilibrium shapes closely approaching a sphere near the melting
point, even though the three-dimensional Potts model with three or more states
does not have a phase transition with a diverging length scale at the melting
point.Comment: 6 pages, 3 figures, submitted to PR
Vicinal silicon surfaces: from step density wave to faceting
This paper investigates faceting mechanisms induced by electromigration in
the regime where atomic steps are transparent. For this purpose we study
several vicinal orientations by means of in-situ (optical diffraction,
electronic microscopy) as well as ex-situ (AFM, microprofilometry)
visualization techniques. The data show that faceting proceeds in two stages.
The first stage is short and leads to the appearance of a step density wave,
with a wavelength roughly independent of the surface orientation. The second
stage is much slower, and leads to the formation of a hill-and-valley
structure, the period of which depends on the initial surface orientation. A
simple continuum model enables us to point out why the wavelength of the step
density wave does not depend on the microscale details of the surface. The
final wavelength is controlled by the competition between elastic step-step
interaction and facet edge energy cost. Finally, the surface stress angular
dependence is shown to emerge as a coarsed-grained picture from the step model.Comment: 26 pages, 9 figure
Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances
A history is given of the applications of the simple expression generalized
from the surmise by Wigner and also by Ibach to extract the strength of the
interaction between steps on a vicinal surface, via the terrace width
distribution (TWD). A concise guide for use with experiments and a summary of
some recent extensions are provided.Comment: 11 pages, 4 figures, reformatted (with revtex) version of refereed
paper for special issue of Applied Physics A entitled "From Surface Science
to Device Physics", in honor of the retirements of Prof. H. Ibach and Prof.
H. L\"ut
Measuring the surface stress polar dependence
While measurements of the polar dependence of the surface free energy are
easily available, measurements of the whole polar dependence of the surface
stress of a crystal do not exist. In this paper is presented a new procedure
that allows, for the first time, the experimental determination of the surface
stress polar dependence of a crystal. For this purpose (1) electromigration is
used to control the kinetic faceting of surface orientations that belong to the
equilibrium shape of the crystal and (2) for each destabilised surface, the
period of faceting as well as the crystallographic angles of the appearing
facets are measured by AFM. The so-obtained data lead to a set of equations
whose mathematical solution, compatible with physical constraints, gives access
to the surface stress polar dependence of the whole crystal and thus to a
better understanding of surface stress properties.Comment: 8 pages, 6 Figure
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