57,580 research outputs found
On the Displacement for Covering a dimensional Cube with Randomly Placed Sensors
Consider sensors placed randomly and independently with the uniform
distribution in a dimensional unit cube (). The sensors have
identical sensing range equal to , for some . We are interested in
moving the sensors from their initial positions to new positions so as to
ensure that the dimensional unit cube is completely covered, i.e., every
point in the dimensional cube is within the range of a sensor. If the
-th sensor is displaced a distance , what is a displacement of minimum
cost? As cost measure for the displacement of the team of sensors we consider
the -total movement defined as the sum , for some
constant . We assume that and are chosen so as to allow full
coverage of the dimensional unit cube and .
The main contribution of the paper is to show the existence of a tradeoff
between the dimensional cube, sensing radius and -total movement. The
main results can be summarized as follows for the case of the dimensional
cube.
If the dimensional cube sensing radius is and
, for some , then we present an algorithm that uses
total expected movement (see Algorithm 2 and
Theorem 5).
If the dimensional cube sensing radius is greater than
and is a natural
number then the total expected movement is
(see Algorithm 3 and Theorem 7).
In addition, we simulate Algorithm 2 and discuss the results of our
simulations
Epitaxial Growth Kinetics with Interacting Coherent Islands
The Stranski-Krastanov growth kinetics of undislocated (coherent)
3-dimensional islands is studied with a self-consistent mean field rate theory
that takes account of elastic interactions between the islands. The latter are
presumed to facilitate the detachment of atoms from the islands with a
consequent decrease in their average size. Semi-quantitative agreement with
experiment is found for the time evolution of the total island density and the
mean island size. When combined with scaling ideas, these results provide a
natural way to understand the often-observed initial increase and subsequent
decrease in the width of the coherent island size distribution.Comment: 4 pages, 4 figure
The Concept of Two Mobilities in Homoepitaxial Growth
A general kinetic concept is introduced which can be used to control growth modes in homoepitaxy. Its basic idea is that during growth of a layer, the characteristics length scale associated with nucleation is deliberately varied. The power of this concept lies in the fact that it can be realized experimentally in a variety of ways and is not restricted to special systems. It helps to understand various effects reported in the literature and may serve as a guideline for future methods of growth manipulation
Scaling of Heteroepitaxial Island Sizes
Monte Carlo simulations of an atomistic solid-on-solid model are used to
study the effect of lattice misfit on the distribution of two-dimensional
islands sizes as a function of coverage in the submonolayer
aggregation regime of epitaxial growth. Misfit promotes the detachment of atoms
from the perimeter of large pseudomorphic islands and thus favors their
dissolution into smaller islands that relieve strain more efficiently. The
number density of islands composed of atoms exhibits scaling in the form
\mbox{)} where is the average island size. Unlike the
case of homoepitaxy, a rate equation theory based on this observation leads to
qualitatively different behavior than observed in the simulations.Comment: 10 pages, LaTeX 2.09, IC-DDV-94-00
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