1,719 research outputs found
Characterization of the Local Lipschitz Constant
A characterization, using polynomials introduced by A. V. Kolushov, is given for the local Lipschitz constant for the best approximation operator in Chebyshev approximation from a Haar set. The characterization is then used to study the existence of uniform local Lipschitz constants
Defect Formation and Kinetics of Atomic Terrace Merging
Pairs of atomic scale terraces on a single crystal metal surface can be made
to merge controllably under suitable conditions to yield steps of double height
and width. We study the effect of various physical parameters on the formation
of defects in a kinetic model of step doubling. We treat this manifestly non-
equilibrium problem by mapping the model onto a 1-D random sequential
adsorption problem and solving this analytically. We also do simulations to
check the validity of our treatment. We find that our treatment effectively
captures the dynamic evolution and the final state of the surface morphology.
We show that the number and nature of the defects formed is controlled by a
single dimensionless parameter . For close to one we show that the
fraction of defects rises linearly with as . We also show that one can arrive at the final state faster and with
fewer defects by changing the parameter with time.Comment: 17 pages, 8 figures. To be submitted to Phys. Rev.
Anomalous Dimension and Spatial Correlations in a Point-Island Model
We examine the island size distribution function and spatial correlation
function of a model for island growth in the submonolayer regime in both 1 and
2 dimensions. In our model the islands do not grow in shape, and a fixed number
of adatoms are added, nucleate, and are trapped at islands as they diffuse.
We study the cases of various critical island sizes for nucleation as a
function of initial coverage. We found anomalous scaling of the island size
distribution for large . Using scaling, random walk theory, a version of
mean-field theory we obtain a closed form for the spatial correlation function.
Our analytic results are verified by Monte Carlo simulations
Diffusional Relaxation in Random Sequential Deposition
The effect of diffusional relaxation on the random sequential deposition
process is studied in the limit of fast deposition. Expression for the coverage
as a function of time are analytically derived for both the short-time and
long-time regimes. These results are tested and compared with numerical
simulations.Comment: 9 pages + 2 figure
Absence of non-trivial asymptotic scaling in the Kashchiev model of polynuclear growth
In this brief comment we show that, contrary to previous claims [Bartelt M C
and Evans J W 1993 {\it J.\ Phys.\ A} 2743], the asymptotic
behaviour of the Kashchiev model of polynuclear growth is trivial in all
spatial dimensions, and therefore lies outside the Kardar-Parisi-Zhang
universality class.Comment: 3 pages, 4 postscript figures, uses eps
Observation of the Radiative Decay D^(*+) → D^+y
We have observed a signal for the decay D^(*+)→D^+γ at a significance of 4 standard deviations. From the measured branching ratio B(D^(*+)→D^+γ)/B(D^(*+)→D^+π^0) = 0.055±0.014±0.010 we find B(D^(*+)→D^+γ) = 0.017±0.004±0.003, where the first uncertainty is statistical and the second is systematic. We also report the highest precision determination of the remaining D^(*+) branching fractions
Nanoscale periodicity in stripe-forming systems at high temperature: Au/W(110)
We observe using low-energy electron microscopy the self-assembly of
monolayer-thick stripes of Au on W(110) near the transition temperature between
stripes and the non-patterned (homogeneous) phase. We demonstrate that the
amplitude of this Au stripe phase decreases with increasing temperature and
vanishes at the order-disorder transition (ODT). The wavelength varies much
more slowly with temperature and coverage than theories of stress-domain
patterns with sharp phase boundaries would predict, and maintains a finite
value of about 100 nm at the ODT. We argue that such nanometer-scale stripes
should often appear near the ODT.Comment: 5 page
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Nanoscopic tip sensors fabricated by gas phase etching of optical glass fibers
Silica-based fiber tips are used in a variety of spectroscopic, micro- or nano-scopic optical sensor applications and photonic micro-devices. The miniaturization of optical sensor systems and the technical implementation using optical fibers can provide new sensor designs with improved properties and functionality for new applications. The selective-etching of specifically doped silica fibers is a promising method in order to form complex photonic micro structures at the end or within fibers such as tips and cavities in various shapes useful for the all-fiber sensor and imaging applications. In the present study, we investigated the preparation of geometrically predefined, nanoscaled fiber tips by taking advantage of the dopant concentration profiles of highly doped step-index fibers. For this purpose, a gas phase etching process using hydrofluoric acid (HF) vapor was applied. The shaping of the fiber tips was based on very different etching rates as a result of the doping characteristics of specific optical fibers. Technological studies on the influence of the etching gas atmosphere on the temporal tip shaping and the final geometry were performed using undoped and doped silica fibers. The influence of the doping characteristics was investigated in phosphorus-, germanium-, fluorine- and boron-doped glass fibers. Narrow exposed as well as protected internal fiber tips in various shapes and tip radiuses down to less than 15 nm were achieved and characterized geometrically and topologically. For investigations into surface plasmon resonance effects, the fiber tips were coated with nanometer-sized silver layers by means of vapour deposition and finally subjected to an annealing treatment
Fluctuations, line tensions, and correlation times of nanoscale islands on surfaces
We analyze in detail the fluctuations and correlations of the (spatial)
Fourier modes of nano-scale single-layer islands on (111) fcc crystal surfaces.
We analytically show that the Fourier modes of the fluctuations couple due to
the anisotropy of the crystal, changing the power spectrum of the fluctuations,
and that the actual eigenmodes of the fluctuations are the appropriate linear
combinations of the Fourier modes. Using kinetic Monte Carlo simulations with
bond-counting parameters that best match realistic energy barriers for hopping
rates, we deduce absolute line tensions as a function of azimuthal orientation
from the analyses of the fluctuation of each individual mode. The
autocorrelation functions of these modes give the scaling of the correlation
times with wavelength, providing us with the rate-limiting kinetics driving the
fluctuations, here step-edge diffusion. The results for the energetic
parameters are in reasonable agreement with available experimental data for
Pb(111) surfaces, and we compare the correlation times of island-edge
fluctuations to relaxation times of quenched Pb crystallites.Comment: 11 pages, 8 figures; to appear in PRB 70, xxx (15 Dec 2004), changes
in MC and its implication
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