990 research outputs found
Characterization of Generalized Haar Spaces
AbstractWe say that a subsetGofC0(T,Rk) is rotation-invariant if {Qg:g∈G{=Gfor anyk×korthogonal matrixQ. LetGbe a rotation-invariant finite-dimensional subspace ofC0(T,Rk) on a connected, locally compact, metric spaceT. We prove thatGis a generalized Haar subspace if and only ifPG(f) is strongly unique of order 2 wheneverPG(f) is a singleton
Error Estimates and Lipschitz Constants for Best Approximation in Continuous Function Spaces
We use a structural characterization of the metric projection PG(f), from the continuous function space to its one-dimensional subspace G, to derive a lower bound of the Hausdorff strong unicity constant (or weak sharp minimum constant) for PG and then show this lower bound can be attained. Then the exact value of Lipschitz constant for PG is computed. The process is a quantitative analysis based on the Gâteaux derivative of PG, a representation of local Lipschitz constants, the equivalence of local and global Lipschitz constants for lower semicontinuous mappings, and construction of functions
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
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
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
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
Fluctuations of steps on crystal surfaces
Fluctuations of isolated and pairs of ascending steps of monoatomic height
are studied in the framework of SOS models, using mainly Monte Carlo
techniques. Below the roughening transistion of the surface, the profiles of
long steps show the same scaling features for terrace and surface diffusion.
For a pair of short steps, their separation distance is found to grow as
at late stages. Above roughening, simulational data on surface
diffusion agree well with the classical continuum theory of Mullins.Comment: 4 pages, 2 eps figure
A lattice gas model of II-VI(001) semiconductor surfaces
We introduce an anisotropic two-dimensional lattice gas model of metal
terminated II-IV(001) seminconductor surfaces. Important properties of this
class of materials are represented by effective NN and NNN interactions, which
result in the competition of two vacancy structures on the surface. We
demonstrate that the experimentally observed c(2x2)-(2x1) transition of the
CdTe(001) surface can be understood as a phase transition in thermal
equilbrium. The model is studied by means of transfer matrix and Monte Carlo
techniques. The analysis shows that the small energy difference of the
competing reconstructions determines to a large extent the nature of the
different phases. Possible implications for further experimental research are
discussed.Comment: 7 pages, 2 figure
Step fluctuations and random walks
The probability distribution p(l) of an atom to return to a step at distance
l from the detachment site, with a random walk in between, is exactly
enumerated. In particular, we study the dependence of p(l) on step roughness,
presence of other reflecting or absorbing steps, interaction between steps and
diffusing atom, as well as concentration of defects on the terrace neighbouring
the step. Applying Monte Carlo techniques, the time evolution of equilibrium
step fluctuations is computed for specific forms of return probabilities.
Results are compared to previous theoretical and experimental findings.Comment: 16 pages, 6 figure
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