18,848 research outputs found
Roughness exponents and grain shapes
In surfaces with grainy features, the local roughness shows a crossover
at a characteristic length , with roughness exponent changing from
to a smaller . The grain shape, the choice of
or height-height correlation function (HHCF) , and the procedure to
calculate root mean-square averages are shown to have remarkable effects on
. With grains of pyramidal shape, can be as low as 0.71,
which is much lower than the previous prediction 0.85 for rounded grains. The
same crossover is observed in the HHCF, but with initial exponent
for flat grains, while for some conical grains it may
increase to . The universality class of the growth process
determines the exponents after the crossover, but has no
effect on the initial exponents and , supporting the
geometric interpretation of their values. For all grain shapes and different
definitions of surface roughness or HHCF, we still observe that the crossover
length is an accurate estimate of the grain size. The exponents obtained
in several recent experimental works on different materials are explained by
those models, with some surface images qualitatively similar to our model
films.Comment: 7 pages, 6 figures and 2 table
Phases of granular segregation in a binary mixture
We present results from an extensive experimental investigation into granular
segregation of a shallow binary mixture in which particles are driven by
frictional interactions with the surface of a vibrating horizontal tray. Three
distinct phases of the mixture are established viz; binary gas (unsegregated),
segregation liquid and segregation crystal. Their ranges of existence are
mapped out as a function of the system's primary control parameters using a
number of measures based on Voronoi tessellation. We study the associated
transitions and show that segregation can be suppressed is the total filling
fraction of the granular layer, , is decreased below a critical value,
, or if the dimensionless acceleration of the driving, , is
increased above a value .Comment: 12 pages, 12 figures, submitted to Phys. Rev.
Finite-size effects in roughness distribution scaling
We study numerically finite-size corrections in scaling relations for
roughness distributions of various interface growth models. The most common
relation, which considers the average roughness . This illustrates how
finite-size corrections can be obtained from roughness distributions scaling.
However, we discard the usual interpretation that the intrinsic width is a
consequence of high surface steps by analyzing data of restricted
solid-on-solid models with various maximal height differences between
neighboring columns. We also observe that large finite-size corrections in the
roughness distributions are usually accompanied by huge corrections in height
distributions and average local slopes, as well as in estimates of scaling
exponents. The molecular-beam epitaxy model of Das Sarma and Tamborenea in 1+1
dimensions is a case example in which none of the proposed scaling relations
works properly, while the other measured quantities do not converge to the
expected asymptotic values. Thus, although roughness distributions are clearly
better than other quantities to determine the universality class of a growing
system, it is not the final solution for this task.Comment: 25 pages, including 9 figures and 1 tabl
Phase transitions and crossovers in reaction-diffusion models with catalyst deactivation
The activity of catalytic materials is reduced during operation by several
mechanisms, one of them being poisoning of catalytic sites by chemisorbed
impurities or products. Here we study the effects of poisoning in two
reaction-diffusion models in one-dimensional lattices with randomly distributed
catalytic sites. Unimolecular and bimolecular single-species reactions are
considered, without reactant input during the operation. The models show
transitions between a phase with continuous decay of reactant concentration and
a phase with asymptotic non-zero reactant concentration and complete poisoning
of the catalyst. The transition boundary depends on the initial reactant and
catalyst concentrations and on the poisoning probability. The critical system
behaves as in the two-species annihilation reaction, with reactant
concentration decaying as t^{-1/4} and the catalytic sites playing the role of
the second species. In the unimolecular reaction, a significant crossover to
the asymptotic scaling is observed even when one of those parameters is 10% far
from criticality. Consequently, an effective power-law decay of concentration
may persist up to long times and lead to an apparent change in the reaction
kinetics. In the bimolecular single-species reaction, the critical scaling is
followed by a two-dimensional rapid decay, thus two crossovers are found.Comment: 8 pages, 7 figure
Crossover in the scaling of island size and capture zone distributions
Simulations of irreversible growth of extended (fractal and square) islands
with critical island sizes i=1 and 2 are performed in broad ranges of coverage
\theta and diffusion-to-deposition ratios R in order to investigate scaling of
island size and capture zone area distributions (ISD, CZD). Large \theta and
small R lead to a crossover from the CZD predicted by the theory of Pimpinelli
and Einstein (PE), with Gaussian right tail, to CZD with simple exponential
decays. The corresponding ISD also cross over from Gaussian or faster decays to
simple exponential ones. For fractal islands, these features are explained by
changes in the island growth kinetics, from a competition for capture of
diffusing adatoms (PE scaling) to aggregation of adatoms with effectively
irrelevant diffusion, which is characteristic of random sequential adsorption
(RSA) without surface diffusion. This interpretation is confirmed by studying
the crossover with similar CZ areas (of order 100 sites) in a model with
freezing of diffusing adatoms that corresponds to i=0. For square islands,
deviations from PE predictions appear for coverages near \theta=0.2 and are
mainly related to island coalescence. Our results show that the range of
applicability of the PE theory is narrow, thus observing the predicted Gaussian
tail of CZD may be difficult in real systems.Comment: 9 pages, 7 figure
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