65 research outputs found
Non-universal coarsening and universal distributions in far-from equilibrium systems
Anomalous coarsening in far-from equilibrium one-dimensional systems is
investigated by simulation and analytic techniques. The minimal hard core
particle (exclusion) models contain mechanisms of aggregated particle
diffusion, with rates epsilon<<1, particle deposition into cluster gaps, but
suppressed for the smallest gaps, and breakup of clusters which are adjacent to
large gaps. Cluster breakup rates vary with the cluster length x as kx^alpha.
The domain growth law x ~ (epsilon t)^z, with z=1/(2+alpha) for alpha>0, is
explained by a scaling picture, as well as the scaling of the density of double
vacancies (at which deposition and cluster breakup are allowed) as 1/[t(epsilon
t)^z]. Numerical simulations for several values of alpha and epsilon confirm
these results. An approximate factorization of the cluster configuration
probability is performed within the master equation resulting from the mapping
to a column picture. The equation for a one-variable scaling function explains
the above results. The probability distributions of cluster lengths scale as
P(x)= 1/(epsilon t)^z g(y), with y=x/(epsilon t)^z. However, those
distributions show a universal tail with the form g(y) ~ exp(-y^{3/2}), which
disagrees with the prediction of the independent cluster approximation. This
result is explained by the connection of the vacancy dynamics with the problem
of particle trapping in an infinite sea of traps and is confirmed by
simulation.Comment: 30 pages (10 figures included), to appear in 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
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
Universality in two-dimensional Kardar-Parisi-Zhang growth
We analyze simulations results of a model proposed for etching of a
crystalline solid and results of other discrete models in the 2+1-dimensional
Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of
orders n=2,3,4 of the heights distribution are estimated. Results for the
etching model, the ballistic deposition (BD) model and the
temperature-dependent body-centered restricted solid-on-solid model (BCSOS)
suggest the universality of the absolute value of the skewness S = W_3 /
(W_2)^(3/2) and of the value of the kurtosis Q = W_4 / (W_2)^2 - 3. The sign of
the skewness is the same of the parameter \lambda of the KPZ equation which
represents the process in the continuum limit. The best numerical estimates,
obtained from the etching model, are |S| = 0.26 +- 0.01 and Q = 0.134 +- 0.015.
For this model, the roughness exponent \alpha = 0.383 +- 0.008 is obtained,
accounting for a constant correction term (intrinsic width) in the scaling of
the squared interface width. This value is slightly below previous estimates of
extensive simulations and rules out the proposal of the exact value \alpha=2/5.
The conclusion is supported by results for the ballistic deposition model.
Independent estimates of the dynamical exponent and of the growth exponent are
1.605 <= z <= 1.64 and \beta = 0.229 +- 0.005, respectively, which are
consistent with the relations \alpha + z = 2 and z = \alpha / \beta.Comment: 8 pages, 9 figures, to be published in Phys. Rev.
Surface and bulk properties of ballistic deposition models with bond breaking
We introduce a new class of growth models, with a surface restructuring
mechanism in which impinging particles may dislodge suspended particles,
previously aggregated on the same column in the deposit. The flux of these
particles is controlled through a probability . These systems present a
crossover, for small values of , from random to correlated (KPZ) growth of
surface roughness, which is studied through scaling arguments and Monte Carlo
simulations on one- and two-dimensional substrates. We show that the crossover
characteristic time scales with according to with and that the interface width at saturation
scales as with , where is
either the maximal number of broken bonds or of dislodged suspended particles.
This result shows that the sets of exponents and or
and found in all previous works focusing on systems with this same
type of crossover are not universal. Using scaling arguments, we show that the
bulk porosity of the deposits scales as for small
values of . This general scaling relation is confirmed by our numerical
simulations and explains previous results present in literature.Comment: 7 pages, 4 figures, 2 table
Crossover of interface growth dynamics during corrosion and passivation
We study a model of corrosion and passivation of a metalic surface in contact
with a solution using scaling arguments and simulation. The passive layer is
porous so that the metal surface is in contact with the solution. The volume
excess of the products may suppress the access of the solution to the metal
surface, but it is then restored by a diffusion mechanism. A metalic site in
contact with the solution or with the porous layer can be passivated with rate
p and volume excess diffuses with rate D. At small times, the corrosion front
linearly grows in time, but the growth velocity shows a t^{-1/2} decrease after
a crossover time of order t_c ~ D/p^2, where the average front height is of
order h_c ~ D/p. A universal scaling relation between h/h_c and t/t_c is
proposed and confirmed by simulation for 0.00005 <= p <= 0.5 in square
lattices. The roughness of the corrosion front shows a crossover from
Kardar-Parisi-Zhang scaling to Laplacian growth (diffusion-limited erosion -
DLE) at t_c. The amplitudes of roughness scaling are obtained by the same kind
of arguments as previously applied to other competitive growth models. The
simulation results confirm their validity. Since the proposed model captures
the essential ingredients of different corrosion processes, we also expect
these universal features to appear in real systems.Comment: 17 pages, including 7 figures; submitted articl
Maximal and minimal height distributions of fluctuating interfaces
We study numerically the maximal and minimal height distributions (MAHD,
MIHD) of the nonlinear interface growth equations of second and fourth order
and of related lattice models in two dimensions. MAHD and MIHD are different
due to the asymmetry of the local height distribution, so that, in each class,
the sign of the relevant nonlinear term determines which one of two universal
curves is the MAHD and the MIHD. The average maximal and minimal heights scale
as the average roughness, in contrast to Edwards-Wilkinson (EW) growth. All
extreme height distributions, including the EW ones, have tails that cannot be
fit by generalized Gumbel distributions.Comment: 13 pages, 6 figure
Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling
We simulated a growth model in 1+1 dimensions in which particles are
aggregated according to the rules of ballistic deposition with probability p or
according to the rules of random deposition with surface relaxation (Family
model) with probability 1-p. For any p>0, this system is in the
Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover
from the Edwards-Wilkinson class (EW) for small p. From the scaling of the
growth velocity, the parameter p is connected to the coefficient of the
nonlinear term of the KPZ equation, lambda, giving lambda ~ p^gamma, with gamma
= 2.1 +- 0.2. Our numerical results confirm the interface width scaling in the
growth regime as W ~ lambda^beta t^beta, and the scaling of the saturation time
as tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 and
strong corrections to scaling for small lambda. This picture is consistent with
a crossover time from EW to KPZ growth in the form t_c ~ lambda^(-4) ~ p^(-8),
in agreement with scaling theories and renormalization group analysis. Some
consequences of the slow crossover in this problem are discussed and may help
investigations of more complex models.Comment: 16 pages, 7 figures; to appear in Phys. Rev.
Scaling of island size and capture zone distributions in submonolayer growth
Island size and capture zone distributions (ISDs, CZDs) are studied
numerically in submonolayer growth with various critical island sizes and
shapes. CZDs scaled by the variance show excellent agreement with the Wigner
surmise, confirming the Pimpinelli-Einstein approach for large CZs / large
island dynamics. The ISD decay as exp(-s^x), with x=4, x approx 2.4 and 2 for
point, fractal, and square islands, respectively. A scaling approach explains
the values of x from the Gaussian decay of CZD and the efficiency of islands to
capture diffusing adatoms.Comment: 12 pages, 3 figure
Self-Attracting Walk on Lattices
We have studied a model of self-attracting walk proposed by Sapozhnikov using
Monte Carlo method. The mean square displacement
and the mean number of visited sites are calculated for
one-, two- and three-dimensional lattice. In one dimension, the walk shows
diffusive behaviour with . However, in two and three dimension, we
observed a non-universal behaviour, i.e., the exponent varies
continuously with the strength of the attracting interaction.Comment: 6 pages, latex, 6 postscript figures, Submitted J.Phys.
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