19,683 research outputs found
Scaling in the crossover from random to correlated growth
In systems where deposition rates are high compared to diffusion, desorption
and other mechanisms that generate correlations, a crossover from random to
correlated growth of surface roughness is expected at a characteristic time
t_0. This crossover is analyzed in lattice models via scaling arguments, with
support from simulation results presented here and in other authors works. We
argue that the amplitudes of the saturation roughness and of the saturation
time scale as {t_0}^{1/2} and t_0, respectively. For models with lateral
aggregation, which typically are in the Kardar-Parisi-Zhang (KPZ) class, we
show that t_0 ~ 1/p, where p is the probability of the correlated aggregation
mechanism to take place. However, t_0 ~ 1/p^2 is obtained in solid-on-solid
models with single particle deposition attempts. This group includes models in
various universality classes, with numerical examples being provided in the
Edwards-Wilkinson (EW), KPZ and Villain-Lai-Das Sarma (nonlinear molecular-beam
epitaxy) classes. Most applications are for two-component models in which
random deposition, with probability 1-p, competes with a correlated aggregation
process with probability p. However, our approach can be extended to other
systems with the same crossover, such as the generalized restricted
solid-on-solid model with maximum height difference S, for large S. Moreover,
the scaling approach applies to all dimensions. In the particular case of
one-dimensional KPZ processes with this crossover, we show that t_0 ~ nu^{-1}
and nu ~ lambda^{2/3}, where nu and lambda are the coefficients of the linear
and nonlinear terms of the associated KPZ equations. The applicability of
previous results on models in the EW and KPZ classes is discussed.Comment: 14 pages + 5 figures, minor changes, version accepted in Phys. Rev.
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
Non-Local Product Rules for Percolation
Despite original claims of a first-order transition in the product rule model
proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies
indicate that this percolation model, in fact, displays a continuous
transition. The distinctive scaling properties of the model at criticality,
however, strongly suggest that it should belong to a different universality
class than ordinary percolation. Here we introduce a generalization of the
product rule that reveals the effect of non-locality on the critical behavior
of the percolation process. Precisely, pairs of unoccupied bonds are chosen
according to a probability that decays as a power-law of their Manhattan
distance, and only that bond connecting clusters whose product of their sizes
is the smallest, becomes occupied. Interestingly, our results for
two-dimensional lattices at criticality shows that the power-law exponent of
the product rule has a significant influence on the finite-size scaling
exponents for the spanning cluster, the conducting backbone, and the cutting
bonds of the system. In all three cases, we observe a continuous variation from
ordinary to (non-local) explosive percolation exponents.Comment: 5 pages, 4 figure
How dense can one pack spheres of arbitrary size distribution?
We present the first systematic algorithm to estimate the maximum packing
density of spheres when the grain sizes are drawn from an arbitrary size
distribution. With an Apollonian filling rule, we implement our technique for
disks in 2d and spheres in 3d. As expected, the densest packing is achieved
with power-law size distributions. We also test the method on homogeneous and
on empirical real distributions, and we propose a scheme to obtain
experimentally accessible distributions of grain sizes with low porosity. Our
method should be helpful in the development of ultra-strong ceramics and high
performance concrete.Comment: 5 pages, 5 figure
Quantum Evolution of Inhomogeneities in Curved Space
We obtain the renormalized equations of motion for matter and semi-classical
gravity in an inhomogeneous space-time. We use the functional Schrodinger
picture and a simple Gaussian approximation to analyze the time evolution of
the model, and we establish the renormalizability of this
non-perturbative approximation. We also show that the energy-momentum tensor in
this approximation is finite once we consider the usual mass and coupling
constant renormalizations, without the need of further geometrical
counter-terms.Comment: 22 page
Experimental determination of the non-extensive entropic parameter
We show how to extract the parameter from experimental data, considering
an inhomogeneous magnetic system composed by many Maxwell-Boltzmann homogeneous
parts, which after integration over the whole system recover the Tsallis
non-extensivity. Analyzing the cluster distribution of
LaSrMnO manganite, obtained through scanning tunnelling
spectroscopy, we measure the parameter and predict the bulk magnetization
with good accuracy. The connection between the Griffiths phase and
non-extensivity is also considered. We conclude that the entropic parameter
embodies information about the dynamics, the key role to describe complex
systems.Comment: Submitted to Phys. Rev. Let
- …