3,237 research outputs found
New method to study stochastic growth equations: a cellular automata perspective
We introduce a new method based on cellular automata dynamics to study
stochastic growth equations. The method defines an interface growth process
which depends on height differences between neighbors. The growth rule assigns
a probability exp for a site to
receive one particle at a time and all the sites are updated
simultaneously. Here and are two parameters and
is a function which depends on height of the site and its neighbors. Its
functional form is specified through discretization of the deterministic part
of the growth equation associated to a given deposition process. In particular,
we apply this method to study two linear equations - the Edwards-Wilkinson (EW)
equation and the Mullins-Herring (MH) equation - and a non-linear one - the
Kardar-Parisi-Zhang (KPZ) equation. Through simulations and statistical
analysis of the height distributions of the profiles, we recover the values for
roughening exponents, which confirm that the processes generated by the method
are indeed in the universality classes of the original growth equations. In
addition, a crossover from Random Deposition to the associated correlated
regime is observed when the parameter is varied.Comment: 6 pages, 7 figure
Scaling Behavior of Driven Interfaces Above the Depinning Transition
We study the depinning transition for models representative of each of the
two universality classes of interface roughening with quenched disorder. For
one of the universality classes, the roughness exponent changes value at the
transition, while the dynamical exponent remains unchanged. We also find that
the prefactor of the width scales with the driving force. We propose several
scaling relations connecting the values of the exponents on both sides of the
transition, and discuss some experimental results in light of these findings.Comment: Revtex 3.0, 4 pages in PRL format + 5 figures (available at
ftp://jhilad.bu.edu/pub/abbhhss/ma-figures.tar.Z ) submitted to Phys Rev Let
A Northern White Family to Mr. Meredith (8 October 1962)
https://egrove.olemiss.edu/mercorr_pro/2063/thumbnail.jp
New set of measures to analyze non-equilibrium structures
We introduce a set of statistical measures that can be used to quantify
non-equilibrium surface growth. They are used to deduce new information about
spatiotemporal dynamics of model systems for spinodal decomposition and surface
deposition. Patterns growth in the Cahn-Hilliard Equation (used to model
spinodal decomposition) are shown to exhibit three distinct stages. Two models
of surface growth, namely the continuous Kardar-Parisi-Zhang (KPZ) model and
the discrete Restricted-Solid-On-Solid (RSOS) model are shown to have different
saturation exponents
Mathematics of random growing interfaces
We establish a thermodynamic limit and Gaussian fluctuations for the height
and surface width of the random interface formed by the deposition of particles
on surfaces. The results hold for the standard ballistic deposition model as
well as the surface relaxation model in the off-lattice setting. The results
are proved with the aid of general limit theorems for stabilizing functionals
of marked Poisson point processes.Comment: 12 page
Dynamic properties in a family of competitive growing models
The properties of a wide variety of growing models, generically called
, are studied by means of numerical simulations and analytic
developments. The study comprises the following models: Ballistic
Deposition, Random Deposition with Surface Relaxation, Das Sarma-Tamboronea,
Kim-Kosterlitz, Lai-Das Sarma, Wolf-Villain, Large Curvature, and three
additional models that are variants of the Ballistic Deposition model.
It is shown that after a growing regime, the interface width becomes
saturated at a crossover time () that, by fixing the sample size,
scales with according to , where
is an exponent. Also, the interface width at saturation () scales
as , where is another
exponent.
It is proved that, in any dimension, the exponents and obey the
following relationship: , where is
the growing exponent for . Furthermore, both exponents exhibit universality
in the limit.
By mapping the behaviour of the average height difference of two neighbouring
sites in discrete models of type and two kinds of random walks, we have
determined the exact value of the exponent .
Finally, by linking four well-established universality classes (namely
Edwards-Wilkinson, Kardar-Parisi-Zhang, Linear-MBE and Non-linear-MBE) with the
properties of both random walks, eight different stochastic equations for all
the competitive models studied are derived.Comment: 23 pages, 6 figures, Submitted to Phys. Rev.
Dynamic scaling and universality in evolution of fluctuating random networks
We found that models of evolving random networks exhibit dynamic scaling
similar to scaling of growing surfaces. It is demonstrated by numerical
simulations of two variants of the model in which nodes are added as well as
removed [Phys. Rev. Lett. 83, 5587 (1999)]. The averaged size and connectivity
of the network increase as power-laws in early times but later saturate.
Saturated values and times of saturation change with paramaters controlling the
local evolution of the network topology. Both saturated values and times of
saturation obey also power-law dependences on controlling parameters. Scaling
exponents are calculated and universal features are discussed.Comment: 7 pages, 6 figures, Europhysics Letters for
Trapping mechanism in overdamped ratchets with quenched noise
A trapping mechanism is observed and proposed as the origin of the anomalous
behavior recently discovered in transport properties of overdamped ratchets
subject to external oscillatory drive in the presence of quenched noise. In
particular, this mechanism is shown to appear whenever the quenched disorder
strength is greater than a threshold value. The minimum disorder strength
required for the existence of traps is determined by studying the trap
structure in a disorder configuration space. An approximation to the trapping
probability density function in a disordered region of finite length included
in an otherwise perfect ratchet lattice is obtained. The mean velocity of the
particles and the diffusion coefficient are found to have a non-monotonic
dependence on the quenched noise strength due to the presence of the traps.Comment: 21 pages, 6 figures, to appear in PR
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