642 research outputs found
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.
An Anisotropic Ballistic Deposition Model with Links to the Ulam Problem and the Tracy-Widom Distribution
We compute exactly the asymptotic distribution of scaled height in a
(1+1)--dimensional anisotropic ballistic deposition model by mapping it to the
Ulam problem of finding the longest nondecreasing subsequence in a random
sequence of integers. Using the known results for the Ulam problem, we show
that the scaled height in our model has the Tracy-Widom distribution appearing
in the theory of random matrices near the edges of the spectrum. Our result
supports the hypothesis that various growth models in dimensions that
belong to the Kardar-Parisi-Zhang universality class perhaps all share the same
universal Tracy-Widom distribution for the suitably scaled height variables.Comment: 5 pages Revtex, 3 .eps figures included, new references adde
A simulational and theoretical study of the spherical electrical double layer for a size-asymmetric electrolyte: the case of big coions
Monte Carlo simulations of a spherical macroion, surrounded by a
size-asymmetric electrolyte in the primitive model, were performed. We
considered 1:1 and 2:2 salts with a size ratio of 2 (i.e., with coions twice
the size of counterions), for several surface charge densities of the
macrosphere. The radial distribution functions, electrostatic potential at the
Helmholtz surfaces, and integrated charge are reported. We compare these
simulational data with original results obtained from the Ornstein-Zernike
integral equation, supplemented by the hypernetted chain/hypernetted chain
(HNC/HNC) and hypernetted chain/mean spherical approximation (HNC/MSA)
closures, and with the corresponding calculations using the modified
Gouy-Chapman and unequal-radius modified Gouy-Chapman theories. The HNC/HNC and
HNC/MSA integral equations formalisms show good concordance with Monte Carlo
"experiments", whereas the notable limitations of point-ion approaches are
evidenced. Most importantly, the simulations confirm our previous theoretical
predictions of the non-dominance of the counterions in the size-asymmetric
spherical electrical double layer [J. Chem. Phys. 123, 034703 (2005)], the
appearance of anomalous curvatures at the outer Helmholtz plane and the
enhancement of charge reversal and screening at high colloidal surface charge
densities due to the ionic size asymmetry.Comment: 11 pages, 7 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.
Abrupt grain boundary melting in ice
The effect of impurities on the grain boundary melting of ice is investigated
through an extension of Derjaguin-Landau-Verwey-Overbeek theory, in which we
include retarded potential effects in a calculation of the full frequency
dependent van der Waals and Coulombic interactions within a grain boundary. At
high dopant concentrations the classical solutal effect dominates the melting
behavior. However, depending on the amount of impurity and the surface charge
density, as temperature decreases, the attractive tail of the dispersion force
interaction begins to compete effectively with the repulsive screened Coulomb
interaction. This leads to a film-thickness/temperature curve that changes
depending on the relative strengths of these interactions and exhibits a
decrease in the film thickness with increasing impurity level. More striking is
the fact that at very large film thicknesses, the repulsive Coulomb interaction
can be effectively screened leading to an abrupt reduction to zero film
thickness.Comment: 8 pages, 1 figur
The Parallel Complexity of Growth Models
This paper investigates the parallel complexity of several non-equilibrium
growth models. Invasion percolation, Eden growth, ballistic deposition and
solid-on-solid growth are all seemingly highly sequential processes that yield
self-similar or self-affine random clusters. Nonetheless, we present fast
parallel randomized algorithms for generating these clusters. The running times
of the algorithms scale as , where is the system size, and the
number of processors required scale as a polynomial in . The algorithms are
based on fast parallel procedures for finding minimum weight paths; they
illuminate the close connection between growth models and self-avoiding paths
in random environments. In addition to their potential practical value, our
algorithms serve to classify these growth models as less complex than other
growth models, such as diffusion-limited aggregation, for which fast parallel
algorithms probably do not exist.Comment: 20 pages, latex, submitted to J. Stat. Phys., UNH-TR94-0
The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study
The hypernetted chain/mean spherical approximation (HNC/MSA) integral
equation is obtained and solved numerically for a totally asymmetric primitive
model electrolyte around a spherical macroparticle. The ensuing radial
distribution functions show a very good agreement when compared to our Monte
Carlo and molecular dynamics simulations for spherical geometry and with
respect to previous anisotropic reference HNC calculations in the planar limit.
We report an analysis of the potential vs charge relationship, radial
distribution functions, mean electrostatic potential and cumulative reduced
charge for representative cases of 1:1 and 2:2 salts with a size asymmetry
ratio of 2. Our results are collated with those of the Modified Gouy-Chapman
(MGC) and unequal radius Modified Gouy-Chapman (URMGC) theories and with those
of HNC/MSA in the restricted primitive model (RPM) to assess the importance of
size asymmetry effects. One of the most striking characteristics found is
that,\textit{contrary to the general belief}, away from the point of zero
charge the properties of an asymmetric electrical double layer (EDL) are not
those corresponding to a symmetric electrolyte with the size and charge of the
counterion, i.e. \textit{counterions do not always dominate}. This behavior
suggests the existence of a new phenomenology in the EDL that genuinely belongs
to a more realistic size-asymmetric model where steric correlations are taken
into account consistently. Such novel features can not be described by
traditional mean field theories like MGC, URMGC or even by enhanced formalisms,
like HNC/MSA, if they are based on the RPM.Comment: 29 pages, 13 figure
Scaling Behavior of Cyclical Surface Growth
The scaling behavior of cyclical surface growth (e.g. deposition/desorption),
with the number of cycles n, is investigated. The roughness of surfaces grown
by two linear primary processes follows a scaling behavior with asymptotic
exponents inherited from the dominant process while the effective amplitudes
are determined by both. Relevant non-linear effects in the primary processes
may remain so or be rendered irrelevant. Numerical simulations for several
pairs of generic primary processes confirm these conclusions. Experimental
results for the surface roughness during cyclical electrodeposition/dissolution
of silver show a power-law dependence on n, consistent with the scaling
description.Comment: 2 figures adde
Effect of Long-Range Interactions in the Conserved Kardar-Parisi-Zhang Equation
The conserved Kardar-Parisi-Zhang equation in the presence of long-range
nonlinear interactions is studied by the dynamic renormalization group method.
The long-range effect produces new fixed points with continuously varying
exponents and gives distinct phase transitions, depending on both the
long-range interaction strength and the substrate dimension . The long-range
interaction makes the surface width less rough than that of the short-range
interaction. In particular, the surface becomes a smooth one with a negative
roughness exponent at the physical dimension d=2.Comment: 4 pages(LaTex), 1 figure(Postscript
Missing and Quenched Gamow Teller Strength
Gamow-Teller strength functions in full spaces are calculated with
sufficient accuracy to ensure that all the states in the resonance region have
been populated. Many of the resulting peaks are weak enough to become
unobservable. The quenching factor necessary to bring into agreement the low
lying observed states with shell model predictions is shown to be due to
nuclear correlations. To within experimental uncertainties it is the same that
is found in one particle transfer and (e,e') reactions. Perfect consistency
between the observed peaks and the calculation is
achieved by assuming an observation threshold of 0.75\% of the total strength,
a value that seems typical in several experimentsComment: 11 pages, 6 figures avalaible upon request, RevTeX, FTUAM-94/0
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