48 research outputs found
Discrete-Event Analytic Technique for Surface Growth Problems
We introduce an approach for calculating non-universal properties of rough
surfaces. The technique uses concepts of distinct surface-configuration
classes, defined by the surface growth rule. The key idea is a mapping between
discrete events that take place on the interface and its elementary local-site
configurations. We construct theoretical probability distributions of
deposition events at saturation for surfaces generated by selected growth
rules. These distributions are then used to compute measurable physical
quantities. Despite the neglect of temporal correlations, our approximate
analytical results are in very good agreement with numerical simulations. This
discrete-event analytic technique can be particularly useful when applied to
quantification problems, which are known to not be suited to continuum methods.Comment: 4 pages, 7 figures, published 17 Feb. 200
Field-driven solid-on-solid interfaces moving under a stochastic Arrhenius dynamic: effects of the barrier height
We present analytical results and kinetic Monte Carlo simulations for the
mobility and microscopic structure of solid-on-solid (SOS) interfaces driven
far from equilibrium by an external force, such as an applied field or
(electro)chemical potential difference. The interfaces evolve under a specific
stochastic dynamic with a local energy barrier (an Arrhenius dynamic), known as
the transition dynamics approximation (TDA). We calculate the average height of
steps on the interface, the average interface velocity, and the skewness of the
interface as functions of the driving force and the height of the energy
barrier. We find that the microscopic interface structure depends quite
strongly on the barrier height. As the barrier becomes higher, the local
interface width decreases and the skewness increases, suggesting increasing
short-range correlations between the step heights.Comment: 6 pages, 5 figs. RevTe
Magnetization Switching in Single-Domain Ferromagnets
A model for single-domain uniaxial ferromagnetic particles with high
anisotropy, the Ising model, is studied. Recent experimental observations have
been made of the probability that the magnetization has not switched. Here an
approach is described in which it is emphasized that a ferromagnetic particle
in an unfavorable field is in fact a metastable system, and the switching is
accomplished through the nucleation and subsequent growth of localized
droplets. Nucleation theory is applied to finite systems to determine the
coercivity as a function of particle size and to calculate the probability of
not switching. Both of these quantities are modified by different boundary
conditions, magnetostatic interactions, and quenched disorder.Comment: 4 pages, LaTeX, 2 figures, documentstyle{elsart} More fits and
Mathematica notebook at http://www.scri.fsu.edu/~novotny/magnetism.html To
appear in J.Mag.Mag.Mater. Conference Proceedings of 7th International
Conference on Magnetism Cairns, Australia, August, 199
Update statistics in conservative parallel discrete event simulations of asynchronous systems
We model the performance of an ideal closed chain of L processing elements
that work in parallel in an asynchronous manner. Their state updates follow a
generic conservative algorithm. The conservative update rule determines the
growth of a virtual time surface. The physics of this growth is reflected in
the utilization (the fraction of working processors) and in the interface
width. We show that it is possible to nake an explicit connection between the
utilization and the macroscopic structure of the virtual time interface. We
exploit this connection to derive the theoretical probability distribution of
updates in the system within an approximate model. It follows that the
theoretical lower bound for the computational speed-up is s=(L+1)/4 for L>3.
Our approach uses simple statistics to count distinct surface configuration
classes consistent with the model growth rule. It enables one to compute
analytically microscopic properties of an interface, which are unavailable by
continuum methods.Comment: 15 pages, 12 figure
Microstructure and velocity of field-driven Ising interfaces moving under a soft stochastic dynamic
We present theoretical and dynamic Monte Carlo simulation results for the
mobility and microscopic structure of 1+1-dimensional Ising interfaces moving
far from equilibrium in an applied field under a single-spin-flip ``soft''
stochastic dynamic. The soft dynamic is characterized by the property that the
effects of changes in field energy and interaction energy factorize in the
transition rate, in contrast to the nonfactorizing nature of the traditional
Glauber and Metropolis rates (``hard'' dynamics). This work extends our
previous studies of the Ising model with a hard dynamic and the unrestricted
SOS model with soft and hard dynamics. [P.A. Rikvold and M. Kolesik, J. Stat.
Phys. 100, 377 (2000); J. Phys. A 35, L117 (2002); Phys. Rev. E 66, 066116
(2002).] The Ising model with soft dynamics is found to have closely similar
properties to the SOS model with the same dynamic. In particular, the local
interface width does not diverge with increasing field, as it does for hard
dynamics. The skewness of the interface at nonzero field is very weak and has
the opposite sign of that obtained with hard dynamics.Comment: 19 pages LaTex with 7 imbedded figure
Computational Lattice-Gas Modeling of the Electrosorption of Small Molecules and Ions
We present two recent applications of lattice-gas modeling techniques to
electrochemical adsorption on catalytically active metal substrates: urea on
Pt(100) and (bi)sulfate on Rh(111). Both involve the specific adsorption of
small molecules or ions on well-characterized single-crystal electrodes, and
they provide a particularly good fit between the adsorbate geometry and the
substrate structure. The close geometric fit facilitates the formation of
ordered submonolayer adsorbate phases in a range of electrode potential
positive of the range in which an adsorbed monolayer of hydrogen is stable. In
both systems the ordered-phase region is separated from the adsorbed- hydrogen
region by a phase transition, signified in cyclic voltammograms by a sharp
current peak. Based on data from {\it in situ\/} radiochemical surface
concentration measurements, cyclic voltammetry, and scanning tunneling micro-
scopy, and {\it ex situ\/} Auger electron spectroscopy and low-energy electron
diffraction, we have developed specific lattice-gas models for the two systems.
These models were studied by group-theoretical ground-state calcu- lations and
numerical Monte Carlo simulations, and effective lattice-gas inter- action
parameters were determined so as to provide agreement with experiments.Comment: 17 pp. uuencoded postscript, FSU-SCRI-94C-9
Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures
We examine a square-lattice nearest-neighbor Ising quantum ferromagnet
coupled to -dimensional phonon baths. Using the density-matrix equation, we
calculate the transition rates between configurations, which determines the
specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo
simulations, we measure the lifetimes of the metastable state. As the magnetic
field approaches at low temperatures, the lifetime prefactor diverges
because the transition rates between certain configurations approaches zero
under these conditions. Near and zero temperature, the divergent
prefactor shows scaling behavior as a function of the field, temperature, and
the dimension of the phonon baths. With proper scaling, the simulation data at
different temperatures and for different dimensions of the baths collapse well
onto two master curves, one for and one for .Comment: published versio
Parallelization of a Dynamic Monte Carlo Algorithm: a Partially Rejection-Free Conservative Approach
We experiment with a massively parallel implementation of an algorithm for
simulating the dynamics of metastable decay in kinetic Ising models. The
parallel scheme is directly applicable to a wide range of stochastic cellular
automata where the discrete events (updates) are Poisson arrivals. For high
performance, we utilize a continuous-time, asynchronous parallel version of the
n-fold way rejection-free algorithm. Each processing element carries an lxl
block of spins, and we employ the fast SHMEM-library routines on the Cray T3E
distributed-memory parallel architecture. Different processing elements have
different local simulated times. To ensure causality, the algorithm handles the
asynchrony in a conservative fashion. Despite relatively low utilization and an
intricate relationship between the average time increment and the size of the
spin blocks, we find that for sufficiently large l the algorithm outperforms
its corresponding parallel Metropolis (non-rejection-free) counterpart. As an
example application, we present results for metastable decay in a model
ferromagnetic or ferroelectric film, observed with a probe of area smaller than
the total system.Comment: 17 pages, 7 figures, RevTex; submitted to the Journal of
Computational Physic
Simulations of metastable decay in two- and three-dimensional models with microscopic dynamics
We present a brief analysis of the crossover phase diagram for the decay of a
metastable phase in a simple dynamic lattice-gas model of a two-phase system.
We illustrate the nucleation-theoretical analysis with dynamic Monte Carlo
simulations of a kinetic Ising lattice gas on square and cubic lattices. We
predict several regimes in which the metastable lifetime has different
functional forms, and provide estimates for the crossovers between the
different regimes. In the multidroplet regime, the
Kolmogorov-Johnson-Mehl-Avrami theory for the time dependence of the
order-parameter decay and the two-point density correlation function allows
extraction of both the order parameter in the metastable phase and the
interfacial velocity from the simulation data.Comment: 14 pages, 4 figures, submitted to J. Non-Crystalline Solids,
conference proceeding for IXth International Conference on the Physics of
Non-Crystalline Solids, October, 199
Microstructure and Velocity of Field-Driven SOS Interfaces: Analytic Approximations and Numerical Results
The local structure of a solid-on-solid (SOS) interface in a two-dimensional
kinetic Ising ferromagnet with single-spin-flip Glauber dynamics, which is
driven far from equilibrium by an applied field, is studied by an analytic
mean-field, nonlinear-response theory [P.A. Rikvold and M. Kolesik, J. Stat.
Phys. 100, 377 (2000)] and by dynamic Monte Carlo simulations. The probability
density of the height of an individual step in the surface is obtained, both
analytically and by simulation. The width of the probability density is found
to increase dramatically with the magnitude of the applied field, with close
agreement between the theoretical predictions and the simulation results.
Excellent agreement between theory and simulations is also found for the
field-dependence and anisotropy of the interface velocity. The joint
distribution of nearest-neighbor step heights is obtained by simulation. It
shows increasing correlations with increasing field, similar to the skewness
observed in other examples of growing surfaces.Comment: 18 pages RevTex4 with imbedded figure