Selected Recent Presentations
Per Arne Rikvold
prikvold@fsu.edu
Invited talk at
Eco Summit 2007
Beijing, China, May 22-26, 2007.
Abstract
I report results on eco-systems generated by individual-based models of
biological co-evolution of species. Emphasis will be on the fluctuations
in community structure, diversity, and population levels occurring
during the evolution process. The evolution process is studied by
kinetic Monte Carlo computer simulations over very long time periods
- up to several tens of millions of generations. The multispecies
evolution models studied contain both autotrophs that are able to
directly utilize an external resource, and heterotrophs that must rely on
consumption of one or more autotrophs or other heterotrophs for
support. The interspecies interactions are based on a Holling Type II
functional response for predators (considering the autotrophs as
predators with respect to the external resource), modified by intra- and
interspecies competition. Time series of diversities and population sizes
over very long simulations of tens of millions of generations display
highly correlated fluctuations that give rise to power spectra of
1/f form,
also known as flicker noise. These model-intrinsic dynamic features
correspond to large, correlated extinction events and similarly
correlated bursts of new species, without the need for external
catastrophic events. A future goal of the research is to study how the
dynamics of extinctions and species-emergence in these models are
influenced by specific external stresses, such as fluctuations in the
external resource level. In the absence of adaptive foraging strategies,
the studied models are quite unstable, switching randomly between
highly diverse and quite species-poor communities. On the other hand,
adaptive foraging is shown to significantly stabilize the resulting
communities, leading to stable, high-diversity eco-systems. The
long-time 1/f noises are relatively unaffected by this effect.
Invited talk at
U.S.-Japan Bilateral Seminar Simulations of Complex Behavior
from Simple Models
Lahaina, HI, July 17-20, 2006.
Abstract
We explore the complex dynamical behavior of simple predator-prey
models of
biological coevolution that account in a reasonably realistic way
for interspecific and intraspecific competition for resources,
as well as adaptive foraging behavior.
In long kinetic Monte Carlo simulations of these models we
find quite robust 1/f-like noise in species diversity and
population sizes, as well as power-law distributions for the
lifetimes of individual species and the durations of quiet
periods of evolutionary stasis.
Invited talk at
SPIE (The International Society for Optical Engineering)
International Symposium on Fluctuations and Noise
Noise in Complex Systems and Stochastic Dynamics III
Austin, TX, May 24-26, 2005
Abstract
Fluctuations in diversity and extinction sizes are discussed and
compared for two different, individual-based models of biological
coevolution. Both models display power-law distributions for
various quantities of evolutionary interest, such as
the lifetimes of individual species, the quiet periods between
evolutionary upheavals larger than a given cutoff, and the sizes
of extinction events. Time series of the diversity and
measures of the size of extinctions give rise to flicker
noise. Surprisingly, the power-law behaviors of the probability
densities of quiet periods in the two models differ, while the
distributions of the lifetimes of individual species are the same.
See: P. A. Rikvold,
arXiv:q-bio:PE/0502046.
Invited talk at
the 207th Meeting of the Electrochemical Society
Quebec City, Canada, May 16-20, 2005
Abstract
The Ziff-Gulari-Barshad (ZGB) model of CO oxidation on a catalytic
surface corresponds to a Langmuir-Hinshelwood process.
For high CO
pressure the model produces a CO poisoned state in agreement with
experiments. If CO desorption is not allowed (corresponding to low
temperature in experiments), the poisoning is irreversible.
However, with a low rate of desorption (corresponding to higher
temperatures), the surface can be decontaminated by reducing the CO
pressure.
The poisoning of the catalytic surface corresponds to a
discontinuous, nonequilibrium phase transition. In the work
reported here, we use the analogy to the dynamics of phase
transformations near equilibrium phase transitions to
analyze the time evolution of the poisoning and decontamination
processes. We find that the time evolution is well described by a
modified form of the classic Kolmogorov-Johnson-Mehl-Avrami (KJMA)
theory of phase transformations. We map out the transition value of
the CO pressure as a function of the desorption rate, and
we show that the dynamics of the poisoning and decontamination
processes differ, depending on whether the pressure is close to or
far away from the transition line. Far from the transition
line, the processes are near deterministic and well described by
the classic KJMA theory, while close to the
transition the time until full poisoning or decontamination is
random and follows an exponential distribution. The pressure range
in which this
stochastic behavior is observed shrinks to zero logarithmically in
the size of the catalytic surface.
By periodically varying the CO pressure about its transition value,
we show that the system can can be made to undergo a Dynamic Phase
Transition (DPT) at a critical value of the period of the pressure
variation. Such DPTs have been observed in magnetic systems subject
to an oscillating field, but to our knowledge it is the first time
one is predicted in a far-from-equilibrium catalytic system. At the
DPT, the CO2 production rate is significantly enhanced,
compared to its maximum value under constant CO pressure. This
enhancement may have practical applications.
See: E. Machado, G. M. Buendía,
P. A. Rikvold, and R. M. Ziff,
arXiv:cond-mat/0506271.
Invited talk at
The 2004 Joint International Meeting of The Electrochemical Society and
The Electrochemical Society of Japan
Honolulu, HI, October 3-8, 2004.
Abstract
We use kinetic Monte Carlo simulations to study the effect of the ratio
between the rate of adsorption/desorption and the rate of lateral
adsorbate diffusion on the structure of submonolayers formed during
electrodeposition. In particular we study the time evolution of the
island size distribution during potential-step and potential-pulse
conditions, in which the electrode potential is brought eiter
permanently or only for a short time beyond the threshold for
submonolayer adsorption. In the former case, the adlayer grows
monotonically toward
saturation, while in the latter, the potential is reversed at a partial
coverage, after which the adlayer desorbs. Below the critical island size,
beyond which islands are more likely to grow than to decay, the size
distribution is relatively independent of the lateral diffusion rate and
well described by a metastable distribution of lattice animals. For
high coverages, the size distribution of large islands is dominated by
coalescence. An striking effect of rapid diffusion is to open a ``gap''
in the island-size distribution, so that the adlayer consists mainly of
very large and very small islands. We also note significant differences
between the structures of growing and desorbing adlayers at the same
coverage.
See: S. Frank, D. E. Roberts, and P. A. Rikvold,
arXiv:cond-mat/0409518.
Invited talk at
U.S. National Science Foundation / European Commission
Workshop: Methods in Computational Materials Science
San Francisco, CA, April 15-16, 2004.
Abstract
Kinetic Monte Carlo simulation is a useful tool to study the dynamics of
physical and chemical systems on mesoscopic and macroscopic time scales
much longer than the picosecond scales accessible with molecular
dynamics. However, the Monte Carlo transition rates are not, in general,
known from first principles. Often it is therefore assumed that 'minor'
differences between dynamics are not very important, as long as they
obey detailed balance and thus eventually bring the system to
thermodynamic equilibrium. In this talk I will show that this view is
too simplistic, and that very significant differences are found in the
structure and mobility of driven interfaces [1], as well as in nucleation
rates at low temperatures [2], between kinetic Ising systems evolving under
different stochastic dynamics. In particular, I will discuss the
differences between "hard" dynamics (such as the standard Glauber and
Metropolis rates), in which the effects of the interactions and the
applied field do not factorize in the transition rate, and "soft"
dynamics that possess such a factorization property. In additin to the
hard and soft Glauber cases, I will also consider rates that contain
local energy barriers between the individual system states [3], including
the one-step-dynamic [4] and the transition-dynamics-approximation [5].
The moral of my story is that great care must be shown in devising
stochastic Monte Carlo dynamics for specific systems if the
time-dependent results are going to be physically meaningful.
1. P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000);
J. Phys. A 35, L117 (2002); Phys. Rev. E 66, 066116 (2002);
Phys. Rev. E 67, 066113 (2003).
2. K. Park, P.A. Rikvold, G.M. Buendia, and M.A. Novotny,
Phys. Rev. Lett. 92, 015701 (2004).
3. G.M. Buendia, P.A. Rikvold, K. Park, and M.A. Novotny, submitted to
J. Chem. Phys, cond-mat/0402537.
4. H.C. Kang and W.H. Weinberg, J. Chem. Phys. 90, 2824 (1989).
5. T. Ala-Nissila, J. Kjoll, and S.C. Ying, Phys. Rev. B 46, 846 (1992).
Invited talk at
Centre Europeen de Calcul Atomique et Moleculaire (CECAM)
Workshop Dynamics of Evolution
Ecole Normale Superieure de Lyon, Lyon, France, July 28-30, 2003.
Abstract
We present a study by linear stability analysis and large-scale Monte
Carlo simulations of a simple model of biological coevolution. Selection
is provided through a reproduction probability that contains
quenched, random interspecies interactions, while genetic variation is
provided through a low mutation rate. Both selection and mutation
act on individual organisms.
Consistent with some current theories of macroevolutionary dynamics,
the model displays intermittent, statistically self-similar
behavior with punctuated equilibria.
The probability density for the lifetimes of ecological
communities is well approximated by a power law with exponent
near -2, and the corresponding power spectral
densities show 1/f noise (flicker noise) over several decades.
The long-lived communities (quasi-steady states) consist of
a relatively small number of mutualistically interacting species,
and they are surrounded by a ``protection zone'' of closely related genotypes
that have a very low probability of invading the resident community.
The extent of the protection zone affects the stability of the community
in a way analogous to the height of the free-energy barrier surrounding
ametastable state in a physical system.
Measures of biological diversity are on average stationary
with no discernible trends, even over our
very long simulation runs of approximately 3.4x1E7 generations.
See: P. A. Rikvold and R. K. P. Zia,
arXiv:nlin.AO/0303010
and
arXiv:nlin.AO/0306023.
Invited talk at
Faraday Discussion 121: The Dynamic Electrode Surface
Fritz-Haber-Institut, Berlin, Germany, April 15-17, 2002
Abstract
We investigate the static and dynamic behaviors of a Br adlayer i
electrochemically deposited onto single-crystal Ag(100)
using an off-lattice model of the adlayer.
Unlike previous studies using a lattice-gas model,
the off-lattice model allows adparticles to be located at any position
within a two-dimensional approximation to the substrate.
Interactions with the substrate are approximated by a corrugation potential.
Using Density Functional Theory (DFT) to calculate surface binding energies,
a sinusoidal approximation to the corrugation potential is constructed.
A variety of techniques, including Monte Carlo and Langevin simulations,
are used to study the behavior of the adlayer.
The lateral root-mean-square (rms) deviation of the adparticles
from the binding sites
is presented along with equilibrium coverage isotherms,
and the thermally activated Arrhenius barrier-hopping model
used in previous dynamic Monte Carlo
simulations is tested.
Proceedings article
S. J. Mitchell, S. Wang, and P. A. Rikvold,
Faraday Discussions 121, 53-69 (2002).
Discussion:
Faraday Discussions 121, 116-120 (2002).
Preprint:
arXiv:cond-mat/0112299.
Dynamics of Magnetization Reversal in Models of Magnetic Nanoparticles
and Ultrathin Films
HTML
(with animations),
PDF
(reduced quality, without animations)
Invited talk at
International Workshop on Nanostructured Magnetic Materials and their
Applications
Gebze Institute of Technology, Gebze, Turkey, September 3-7, 2001.
Abstract
We present numerical and theoretical results for models of magnetization
switching in nanoparticles and ultrathin films. The models and
computational methods include kinetic Ising models of highly anisotropic
magnets which are simulated by dynamic Monte Carlo methods, and
micromagnetics models of continuum-spin systems that are studied by
finite-temperature Langevin simulations. The theoretical analysis builds
on the fact that a magnetic particle that is magnetized in a direction
antiparallel to the applied field is in a metastable state. Nucleation
theory is therefore used to analyze magnetization reversal as the decay of
this metastable phase to equilibrium. We present results on magnetization
reversal in pure systems, as well as effects of impurities and surfaces,
and hysteresis in magnets driven by oscillating external fields.
Proceedings article
P. A. Rikvold, G. Brown, S. J. Mitchell, and M. A. Novotny.
In Nanostructured Magnetic Materials and their Applications,
edited by D. Shi, B. Aktas, L. Pust, and F. Mikailov,
Springer Lecture Notes in Physics, Vol. 593
(Springer, Berlin, 2002), pp. 164-182.
Preprint:
arXiv:cond-mat/0110103.
The cond-mat preprint version does not contain Fig. 1. A PDF file with
all figures is found
here.
Analytic Approximations for the Velocity of Field-driven
Ising and SOS Interfaces
HTML
(with animations),
PDF
(reduced quality, without animations)
Invited talk at
University of California at Los Angeles
Institute of Pure and Applied Mathematics
Workshop on Material Interfaces and Geometrically Based Motions
Los Angeles, CA, April 23-27, 2001
Abstract
We present an analytic nonlinear-response approximation which yields
estimates for the field, temperature, and orientation dependences of the
velocity of an interface in a two-dimensional kinetic Ising model, driven
by a nonzero field at temperatures below the bulk critical temperature [1].
The interface mobility depends on the local interface structure,
and the Solid-on-Solid (SOS) approximation is used to estimate field-dependent
mean spin-class populations, from which the mean interface velocity can be
obtained for any specific single-spin-flip dynamic. In the low-temperature
limit the standard polynuclear growth and single-step models are
recovered for interfaces making small and large angles with the
latice-symmetry directions, respectively. In the case of the Glauber
dynamic the analytic results are compared with Monte Carlo simulations.
Very satisfactory agreement is found in a wide range of field, temperature,
and interface orientation, both for the Ising model and for a modified model
in which the interface is constrained to maintain an SOS configuration at all
times. For the latter model we also present results for the correlations
between nearest-neighbor step heights, illustrating how the up-down symmetry
of the interface is gradually destroyed as the field is increased.
[1]
P. A. Rikvold and M. Kolesik.
J. Stat. Phys. 100, 377-403 (2000).
Preprint:
cond-mat/9909188.
Dynamic Simulations of X-ray Scattering
Intensities and Cyclic Voltammograms for
Halide Electrosorption on Single-crystal Silver
HTML
(with animations),
PDF
(reduced quality, without animations)
Invited talk at
Symposium on Electrochemical Surface Science on the
Molecular/Atomic Scale at the
2000 International Chemical Congress of Pacific Basin Societies
(PACIFICHEM 2000)
Honolulu, HI, December 14-19, 2000
Abstract
We present new results from dynamic Monte Carlo simulations of the dynamics
of halide adsorption on single-crystal noble-metal electrodes, in particular Br
on Ag(100) [1,2]. This system undergoes a continuous phase transition between a
disordered phase for negative electrode potentials, and an ordered c(2X2) phase
for positive potentials. The dynamic Monte Carlo algorithm includes adsorption,
desorption, and nearest- and next-nearest neighbor diffusion, with barriers
estimated from ab initio calculations. Using this algorithm, we perform
simulations that predict the time dependent intensities of surface X-ray
scattering experiments following sudden potential steps across the phase
transition. We also provide simulated cyclic voltammograms and current
transients following positive and negative potential steps.
[1] S. J. Mitchell, G. Brown, and P. A. Rikvold,
J. Electroanal. Chem. 493, 68-74 (2000).
Preprint:
arXiv:cond-mat/0005249.
[2] S. J. Mitchell, G. Brown, and P. A. Rikvold,
Surf. Sci. 471, 125-142 (2001).
Preprint:
arXiv:cond-mat/0007079.
Nucleation Theory and the Decay of Metastable Phases
HTML
(with animations),
PDF
(reduced quality, without animations)
Invited departmental colloquium at
The Department of Physics, University of Missouri at Rolla
December 7, 2000
Abstract
Metastable phases are ubiquitous in nature, with examples ranging from
supercooled water to the quark-gluon plasma. Such phases are easily
mistaken for true equilibrium phases, and unless they are strongly
perturbed, they can exist for a very long time. Typically, a metastable
phase decays suddenly to the true equilibrium through the random nucleation of
one or many critical droplets of the equilibrium phase. In this talk I will
discuss some aspects of the nucleation theory of metstable decay, with
particular emphasis on finite-size effects that are important when
considering real systems. The principles will be illustrated with
simulation results on magnetization switching in models of magnetic
nanoparticles and ultrathin films. As the recording density of magnetic
disks rapidly increases, this is an area of critical interest to the
computer industry.
Invited lecture at
Symposium on Computer Simulation in Electrochemistry at the
220th American Chemical Society National Meeting,
Washington, DC, August 20-24, 2000.
Abstract
We present new results from dynamic Monte Carlo simulations of the dynamics of
bromine electrosorption on single-crystal Ag(100). This system has a
continuous phase transition which
separates a disordered phase at negative electrode potentials from an
ordered c(2X2) phase at positive potentials [1]. Our dynamic Monte Carlo algorithm
includes adsorption, desorption, and nearest- and next-nearest neighbor lateral
diffusion, with barriers estimated from ab-initio calculations in the
literature. With this algorithm we simulate cyclic voltammograms and current
transients following positive and negative potential steps [2], as well as
time-dependent intensities of surtace X-ray
scattering experiments following sudden potential steps across the phase
transition [3].
[1] B.M Ocko, J.X. Wang, and Th. Wandlowski, Phys. Rev. Lett. 79, 1511 (1997).
[2] S.J. Mitchell, G. Brown, and P.A. Rikvold,
J. Electroanal. Chem. 493, 68-74 (2000).
Preprint:
cond-mat/0005249.
[3] S.J. Mitchell, G. Brown, and P.A. Rikvold,
Surf. Sci. 471, 125-142 (2001).
Preprint:
cond-mat/0007079.
Contributed poster at
Gordon Research Conference on Physics Research and
Education, Plymouth, NH, June 11-16, 2000.
Abstract
It has struck us how students at all levels often have very weak intuition
about the physical world. This is probably partly
due to the increasing sophistication of our surroundings. While children of
previous generations played with mechanical
toys whose workings they could actually observe, today's children are
surrounded by electronic toys and appliances. To
understand the workings of those often requires an advanced degree in
physics or engineering, and all that is visible with
the naked eye are a few plastic squares with metal contacts. Partly to
help foster the physical intuition of students at
various levels, and partly as a way of amusing ourselves, we have devised
a few models from standard LEGO parts, that
illustrate some of the principles of mechanics, thermodynamics, and robotics.
These include several compressed-air
engines modeled on historic steam engines and locomotives, and a robot that
sorts LEGO bricks according to color. The
models have been used as demonstrations in introductory university physics
classes, and in a one-semester mentorship
program with middle-school students.
Contributed talk at
The March Meeting of the American Physical Society, Minneapolis, MN,
March 20-24, 2000.
Abstract
Numerical and analytical results [
G. Brown, et al., Phys. Rev. E 56, 6601 (1997);
60, 5151 (1999)]
applicable to the
time-dependent intensity covariance of the speckle intensity at wave
vector k are presented. That the covariance can
be used to experimentally measure the two-time structure factor of
phase-segregating materials is established by direct
comparision of numerical estimates of both quantities. The relationship is
observed to break down only at very large k.
For systems in which the characteristic domain size grows with time tau
as R = [B tau]^n, the scaling behavior of the
two-time structure factor is obtained analytically from geometric arguments
based on a simple moving-interface picture
at both large and small t-bar = k^{1/n} B (tau_1 + tau_2)/2.
Specifically, the asymptotic scaling of the two-time structure
factor for small t-bar is in terms of delta t / t-bar,
with delta t = k^{1/n} B|tau_2 - tau_1| .
For large t-bar, the appropriate
scaling variable is delta t / t-bar^{1-n}. These predictions have been
verified in recent experiments [
A. Malik, et al., Phys. Rev. Lett. 81, 5832 (1998);
F. Livet, et al. (unpublished)]. In the large t-bar limit, an analytic
scaling function is
obtained that agrees well with the simulation results.
Invited lecture at
1999 Joint International Meeting of the
Electrochemical Society and the Electrochemical Society of Japan.
Honolulu, HI, October 18-22, 1999.
Abstract
Modern in situ experimental techniques to
study the microscopic structure of electrode--electrolyte interfaces,
such as synchrotron X-ray diffraction [1,2] and various scanning
microscopies, are providing increasingly detailed information
that can be compared with theoretical model studies.
A theoretical method which is particularly well suited to modeling the
microscopic structure of chemisorbed single- and multi-adsorbate systems
is Monte Carlo simulation of lattice-gas models [3]. Such models describe the
adsorbate layer by a Hamiltonian which gives the energies of different
microscopic adsorbate configurations [3,4].
Here we present results from equilibrium and dynamic
Monte Carlo simulations of the
electrosorption of Br on single-crystal Ag(100). In recent X-ray scattering
studies this system was shown to undergo a continuous order-disorder
transition from a disordered low-coverage phase at low potentials to an
ordered c(2X2) phase at higher potentials. The transition was found to
be in the universality class of the two-dimensional Ising model,
as expected from the symmetry of the ordered phase [1]. For the
electrolyte compositions used in the experiments, the
critical value of the electrode potential lies in the range
-0.8 to -0.6V vs SCE, with lower transition potentials
corresponding to higher Br concentrations [5].
Following Koper [6] we performed equilibrium Monte Carlo simulations of
a lattice-gas model in which the Br adsorbs at the four-fold hollow sites
on the Ag(100) surface. Consistent with Koper's results, we find that the
equilibrium
isotherms are well represented by a lattice-gas model with
strongly repulsive nearest-neighbor interactions, which can be approximated
by nearest-neighbor exclusion (the hard-square model),
plus a repulsive dipole-dipole interactions which falls off as
r-3.
The dynamic simulations use an algorithm which allows the following moves:
-
Adsorption and desorption.
-
Diffusion between nearest-neighbor sites.
-
Diffusion between next-nearest neighbor sites.
The rate for each process is determined by thermal excitation across a
transition state whose free energy is determined by a barrier value and,
through a Butler-Volmer approximation, by the electrochemical potentials of
the initial and final states [2,7]. The barriers are estimated from
ab initio calculations [8] of the differences between the Br binding
energies at four-fold hollow, bridge, and on-top sites.
Nearest-neighbor diffusion corresponds to moving between two hollow sites
across a bridge site, while next-nearest-neighbor diffusion involves
going across an on-top site. The barrier for adsorption/desorption is
estimated to be on the order of twice the next-nearest-neighbor barrier.
Using this dynamic Monte Carlo algorithm we calculate the Br coverage and the
c(2X2) order parameter as functions of time, following rapid potential
steps across the phase transition. Data for the time-dependent
scattering intensities near
the (1/2,1/2) and (1,1) diffraction peaks are also presented.
In agreement with the theoretical expectation for phase-ordering systems
with non-conserved order parameter, the characteristic size of the
ordered-phase domains is observed to grow as (time)1/2.
-
B. M. Ocko, J. X. Wang, and T. Wandlowski,
Phys. Rev. Lett. 79, 1511 (1997).
-
G. Brown, P. A. Rikvold, S. J. Mitchell, and M. A. Novotny,
in Interfacial Electrochemistry: Theory, Experiment,
and Applications, edited by A. Wieckowski
(Marcel Dekker, New York, 1999).
Preprint:
cond-mat/9805126.
-
P. A. Rikvold, J. B. Collins, G. D. Hansen,
and J. D. Gunton,
Surf. Sci. 203, 500 (1988).
Abstract.
-
L. Blum, Adv. Chem. Phys. 78, 171 (1990).
-
J. X. Wang, T. Wandlowski, and B. M. Ocko,
Electrochem. Soc. Proc. 97-17, 293 (1997).
-
M. T. M. Koper, J. Electroanal. Chem. 450, 189 (1998).
-
P. A. Rikvold, G. Brown, M. A. Novotny, and A. Wieckowski,
Coll. Surf. A 134, 3 (1998)
Preprint:
cond-mat/9703209;
G. Brown, P. A. Rikvold, M. A. Novotny, and A. Wieckowski,
J. Electrochem. Soc. 146, 1035 (1999) .
Preprint:
cond-mat/9709320.
Related MPEG animations at
this URL.
-
A. Ignaczak and J. A. N. F. Gomes,
J.Electroanal. Chem. 420, 71 (1997).
Invited lecture at
International Materials Research Congress.
Cancun, Mexico, August 29 - September 2, 1999.
Abstract
Anisotropic, single-domain ferromagnetic particles are promising
for technological applications such as ultra-high density recording
media. Since such particles do not have
domain walls in equilibrium, traditional wall-motion
descriptions of the switching are inadequate.
Here we describe an approach which emphasizes that a ferromagnetic
particle in an unfavorable field is metastable.
Switching from the antiparallel to the parallel magnetization
state occurs through random nucleation and growth of
droplets, inside which the magnetization is parallel to the field [1,2]. We
summarize relevant results of nucleation theory and present
simulations of model single-domain
ferromagnets. Since metastable decay involves microscopic and macroscopic
time scales separated by many orders of magnitude,
sophisticated algorithms are needed [3].
We present comparisons between our results and experiments,
including the often observed maximum in the switching field as a function
of grain size,
recent observations of a maximum of the coercivity versus coverage in
magnetic sesquilayers, and new results on the frequency dependence of
hysteresis-loop areas at very low frequencies.
-
``Magnetization Switching in Nanoscale Ferromagnetic Grains:
Description by a Kinetic Ising Model.''
H. L. Richards, S. W. Sides, M. A. Novotny,
and P. A. Rikvold.
J. Magn. Magn. Mater. 150, 37-50 (1995).
Preprint:
cond-mat/9412120.
-
``Nucleation Theory of Magnetization Reversal in Nanoscale Ferromagnets.''
P. A. Rikvold, M. A. Novotny, M. Kolesik,
and H. L. Richards.
In Dynamical Properties of Unconventional Magnetic Systems,
edited by A. T. Skjeltorp and D. Sherrington.
NATO Science Series E: Applied Sciences
(Kluwer, Dordrecht, 1998), Vol. 349, pp. 307-316.
Preprint:
cond-mat/9705189.
Invited lecture at
Workshop on Parallel Algorithms, Computational
Efficiency, and Multiscale Materials Simulations.
New Orleans, LA, April 2-3, 1999.
Abstract
We summarize some algorithms developed in our group to accelerate
simulations of metastable decay, without changing the underlying
dynamics. These include the Constrained Transfer Matrix (CTM) method,
the Monte Carlo with Absorbing Markov Chains (MCAMC) method, serial and
massively parallel implementations of the n-fold Way method of
Bortz, Kalos, and Lebowitz, and the Projective Dynamics method.
Metastable life times up to 1060 Monte Carlo Steps per Site
(MCSS) have been measured with these methods.
Invited lecture at
The Twelfth Workshop on Computer Simulation Studies in Condensed Matter
Phyiscs.
Center for Simulational Physics, The University of Georgia, Athens, GA,
March 8-12, 1999.
Abstract
We briefly introduce hysteresis
in spatially extended systems and the
dynamic phase transition
observed as the frequency of the oscillating field
increases beyond a critical value.
Hysteresis and the decay of metastable phases
are closely related
phenomena, and a dynamic phase transition can occur only for field amplitudes,
temperatures, and system sizes at which the metastable
phase decays through nucleation and growth of many droplets.
We present preliminary results from extensive
Monte Carlo simulations
of a two-dimensional kinetic Ising model
in a square-wave
oscillating field and estimate critical exponents
by finite-size scaling
techniques adapted from equilibrium
critical phenomena.
The estimates are consistent with the
universality class
of the two-dimensional
equilibrium Ising model and inconsistent with two-dimensional random
percolation.
However, we are not aware of any theoretical arguments indicating
why this should be so. Thus, the question of the universality
class of this nonequilibrium critical phenomenon remains open.
Proceedings article
``Dynamic Phase Transition and Hysteresis in Kinetic Ising Models.''
P. A. Rikvold, G. Korniss, C. J. White, M. A. Novotny,
and S. W. Sides.
In Computer Simulation Studies in Condensed Matter Physics XII,
edited by D. P. Landau, S. P. Lewis, and H. B. Schüttler,
(Springer, Berlin, 2000), pp. 105-119.
Preprint:
cond-mat/9904028.
Invited lecture at
International Symposium Beyond Statistical Mechanics
In honor of Professor Jens Feder on his 60th birthday.
The Norwegian Academy of Science and Letters, Oslo, Norway,
January 11-12, 1999.
Abstract
Hysteresis is considered for a kinetic Ising model in an oscillating
field. The system has a dynamic phase transition (DPT) at a specific
frequency of the applied field.
Finite-size scaling estimates are provided for the critical frequency and the
critical indices alpha, gamma, and nu, and it is argued that the DPT
corresponds to a nontrivial critical point.
Invited lecture at
International Workshop on Nonequilibrium Dynamics
Center for Nonlinear Science, Los Alamos National Laboratory,
Los Alamos, NM
April 20-22, 1998
Abstract
We consider hysteresis for a two-dimensional,
spin-1/2, nearest-neighbor, kinetic Ising
ferromagnet in an oscillating
field, using Monte Carlo simulations.
The period-averaged magnetization
is the order parameter for a proposed dynamic phase transition (DPT).
To quantify the nature of this transition,
we present the first finite-size scaling study of the DPT
for this model.
Evidence of a diverging correlation length is given,
and we provide estimates of the transition frequency and the
critical indices beta, gamma, and nu.
Invited lecture at
International Symposium on Current Issues in
Non-Equilibrium Statistical Mechanics and Materials
In honor of Professor James D. Gunton on his 60th birthday
Lehigh University, Bethlehem, PA, October 24-25, 1997
Abstract
The Kolmogorov-Johnson-Mehl-Avrami (KJMA) approximation, or ``Avrami's Law,''
for the decay of a metastable phase was proposed almost sixty years ago.
It amounts to an extremely simple approximation, which has come to be widely
used in areas from metallurgy to food science and cosmology. Despite its
simplicity and popularity, few direct numerical tests of its range of
validity have been performed for a simple model system. Here we present such
a test for the two-dimensional kinetic Ising model
in an applied field. Despite its simplicity, we find the approximation
amazingly accurate and robust.
Invited lecture at
The 1997 Joint International Meeting of The
Electrochemical Society and The International Society of
Electrochemistry
Paris, France, August 31 - September 5, 1997
Abstract
We present results of dynamical Monte Carlo simulations of potential-step
experiments for the underpotential deposition of copper with sulfate
on gold (111)
single-crystal electrodes. The results are in good, semiquantitative
agreement with experimental results by Hölzle et al. and indicate the
applicability of dynamic simulations to electrochemical adsorption problems.
Invited lecture at
NATO Advanced Study Institute
Dynamical Properties of Unconventional Magnetic Systems
Geilo, Norway, April 2-12, 1997
Abstract
Highly anisotropic, single-domain ferromagnetic particles are currently
considered for applications in ultra-high density magnetic recording
media. Since such particles do not have internal domain walls in equilibrium,
traditional wall-motion descriptions of the switching dynamics are
inadequate. Recent observations of individual particles by methods such as
Magnetic Force Microscopy (MFM) also indicate that the dynamics is not well
described by the Néel-Brown theory of uniform magnetization rotation.
Here we describe an approach in which it is emphasized that a ferromagnetic
particle in an unfavorable field is in fact a metastable system, like a
supersaturated solution or vapor. The switching is accomplished through the
nucleation and subsequent growth of localized droplets, inside which the
magnetization has its equilibrium value. We summarize relevant results of
nucleation theory and present data from Monte Carlo simulations of kinetic
Ising models of single-domain ferromagnets. The nucleation and growth
processes are modified by a variety of boundary conditions, magnetostatic
interactions, and impurities. We emphasize the effects of the particle size
on the switching dynamics and present qualitative and quantitative
comparisons between our results and experiments. These results include the
often observed maximum in the switching field as a function of grain size,
as well as recent observation of a maximum of the coercivity versus coverage
in magnetic sesquilayers.
Proceedings article
``Nucleation Theory of Magnetization Reversal in Nanoscale
Ferromagnets.''
P. A. Rikvold, M. A. Novotny, M. Kolesik,
and H. L. Richards.
In Dynamical Properties of Unconventional Magnetic Systems,
edited by A. T. Skjeltorp and D. Sherrington.
NATO Science Series E: Applied Sciences
(Kluwer, Dordrecht, 1998), Vol. 349, pp. 307-316.
Preprint:
cond-mat/9705189.
Related MPEG animations at
this URL.
Invited lecture at
The National Meeting of the American Chemical
Society
Symposium on Electrochemical Surface Science on the International
Scene
Orlando, FL, August, 1996
Abstract
We discuss applications of statistical-mechanical lattice-gas models to
electrochemical adsorption. We summarize studies of adsorption on
single-crystal electrodes, presenting simulated and experimental coverages and
voltammetric currents for urea on Pt(100) and the underpotential deposition
of Cu on Au(111) in sulfuric acid. We also discuss
an extension of the method to study
time-dependent phenomena far from equilibrium.
Proceedings article
``Equilibrium and Nonequilibrium Applications of
Lattice-Gas Models in Electrochemistry.''
P. A. Rikvold, G. Brown, M. A. Novotny, and
A. Wieckowski.
Colloids and Surfaces A: Physicochemical and Engineering
Aspects 134, 3-14 (1998).
Preprint:
cond-mat/9703209.
Invited lecture at
Second East-West Surface Science Workshop (EWSSW96)
Pamporovo, Bulgaria, February 17-25, 1996
Abstract
A technique of statistical-mechanical lattice-gas modeling
of chemisorption, applicable to electrochemical systems
dominated by lateral interactions, is reviewed.
A strategy for applying
the method to specific systems is outlined. This includes
microscopic model formulation, calculation of zero-temperature phase
diagrams, numerical calculation of thermodynamical
and structural quantities at nonzero temperatures,
and estimation of the effective, lateral interaction energies.
The general discussion is illustrated by applications to the following
specific problems.
The poisoning by sulfur
of hydrogen adsorption on platinum (111),
the electrochemical adsorption
of organics on polycrystalline copper and nickel and of urea
on single-crystal
platinum (100), and the underpotential deposition of
copper on single-crystal gold (111).
Proceedings article
``Phase Transitions in Electrochemical Adsorption.''
P. A. Rikvold and A. Wieckowski.
In Thin Films and Phase Transitions on Surfaces;
Proceedings of the Second East-West Surface Science
Workshop, EWSSW96, Pamporovo, Bulgaria, February 18-24, 1996,
edited by M. Michailov
(Institute of Physical Chemistry,
Bulgarian Academy of Sciences, Sofia, 1996), pp. 58-75.
Abstract.
Invited lecture at
International Union for Vacuum Science, Technology, and
Applications
Workshop on Surface Science and Electrochemistry
San Benedetto del Tronto, Italy, September 12-16, 1994
Abstract
Lattice-gas modeling is applied to
electrochemical adsorption on catalytically active metal substrates: urea on
Pt(100) and (bi)sulfate on Rh(111). Both involve specific adsorption of
small molecules or ions on single-crystal electrodes.
Ordered submonolayer adsorbate phases are formed
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 in situ radiochemical surface
concentration measurements, cyclic voltammetry, and scanning tunneling
microscopy,
and ex situ Auger electron spectroscopy and low-energy electron
diffraction, we have developed specific models for the two
systems. These models were studied by group-theoretical ground-state
calculations and numerical Monte Carlo simulations, and effective interaction
parameters were determined so as to provide agreement with experiments.
Proceedings article
``Computational Lattice-Gas Modeling of the Electrosorption of
Small Molecules and Ions.''
P. A. Rikvold, M. Gamboa-Aldeco, J. Zhang, M. Han,
H. L. Richards, Q. Wang, and A. Wieckowski.
Surf. Sci. 335, 389-400 (1995).
Preprint:
cond-mat/9409121.
Related MPEG animations at
this URL.
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