Response of a Model of CO Oxidation with CO Desorption and Diffusion to a Periodic External CO Pressure

We present a study of the dynamical behavior of a Ziff-Gulari-Barshad model with CO desorption and lateral diffusion. Depending on the values of the desorption and diffusion parameters, the system presents a discontinuous phase transition between low and high CO coverage phases. We calculate several points on the coexistence curve between these phases. Inclusion of the diffusion term produces a significant increase in the CO_2 production rate. We further applied a square-wave periodic pressure variation of the partial CO pressure with parameters that can be tuned to modify the catalytic activity. Contrary to the diffusion-free case, this driven system does not present a further enhancement of the catalytic activity, beyond the increase induced by the diffusion under constant CO pressure.Comment: 5 pages, RevTe

Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors.Concerning the kinetics, it is shown that the extended volume evolves with time according to alpha_ex=[exp(kappa Ct)]^m+1, where t' is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters

Values and Heritage Conservation: Research Report, The Getty Conservation Institute, Los Angeles

Researches values and benefits of cultural heritage conservation undertaken by GCI through its Agora initiative as a means of articulating and furthering ideas that have emerged from the conservation field in recent years

Avrami exponent under transient and heterogeneous nucleation transformation conditions

The Kolmogorov-Johnson-Mehl-Avrami model for isothermal transformation kinetics is universal under specific assumptions. However, the experimental Avrami exponent deviates from the universal value. In this context, we study the effect of transient heterogeneous nucleation on the Avrami exponent for bulk materials and also for transformations leading to nanostructured materials. All transformations are assumed to be polymorphic. A discrete version of the KJMA model is modified for this purpose. Scaling relations for transformations under different conditions are reported.Comment: 19 pages, 6 figures Accepted for publication in Journal of Non-Crystalline Solid

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

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

Can randomness alone tune the fractal dimension?

We present a generalized stochastic Cantor set by means of a simple {\it cut and delete process} and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, $m$ and $b$, are introduced which tune the relative strength of the two processes and the degree of randomness respectively. In doing so, we have identified a new set with a wide spectrum of subsets produced by tuning either $m$ or $b$. Measuring the size of the resulting set in terms of fractal dimension, we show that the fractal dimension increases with increasing order and reaches its maximum value when the randomness is completely ceased.Comment: 6 pages 2-column RevTeX, Two figures (presented in the APCTP International Symposium on Slow Dynamical Processes in Nature, Nov. 2001, Seoul, Korea

Easy collective polarization switching in ferroelectrics

The actual mechanism of polarization switching in ferroelectrics remains a puzzle for many decades, since the usually estimated barrier for nucleation and growth is insurmountable ("paradox of the coercive field"). To analyze the mechanisms of the nucleation we consider the exactly solvable case of a ferroelectric film with a "dead" layer at the interface with electrodes. The classical nucleation is easier in this case but still impossible, since the calculated barrier is huge. We have found that the {\em interaction} between the nuclei is, however, long range, hence one has to study an {\em ensemble} of the nuclei. We show that there are the ensembles of small (embryonic) nuclei that grow {\em without the barrier}. We submit that the interaction between nuclei is the key point for solving the paradox.Comment: 5 pages, REVTeX 3.1 with one eps-figure. Corrected discussion of single stripe and cylindrical nuclei, and their interaction. The estimate for equilibrium density of embryonic nuclei is added. To appear in Phys. Rev. Letter

Kinetic model of DNA replication in eukaryotic organisms

We formulate a kinetic model of DNA replication that quantitatively describes recent results on DNA replication in the in vitro system of Xenopus laevis prior to the mid-blastula transition. The model describes well a large amount of different data within a simple theoretical framework. This allows one, for the first time, to determine the parameters governing the DNA replication program in a eukaryote on a genome-wide basis. In particular, we have determined the frequency of origin activation in time and space during the cell cycle. Although we focus on a specific stage of development, this model can easily be adapted to describe replication in many other organisms, including budding yeast.Comment: 10 pages, 6 figures: see also cond-mat/0306546 & physics/030615

Mean Field Theory of Polynuclear Surface Growth

We study statistical properties of a continuum model of polynuclear surface growth on an infinite substrate. We develop a self-consistent mean-field theory which is solved to deduce the growth velocity and the extremal behavior of the coverage. Numerical simulations show that this theory gives an improved approximation for the coverage compare to the previous linear recursion relations approach. Furthermore, these two approximations provide useful upper and lower bounds for a number of characteristics including the coverage, growth velocity, and the roughness exponent.Comment: revtex, 7 pages, 4 fig