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

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

Exact results for nucleation-and-growth in one dimension

We study statistical properties of the Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model in one dimension. We obtain exact results for the gap density as well as the island distribution. When all nucleation events occur simultaneously, the island distribution has discontinuous derivatives on the rays x_n(t)=nt, n=1,2,3... We introduce an accelerated growth mechanism where the velocity increases linearly with the island size. We solve for the inter-island gap density and show that the system reaches complete coverage in a finite time and that the near-critical behavior of the system is robust, i.e., it is insensitive to details such as the nucleation mechanism.Comment: 9 pages, revtex, also available from http://arnold.uchicago.edu/~ebn

Computational Methods to Study Kinetics of DNA Replication

New technologies such as DNA combing have led to the availability of large quanti-ties of data that describe the state of DNA while undergoing replication in S phase. In this chapter, we describe methods used to extract various parameters of replica-tion — fork velocity, origin initiation rate, fork density, numbers of potential and utilized origins — from such data. We first present a version of the technique that applies to “ideal ” data. We then show how to deal with a number of real-world complications, such as the asynchrony of starting times of a population of cells, the finite length of fragments used in the analysis, and the finite amount of DNA in a chromosome. Key words: DNA replication, replication fork velocity, origin initiation

Dynamic Phase Transition, Universality, and Finite-size Scaling in the Two-dimensional Kinetic Ising Model in an Oscillating Field

We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multi-droplet regime where the metastable phase decays through nucleation and growth of many droplets of the stable phase. At a critical frequency, the system undergoes a genuine non-equilibrium phase transition, in which the symmetry-broken phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. We investigate the universal aspects of this dynamic phase transition at various temperatures and field amplitudes via large-scale Monte Carlo simulations, employing finite-size scaling techniques adopted from equilibrium critical phenomena. The critical exponents, the fixed-point value of the fourth-order cumulant, and the critical order-parameter distribution all are consistent with the universality class of the two-dimensional equilibrium Ising model. We also study the cross-over from the multi-droplet to the strong-field regime, where the transition disappears

Computer simulation of crystallization kinetics with non-Poisson distributed nuclei

The influence of non-uniform distribution of nuclei on crystallization kinetics of amorphous materials is investigated. This case cannot be described by the well-known Johnson-Mehl-Avrami (JMA) equation, which is only valid under the assumption of a spatially homogeneous nucleation probability. The results of computer simulations of crystallization kinetics with nuclei distributed according to a cluster and a hardcore distribution are compared with JMA kinetics. The effects of the different distributions on the so-called Avrami exponent $n$ are shown. Furthermore, we calculate the small-angle scattering curves of the simulated structures which can be used to distinguish experimentally between the three nucleation models under consideration.Comment: 14 pages including 7 postscript figures, uses epsf.sty and ioplppt.st

Co-firing of biomass with coals Part 1. Thermogravimetric kinetic analysis of combustion of fir (abies bornmulleriana) wood

The chemical composition and reactivity of fir (Abies bornmulleriana) wood under non-isothermal thermogravimetric (TG) conditions were studied. Oxidation of the wood sample at temperatures near 600 A degrees C caused the loss of aliphatics from the structure of the wood and created a char heavily containing C-O functionalities and of highly aromatic character. On-line FTIR recordings of the combustion of wood indicated the oxidation of carbonaceous and hydrogen content of the wood and release of some hydrocarbons due to pyrolysis reactions that occurred during combustion of the wood. TG analysis was used to study combustion of fir wood. Non-isothermal TG data were used to evaluate the kinetics of the combustion of this carbonaceous material. The article reports application of Ozawa-Flynn-Wall model to deal with non-isothermal TG data for the evaluation of the activation energy corresponding to the combustion of the fir wood. The average activation energy related to fir wood combustion was 128.9 kJ/mol, and the average reaction order for the combustion of wood was calculated as 0.30

Metastable lifetimes in a kinetic Ising model: Dependence on field and system size

The lifetimes of metastable states in kinetic Ising ferromagnets are studied by droplet theory and Monte Carlo simulation, in order to determine their dependences on applied field and system size. For a wide range of fields, the dominant field dependence is universal for local dynamics and has the form of an exponential in the inverse field, modified by universal and nonuniversal power-law prefactors. Quantitative droplet-theory predictions are numerically verified, and small deviations are shown to depend nonuniversally on the details of the dynamics. We identify four distinct field intervals in which the field dependence and statistical properties of the lifetimes are different. The field marking the crossover between the weak-field regime, in which the decay is dominated by a single droplet, and the intermediate-field regime, in which it is dominated by a finite droplet density, vanishes logarithmically with system size. As a consequence the slow decay characteristic of the former regime may be observable in systems that are macroscopic as far as their equilibrium properties are concerned.Comment: 18 pages single spaced. RevTex Version 3. FSU-SCRI-94-1

Structure, Photophysics and the Order-Disorder Transition to the Beta Phase in Poly(9,9-(di -n,n-octyl)fluorene)

X-ray diffraction, UV-vis absorption and photoluminescence (PL) spectroscopy have been used to study the well-known order-disorder transition (ODT) to the beta phase in poly(9,9-(di n,n-octyl)fluorene)) (PF8) thin film samples through combination of time-dependent and temperature-dependent measurements. The ODT is well described by a simple Avrami picture of one-dimensional nucleation and growth but crystallization, on cooling, proceeds only after molecular-level conformational relaxation to the so called beta phase. Rapid thermal quenching is employed for PF8 studies of pure alpha phase samples while extended low-temperature annealing is used for improved beta phase formation. Low temperature PL studies reveal sharp Franck-Condon type emission bands and, in the beta phase, two distinguishable vibronic sub-bands with energies of approximately 199 and 158 meV at 25 K. This improved molecular level structural order leads to a more complete analysis of the higher-order vibronic bands. A net Huang-Rhys coupling parameter of just under 0.7 is typically observed but the relative contributions by the two distinguishable vibronic sub-bands exhibit an anomalous temperature dependence. The PL studies also identify strongly correlated behavior between the relative beta phase 0-0 PL peak position and peak width. This relationship is modeled under the assumption that emission represents excitons in thermodynamic equilibrium from states at the bottom of a quasi-one-dimensional exciton band. The crystalline phase, as observed in annealed thin-film samples, has scattering peaks which are incompatible with a simple hexagonal packing of the PF8 chains.Comment: Submitted to PRB, 12 files; 1 tex, 1 bbl, 10 eps figure

A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy $F(m)$ and are designed to give the correct equilibrium distribution for $m$. The connection between macroscopic dynamics and the underlying microscopic dynamic are considered in the context of a projection- operator formalism. Application to the square-lattice nearest-neighbor Ising ferromagnet gives good agreement with droplet theory and Monte Carlo simulations of the underlying microscopic dynamic. This includes quantitative agreement for the exponential dependence of the lifetime on the inverse of the applied field $H$, and the observation of distinct field regions in which the derivative of the lifetime with respect to $1/H$ depends differently on $H$. In addition, at very low temperatures we observe oscillatory behavior of this derivative with respect to $H$, due to the discreteness of the lattice and in agreement with rigorous results. Similarities and differences between this work and earlier works on finite Ising models in the fixed-magnetization ensemble are discussed.Comment: 44 pages RevTeX3, 11 uuencoded Postscript figs. in separate file