Noise-assisted Mound Coarsening in Epitaxial Growth

We propose deposition noise to be an important factor in unstable epitaxial growth of thin films. Our analysis yields a geometrical relation H=(RWL)^2 between the typical mound height W, mound size L, and the film thickness H. Simulations of realistic systems show that the parameter R is a characteristic of the growth conditions, and generally lies in the range 0.2-0.7. The constancy of R in late-stage coarsening yields a scaling relation between the coarsening exponent 1/z and the mound height exponent \beta which, in the case of saturated mound slope, gives \beta = 1/z = 1/4.Comment: 4 pages, RevTex Macros, 3 eps figure

Topics in constrained and unconstrained ordination

In this paper, we reflect on a number of aspects of ordination methods: how should absences be treated in ordination and how do model-based methods, including Gaussian ordination and methods using generalized linear models, relate to the usual least-squares (eigenvector) methods based on (log-) transformed data. We defend detrended correspondence analysis by theoretical arguments and by reanalyzing data that previously gave bad results. We show by examples that constrained ordination can yield more informative views on effects of interest compared to unconstrained ordination (where such effects can be invisible) and show how constrained axes can be interpreted. Constrained ordination uses an ANOVA/regression approach to enable the user to focus on particular aspects of species community data, in particular the effects of qualitative and quantitative environmental variables. We close with an analysis examining the interaction effects between two factors, and we demonstrate how principal response curves can help in their visualisation. Example data and Canoco 5 projects are provided as Supplementary Material

Competition among native and invasive Phragmites australis populations: An experimental test of the effects of invasion status, genome size, and ploidy level

Among the traits whose relevance for plant invasions has recently been suggested are genome size (the amount of nuclear DNA) and ploidy level. So far, research on the role of genome size in invasiveness has been mostly based on indirect evidence by comparing species with different genome sizes, but how karyological traits influence competition at the intraspecific level remains unknown. We addressed these questions in a common-garden experiment evaluating the outcome of direct intraspecific competition among 20 populations of Phragmites australis, represented by clones collected in North America and Europe, and differing in their status (native and invasive), genome size (small and large), and ploidy levels (tetraploid, hexaploid, or octoploid). Each clone was planted in competition with one of the others in all possible combinations with three replicates in 45-L pots. Upon harvest, the identity of 21 shoots sampled per pot was revealed by flow cytometry and DNA analysis. Differences in performance were examined using relative proportions of shoots of each clone, ratios of their aboveground biomass, and relative yield total (RYT). The performance of the clones in competition primarily depended on the clone status (native vs. invasive). Measured in terms of shoot number or aboveground biomass, the strongest signal observed was that North American native clones always lost in competition to the other two groups. In addition, North American native clones were suppressed by European natives to a similar degree as by North American invasives. North American invasive clones had the largest average shoot biomass, but only by a limited, nonsignificant difference due to genome size. There was no effect of ploidy on competition. Since the North American invaders of European origin are able to outcompete the native North American clones, we suggest that their high competitiveness acts as an important driver in the early stages of their invasion

Particle currents and the distribution of terrace sizes in unstable epitaxial growth

A solid-on-solid model of epitaxial growth in 1+1 dimensions is investigated in which slope dependent upward and downward particle currents compete on the surface. The microscopic mechanisms which give rise to these currents are the smoothening incorporation of particles upon deposition and an Ehrlich-Schwoebel barrier which hinders inter-layer transport at step edges. We calculate the distribution of terrace sizes and the resulting currents on a stepped surface with a given inclination angle. The cancellation of the competing effects leads to the selection of a stable magic slope. Simulation results are in very good agreement with the theoretical findings.Comment: 4 pages, including 3 figure

Diamond Solitaire

We investigate the game of peg solitaire on different board shapes, and find those of diamond or rhombus shape have interesting properties. When one peg captures many pegs consecutively, this is called a sweep. Rhombus boards of side 6 have the property that no matter which peg is missing at the start, the game can be solved to one peg using a maximal sweep of length 16. We show how to construct a solution on a rhombus board of side 6i, where the final move is a maximal sweep of length r, where r=(9i-1)(3i-1) is a "rhombic matchstick number".Comment: 11 pages, 12 figure

Coarsening of Surface Structures in Unstable Epitaxial Growth

We study unstable epitaxy on singular surfaces using continuum equations with a prescribed slope-dependent surface current. We derive scaling relations for the late stage of growth, where power law coarsening of the mound morphology is observed. For the lateral size of mounds we obtain $\xi \sim t^{1/z}$ with $z \geq 4$. An analytic treatment within a self-consistent mean-field approximation predicts multiscaling of the height-height correlation function, while the direct numerical solution of the continuum equation shows conventional scaling with z=4, independent of the shape of the surface current.Comment: 15 pages, Latex. Submitted to PR

Impurity-induced diffusion bias in epitaxial growth

We introduce two models for the action of impurities in epitaxial growth. In the first, the interaction between the diffusing adatoms and the impurities is ``barrier''-like and, in the second, it is ``trap''-like. For the barrier model, we find a symmetry breaking effect that leads to an overall down-hill current. As expected, such a current produces Edwards-Wilkinson scaling. For the trap model, no symmetry breaking occurs and the scaling behavior appears to be of the conserved-KPZ type.Comment: 5 pages(with the 5 figures), latex, revtex3.0, epsf, rotate, multico

Nonuniversal mound formation in nonequilibrium surface growth

We demonstrate, using well-established nonequilibrium limited-mobility solid-on-solid growth models, that mound formation in the dynamical surface growth morphology does not necessarily imply the existence of a surface edge diffusion bias (the Schwoebel barrier). We find mounded morphologies in several nonequilibrium growth models which incorporate no Schwoebel barrier. Our numerical results indicate that mounded morphologies in nonequilibrium surface growth may arise from a number of distinct physical mechanisms, with the Schwoebel instability being one of them.Comment: 5 pages, 4 ps figures included, accepted for publication in Surface Science Letter