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

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

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

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

Numerical test of the damping time of layer-by-layer growth on stochastic models

We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.Comment: 4 pages, source LaTeX file and 5 PS figure