18 research outputs found
Non-conserved dynamics of steps on vicinal surfaces during electromigration-induced step bunching
We report new results on the non-conserved dynamics of parallel steps on
vicinal surfaces in the case of sublimation with electromigration and step-step
interactions. The derived equations are valid in the quasistatic approximation
and in the limit , where is the inverse
electromigration length, the diffusion length, the kinetic
lengths and the terrace widths. The coupling between crystal sublimation
and step-step interactions induces non-linear, non-conservative terms in the
equations of motion. Depending on the initial conditions, this leads to
interrupted coarsening, anticoarsening of step bunches or periodic switching
between step trains of different numbers of bunches.Comment: 11 pages, 4 figures; revised and extended versio
Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models
Both community ecology and conservation biology seek further understanding of
factors governing the advance of an invasive species. We model biological
invasion as an individual-based, stochastic process on a two-dimensional
landscape. An ecologically superior invader and a resident species compete for
space preemptively. Our general model includes the basic contact process and a
variant of the Eden model as special cases. We employ the concept of a
"roughened" front to quantify effects of discreteness and stochasticity on
invasion; we emphasize the probability distribution of the front-runner's
relative position. That is, we analyze the location of the most advanced
invader as the extreme deviation about the front's mean position. We find that
a class of models with different assumptions about neighborhood interactions
exhibit universal characteristics. That is, key features of the invasion
dynamics span a class of models, independently of locally detailed demographic
rules. Our results integrate theories of invasive spatial growth and generate
novel hypotheses linking habitat or landscape size (length of the invading
front) to invasion velocity, and to the relative position of the most advanced
invader.Comment: The original publication is available at
www.springerlink.com/content/8528v8563r7u2742