50 research outputs found
Quasi-stationary regime of a branching random walk in presence of an absorbing wall
A branching random walk in presence of an absorbing wall moving at a constant
velocity undergoes a phase transition as the velocity of the wall
varies. Below the critical velocity , the population has a non-zero
survival probability and when the population survives its size grows
exponentially. We investigate the histories of the population conditioned on
having a single survivor at some final time . We study the quasi-stationary
regime for when is large. To do so, one can construct a modified
stochastic process which is equivalent to the original process conditioned on
having a single survivor at final time . We then use this construction to
show that the properties of the quasi-stationary regime are universal when
. We also solve exactly a simple version of the problem, the
exponential model, for which the study of the quasi-stationary regime can be
reduced to the analysis of a single one-dimensional map.Comment: 2 figures, minor corrections, one reference adde
Patchiness and Demographic Noise in Three Ecological Examples
Understanding the causes and effects of spatial aggregation is one of the
most fundamental problems in ecology. Aggregation is an emergent phenomenon
arising from the interactions between the individuals of the population, able
to sense only -at most- local densities of their cohorts. Thus, taking into
account the individual-level interactions and fluctuations is essential to
reach a correct description of the population. Classic deterministic equations
are suitable to describe some aspects of the population, but leave out features
related to the stochasticity inherent to the discreteness of the individuals.
Stochastic equations for the population do account for these
fluctuation-generated effects by means of demographic noise terms but, owing to
their complexity, they can be difficult (or, at times, impossible) to deal
with. Even when they can be written in a simple form, they are still difficult
to numerically integrate due to the presence of the "square-root" intrinsic
noise. In this paper, we discuss a simple way to add the effect of demographic
stochasticity to three classic, deterministic ecological examples where
aggregation plays an important role. We study the resulting equations using a
recently-introduced integration scheme especially devised to integrate
numerically stochastic equations with demographic noise. Aimed at scrutinizing
the ability of these stochastic examples to show aggregation, we find that the
three systems not only show patchy configurations, but also undergo a phase
transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy
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
The Kuiper Belt and Other Debris Disks
We discuss the current knowledge of the Solar system, focusing on bodies in
the outer regions, on the information they provide concerning Solar system
formation, and on the possible relationships that may exist between our system
and the debris disks of other stars. Beyond the domains of the Terrestrial and
giant planets, the comets in the Kuiper belt and the Oort cloud preserve some
of our most pristine materials. The Kuiper belt, in particular, is a
collisional dust source and a scientific bridge to the dusty "debris disks"
observed around many nearby main-sequence stars. Study of the Solar system
provides a level of detail that we cannot discern in the distant disks while
observations of the disks may help to set the Solar system in proper context.Comment: 50 pages, 25 Figures. To appear in conference proceedings book
"Astrophysics in the Next Decade