10 research outputs found
Adaptation of Autocatalytic Fluctuations to Diffusive Noise
Evolution of a system of diffusing and proliferating mortal reactants is
analyzed in the presence of randomly moving catalysts. While the continuum
description of the problem predicts reactant extinction as the average growth
rate becomes negative, growth rate fluctuations induced by the discrete nature
of the agents are shown to allow for an active phase, where reactants
proliferate as their spatial configuration adapts to the fluctuations of the
catalysts density. The model is explored by employing field theoretical
techniques, numerical simulations and strong coupling analysis. For d<=2, the
system is shown to exhibits an active phase at any growth rate, while for d>2 a
kinetic phase transition is predicted. The applicability of this model as a
prototype for a host of phenomena which exhibit self organization is discussed.Comment: 6 pages 6 figur
Resonant nucleation of spatio-temporal order via parametric modal amplification
We investigate, analytically and numerically, the emergence of
spatio-temporal order in nonequilibrium scalar field theories. The onset of
order is triggered by destabilizing interactions (DIs), which instantaneously
change the interacting potential from a single to a double-well, tunable to be
either degenerate (SDW) or nondegenerate (ADW). For the SDW case, we observe
the emergence of spatio-temporal coherent structures known as oscillons. We
show that this emergence is initially synchronized, the result of parametric
amplification of the relevant oscillon modes. We also discuss how these ordered
structures act as bottlenecks for equipartition. For ADW potentials, we show
how the same parametric amplification mechanism may trigger the rapid decay of
a metastable state. For a range of temperatures, the decay rates associated
with this resonant nucleation can be orders of magnitude larger than those
computed by homogeneous nucleation, with time-scales given by a simple power
law, , where depends weakly on the
temperature and is the free-energy barrier of a critical
fluctuation.Comment: 38 pages, 20 figures now included within the tex
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
Enhancement of pair correlation in a one-dimensional hybridization model
We propose an integrable model of one-dimensional (1D) interacting electrons
coupled with the local orbitals arrayed periodically in the chain. Since the
local orbitals are introduced in a way that double occupation is forbidden, the
model keeps the main feature of the periodic Anderson model with an interacting
host. For the attractive interaction, it is found that the local orbitals
enhance the effective mass of the Cooper-pair-like singlets and also the pair
correlation in the ground state. However, the persistent current is depressed
in this case. For the repulsive interaction case, the Hamiltonian is
non-Hermitian but allows Cooper pair solutions with small momenta, which are
induced by the hybridization between the extended state and the local orbitals.Comment: 11 page revtex, no figur
Population dynamics in compressible flows
Organisms often grow, migrate and compete in liquid environments, as well as
on solid surfaces. However, relatively little is known about what happens when
competing species are mixed and compressed by fluid turbulence. In these
lectures we review our recent work on population dynamics and population
genetics in compressible velocity fields of one and two dimensions. We discuss
why compressible turbulence is relevant for population dynamics in the ocean
and we consider cases both where the velocity field is turbulent and when it is
static. Furthermore, we investigate populations in terms of a continuos density
field and when the populations are treated via discrete particles. In the last
case we focus on the competition and fixation of one species compared to
anotherComment: 16 pages, talk delivered at the Geilo Winter School 201