127 research outputs found
Biodiversity in model ecosystems, II: Species assembly and food web structure
This is the second of two papers dedicated to the relationship between
population models of competition and biodiversity. Here we consider species
assembly models where the population dynamics is kept far from fixed points
through the continuous introduction of new species, and generalize to such
models thecoexistence condition derived for systems at the fixed point. The
ecological overlap between species with shared preys, that we define here,
provides a quantitative measure of the effective interspecies competition and
of the trophic network topology. We obtain distributions of the overlap from
simulations of a new model based both on immigration and speciation, and show
that they are in good agreement with those measured for three large natural
food webs. As discussed in the first paper, rapid environmental fluctuations,
interacting with the condition for coexistence of competing species, limit the
maximal biodiversity that a trophic level can host. This horizontal limitation
to biodiversity is here combined with either dissipation of energy or growth of
fluctuations, which in our model limit the length of food webs in the vertical
direction. These ingredients yield an effective model of food webs that produce
a biodiversity profile with a maximum at an intermediate trophic level, in
agreement with field studies
Biodiversity in model ecosystems, I: Coexistence conditions for competing species
This is the first of two papers where we discuss the limits imposed by
competition to the biodiversity of species communities. In this first paper we
study the coexistence of competing species at the fixed point of population
dynamic equations. For many simple models, this imposes a limit on the width of
the productivity distribution, which is more severe the more diverse the
ecosystem is (Chesson, 1994). Here we review and generalize this analysis,
beyond the ``mean-field''-like approximation of the competition matrix used in
previous works, and extend it to structured food webs. In all cases analysed,
we obtain qualitatively similar relations between biodiversity and competition:
the narrower the productivity distribution is, the more species can stably
coexist. We discuss how this result, considered together with environmental
fluctuations, limits the maximal biodiversity that a trophic level can host
Vicinal Surfaces and the Calogero-Sutherland Model
A miscut (vicinal) crystal surface can be regarded as an array of meandering
but non-crossing steps. Interactions between the steps are shown to induce a
faceting transition of the surface between a homogeneous Luttinger liquid state
and a low-temperature regime consisting of local step clusters in coexistence
with ideal facets. This morphological transition is governed by a hitherto
neglected critical line of the well-known Calogero-Sutherland model. Its exact
solution yields expressions for measurable quantities that compare favorably
with recent experiments on Si surfaces.Comment: 4 pages, revtex, 2 figures (.eps
Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations
We study the KPZ equation (in D = 2, 3 and 4 spatial dimensions) by using a
RSOS discretization of the surface. We measure the critical exponents very
precisely, and we show that the rational guess is not appropriate, and that 4D
is not the upper critical dimension. We are also able to determine very
precisely the exponent of the sub-leading scaling corrections, that turns out
to be close to 1 in all cases. We introduce and use a {\em multi-surface
coding} technique, that allow a gain of order 30 over usual numerical
simulations.Comment: 10 pages, 8 eps figures (2 figures added). Published versio
Renormalization group study of one-dimensional systems with roughening transitions
A recently introduced real space renormalization group technique, developed
for the analysis of processes in the Kardar-Parisi-Zhang universality class, is
generalized and tested by applying it to a different family of surface growth
processes.
In particular, we consider a growth model exhibiting a rich phenomenology
even in one dimension. It has four different phases and a directed percolation
related roughening transition. The renormalization method reproduces extremely
well all the phase diagram, the roughness exponents in all the phases and the
separatrix among them. This proves the versatility of the method and elucidates
interesting physical mechanisms.Comment: Submitted to Phys. Rev.
Patterns in the Kardar-Parisi-Zhang equation
We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang
equation for the kinetic growth of an interface in higher dimensions. The weak
noise approach provides a many body picture of a growing interface in terms of
a network of localized growth modes. Scaling in 1d is associated with a gapless
domain wall mode. The method also provides an independent argument for the
existence of an upper critical dimension.Comment: 8 pages revtex, 4 eps figure
On Growth, Disorder, and Field Theory
This article reviews recent developments in statistical field theory far from
equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic
surface growth and its mathematical relatives, namely the stochastic Burgers
equation in fluid mechanics and directed polymers in a medium with quenched
disorder. At strong stochastic driving -- or at strong disorder, respectively
-- these systems develop nonperturbative scale-invariance. Presumably exact
values of the scaling exponents follow from a self-consistent asymptotic
theory. This theory is based on the concept of an operator product expansion
formed by the local scaling fields. The key difference to standard Lagrangian
field theory is the appearance of a dangerous irrelevant coupling constant
generating dynamical anomalies in the continuum limit.Comment: review article, 50 pages (latex), 10 figures (eps), minor
modification of original versio
A minimal stochastic model for influenza evolution
We introduce and discuss a minimal individual-based model for influenza
dynamics. The model takes into account the effects of specific immunization
against viral strains, but also infectivity randomness and the presence of a
short-lived strain transcending immunity recently suggested in the literature.
We show by simulations that the resulting model exhibits substitution of viral
strains along the years, but that their divergence remains bounded. We also
show that dropping any of these features results in a drastically different
behavior, leading either to the extinction of the disease, to the proliferation
of the viral strains, or to their divergence
Canonical phase space approach to the noisy Burgers equation
Presenting a general phase approach to stochastic processes we analyze in
particular the Fokker-Planck equation for the noisy Burgers equation and
discuss the time dependent and stationary probability distributions. In one
dimension we derive the long-time skew distribution approaching the symmetric
stationary Gaussian distribution. In the short time regime we discuss
heuristically the nonlinear soliton contributions and derive an expression for
the distribution in accordance with the directed polymer-replica model and
asymmetric exclusion model results.Comment: 4 pages, Revtex file, submitted to Phys. Rev. Lett. a reference has
been added and a few typos correcte
Bundles of Interacting Strings in Two Dimensions
Bundles of strings which interact via short-ranged pair potentials are
studied in two dimensions. The corresponding transfer matrix problem is solved
analytically for arbitrary string number N by Bethe ansatz methods. Bundles
consisting of N identical strings exhibit a unique unbinding transition. If the
string bundle interacts with a hard wall, the bundle may unbind from the wall
via a unique transition or a sequence of N successive transitions. In all
cases, the critical exponents are independent of N and the density profile of
the strings exhibits a scaling form that approaches a mean-field profile in the
limit of large N.Comment: 8 pages (latex) with two figure
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