120 research outputs found
The generalized contact process with n absorbing states
We investigate the critical properties of a one dimensional stochastic
lattice model with n (permutation symmetric) absorbing states. We analyze the
cases with by means of the non-hermitian density matrix
renormalization group. For n=1 and n=2 we find that the model is respectively
in the directed percolation and parity conserving universality class,
consistent with previous studies. For n=3 and n=4, the model is in the active
phase in the whole parameter space and the critical point is shifted to the
limit of one infinite reaction rate. We show that in this limit the dynamics of
the model can be mapped onto that of a zero temperature n-state Potts model. On
the basis of our numerical and analytical results we conjecture that the model
is in the same universality class for all with exponents , and . These exponents
coincide with those of the multispecies (bosonic) branching annihilating random
walks. For n=3 we also show that, upon breaking the symmetry to a lower one
(), one gets a transition either in the directed percolation, or in the
parity conserving class, depending on the choice of parameters.Comment: 10 pages, RevTeX, and 10 PostScript figures include
Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction
We study the zero temperature coarsening dynamics in an Ising chain in
presence of a dynamically induced field that favors locally the `-' phase
compared to the `+' phase. At late times, while the `+' domains still coarsen
as , the `-' domains coarsen slightly faster as . As
a result, at late times, the magnetization decays slowly as, . We establish this behavior both analytically within an
independent interval approximation (IIA) and numerically. In the zero volume
fraction limit of the `+' phase, we argue that the IIA becomes asymptotically
exact. Our model can be alternately viewed as a simple Ising model for granular
compaction. At late times in our model, the system decays into a fully compact
state (where all spins are `-') in a slow logarithmic manner , a fact that has been observed in recent experiments on granular systems.Comment: 4 pages Revtex, 3 eps figures, supersedes cond-mat/000221
Slow Relaxation in a Constrained Ising Spin Chain: a Toy Model for Granular Compaction
We present detailed analytical studies on the zero temperature coarsening
dynamics in an Ising spin chain in presence of a dynamically induced field that
favors locally the `-' phase compared to the `+' phase. We show that the
presence of such a local kinetic bias drives the system into a late time state
with average magnetization m=-1. However the magnetization relaxes into this
final value extremely slowly in an inverse logarithmic fashion. We further map
this spin model exactly onto a simple lattice model of granular compaction that
includes the minimal microscopic moves needed for compaction. This toy model
then predicts analytically an inverse logarithmic law for the growth of density
of granular particles, as seen in recent experiments and thereby provides a new
mechanism for the inverse logarithmic relaxation. Our analysis utilizes an
independent interval approximation for the particle and the hole clusters and
is argued to be exact at late times (supported also by numerical simulations).Comment: 9 pages RevTeX, 1 figures (.eps
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
On universality in aging ferromagnets
This work is a contribution to the study of universality in
out-of-equilibrium lattice models undergoing a second-order phase transition at
equilibrium. The experimental protocol that we have chosen is the following:
the system is prepared in its high-temperature phase and then quenched at the
critical temperature . We investigated by mean of Monte Carlo simulations
two quantities that are believed to take universal values: the exponent
obtained from the decay of autocorrelation functions and the
asymptotic value of the fluctuation-dissipation ratio . This
protocol was applied to the Ising model, the 3-state clock model and the
4-state Potts model on square, triangular and honeycomb lattices and to the
Ashkin-Teller model at the point belonging at equilibrium to the 3-state Potts
model universality class and to a multispin Ising model and the Baxter-Wu model
both belonging to the 4-state Potts model universality class at equilibrium.Comment: 17 page
Outbreak size distributions in epidemics with multiple stages
Multiple-type branching processes that model the spread of infectious
diseases are investigated. In these stochastic processes, the disease goes
through multiple stages before it eventually disappears. We mostly focus on the
critical multistage Susceptible-Infected-Recovered (SIR) infection process. In
the infinite population limit, we compute the outbreak size distributions and
show that asymptotic results apply to more general multiple-type critical
branching processes. Finally using heuristic arguments and simulations we
establish scaling laws for a multistage SIR model in a finite population.Comment: 7 pages, 2 figures; added references, final versio
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
The non-equilibrium response of the critical Ising model: Universal scaling properties and Local Scale Invariance
Motivated by recent numerical findings [M. Henkel, T. Enss, and M. Pleimling,
J. Phys. A: Math. Gen. 39 (2006) L589] we re-examine via Monte Carlo
simulations the linear response function of the two-dimensional Ising model
with Glauber dynamics quenched to the critical point. At variance with the
results of Henkel et al., we detect discrepancies between the actual scaling
behavior of the response function and the prediction of Local Scale Invariance.
Such differences are clearly visible in the impulse autoresponse function,
whereas they are drastically reduced in integrated response functions.
Accordingly, the scaling form predicted on the basis of Local Scale Invariance
simply provides an accurate fitting form for some quantities but cannot be
considered to be exact.Comment: 25 pages, 4 figure
Surface Covering of Downed Logs: Drivers of a Neglected Process in Dead Wood Ecology
Many species use coarse woody debris (CWD) and are disadvantaged by the forestry-induced loss of this resource. A neglected process affecting CWD is the covering of the surfaces of downed logs caused by sinking into the ground (increasing soil contact, mostly covering the underside of the log), and dense overgrowth by ground vegetation. Such cover is likely to profoundly influence the quality and accessibility of CWD for wood-inhabiting organisms, but the factors affecting covering are largely unknown. In a five-year experiment we determined predictors of covering rate of fresh logs in boreal forests and clear-cuts. Logs with branches were little covered because they had low longitudinal ground contact. For branchless logs, longitudinal ground contact was most strongly related to estimated peat depth (positive relation). The strongest predictor for total cover of branchless logs was longitudinal ground contact. To evaluate the effect on cover of factors other than longitudinal ground contact, we separately analyzed data from only those log sections that were in contact with the ground. Four factors were prominent predictors of percentage cover of such log sections: estimated peat depth, canopy shade (both increasing cover), potential solar radiation calculated from slope and slope aspect, and diameter of the log (both reducing cover). Peat increased cover directly through its low resistance, which allowed logs to sink and soil contact to increase. High moisture and low temperatures in pole-ward facing slopes and under a canopy favor peat formation through lowered decomposition and enhanced growth of peat-forming mosses, which also proved to rapidly overgrow logs. We found that in some boreal forests, peat and fast-growing mosses can rapidly cover logs lying on the ground. When actively introducing CWD for conservation purposes, we recommend that such rapid covering is avoided, thereby most likely improving the CWD's longevity as habitat for many species
Where are we now with European forest multi-taxon biodiversity and where can we head to?
The European biodiversity and forest strategies rely on forest sustainable management (SFM) to conserve forest biodiversity. However, current sustainability assessments hardly account for direct biodiversity indicators. We focused on forest multi-taxon biodiversity to: i) gather and map the existing information; ii) identify knowledge and research gaps; iii) discuss its research potential. We established a research network to fit data on species, standing trees, lying deadwood and sampling unit description from 34 local datasets across 3591 sampling units. A total of 8724 species were represented, with the share of common and rare species varying across taxonomic classes: some included many species with several rare ones (e.g., Insecta); others (e.g., Bryopsida) were represented by few common species. Tree-related structural attributes were sampled in a subset of sampling units (2889; 2356; 2309 and 1388 respectively for diameter, height, deadwood and microhabitats). Overall, multi-taxon studies are biased towards mature forests and may underrepresent the species related to other developmental phases. European forest compositional categories were all represented, but beech forests were over-represented as compared to thermophilous and boreal forests. Most sampling units (94%) were referred to a habitat type of conservation concern. Existing information may support European conservation and SFM strategies in: (i) methodological harmonization and coordinated monitoring; (ii) definition and testing of SFM indicators and thresholds; (iii) data-driven assessment of the effects of environmental and management drivers on multi-taxon forest biological and functional diversity, (iv) multi-scale forest monitoring integrating in-situ and remotely sensed information
- …