347 research outputs found
Metastability in Markov processes
We present a formalism to describe slowly decaying systems in the context of
finite Markov chains obeying detailed balance. We show that phase space can be
partitioned into approximately decoupled regions, in which one may introduce
restricted Markov chains which are close to the original process but do not
leave these regions. Within this context, we identify the conditions under
which the decaying system can be considered to be in a metastable state.
Furthermore, we show that such metastable states can be described in
thermodynamic terms and define their free energy. This is accomplished showing
that the probability distribution describing the metastable state is indeed
proportional to the equilibrium distribution, as is commonly assumed. We test
the formalism numerically in the case of the two-dimensional kinetic Ising
model, using the Wang--Landau algorithm to show this proportionality
explicitly, and confirm that the proportionality constant is as derived in the
theory. Finally, we extend the formalism to situations in which a system can
have several metastable states.Comment: 30 pages, 5 figures; version with one higher quality figure available
at http://www.fis.unam.mx/~dsanders
Phase transitions in systems of self-propelled agents and related network models
An important characteristic of flocks of birds, school of fish, and many
similar assemblies of self-propelled particles is the emergence of states of
collective order in which the particles move in the same direction. When noise
is added into the system, the onset of such collective order occurs through a
dynamical phase transition controlled by the noise intensity. While originally
thought to be continuous, the phase transition has been claimed to be
discontinuous on the basis of recently reported numerical evidence. We address
this issue by analyzing two representative network models closely related to
systems of self-propelled particles. We present analytical as well as numerical
results showing that the nature of the phase transition depends crucially on
the way in which noise is introduced into the system.Comment: Four pages, four figures. Submitted to PR
Transport Properties of the Diluted Lorentz Slab
We study the behavior of a point particle incident from the left on a slab of
a randomly diluted triangular array of circular scatterers. Various scattering
properties, such as the reflection and transmission probabilities and the
scattering time are studied as a function of thickness and dilution. We show
that a diffusion model satisfactorily describes the mentioned scattering
properties. We also show how some of these quantities can be evaluated exactly
and their agreement with numerical experiments. Our results exhibit the
dependence of these scattering data on the mean free path. This dependence
again shows excellent agreement with the predictions of a Brownian motion
model.Comment: 14 pages of text in LaTeX, 7 figures in Postscrip
The Reaction-Diffusion Front for in One Dimension
We study theoretically and numerically the steady state diffusion controlled
reaction , where currents of and particles
are applied at opposite boundaries. For a reaction rate , and equal
diffusion constants , we find that when the
reaction front is well described by mean field theory. However, for , the front acquires a Gaussian profile - a result of
noise induced wandering of the reaction front center. We make a theoretical
prediction for this profile which is in good agreement with simulation.
Finally, we investigate the intrinsic (non-wandering) front width and find
results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure
Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension
Extensive simulations are performed of the diffusion-limited reaction
AB in one dimension, with initially separated reagents. The reaction
rate profile, and the probability distributions of the separation and midpoint
of the nearest-neighbour pair of A and B particles, are all shown to exhibit
dynamic scaling, independently of the presence of fluctuations in the initial
state and of an exclusion principle in the model. The data is consistent with
all lengthscales behaving as as . Evidence of
multiscaling, found by other authors, is discussed in the light of these
findings.Comment: Resubmitted as TeX rather than Postscript file. RevTeX version 3.0,
10 pages with 16 Encapsulated Postscript figures (need epsf). University of
Geneva preprint UGVA/DPT 1994/10-85
Phase transitions in swarming systems: A recent debate
In this work we consider the phase transition from ordered to disordered
states that occur in the Vicsek model of self-propelled particles. This model
was proposed to describe the emergence of collective order in swarming systems.
When noise is added to the motion of the particles, the onset of collective
order occurs through a dynamical phase transition. Based on their numerical
results, Vicsek and his colleagues originally concluded that this phase
transition was of second order (continuous). However, recent numerical evidence
seems to indicate that the phase transition might be of first order
(discontinuous), thus challenging Vicsek's original results. In this work we
review the evidence supporting both aspects of this debate. We also show new
numerical results indicating that the apparent discontinuity of the phase
transition may in fact be a numerical artifact produced by the artificial
periodicity of the boundary conditions.Comment: 18 pages, 16 figure
The statistics of diffusive flux
We calculate the explicit probability distribution function for the flux
between sites in a simple discrete time diffusive system composed of
independent random walkers. We highlight some of the features of the
distribution and we discuss its relation to the local instantaneous entropy
production in the system. Our results are applicable both to equilibrium and
non-equilibrium steady states as well as for certain time dependent situations.Comment: 12 pages, 1 figur
Localisation Transition of A Dynamic Reaction Front
We study the reaction-diffusion process with injection of
each species at opposite boundaries of a one-dimensional lattice and bulk
driving of each species in opposing directions with a hardcore interaction. The
system shows the novel feature of phase transitions between localised and
delocalised reaction zones as the injection rate or reaction rate is varied. An
approximate analytical form for the phase diagram is derived by relating both
the domain of reactants and the domain of reactants to asymmetric
exclusion processes with open boundaries, a system for which the phase diagram
is known exactly, giving rise to three phases. The reaction zone width is
described by a finite size scaling form relating the early time growth,
relaxation time and saturation width exponents. In each phase the exponents are
distinct from the previously studied case where the reactants diffuse
isotropically.Comment: 13 pages, latex, uses eps
Order statistics for d-dimensional diffusion processes
We present results for the ordered sequence of first passage times of arrival
of N random walkers at a boundary in Euclidean spaces of d dimensions
Recuperación de las interacciones entre el haya (Fagus sylvatica) y los hongos ectomicorrícicos 140 años después del fin de la actividad minera
Even the increasing use of restoration, it does not always imply a shortterm answer in ecosystems that guarantees the recovery of their structure, functions, and services. So far, most studies evaluating ecosystem recovery have used metrics that ignore the complexity needed to structure communities of organisms that form ecosystems. Here, we analyze the recovery of species interactions (metric with a certain level of complexity) in a large time scale ('100 years). In particular, we characterized, using molecular identification, the ectomicorrhyzal (EcM) fungal communities present in 18 beech trees inside and seven outside an ancient iron in Navarra (northern Spain), in use from the XIV century until 140 years ago, as well as seven beech trees from a nearby oldgrowth forest. Species richness of EcM fungi was similar for the three locations, while differences were found for species composition in the area damaged by mining and compare to outside the mine and the reference beech forest. Our results suggest the need to assess ecosystem recovery with more complex metrics (e.g. architecture of interaction networks) in order to accurately estimate the real time required for ecosystems to fully recover. © 2019 Los Autores.Este trabajo ha sido financiado por el Plan Nacional de Investigación RETOS (CGL2015-70452-R) y la acreditación de excelencia “María de Maeztu” 2018-2022 (MDM-2017-0714). ARU fue financiada por el programa de becas predoctorales (2016) de la Fundación Tatiana Guzman el Bueno
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