1,166 research outputs found
Path-integral representation for a stochastic sandpile
We introduce an operator description for a stochastic sandpile model with a
conserved particle density, and develop a path-integral representation for its
evolution. The resulting (exact) expression for the effective action highlights
certain interesting features of the model, for example, that it is nominally
massless, and that the dynamics is via cooperative diffusion. Using the
path-integral formalism, we construct a diagrammatic perturbation theory,
yielding a series expansion for the activity density in powers of the time.Comment: 22 pages, 6 figure
Absorbing-state phase transitions with extremal dynamics
Extremal dynamics represents a path to self-organized criticality in which
the order parameter is tuned to a value of zero. The order parameter is
associated with a phase transition to an absorbing state. Given a process that
exhibits a phase transition to an absorbing state, we define an ``extremal
absorbing" process, providing the link to the associated extremal
(nonabsorbing) process. Stationary properties of the latter correspond to those
at the absorbing-state phase transition in the former. Studying the absorbing
version of an extremal dynamics model allows to determine certain critical
exponents that are not otherwise accessible. In the case of the Bak-Sneppen
(BS) model, the absorbing version is closely related to the "-avalanche"
introduced by Paczuski, Maslov and Bak [Phys. Rev. E {\bf 53}, 414 (1996)], or,
in spreading simulations to the "BS branching process" also studied by these
authors. The corresponding nonextremal process belongs to the directed
percolation universality class. We revisit the absorbing BS model, obtaining
refined estimates for the threshold and critical exponents in one dimension. We
also study an extremal version of the usual contact process, using mean-field
theory and simulation. The extremal condition slows the spread of activity and
modifies the critical behavior radically, defining an ``extremal directed
percolation" universality class of absorbing-state phase transitions.
Asymmetric updating is a relevant perturbation for this class, even though it
is irrelevant for the corresponding nonextremal class.Comment: 24 pages, 11 figure
Asymptotic behavior of the order parameter in a stochastic sandpile
We derive the first four terms in a series for the order paramater (the
stationary activity density rho) in the supercritical regime of a
one-dimensional stochastic sandpile; in the two-dimensional case the first
three terms are reported. We reorganize the pertubation theory for the model,
recently derived using a path-integral formalism [R. Dickman e R. Vidigal, J.
Phys. A 35, 7269 (2002)], to obtain an expansion for stationary properties.
Since the process has a strictly conserved particle density p, the Fourier mode
N^{-1} psi_{k=0} -> p, when the number of sites N -> infinity, and so is not a
random variable. Isolating this mode, we obtain a new effective action leading
to an expansion for rho in the parameter kappa = 1/(1+4p). This requires
enumeration and numerical evaluation of more than 200 000 diagrams, for which
task we develop a computational algorithm. Predictions derived from this series
are in good accord with simulation results. We also discuss the nature of
correlation functions and one-site reduced densities in the small-kappa
(large-p) limit.Comment: 18 pages, 5 figure
Sandpiles with height restrictions
We study stochastic sandpile models with a height restriction in one and two
dimensions. A site can topple if it has a height of two, as in Manna's model,
but, in contrast to previously studied sandpiles, here the height (or number of
particles per site), cannot exceed two. This yields a considerable
simplification over the unrestricted case, in which the number of states per
site is unbounded. Two toppling rules are considered: in one, the particles are
redistributed independently, while the other involves some cooperativity. We
study the fixed-energy system (no input or loss of particles) using cluster
approximations and extensive simulations, and find that it exhibits a
continuous phase transition to an absorbing state at a critical value zeta_c of
the particle density. The critical exponents agree with those of the
unrestricted Manna sandpile.Comment: 10 pages, 14 figure
Proline Biosynthesis Is Required for Endoplasmic Reticulum Stress Tolerance in \u3ci\u3eSaccharomyces cerevisiae\u3c/i\u3e
Background: Proline is an important amino acid for stress resistance in different organisms.
Results: Depletion of proline biosynthesis disrupts redox homeostasis and increases sensitivity to endoplasmic reticulum (ER) stress in yeast.
Conclusion: Proline biosynthesis is critical for maintaining the intracellular redox environment and the UPR during ER stress.
Significance: Proline metabolism is shown to have an important role in ER stress tolerance that was previously unknown
Activated Random Walkers: Facts, Conjectures and Challenges
We study a particle system with hopping (random walk) dynamics on the integer
lattice . The particles can exist in two states, active or
inactive (sleeping); only the former can hop. The dynamics conserves the number
of particles; there is no limit on the number of particles at a given site.
Isolated active particles fall asleep at rate , and then remain
asleep until joined by another particle at the same site. The state in which
all particles are inactive is absorbing. Whether activity continues at long
times depends on the relation between the particle density and the
sleeping rate . We discuss the general case, and then, for the
one-dimensional totally asymmetric case, study the phase transition between an
active phase (for sufficiently large particle densities and/or small )
and an absorbing one. We also present arguments regarding the asymptotic mean
hopping velocity in the active phase, the rate of fixation in the absorbing
phase, and survival of the infinite system at criticality. Using mean-field
theory and Monte Carlo simulation, we locate the phase boundary. The phase
transition appears to be continuous in both the symmetric and asymmetric
versions of the process, but the critical behavior is very different. The
former case is characterized by simple integer or rational values for critical
exponents (, for example), and the phase diagram is in accord with
the prediction of mean-field theory. We present evidence that the symmetric
version belongs to the universality class of conserved stochastic sandpiles,
also known as conserved directed percolation. Simulations also reveal an
interesting transient phenomenon of damped oscillations in the activity
density
On the absorbing-state phase transition in the one-dimensional triplet creation model
We study the lattice reaction diffusion model 3A -> 4A, A -> 0 (``triplet
creation") using numerical simulations and n-site approximations. The
simulation results provide evidence of a discontinuous phase transition at high
diffusion rates. In this regime the order parameter appears to be a
discontinuous function of the creation rate; no evidence of a stable interface
between active and absorbing phases is found. Based on an effective mapping to
a modified compact directed percolation process, shall nevertheless argue that
the transition is continuous, despite the seemingly discontinuous phase
transition suggested by studies of finite systems.Comment: 23 pages, 11 figure
Kinetic description of avalanching systems
Avalanching systems are treated analytically using the renormalization group
(in the self-organized-criticality regime) or mean-field approximation,
respectively. The latter describes the state in terms of the mean number of
active and passive sites, without addressing the inhomogeneity in their
distribution. This paper goes one step further by proposing a kinetic
description of avalanching systems making use of the distribution function for
clusters of active sites. We illustrate application of the kinetic formalism to
a model proposed for the description of the avalanching processes in the
reconnecting current sheet of the Earth magnetosphere.Comment: 9 page
Critical Dynamics of the Contact Process with Quenched Disorder
We study critical spreading dynamics in the two-dimensional contact process
(CP) with quenched disorder in the form of random dilution. In the pure model,
spreading from a single particle at the critical point is
characterized by the critical exponents of directed percolation: in
dimensions, , , and . Disorder causes a
dramatic change in the critical exponents, to , , and . These exponents govern spreading following
a long crossover period. The usual hyperscaling relation, , is violated. Our results support the conjecture by Bramson, Durrett, and
Schonmann [Ann. Prob. {\bf 19}, 960 (1991)], that in two or more dimensions the
disordered CP has only a single phase transition.Comment: 11 pages, REVTeX, four figures available on reques
Survival-extinction phase transition in a bit-string population with mutation
A bit-string model for the evolution of a population of haploid organisms,
subject to competition, reproduction with mutation and selection is studied,
using mean field theory and Monte Carlo simulations. We show that, depending on
environmental flexibility and genetic variability, the model exhibits a phase
transtion between extinction and survival. The mean-field theory describes the
infinite-size limit, while simulations are used to study quasi-stationary
properties.Comment: 11 pages, 5 figure
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