1,162 research outputs found
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
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
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
A globally accurate theory for a class of binary mixture models
Using the self-consistent Ornstein-Zernike approximation (SCOZA) results for
the 3D Ising model, we obtain phase diagrams for binary mixtures described by
decorated models. We obtain the plait point, binodals, and closed-loop
coexistence curves for the models proposed by Widom, Clark, Neece, and Wheeler.
The results are in good agreement with series expansions and experiments.Comment: 16 pages, 10 figure
Self-organized Criticality and Absorbing States: Lessons from the Ising Model
We investigate a suggested path to self-organized criticality. Originally,
this path was devised to "generate criticality" in systems displaying an
absorbing-state phase transition, but closer examination of the mechanism
reveals that it can be used for any continuous phase transition. We used the
Ising model as well as the Manna model to demonstrate how the finite-size
scaling exponents depend on the tuning of driving and dissipation rates with
system size.Our findings limit the explanatory power of the mechanism to
non-universal critical behavior.Comment: 5 pages, 2 figures, REVTeX
Theory of the NO+CO surface reaction model
We derive a pair approximation (PA) for the NO+CO model with instantaneous
reactions. For both the triangular and square lattices, the PA, derived here
using a simpler approach, yields a phase diagram with an active state for
CO-fractions y in the interval y_1 < y < y_2, with a continuous (discontinuous)
phase transition to a poisoned state at y_1 (y_2). This is in qualitative
agreement with simulation for the triangular lattice, where our theory gives a
rather accurate prediction for y_2. To obtain the correct phase diagram for the
square lattice, i.e., no active state, we reformulate the PA using sublattices.
The (formerly) active regime is then replaced by a poisoned state with broken
symmetry (unequal sub- lattice coverages), as observed recently by Kortluke et
al. [Chem. Phys. Lett. 275, 85 (1997)]. In contrast with their approach, in
which the active state persists, although reduced in extent, we report here the
first qualitatively correct theory of the NO+CO model on the square lattice.
Surface diffusion of nitrogen can lead to an active state in this case. In one
dimension, the PA predicts that diffusion is required for the existence of an
active state.Comment: 15 pages, 9 figure
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
Nonequilibrium phase transition on a randomly diluted lattice
We show that the interplay between geometric criticality and dynamical
fluctuations leads to a novel universality class of the contact process on a
randomly diluted lattice. The nonequilibrium phase transition across the
percolation threshold of the lattice is characterized by unconventional
activated (exponential) dynamical scaling and strong Griffiths effects. We
calculate the critical behavior in two and three space dimensions, and we also
relate our results to the recently found infinite-randomness fixed point in the
disordered one-dimensional contact process.Comment: 4 pages, 1 eps figure, final version as publishe
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
Modelling of quasi-optical arrays
A model for analyzing quasi-optical grid amplifiers based on a finite-element electromagnetic simulator is presented. This model is deduced from the simulation of the whole unit cell and takes into account mutual coupling effects. By using this model, the gain of a 10Ă—10 grid amplifier has been accurately predicted. To further test the validity of the model three passive structures with different loads have been fabricated and tested using a new focused-beam network analyzer that we developed
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