537 research outputs found
Theory of Branching and Annihilating Random Walks
A systematic theory for the diffusion--limited reaction processes and is developed. Fluctuations are taken into account via
the field--theoretic dynamical renormalization group. For even the mean
field rate equation, which predicts only an active phase, remains qualitatively
correct near dimensions; but below a nontrivial
transition to an inactive phase governed by power law behavior appears. For
odd there is a dynamic phase transition for any which is described
by the directed percolation universality class.Comment: 4 pages, revtex, no figures; final version with slight changes, now
accepted for publication in Phys. Rev. Let
Interacting Monomer-Dimer Model with Infinitely Many Absorbing States
We study a modified version of the interacting monomer-dimer (IMD) model that
has infinitely many absorbing (IMA) states. Unlike all other previously studied
models with IMA states, the absorbing states can be divided into two equivalent
groups which are dynamically separated infinitely far apart. Monte Carlo
simulations show that this model belongs to the directed Ising universality
class like the ordinary IMD model with two equivalent absorbing states. This
model is the first model with IMA states which does not belong to the directed
percolation (DP) universality class. The DP universality class can be restored
in two ways, i.e., by connecting the two equivalent groups dynamically or by
introducing a symmetry-breaking field between the two groups.Comment: 5 pages, 5 figure
Numerical Study of a Field Theory for Directed Percolation
A numerical method is devised for study of stochastic partial differential
equations describing directed percolation, the contact process, and other
models with a continuous transition to an absorbing state. Owing to the
heightened sensitivity to fluctuationsattending multiplicative noise in the
vicinity of an absorbing state, a useful method requires discretization of the
field variable as well as of space and time. When applied to the field theory
for directed percolation in 1+1 dimensions, the method yields critical
exponents which compare well against accepted values.Comment: 18 pages, LaTeX, 6 figures available upon request LC-CM-94-00
Nonequilibrium Critical Dynamics of a Three Species Monomer-Monomer Model
We study a three species monomer-monomer catalytic surface reaction model
with a reactive steady state bordered by three equivalent unreactive phases
where the surface is saturated with one species. The transition from the
reactive to a saturated phase shows directed percolation critical behavior.
Each pair of these reactive-saturated phase boundaries join at a bicritical
point where the universal behavior is in the even branching annihilating random
walk class. We find the crossover exponent from bicritical to critical behavior
and a new exponent associated with the bicritical interface dynamics.Comment: 4 pages RevTex. 4 eps figures included with psfig.sty. Uses
multicol.sty. Accepted for publication in PR
Does hardcore interaction change absorbing type critical phenomena?
It has been generally believed that hardcore interaction is irrelevant to
absorbing type critical phenomena because the particle density is so low near
an absorbing phase transition. We study the effect of hardcore interaction on
the N species branching annihilating random walks with two offspring and report
that hardcore interaction drastically changes the absorbing type critical
phenomena in a nontrivial way. Through Langevin equation type approach, we
predict analytically the values of the scaling exponents, in one dimension for all N > 1. Direct numerical
simulations confirm our prediction. When the diffusion coefficients for
different species are not identical, and vary
continuously with the ratios between the coefficients.Comment: 4 pages, 1 figur
Criticality of natural absorbing states
We study a recently introduced ladder model which undergoes a transition
between an active and an infinitely degenerate absorbing phase. In some cases
the critical behaviour of the model is the same as that of the branching
annihilating random walk with species both with and without hard-core
interaction. We show that certain static characteristics of the so-called
natural absorbing states develop power law singularities which signal the
approach of the critical point. These results are also explained using random
walk arguments. In addition to that we show that when dynamics of our model is
considered as a minimum finding procedure, it has the best efficiency very
close to the critical point.Comment: 6 page
Damage spreading for one-dimensional, non-equilibrium models with parity conserving phase transitions
The damage spreading (DS) transitions of two one-dimensional stochastic
cellular automata suggested by Grassberger (A and B) and the kinetic Ising
model of Menyh\'ard (NEKIM) have been investigated on the level of kinks and
spins. On the level of spins the parity conservation is not satisfied and
therefore studying these models provides a convenient tool to understand the
dependence of DS properties on symmetries. For the model B the critical point
and the DS transition point is well separated and directed percolation damage
spreading transition universality was found for spin damage as well as for kink
damage in spite of the conservation of damage variables modulo 2 in the latter
case. For the A stochastic cellular automaton, and the NEKIM model the two
transition points coincide with drastic effects on the damage of spin and kink
variables showing different time dependent behaviours. While the kink DS
transition is continuous and shows regular PC class universality, the spin
damage exhibits a discontinuous phase transition with compact clusters and PC
like dynamical scaling (), () and () exponents whereas
the static exponents determined by FSS are consistent with that of the spins of
the NEKIM model at the PC transition point. The generalised hyper-scaling law
is satisfied.Comment: 11 pages, 20 figures embedded in the text, minor changes in the text,
a new table and new references are adde
One-dimensional Nonequilibrium Kinetic Ising Models with local spin-symmetry breaking: N-component branching annihilation transition at zero branching rate
The effects of locally broken spin symmetry are investigated in one
dimensional nonequilibrium kinetic Ising systems via computer simulations and
cluster mean field calculations. Besides a line of directed percolation
transitions, a line of transitions belonging to N-component, two-offspring
branching annihilating random-walk class (N-BARW2) is revealed in the phase
diagram at zero branching rate. In this way a spin model for N-BARW2
transitions is proposed for the first time.Comment: 6 pages, 5 figures included, 2 new tables added, to appear in PR
Cation distribution in manganese cobaltite spinels Co3−xMnxO4 (0 ≤ x ≤ 1) determined by thermal analysis
Thermogravimetric analysis was used in order to study the reduction in air of submicronic powders of Co3−x Mn x O4 spinels, with 0 ≤ x ≤ 1. For x = 0 (i.e. Co3O4), cation reduction occurred in a single step. It involved the CoIII ions at the octahedral sites, which were reduced to Co2+ on producing CoO. For 0 < x ≤ 1, the reduction occurred in two stages at increasing temperature with increasing amounts of manganese. The first step corresponded to the reduction of octahedral CoIII ions and the second was attributed to the reduction of octahedral Mn4+ ions to Mn3+. From the individual weight losses and the electrical neutrality of the lattice, the CoIII and Mn4+ ion concentrations were calculated. The distribution of cobalt and manganese ions present on each crystallographic site of the spinel was determined. In contrast to most previous studies that took into account either CoIII and Mn3+ or Co2+, CoIII and Mn4+ only, our thermal analysis study showed that Co2+/CoIII and Mn3+/Mn4+ pairs occupy the octahedral sites. These results were used to explain the resistivity measurements carried out on dense ceramics prepared from our powders sintered at low temperature (700–750 °C) in a Spark Plasma Sintering apparatus
The three species monomer-monomer model: A mean-field analysis and Monte Carlo study
We study the phase diagram and critical behavior of a one dimensional three
species monomer-monomer surface reaction model. Static Monte Carlo simulations
show a phase diagram consisting of a reactive steady state bordered by three
equivalent unreactive phases where the surface is saturated with one monomer
species. The transitions from the reactive to saturated phases are all
continuous, while the transitions between poisoned phases are first-order, with
bicritical points where the reactive phase meets two poisoned phases. A
mean-field cluster analysis predicts all of the qualitative features of the
phase diagram only when correlations up to triplets of adjacent sites are
included. Dynamic Monte Carlo simulations show that the transition from the
reactive to a saturated phase show critical behavior in the directed
percolation universality class, while the bicritical point shows critical
behavior in the even branching annihilating random walk class. The crossover
from bicritical to critical behavior is also studied.Comment: 16 pages using RevTeX, plus 10 figures. Uses psfig.st
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