29,375 research outputs found
Low-density series expansions for directed percolation II: The square lattice with a wall
A new algorithm for the derivation of low-density expansions has been used to
greatly extend the series for moments of the pair-connectedness on the directed
square lattice near an impenetrable wall. Analysis of the series yields very
accurate estimates for the critical point and exponents. In particular, the
estimate for the exponent characterizing the average cluster length near the
wall, , appears to exclude the conjecture . The
critical point and the exponents and have the
same values as for the bulk problem.Comment: 8 pages, 1 figur
Nonuniversal Critical Spreading in Two Dimensions
Continuous phase transitions are studied in a two dimensional nonequilibrium
model with an infinite number of absorbing configurations. Spreading from a
localized source is characterized by nonuniversal critical exponents, which
vary continuously with the density phi in the surrounding region. The exponent
delta changes by more than an order of magnitude, and eta changes sign. The
location of the critical point also depends on phi, which has important
implications for scaling. As expected on the basis of universality, the static
critical behavior belongs to the directed percolation class.Comment: 21 pages, REVTeX, figures available upon reques
Reentrant phase diagram of branching annihilating random walks with one and two offsprings
We investigate the phase diagram of branching annihilating random walks with
one and two offsprings in one dimension. A walker can hop to a nearest neighbor
site or branch with one or two offsprings with relative ratio. Two walkers
annihilate immediately when they meet. In general, this model exhibits a
continuous phase transition from an active state into the absorbing state
(vacuum) at a finite hopping probability. We map out the phase diagram by Monte
Carlo simulations which shows a reentrant phase transition from vacuum to an
active state and finally into vacuum again as the relative rate of the
two-offspring branching process increases. This reentrant property apparently
contradicts the conventional wisdom that increasing the number of offsprings
will tend to make the system more active. We show that the reentrant property
is due to the static reflection symmetry of two-offspring branching processes
and the conventional wisdom is recovered when the dynamic reflection symmetry
is introduced instead of the static one.Comment: 14 pages, Revtex, 4 figures (one PS figure file upon request)
(submitted to Phy. Rev. E
One Dimensional Nonequilibrium Kinetic Ising Models with Branching Annihilating Random Walk
Nonequilibrium kinetic Ising models evolving under the competing effect of
spin flips at zero temperature and nearest neighbour spin exchanges at
are investigated numerically from the point of view of a phase
transition. Branching annihilating random walk of the ferromagnetic domain
boundaries determines the steady state of the system for a range of parameters
of the model. Critical exponents obtained by simulation are found to agree,
within error, with those in Grassberger's cellular automata.Comment: 10 pages, Latex, figures upon request, SZFKI 05/9
Dimensional reduction in a model with infinitely many absorbing states
Using Monte Carlo method we study a two-dimensional model with infinitely
many absorbing states. Our estimation of the critical exponent beta=0.273(5)
suggests that the model belongs to the (1+1) rather than (2+1)
directed-percolation universality class. We also show that for a large class of
absorbing states the dynamic Monte Carlo method leads to spurious dynamical
transitions.Comment: 6 pages, 4 figures, Phys.Rev. E, Dec. 199
Critical behavior of a one-dimensional monomer-dimer reaction model with lateral interactions
A monomer-dimer reaction lattice model with lateral repulsion among the same
species is studied using a mean-field analysis and Monte Carlo simulations. For
weak repulsions, the model exhibits a first-order irreversible phase transition
between two absorbing states saturated by each different species. Increasing
the repulsion, a reactive stationary state appears in addition to the saturated
states. The irreversible phase transitions from the reactive phase to any of
the saturated states are continuous and belong to the directed percolation
universality class. However, a different critical behavior is found at the
point where the directed percolation phase boundaries meet. The values of the
critical exponents calculated at the bicritical point are in good agreement
with the exponents corresponding to the parity-conserving universality class.
Since the adsorption-reaction processes does not lead to a non-trivial local
parity-conserving dynamics, this result confirms that the twofold symmetry
between absorbing states plays a relevant role in determining the universality
class. The value of the exponent , which characterizes the
fluctuations of an interface at the bicritical point, supports the
Bassler-Brown's conjecture which states that this is a new exponent in the
parity-conserving universality class.Comment: 19 pages, 22 figures, to be published in Phys. Rev
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
Fear and its implications for stock markets
The value of stocks, indices and other assets, are examples of stochastic
processes with unpredictable dynamics. In this paper, we discuss asymmetries in
short term price movements that can not be associated with a long term positive
trend. These empirical asymmetries predict that stock index drops are more
common on a relatively short time scale than the corresponding raises. We
present several empirical examples of such asymmetries. Furthermore, a simple
model featuring occasional short periods of synchronized dropping prices for
all stocks constituting the index is introduced with the aim of explaining
these facts. The collective negative price movements are imagined triggered by
external factors in our society, as well as internal to the economy, that
create fear of the future among investors. This is parameterized by a ``fear
factor'' defining the frequency of synchronized events. It is demonstrated that
such a simple fear factor model can reproduce several empirical facts
concerning index asymmetries. It is also pointed out that in its simplest form,
the model has certain shortcomings.Comment: 5 pages, 5 figures. Submitted to the Proceedings of Applications of
Physics in Financial Analysis 5, Turin 200
Study of the one-dimensional off-lattice hot-monomer reaction model
Hot monomers are particles having a transient mobility (a ballistic flight)
prior to being definitely absorbed on a surface. After arriving at a surface,
the excess energy coming from the kinetic energy in the gas phase is dissipated
through degrees of freedom parallel to the surface plane. In this paper we
study the hot monomer-monomer adsorption-reaction process on a continuum
(off-lattice) one-dimensional space by means of Monte Carlo simulations. The
system exhibits second-order irreversible phase transition between a reactive
and saturated (absorbing) phases which belong to the directed percolation (DP)
universality class. This result is interpreted by means of a coarse-grained
Langevin description which allows as to extend the DP conjecture to transitions
occurring in continuous media.Comment: 13 pages, 5 figures, final version to appear in J. Phys.
Measurements and Monte-Carlo simulations of the particle self-shielding effect of B4C grains in neutron shielding concrete
A combined measurement and Monte-Carlo simulation study was carried out in
order to characterize the particle self-shielding effect of B4C grains in
neutron shielding concrete. Several batches of a specialized neutron shielding
concrete, with varying B4C grain sizes, were exposed to a 2 {\AA} neutron beam
at the R2D2 test beamline at the Institute for Energy Technology located in
Kjeller, Norway. The direct and scattered neutrons were detected with a neutron
detector placed behind the concrete blocks and the results were compared to
Geant4 simulations. The particle self-shielding effect was included in the
Geant4 simulations by calculating effective neutron cross-sections during the
Monte-Carlo simulation process. It is shown that this method well reproduces
the measured results. Our results show that shielding calculations for
low-energy neutrons using such materials would lead to an underestimate of the
shielding required for a certain design scenario if the particle self-shielding
effect is not included in the calculations.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0
license http://creativecommons.org/licenses/by-nc-nd/4.0
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