16,802 research outputs found
Correlated Initial Conditions in Directed Percolation
We investigate the influence of correlated initial conditions on the temporal
evolution of a (d+1)-dimensional critical directed percolation process.
Generating initial states with correlations ~r^(sigma-d) we
observe that the density of active sites in Monte-Carlo simulations evolves as
rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in
the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an
exact field-theoretical renormalization group calculation.Comment: 10 pages, RevTeX, including 5 encapsulated postscript figure
Geotechnical Prediction and Performance of Eastern Scheldt Storm Surge Barrier
The construction of the Eastern Scheldt storm surge barrier was completed in 1986. The monitoring system meant to verify the functioning of the barrier during storm conditions became operational in 1988. Data concerning the geotechnical response was collected during the 4 days storm period between February 26 and March 2, 1990. In the paper some results are described. Conclusions with respect to the expected behaviour of the barrier during more extreme storms in future will be drawn in near future
Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process
A general field theoretic model of directed percolation with many colors that
is equivalent to a population model (Gribov process) with many species near
their extinction thresholds is presented. It is shown that the multicritical
behavior is always described by the well known exponents of Reggeon field
theory. In addition this universal model shows an instability that leads in
general to a total asymmetry between each pair of species of a cooperative
society.Comment: 4 pages, 2 Postscript figures, uses multicol.sty, submitte
Spreading with immunization in high dimensions
We investigate a model of epidemic spreading with partial immunization which
is controlled by two probabilities, namely, for first infections, , and
reinfections, . When the two probabilities are equal, the model reduces to
directed percolation, while for perfect immunization one obtains the general
epidemic process belonging to the universality class of dynamical percolation.
We focus on the critical behavior in the vicinity of the directed percolation
point, especially in high dimensions . It is argued that the clusters of
immune sites are compact for . This observation implies that a
recently introduced scaling argument, suggesting a stretched exponential decay
of the survival probability for , in one spatial dimension,
where denotes the critical threshold for directed percolation, should
apply in any dimension and maybe for as well. Moreover, we
show that the phase transition line, connecting the critical points of directed
percolation and of dynamical percolation, terminates in the critical point of
directed percolation with vanishing slope for and with finite slope for
. Furthermore, an exponent is identified for the temporal correlation
length for the case of and , , which
is different from the exponent of directed percolation. We also
improve numerical estimates of several critical parameters and exponents,
especially for dynamical percolation in .Comment: LaTeX, IOP-style, 18 pages, 9 eps figures, minor changes, additional
reference
Development of Stresses in Cohesionless Poured Sand
The pressure distribution beneath a conical sandpile, created by pouring sand
from a point source onto a rough rigid support, shows a pronounced minimum
below the apex (`the dip'). Recent work of the authors has attempted to explain
this phenomenon by invoking local rules for stress propagation that depend on
the local geometry, and hence on the construction history, of the medium. We
discuss the fundamental difference between such approaches, which lead to
hyperbolic differential equations, and elastoplastic models, for which the
equations are elliptic within any elastic zones present .... This displacement
field appears to be either ill-defined, or defined relative to a reference
state whose physical existence is in doubt. Insofar as their predictions depend
on physical factors unknown and outside experimental control, such
elastoplastic models predict that the observations should be intrinsically
irreproducible .... Our hyperbolic models are based instead on a physical
picture of the material, in which (a) the load is supported by a skeletal
network of force chains ("stress paths") whose geometry depends on construction
history; (b) this network is `fragile' or marginally stable, in a sense that we
define. .... We point out that our hyperbolic models can nonetheless be
reconciled with elastoplastic ideas by taking the limit of an extremely
anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps.
Philosophical Transactions A, Royal Society, submitted 02/9
Renormalization group of probabilistic cellular automata with one absorbing state
We apply a recently proposed dynamically driven renormalization group scheme
to probabilistic cellular automata having one absorbing state. We have found
just one unstable fixed point with one relevant direction. In the limit of
small transition probability one of the cellular automata reduces to the
contact process revealing that the cellular automata are in the same
universality class as that process, as expected. Better numerical results are
obtained as the approximations for the stationary distribution are improved.Comment: Errors in some formulas have been corrected. Additional material
available at http://mestre.if.usp.br/~javie
Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions
We develop a method of constructing percolation clusters that allows us to
build very large clusters using very little computer memory by limiting the
maximum number of sites for which we maintain state information to a number of
the order of the number of sites in the largest chemical shell of the cluster
being created. The memory required to grow a cluster of mass s is of the order
of bytes where ranges from 0.4 for 2-dimensional lattices
to 0.5 for 6- (or higher)-dimensional lattices. We use this method to estimate
, the exponent relating the minimum path to the
Euclidean distance r, for 4D and 5D hypercubic lattices. Analyzing both site
and bond percolation, we find (4D) and
(5D). In order to determine
to high precision, and without bias, it was necessary to
first find precise values for the percolation threshold, :
(4D) and (5D) for site and
(4D) and (5D) for bond
percolation. We also calculate the Fisher exponent, , determined in the
course of calculating the values of : (4D) and
(5D)
- …