690 research outputs found
Epidemic analysis of the second-order transition in the Ziff-Gulari-Barshad surface-reaction model
We study the dynamic behavior of the Ziff-Gulari-Barshad (ZGB) irreversible
surface-reaction model around its kinetic second-order phase transition, using
both epidemic and poisoning-time analyses. We find that the critical point is
given by p_1 = 0.3873682 \pm 0.0000015, which is lower than the previous value.
We also obtain precise values of the dynamical critical exponents z, \delta,
and \eta which provide further numerical evidence that this transition is in
the same universality class as directed percolation.Comment: REVTEX, 4 pages, 5 figures, Submitted to Physical Review
Efficient Monte Carlo algorithm and high-precision results for percolation
We present a new Monte Carlo algorithm for studying site or bond percolation
on any lattice. The algorithm allows us to calculate quantities such as the
cluster size distribution or spanning probability over the entire range of site
or bond occupation probabilities from zero to one in a single run which takes
an amount of time scaling linearly with the number of sites on the lattice. We
use our algorithm to determine that the percolation transition occurs at
occupation probability 0.59274621(13) for site percolation on the square
lattice and to provide clear numerical confirmation of the conjectured
4/3-power stretched-exponential tails in the spanning probability functions.Comment: 8 pages, including 3 postscript figures, minor corrections in this
version, plus updated figures for the position of the percolation transitio
Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices
Extensive Monte-Carlo simulations were performed to study bond percolation on
the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic
(b.c.c.) lattices, using an epidemic kind of approach. These simulations
provide very precise values of the critical thresholds for each of the
lattices: pc(s.c.) = 0.248 812 6(5), pc(f.c.c.) = 0.120 163 5(10), and
pc(b.c.c.) = 0.180 287 5(10). For p close to pc, the results follow the
expected finite-size and scaling behavior, with values for the Fisher exponent
(2.189(2)), the finite-size correction exponent (0.64(2)), and
the scaling function exponent (0.445(1)) confirmed to be universal.Comment: 16 pgs, 7 figures, LaTeX, to be published in Phys. Rev.
Response of a Model of CO Oxidation with CO Desorption and Diffusion to a Periodic External CO Pressure
We present a study of the dynamical behavior of a Ziff-Gulari-Barshad model
with CO desorption and lateral diffusion. Depending on the values of the
desorption and diffusion parameters, the system presents a discontinuous phase
transition between low and high CO coverage phases. We calculate several points
on the coexistence curve between these phases. Inclusion of the diffusion term
produces a significant increase in the CO_2 production rate. We further applied
a square-wave periodic pressure variation of the partial CO pressure with
parameters that can be tuned to modify the catalytic activity. Contrary to the
diffusion-free case, this driven system does not present a further enhancement
of the catalytic activity, beyond the increase induced by the diffusion under
constant CO pressure.Comment: 5 pages, RevTe
Fragmentation with a Steady Source
We investigate fragmentation processes with a steady input of fragments. We
find that the size distribution approaches a stationary form which exhibits a
power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic
behavior is robust as it is independent of the details of the input as well as
the spatial dimension. The full time dependent behavior is obtained
analytically for arbitrary inputs, and is found to exhibit a universal scaling
behavior.Comment: 4 page
Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
Two random-walk related problems which have been studied independently in the
past, the expected maximum of a random walker in one dimension and the flux to
a spherical trap of particles undergoing discrete jumps in three dimensions,
are shown to be closely related to each other and are studied using a unified
approach as a solution to a Wiener-Hopf problem. For the flux problem, this
work shows that a constant c = 0.29795219 which appeared in the context of the
boundary extrapolation length, and was previously found only numerically, can
be derived explicitly. The same constant enters in higher-order corrections to
the expected-maximum asymptotics. As a byproduct, we also prove a new universal
result in the context of the flux problem which is an analogue of the Sparre
Andersen theorem proved in the context of the random walker's maximum.Comment: Two figs. Accepted for publication, Journal of Statistical Physic
Preliminary Investigation of Spoiler Lateral Control on a 42 Degree Sweptback Wing at Transonic Speeds
New Results for Diffusion in Lorentz Lattice Gas Cellular Automata
New calculations to over ten million time steps have revealed a more complex
diffusive behavior than previously reported, of a point particle on a square
and triangular lattice randomly occupied by mirror or rotator scatterers. For
the square lattice fully occupied by mirrors where extended closed particle
orbits occur, anomalous diffusion was still found. However, for a not fully
occupied lattice the super diffusion, first noticed by Owczarek and Prellberg
for a particular concentration, obtains for all concentrations. For the square
lattice occupied by rotators and the triangular lattice occupied by mirrors or
rotators, an absence of diffusion (trapping) was found for all concentrations,
except on critical lines, where anomalous diffusion (extended closed orbits)
occurs and hyperscaling holds for all closed orbits with {\em universal}
exponents and . Only one point on these critical lines can be related to a
corresponding percolation problem. The questions arise therefore whether the
other critical points can be mapped onto a new percolation-like problem, and of
the dynamical significance of hyperscaling.Comment: 52 pages, including 18 figures on the last 22 pages, email:
[email protected]
The harmonic measure of diffusion-limited aggregates including rare events
We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results include probabilities as small as 10- 80. We find the multifractal D(q) spectrum including regions of small and negative q. Our algorithm allows us to obtain the harmonic measure for clusters more than an order of magnitude larger than those achieved using the method of iterative conformal maps, which is the previous best method. We find a phase transition in the singularity spectrum f(α) at α≈14 and also find a minimum q of D(q), qmin=0.9±0.05
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