673 research outputs found
Pair Connectedness and Shortest Path Scaling in Critical Percolation
We present high statistics data on the distribution of shortest path lengths
between two near-by points on the same cluster at the percolation threshold.
Our data are based on a new and very efficient algorithm. For they
clearly disprove a recent conjecture by M. Porto et al., Phys. Rev. {\bf E 58},
R5205 (1998). Our data also provide upper bounds on the probability that two
near-by points are on different infinite clusters.Comment: 7 pages, including 4 postscript figure
Critical Behaviour of the Drossel-Schwabl Forest Fire Model
We present high statistics Monte Carlo results for the Drossel-Schwabl forest
fire model in 2 dimensions. They extend to much larger lattices (up to
) than previous simulations and reach much closer to the
critical point (up to ). They are incompatible with
all previous conjectures for the (extrapolated) critical behaviour, although
they in general agree well with previous simulations wherever they can be
directly compared. Instead, they suggest that scaling laws observed in previous
simulations are spurious, and that the density of trees in the critical
state was grossly underestimated. While previous simulations gave , we conjecture that actually is equal to the critical threshold
for site percolation in . This is however still far from
the densities reachable with present day computers, and we estimate that we
would need many orders of magnitude higher CPU times and storage capacities to
reach the true critical behaviour -- which might or might not be that of
ordinary percolation.Comment: 8 pages, including 9 figures, RevTe
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
Lower Bounds on Mutual Information
We correct claims about lower bounds on mutual information (MI) between
real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf
69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of
linear correlations depend on the marginal (single variable) distributions.
This is so in spite of the invariance of MI under reparametrizations, because
linear correlations are not invariant under them. The simplest bounds are
obtained for Gaussians, but the most interesting ones for practical purposes
are obtained for uniform marginal distributions. The latter can be enforced in
general by using the ranks of the individual variables instead of their actual
values, in which case one obtains bounds on MI in terms of Spearman correlation
coefficients. We show with gene expression data that these bounds are in
general non-trivial, and the degree of their (non-)saturation yields valuable
insight.Comment: 4 page
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.
Generalized Scaling for Models with Multiple Absorbing States
At a continuous transition into a nonunique absorbing state, particle systems
may exhibit nonuniversal critical behavior, in apparent violation of
hyperscaling. We propose a generalized scaling theory for dynamic critical
behavior at a transition into an absorbing state, which is capable of
describing exponents which vary according to the initial configuration. The
resulting hyperscaling relation is supported by simulations of two lattice
models.Comment: Latex 9 page
Glassy phases in Random Heteropolymers with correlated sequences
We develop a new analytic approach for the study of lattice heteropolymers,
and apply it to copolymers with correlated Markovian sequences. According to
our analysis, heteropolymers present three different dense phases depending
upon the temperature, the nature of the monomer interactions, and the sequence
correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a
``frozen glass'' phase. The presence of the new intermediate ``soft glass''
phase is predicted for instance in the case of polyampholytes with sequences
that favor the alternation of monomers.
Our approach is based on the cavity method, a refined Bethe Peierls
approximation adapted to frustrated systems. It amounts to a mean field
treatment in which the nearest neighbor correlations, which are crucial in the
dense phases of heteropolymers, are handled exactly. This approach is powerful
and versatile, it can be improved systematically and generalized to other
polymeric systems
Intriguing Heat Conduction of a Polymer Chain
We study heat conduction in a one-dimensional chain of particles with
longitudinal as well as transverse motions. The particles are connected by
two-dimensional harmonic springs together with bending angle interactions.
Using equilibrium and nonequilibrium molecular dynamics, three types of thermal
conducting behaviors are found: a logarithmic divergence with system sizes for
large transverse coupling, 1/3 power-law at intermediate coupling, and 2/5
power-law at low temperatures and weak coupling. The results are consistent
with a simple mode-coupling analysis of the same model. The 1/3 power-law
divergence should be a generic feature for models with transverse motions.Comment: 4 page
Field theory of directed percolation with long-range spreading
It is well established that the phase transition between survival and
extinction in spreading models with short-range interactions is generically
associated with the directed percolation (DP) universality class. In many
realistic spreading processes, however, interactions are long ranged and well
described by L\'{e}vy-flights, i.e., by a probability distribution that decays
in dimensions with distance as . We employ the powerful
methods of renormalized field theory to study DP with such long range,
L\'{e}vy-flight spreading in some depth. Our results unambiguously corroborate
earlier findings that there are four renormalization group fixed points
corresponding to, respectively, short-range Gaussian, L\'{e}vy Gaussian,
short-range DP and L\'{e}vy DP, and that there are four lines in the plane which separate the stability regions of these fixed points. When the
stability line between short-range DP and L\'{e}vy DP is crossed, all critical
exponents change continuously. We calculate the exponents describing L\'{e}vy
DP to second order in -expansion, and we compare our analytical
results to the results of existing numerical simulations. Furthermore, we
calculate the leading logarithmic corrections for several dynamical
observables.Comment: 12 pages, 3 figure
Irreversible phase transitions induced by an oscillatory input
A novel kind of irreversible phase transitions (IPT's) driven by an
oscillatory input parameter is studied by means of computer simulations. Second
order IPT's showing scale invariance in relevant dynamic critical properties
are found to belong to the universality class of directed percolation. In
contrast, the absence of universality is observed for first order IPT's.Comment: 18 pages (Revtex); 8 figures (.ps); submitted to Europhysics Letters,
December 9th, 199
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