2,097 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 $d=2$ 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

### Universality of critically pinned interfaces in 2-dimensional isotropic random media

Based on extensive simulations, we conjecture that critically pinned
interfaces in 2-dimensional isotropic random media with short range
correlations are always in the universality class of ordinary percolation.
Thus, in contrast to interfaces in $>2$ dimensions, there is no distinction
between fractal (i.e., percolative) and rough but non-fractal interfaces. Our
claim includes interfaces in zero-temperature random field Ising models (both
with and without spontaneous nucleation), in heterogeneous bootstrap
percolation, and in susceptible-weakened-infected-removed (SWIR) epidemics. It
does not include models with long range correlations in the randomness, and
models where overhangs are explicitly forbidden (which would imply non-isotropy
of the medium).Comment: 5 pages (including 8 figures) of main text + 5 pages (including 7
figures) supplemental materia

### 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
$65536\times 65536$) than previous simulations and reach much closer to the
critical point (up to $\theta \equiv p/f = 256000$). 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 $\rho$ of trees in the critical
state was grossly underestimated. While previous simulations gave $\rho\approx
0.408$, we conjecture that $\rho$ actually is equal to the critical threshold
$p_c = 0.592...$ for site percolation in $d=2$. 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

### Free energy and extension of a semiflexible polymer in cylindrical confining geometries

We consider a long, semiflexible polymer, with persistence length $P$ and
contour length $L$, fluctuating in a narrow cylindrical channel of diameter
$D$. In the regime $D\ll P\ll L$ the free energy of confinement $\Delta F$ and
the length of the channel $R_\parallel$ occupied by the polymer are given by
Odijk's relations $\Delta F/R_\parallel=A_\circ k_BTP^{-1/3}D^{-2/3}$ and
$R_\parallel=L[1-\alpha_\circ(D/P)^{2/3}]$, where $A_\circ$ and $\alpha_\circ$
are dimensionless amplitudes. Using a simulation algorithm inspired by PERM
(Pruned Enriched Rosenbluth Method), which yields results for very long
polymers, we determine $A_\circ$ and $\alpha_\circ$ and the analogous
amplitudes for a channel with a rectangular cross section. For a semiflexible
polymer confined to the surface of a cylinder, the corresponding amplitudes are
derived with an exact analytic approach. The results are relevant for
interpreting experiments on biopolymers in microchannels or microfluidic
devices.Comment: 15 pages without figures, 5 figure

### Self-organized criticality and directed percolation

A sandpile model with stochastic toppling rule is studied. The control
parameters and the phase diagram are determined through a MF approach, the
subcritical and critical regions are analyzed. The model is found to have some
similarities with directed percolation, but the existence of different boundary
conditions and conservation law leads to a different universality class, where
the critical state is extended to a line segment due to self-organization.
These results are supported with numerical simulations in one dimension. The
present model constitute a simple model which capture the essential difference
between ordinary nonequilibrium critical phenomena, like DP, and self-organized
criticality.Comment: 9 pages, 10 eps figs, revtex, submitted to J. Phys.

### 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

### Scaling of loop-erased walks in 2 to 4 dimensions

We simulate loop-erased random walks on simple (hyper-)cubic lattices of
dimensions 2,3, and 4. These simulations were mainly motivated to test recent
two loop renormalization group predictions for logarithmic corrections in
$d=4$, simulations in lower dimensions were done for completeness and in order
to test the algorithm. In $d=2$, we verify with high precision the prediction
$D=5/4$, where the number of steps $n$ after erasure scales with the number $N$
of steps before erasure as $n\sim N^{D/2}$. In $d=3$ we again find a power law,
but with an exponent different from the one found in the most precise previous
simulations: $D = 1.6236\pm 0.0004$. Finally, we see clear deviations from the
naive scaling $n\sim N$ in $d=4$. While they agree only qualitatively with the
leading logarithmic corrections predicted by several authors, their agreement
with the two-loop prediction is nearly perfect.Comment: 3 pages, including 3 figure

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