1,286 research outputs found
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
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.
Polymers Confined between Two Parallel Plane Walls
Single three dimensional polymers confined to a slab, i.e. to the region
between two parallel plane walls, are studied by Monte Carlo simulations. They
are described by -step walks on a simple cubic lattice confined to the
region . The simulations cover both regions (where is the Flory radius, with ), as
well as the cross-over region in between. Chain lengths are up to ,
slab widths up to D=120. In order to test the analysis program and to check for
finite size corrections, we actually studied three different models: (a)
Ordinary random walks (mimicking -polymers); (b) Self-avoiding walks
(SAW); and (c) Domb-Joyce walks with the self-repulsion tuned to the point
where finite size corrections for free (unrestricted) chains are minimal. For
the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with
Markovian anticipation. In addition to the partition sum (which gives us a
direct estimate of the forces exerted onto the walls), we measure the density
profiles of monomers and of end points transverse to the slab, and the radial
extent of the chain parallel to the walls. All scaling laws and some of the
universal amplitude ratios are compared to theoretical predictions.Comment: 8 pages, 14 figures include
Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
Two replicas of spatially extended chaotic systems synchronize to a common
spatio-temporal chaotic state when coupled above a critical strength. As a
prototype of each single spatio-temporal chaotic system a lattice of maps
interacting via power-law coupling is considered. The synchronization
transition is studied as a non-equilibrium phase transition, and its critical
properties are analyzed at varying the spatial interaction range as well as the
nonlinearity of the dynamical units composing each system. In particular,
continuous and discontinuous local maps are considered. In both cases the
transitions are of the second order with critical indexes varying with the
exponent characterizing the interaction range. For discontinuous maps it is
numerically shown that the transition belongs to the {\it anomalous directed
percolation} (ADP) family of universality classes, previously identified for
L{\'e}vy-flight spreading of epidemic processes. For continuous maps, the
critical exponents are different from those characterizing ADP, but apart from
the nearest-neighbor case, the identification of the corresponding universality
classes remains an open problem. Finally, to test the influence of
deterministic correlations for the studied synchronization transitions, the
chaotic dynamical evolutions are substituted by suitable stochastic models. In
this framework and for the discontinuous case, it is possible to derive an
effective Langevin description that corresponds to that proposed for ADP.Comment: 12 pages, 5 figures Comments are welcom
Systematic Series Expansions for Processes on Networks
We use series expansions to study dynamics of equilibrium and non-equilibrium
systems on networks. This analytical method enables us to include detailed
non-universal effects of the network structure. We show that even low order
calculations produce results which compare accurately to numerical simulation,
while the results can be systematically improved. We show that certain commonly
accepted analytical results for the critical point on networks with a broad
degree distribution need to be modified in certain cases due to
disassortativity; the present method is able to take into account the
assortativity at sufficiently high order, while previous results correspond to
leading and second order approximations in this method. Finally, we apply this
method to real-world data.Comment: 4 pages, 3 figure
Synchronization of Coupled Systems with Spatiotemporal Chaos
We argue that the synchronization transition of stochastically coupled
cellular automata, discovered recently by L.G. Morelli {\it et al.} (Phys. Rev.
{\bf 58 E}, R8 (1998)), is generically in the directed percolation universality
class. In particular, this holds numerically for the specific example studied
by these authors, in contrast to their claim. For real-valued systems with
spatiotemporal chaos such as coupled map lattices, we claim that the
synchronization transition is generically in the universality class of the
Kardar-Parisi-Zhang equation with a nonlinear growth limiting term.Comment: 4 pages, including 3 figures; submitted to Phys. Rev.
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
Damage spreading and dynamic stability of kinetic Ising models
We investigate how the time evolution of different kinetic Ising models
depends on the initial conditions of the dynamics. To this end we consider the
simultaneous evolution of two identical systems subjected to the same thermal
noise. We derive a master equation for the time evolution of a joint
probability distribution of the two systems. This equation is then solved
within an effective-field approach. By analyzing the fixed points of the master
equation and their stability we identify regular and chaotic phases.Comment: 4 pages RevTeX, 2 Postscript figure
Stretched Polymers in a Poor Solvent
Stretched polymers with attractive interaction are studied in two and three
dimensions. They are described by biased self-avoiding random walks with
nearest neighbour attraction. The bias corresponds to opposite forces applied
to the first and last monomers. We show that both in and a phase
transition occurs as this force is increased beyond a critical value, where the
polymer changes from a collapsed globule to a stretched configuration. This
transition is second order in and first order in . For we
predict the transition point quantitatively from properties of the unstretched
polymer. This is not possible in , but even there we can estimate the
transition point precisely, and we can study the scaling at temperatures
slightly below the collapse temperature of the unstretched polymer. We find
very large finite size corrections which would make very difficult the estimate
of the transition point from straightforward simulations.Comment: 10 pages, 16 figure
Bias Analysis in Entropy Estimation
We consider the problem of finite sample corrections for entropy estimation.
New estimates of the Shannon entropy are proposed and their systematic error
(the bias) is computed analytically. We find that our results cover correction
formulas of current entropy estimates recently discussed in literature. The
trade-off between bias reduction and the increase of the corresponding
statistical error is analyzed.Comment: 5 pages, 3 figure
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