107 research outputs found
Invading interfaces and blocking surfaces in high dimensional disordered systems
We study the high-dimensional properties of an invading front in a disordered
medium with random pinning forces. We concentrate on interfaces described by
bounded slope models belonging to the quenched KPZ universality class. We find
a number of qualitative transitions in the behavior of the invasion process as
dimensionality increases. In low dimensions the system is characterized
by two different roughness exponents, the roughness of individual avalanches
and the overall interface roughness. We use the similarity of the dynamics of
an avalanche with the dynamics of invasion percolation to show that above
avalanches become flat and the invasion is well described as an annealed
process with correlated noise. In fact, for the overall roughness is
the same as the annealed roughness. In very large dimensions, strong
fluctuations begin to dominate the size distribution of avalanches, and this
phenomenon is studied on the Cayley tree, which serves as an infinite
dimensional limit. We present numerical simulations in which we measured the
values of the critical exponents of the depinning transition, both in finite
dimensional lattices with and on the Cayley tree, which support our
qualitative predictions. We find that the critical exponents in are very
close to their values on the Cayley tree, and we conjecture on this basis the
existence of a further dimension, where mean field behavior is obtained.Comment: 12 pages, REVTeX with 2 postscript figure
On the random neighbor Olami-Feder-Christensen slip-stick model
We reconsider the treatment of Lise and Jensen (Phys. Rev. Lett. 76, 2326
(1996)) on the random neighbor Olami-Feder-Christensen stik-slip model, and
examine the strong dependence of the results on the approximations used for the
distribution of states p(E).Comment: 6pages, 3 figures. To be published in PRE as a brief repor
Anomalous Height Fluctuation Width in Crossover from Random to Coherent Surface Growths
We study an anomalous behavior of the height fluctuation width in the
crossover from random to coherent growths of surface for a stochastic model. In
the model, random numbers are assigned on perimeter sites of surface,
representing pinning strengths of disordered media. At each time, surface is
advanced at the site having minimum pinning strength in a random subset of
system rather than having global minimum. The subset is composed of a randomly
selected site and its neighbors. The height fluctuation width
exhibits the non-monotonic behavior with and it has a
minimum at . It is found numerically that scales as
, and the height fluctuation width at that minimum,
, scales as in 1+1 dimensions. It is found that
the subset-size is the characteristic size of the crossover from
the random surface growth in the KPZ universality, to the coherent surface
growth in the directed percolation universality.Comment: 13 postscript file
Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model
We present the analytic solution of the self-organized critical (SOC)
forest-fire model in one dimension proving SOC in systems without conservation
laws by analytic means. Under the condition that the system is in the steady
state and very close to the critical point, we calculate the probability that a
string of neighboring sites is occupied by a given configuration of trees.
The critical exponent describing the size distribution of forest clusters is
exactly and does not change under certain changes of the model
rules. Computer simulations confirm the analytic results.Comment: 12 pages REVTEX, 2 figures upon request, dro/93/
Anisotropic Interface Depinning - Numerical Results
We study numerically a stochastic differential equation describing an
interface driven along the hard direction of an anisotropic random medium. The
interface is subject to a homogeneous driving force, random pinning forces and
the surface tension. In addition, a nonlinear term due to the anisotropy of the
medium is included. The critical exponents characterizing the depinning
transition are determined numerically for a one-dimensional interface. The
results are the same, within errors, as those of the ``Directed Percolation
Depinning'' (DPD) model. We therefore expect that the critical exponents of the
stochastic differential equation are exactly given by the exponents obtained by
a mapping of the DPD model to directed percolation. We find that a moving
interface near the depinning transition is not self-affine and shows a behavior
similar to the DPD model.Comment: 9 pages, 13 figures, REVTe
Pulse-coupled relaxation oscillators: from biological synchronization to Self-Organized Criticality
It is shown that globally-coupled oscillators with pulse interaction can
synchronize under broader conditions than widely believed from a theorem of
Mirollo \& Strogatz \cite{MirolloII}. This behavior is stable against frozen
disorder. Beside the relevance to biology, it is argued that synchronization in
relaxation oscillator models is related to Self-Organized Criticality in
Stick-Slip-like models.Comment: 4 pages, RevTeX, 1 uuencoded postscript figure in separate file,
accepted for publication in Phys. Rev. Lett
Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators
We introduce two coupled map lattice models with nonconservative interactions
and a continuous nonlinear driving. Depending on both the degree of
conservation and the convexity of the driving we find different behaviors,
ranging from self-organized criticality, in the sense that the distribution of
events (avalanches) obeys a power law, to a macroscopic synchronization of the
population of oscillators, with avalanches of the size of the system.Comment: 4 pages, Revtex 3.0, 3 PostScript figures available upon request to
[email protected]
Breakdown of self-organized criticality
We introduce two sandpile models which show the same behavior of real
sandpiles, that is, an almost self-organized critical behavior for small
systems and the dominance of large avalanches as the system size increases. The
systems become fully self-organized critical, with the critical exponents of
the Bak, Tang and Wiesenfeld model, as the system parameters are changed,
showing that these systems can make a bridge between the well known theoretical
and numerical results and what is observed in real experiments. We find that a
simple mechanism determines the boundary where self-organized can or cannot
exist, which is the presence of local chaos.Comment: 3 pages, 4 figure
On the robustness of scale invariance in SOC models
A random neighbor extremal stick-slip model is introduced. In the
thermodynamic limit, the distribution of states has a simple analytical form
and the mean avalanche size, as a function of the coupling parameter, is
exactly calculable. The system is critical only at a special point Jc in the
coupling parameter space. However, the critical region around this point, where
approximate scale invariance holds, is very large, suggesting a mechanism for
explaining the ubiquity of scale invariance in Nature.Comment: 6 pages, 4 figures; submitted to Physical Review E;
http://link.aps.org/doi/10.1103/PhysRevE.59.496
Synchronization in coupled map lattices as an interface depinning
We study an SOS model whose dynamics is inspired by recent studies of the
synchronization transition in coupled map lattices (CML). The synchronization
of CML is thus related with a depinning of interface from a binding wall.
Critical behaviour of our SOS model depends on a specific form of binding
(i.e., transition rates of the dynamics). For an exponentially decaying binding
the depinning belongs to the directed percolation universality class. Other
types of depinning, including the one with a line of critical points, are
observed for a power-law binding.Comment: 4 pages, Phys.Rev.E (in press
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