90 research outputs found
Self-Organized Criticality in a Fibre-Bundle type model
The dynamics of a fibre-bundle type model with equal load sharing rule is
numerically studied. The system, formed by N elements, is driven by a slow
increase of the load upon it which is removed in a novel way through internal
transfers to the elements broken during avalanches. When an avalanche ends,
failed elements are regenerated with strengths taken from a probability
distribution. For a large enough N and certain restrictions on the distribution
of individual strengths, the system reaches a self-organized critical state
where the spectrum of avalanche sizes is a power law with an exponent
.Comment: 10 pages, 6 figures. To be published in Physica
Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane
We consider flame front propagation in channel geometries. The steady state
solution in this problem is space dependent, and therefore the linear stability
analysis is described by a partial integro-differential equation with a space
dependent coefficient. Accordingly it involves complicated eigenfunctions. We
show that the analysis can be performed to required detail using a finite order
dynamical system in terms of the dynamics of singularities in the complex
plane, yielding detailed understanding of the physics of the eigenfunctions and
eigenvalues.Comment: 17 pages 7 figure
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]
Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II
The current paper is a corrected version of our previous paper
arXiv:adap-org/9608001. Similarly to previous version we investigate the
problem of flame propagation. This problem is studied as an example of unstable
fronts that wrinkle on many scales. The analytic tool of pole expansion in the
complex plane is employed to address the interaction of the unstable growth
process with random initial conditions and perturbations. We argue that the
effect of random noise is immense and that it can never be neglected in
sufficiently large systems. We present simulations that lead to scaling laws
for the velocity and acceleration of the front as a function of the system size
and the level of noise, and analytic arguments that explain these results in
terms of the noisy pole dynamics.This version corrects some very critical
errors made in arXiv:adap-org/9608001 and makes more detailed description of
excess number of poles in system, number of poles that appear in the system in
unit of time, life time of pole. It allows us to understand more correctly
dependence of the system parameters on noise than in arXiv:adap-org/9608001Comment: 23 pages, 4 figures,revised, version accepted for publication in
journal "Combustion, Explosion and Shock Waves". arXiv admin note:
substantial text overlap with arXiv:nlin/0302021, arXiv:adap-org/9608001,
arXiv:nlin/030201
Fingering Instability in Combustion
A thin solid (e.g., paper), burning against an oxidizing wind, develops a
fingering instability with two decoupled length scales. The spacing between
fingers is determined by the P\'eclet number (ratio between advection and
diffusion). The finger width is determined by the degree two dimensionality.
Dense fingers develop by recurrent tip splitting. The effect is observed when
vertical mass transport (due to gravity) is suppressed. The experimental
results quantitatively verify a model based on diffusion limited transport
Unified Scaling Law for Earthquakes
We show that the distribution of waiting times between earthquakes occurring
in California obeys a simple unified scaling law valid from tens of seconds to
tens of years, see Eq. (1) and Fig. 4. The short time clustering, commonly
referred to as aftershocks, is nothing but the short time limit of the general
hierarchical properties of earthquakes. There is no unique operational way of
distinguishing between main shocks and aftershocks. In the unified law, the
Gutenberg-Richter b-value, the exponent -1 of the Omori law for aftershocks,
and the fractal dimension d_f of earthquakes appear as critical indices.Comment: 4 pages, 4 figure
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
Predictability of Self-Organizing Systems
We study the predictability of large events in self-organizing systems. We
focus on a set of models which have been studied as analogs of earthquake
faults and fault systems, and apply methods based on techniques which are of
current interest in seismology. In all cases we find detectable correlations
between precursory smaller events and the large events we aim to forecast. We
compare predictions based on different patterns of precursory events and find
that for all of the models a new precursor based on the spatial distribution of
activity outperforms more traditional measures based on temporal variations in
the local activity.Comment: 15 pages, plain.tex with special macros included, 4 figure
Symmetries and Fixed Point Stability of Stochastic Differential Equations Modeling Self-Organized Criticality
A stochastic nonlinear partial differential equation is built for two
different models exhibiting self-organized criticality, the Bak, Tang, and
Wiesenfeld (BTW) sandpile model and the Zhang's model. The dynamic
renormalization group (DRG) enables to compute the critical exponents. However,
the nontrivial stable fixed point of the DRG transformation is unreachable for
the original parameters of the models. We introduce an alternative
regularization of the step function involved in the threshold condition, which
breaks the symmetry of the BTW model. Although the symmetry properties of the
two models are different, it is shown that they both belong to the same
universality class. In this case the DRG procedure leads to a symmetric
behavior for both models, restoring the broken symmetry, and makes accessible
the nontrivial fixed point. This technique could also be applied to other
problems with threshold dynamics.Comment: 19 pages, RevTex, includes 6 PostScript figures, Phys. Rev. E (March
97?
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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