7 research outputs found
Avalanches in the Weakly Driven Frenkel-Kontorova Model
A damped chain of particles with harmonic nearest-neighbor interactions in a
spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is
studied numerically. One end of the chain is pulled slowly which acts as a weak
driving mechanism. The numerical study was performed in the limit of infinitely
weak driving. The model exhibits avalanches starting at the pulled end of the
chain. The dynamics of the avalanches and their size and strength distributions
are studied in detail. The behavior depends on the value of the damping
constant. For moderate values a erratic sequence of avalanches of all sizes
occurs. The avalanche distributions are power-laws which is a key feature of
self-organized criticality (SOC). It will be shown that the system selects a
state where perturbations are just able to propagate through the whole system.
For strong damping a regular behavior occurs where a sequence of states
reappears periodically but shifted by an integer multiple of the period of the
external potential. There is a broad transition regime between regular and
irregular behavior, which is characterized by multistability between regular
and irregular behavior. The avalanches are build up by sound waves and shock
waves. Shock waves can turn their direction of propagation, or they can split
into two pulses propagating in opposite directions leading to transient
spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in
Phys. Rev.
Critical States in a Dissipative Sandpile Model
A directed dissipative sandpile model is studied in the two-dimension.
Numerical results indicate that the long time steady states of this model are
critical when grains are dropped only at the top or, everywhere. The critical
behaviour is mean-field like. We discuss the role of infinite avalanches of
dissipative models in periodic systems in determining the critical behaviour of
same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included
On Synchronization in a Lattice Model of Pulse-Coupled Oscillators
We analyze the collective behavior of a lattice model of pulse-coupled
oscillators. By means of computer simulations we find the relation between the
intrinsic dynamics of each member of the population and their mutual
interaction that ensures, in a general context, the existence of a fully
synchronized regime. This condition turns out to be the same than the obtained
for the globally coupled population. When the condition is not completely
satisfied we find different spatial structures. This also gives some hints
about self-organized criticality.Comment: 4 pages, RevTex, 1 PostScript available upon request, To appear in
Phys. Rev. Let