12 research outputs found
Crossover phenomenon in self-organized critical sandpile models
We consider a stochastic sandpile where the sand-grains of unstable sites are
randomly distributed to the nearest neighbors. Increasing the value of the
threshold condition the stochastic character of the distribution is lost and a
crossover to the scaling behavior of a different sandpile model takes place
where the sand-grains are equally transferred to the nearest neighbors. The
crossover behavior is numerically analyzed in detail, especially we consider
the exponents which determine the scaling behavior.Comment: 6 pages, 9 figures, accepted for publication in Physical Review
Strong Phase Separation in a Model of Sedimenting Lattices
We study the steady state resulting from instabilities in crystals driven
through a dissipative medium, for instance, a colloidal crystal which is
steadily sedimenting through a viscous fluid. The problem involves two coupled
fields, the density and the tilt; the latter describes the orientation of the
mass tensor with respect to the driving field. We map the problem to a 1-d
lattice model with two coupled species of spins evolving through conserved
dynamics. In the steady state of this model each of the two species shows
macroscopic phase separation. This phase separation is robust and survives at
all temperatures or noise levels--- hence the term Strong Phase Separation.
This sort of phase separation can be understood in terms of barriers to
remixing which grow with system size and result in a logarithmically slow
approach to the steady state. In a particular symmetric limit, it is shown that
the condition of detailed balance holds with a Hamiltonian which has
infinite-ranged interactions, even though the initial model has only local
dynamics. The long-ranged character of the interactions is responsible for
phase separation, and for the fact that it persists at all temperatures.
Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses
epsf, three ps figure
Scaling in a Nonconservative Earthquake Model of Self-Organised Criticality
We numerically investigate the Olami-Feder-Christensen model for earthquakes
in order to characterise its scaling behaviour. We show that ordinary finite
size scaling in the model is violated due to global, system wide events.
Nevertheless we find that subsystems of linear dimension small compared to the
overall system size obey finite (subsystem) size scaling, with universal
critical coefficients, for the earthquake events localised within the
subsystem. We provide evidence, moreover, that large earthquakes responsible
for breaking finite size scaling are initiated predominantly near the boundary.Comment: 6 pages, 6 figures, to be published in Phys. Rev. E; references
sorted correctl
Stochastic dynamics of a sheared granular medium
45.70.-n Granular systems, 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion, 02.50.-r Probability theory, stochastic processes, and statistics,