305 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
Positive Feedback, Memory and the Predictability of Earthquakes
We review the "critical point" concept for large earthquakes and enlarge it
in the framework of so-called "finite-time singularities". The singular
behavior associated with accelerated seismic release is shown to result from a
positive feedback of the seismic activity on its release rate. The most
important mechanisms for such positive feedback are presented. We introduce and
solve analytically a novel simple model of geometrical positive feedback in
which the stress shadow cast by the last large earthquake is progressively
fragmented by the increasing tectonic stress. Finally, we present a somewhat
speculative figure that tends to support a mechanism based on the decay of
stress shadows. This figure suggests that a large earthquake in Southern
California of size similar to the 1812 great event is maturing.Comment: PostScript document of 18 pages + 2 eps figure
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