9,261 research outputs found
Theory of Self-organized Criticality for Problems with Extremal Dynamics
We introduce a general theoretical scheme for a class of phenomena
characterized by an extremal dynamics and quenched disorder. The approach is
based on a transformation of the quenched dynamics into a stochastic one with
cognitive memory and on other concepts which permit a mathematical
characterization of the self-organized nature of the avalanche type dynamics.
In addition it is possible to compute the relevant critical exponents directly
from the microscopic model. A specific application to Invasion Percolation is
presented but the approach can be easily extended to various other problems.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to
Europhys. Let
An extremal model for amorphous media plasticity
An extremal model for the plasticity of amorphous materials is studied in a
simple two-dimensional anti-plane geometry. The steady-state is analyzed
through numerical simulations. Long-range spatial and temporal correlations in
local slip events are shown to develop, leading to non-trivial and highly
anisotropic scaling laws. In particular, the plastic strain is shown to
statistically concentrate over a region which tends to align perpendicular to
the displacement gradient. By construction, the model can be seen as giving
rise to a depinning transition, the threshold of which (i.e. the macroscopic
yield stress) also reveal scaling properties reflecting the localization of the
activity.Comment: 4 pages, 5 figure
Discrepancy between sub-critical and fast rupture roughness: a cumulant analysis
We study the roughness of a crack interface in a sheet of paper. We
distinguish between slow (sub-critical) and fast crack growth regimes. We show
that the fracture roughness is different in the two regimes using a new method
based on a multifractal formalism recently developed in the turbulence
literature. Deviations from monofractality also appear to be different in both
regimes
Branching Transition of a Directed Polymer in Random Medium
A directed polymer is allowed to branch, with configurations determined by
global energy optimization and disorder. A finite size scaling analysis in 2D
shows that, if disorder makes branching more and more favorable, a critical
transition occurs from the linear scaling regime first studied by Huse and
Henley [Phys. Rev. Lett. 54, 2708 (1985)] to a fully branched, compact one. At
criticality clear evidence is obtained that the polymer branches at all scales
with dimension and roughness exponent satisfying , and energy fluctuation exponent , in terms of longitudinal distanceComment: REVTEX, 4 pages, 3 encapsulated eps figure
Roughness of fracture surfaces
We study the fracture surface of three dimensional samples through a model
for quasi-static fractures known as Born Model. We find for the roughness
exponent a value of 0.5 expected for ``small length scales'' in microfracturing
experiments. Our simulations confirm that at small length scales the fracture
can be considered as quasi-static. The isotropy of the roughness exponent on
the crack surface is also shown. Finally, considering the crack front, we
compute the roughness exponents for longitudinal and transverse fluctuations of
the crack line (both 0.5). They result in agreement with experimental data, and
supports the possible application of the model of line depinning in the case of
long-range interactions.Comment: 10 pages, 5 figures, Late
Slow decay of concentration variance due to no-slip walls in chaotic mixing
Chaotic mixing in a closed vessel is studied experimentally and numerically
in different 2-D flow configurations. For a purely hyperbolic phase space, it
is well-known that concentration fluctuations converge to an eigenmode of the
advection-diffusion operator and decay exponentially with time. We illustrate
how the unstable manifold of hyperbolic periodic points dominates the resulting
persistent pattern. We show for different physical viscous flows that, in the
case of a fully chaotic Poincare section, parabolic periodic points at the
walls lead to slower (algebraic) decay. A persistent pattern, the backbone of
which is the unstable manifold of parabolic points, can be observed. However,
slow stretching at the wall forbids the rapid propagation of stretched
filaments throughout the whole domain, and hence delays the formation of an
eigenmode until it is no longer experimentally observable. Inspired by the
baker's map, we introduce a 1-D model with a parabolic point that gives a good
account of the slow decay observed in experiments. We derive a universal decay
law for such systems parametrized by the rate at which a particle approaches
the no-slip wall.Comment: 17 pages, 12 figure
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