8,571 research outputs found
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
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
Large scale numerical simulations of "ultrametric" long-range depinning
The depinning of an elastic line interacting with a quenched disorder is
studied for long range interactions, applicable to crack propagation or
wetting. An ultrametric distance is introduced instead of the Euclidean
distance, allowing for a drastic reduction of the numerical complexity of the
problem. Based on large scale simulations, two to three orders of magnitude
larger than previously considered, we obtain a very precise determination of
critical exponents which are shown to be indistinguishable from their Euclidean
metric counterparts. Moreover the scaling functions are shown to be unchanged.
The choice of an ultrametric distance thus does not affect the universality
class of the depinning transition and opens the way to an analytic real space
renormalization group approach.Comment: submitted to Phys. Rev.
Dynamics of vortices in weakly interacting Bose-Einstein condensates
We study the dynamics of vortices in ideal and weakly interacting
Bose-Einstein condensates using a Ritz minimization method to solve the
two-dimensional Gross-Pitaevskii equation. For different initial vortex
configurations we calculate the trajectories of the vortices. We find
conditions under which a vortex-antivortex pair annihilates and is created
again. For the case of three vortices we show that at certain times two
additional vortices may be created, which move through the condensate and
annihilate each other again. For a noninteracting condensate this process is
periodic, whereas for small interactions the essential features persist, but
the periodicity is lost. The results are compared to exact numerical solutions
of the Gross-Pitaevskii equation confirming our analytical findings.Comment: 8 pages, 7 figures, one reference updated, typos correcte
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
Roughness of Crack Interfaces in Two-Dimensional Beam Lattices
The roughness of crack interfaces is reported in quasistatic fracture, using
an elastic network of beams with random breaking thresholds. For strong
disorders we obtain 0.86(3) for the roughness exponent, a result which is very
different from the minimum energy surface exponent, i.e., the value 2/3. A
cross-over to lower values is observed as the disorder is reduced, the exponent
in these cases being strongly dependent on the disorder.Comment: 9 pages, RevTeX, 3 figure
Walls Inhibit Chaotic Mixing
We report on experiments of chaotic mixing in a closed vessel, in which a
highly viscous fluid is stirred by a moving rod. We analyze quantitatively how
the concentration field of a low-diffusivity dye relaxes towards homogeneity,
and we observe a slow algebraic decay of the inhomogeneity, at odds with the
exponential decay predicted by most previous studies. Visual observations
reveal the dominant role of the vessel wall, which strongly influences the
concentration field in the entire domain and causes the anomalous scaling. A
simplified 1D model supports our experimental results. Quantitative analysis of
the concentration pattern leads to scalings for the distributions and the
variance of the concentration field consistent with experimental and numerical
results.Comment: 4 pages, 3 figure
Cleavage of C3 by Neutral Proteases from Granulocytes in Pleural Empyema
The possibility of direct inactivation of C3 by granular enzymes from polymorphonuclear leukocytes(PMNLs) in pleural empyema was examined. As a group, pleural empyema from 10 patients with purulent effusions and a positive bacteriologic culture cleaved significantly more 125I-labeled C3 bound to Sepharose (18.4% ± 7.3%) than did 19sterile pleural effusions (2.4% ± 0.9%; P << 0.001)and sonicates from bacterial strains commonly found in empyema (1.4% ± 0.2%). Granular enzymesfrom 7 × 106 PMNLs cleaved 78.5% of 125I-labeled C3 bound to Sepharose. When proteolysis of 125I-labeled C3 after incubation with pleural empyema or PMNL granular enzymes was examined with polyacrylamide gel electrophoresis, breakdown products were similar. Granulocyte elastase-like activity was detected in four samples of pleural empyema. Granulocyte elastase inhibitors, as well as 10% human serum, effectively suppressed cleavage of C3 and elastase-like activity. In pleural empyemas, granular enzymes from PMNLs, especially elastase, apparently contribute to low complement-mediated opsonic activity by direct inactivation of C
Tolerance and Sensitivity in the Fuse Network
We show that depending on the disorder, a small noise added to the threshold
distribution of the fuse network may or may not completely change the
subsequent breakdown process. When the threshold distribution has a lower
cutoff at a finite value and a power law dependence towards large thresholds
with an exponent which is less than , the network is not sensitive
to the added noise, otherwise it is. The transition between sensitivity or not
appears to be second order, and is related to a localization-delocalization
transition earlier observed in such systems.Comment: 12 pages, 3 figures available upon request, plain Te
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