11 research outputs found
Growing interfaces uncover universal fluctuations behind scale invariance
Stochastic motion of a point -- known as Brownian motion -- has many
successful applications in science, thanks to its scale invariance and
consequent universal features such as Gaussian fluctuations. In contrast, the
stochastic motion of a line, though it is also scale-invariant and arises in
nature as various types of interface growth, is far less understood. The two
major missing ingredients are: an experiment that allows a quantitative
comparison with theory and an analytic solution of the Kardar-Parisi-Zhang
(KPZ) equation, a prototypical equation for describing growing interfaces. Here
we solve both problems, showing unprecedented universality beyond the scaling
laws. We investigate growing interfaces of liquid-crystal turbulence and find
not only universal scaling, but universal distributions of interface positions.
They obey the largest-eigenvalue distributions of random matrices and depend on
whether the interface is curved or flat, albeit universal in each case. Our
exact solution of the KPZ equation provides theoretical explanations.Comment: 5 pages, 3 figures, supplementary information available on Journal
pag
Fracture in Three-Dimensional Fuse Networks
We report on large scale numerical simulations of fracture surfaces using
random fuse networks for two very different disorders. There are some
properties and exponents that are different for the two distributions, but
others, notably the roughness exponents, seem universal. For the universal
roughness exponent we found a value of zeta = 0.62 +/- 0.05. In contrast to
what is observed in two dimensions, this value is lower than that reported in
experimental studies of brittle fractures, and rules out the minimal energy
surface exponent, 0.41 +/- 0.01.Comment: 4 pages, RevTeX, 5 figures, Postscrip
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
Anomalous roughening of wood fractured surfaces
Scaling properties of wood fractured surfaces are obtained from samples of
three different sizes. Two different woods are studied: Norway spruce and
Maritime pine. Fracture surfaces are shown to display an anomalous dynamic
scaling of the crack roughness. This anomalous scaling behavior involves the
existence of two different and independent roughness exponents. We determine
the local roughness exponents to be 0.87 for spruce and 0.88
for pine. These results are consistent with the conjecture of a universal local
roughness exponent. The global roughness exponent is different for both woods,
= 1.60 for spruce and = 1.35 for pine. We argue that the global
roughness exponent is a good index for material characterization.Comment: 7 two columns pages plus 8 ps figures, uses psfig. To appear in
Physical Review
Anomalous Roughening in Experiments of Interfaces in Hele-Shaw Flows with Strong Quenched Disorder
We report experimental evidences of anomalous kinetic roughening in the
stable displacement of an oil-air interface in a Hele-Shaw cell with strong
quenched disorder. The disorder consists on a random modulation of the gap
spacing transverse to the growth direction (tracks). We have performed
experiments varying average interface velocity and gap spacing, and measured
the scaling exponents. We have obtained beta=0.50, beta*=0.25, alpha=1.0,
alpha_l=0.5, and z=2. When there is no fluid injection, the interface is driven
solely by capillary forces, and a higher value of beta around beta=0.65 is
measured. The presence of multiscaling and the particular morphology of the
interfaces, characterized by high slopes that follow a L\'evy distribution,
confirms the existence of anomalous scaling. From a detailed study of the
motion of the oil--air interface we show that the anomaly is a consequence of
different local velocities over tracks plus the coupling in the motion between
neighboring tracks. The anomaly disappears at high interface velocities, weak
capillary forces, or when the disorder is not sufficiently persistent in the
growth direction. We have also observed the absence of scaling when the
disorder is very strong or when a regular modulation of the gap spacing is
introduced.Comment: 14 pages, 17 figure
Size Effect in Fracture: Roughening of Crack Surfaces and Asymptotic Analysis
Recently the scaling laws describing the roughness development of fracture
surfaces was proposed to be related to the macroscopic elastic energy released
during crack propagation [Mor00]. On this basis, an energy-based asymptotic
analysis allows to extend the link to the nominal strength of structures. We
show that a Family-Vicsek scaling leads to the classical size effect of linear
elastic fracture mechanics. On the contrary, in the case of an anomalous
scaling, there is a smooth transition from the case of no size effect, for
small structure sizes, to a power law size effect which appears weaker than the
linear elastic fracture mechanics one, in the case of large sizes. This
prediction is confirmed by fracture experiments on wood.Comment: 9 pages, 6 figures, accepted for publication in Physical Review
Statistical Physics of Fracture Surfaces Morphology
Experiments on fracture surface morphologies offer increasing amounts of data
that can be analyzed using methods of statistical physics. One finds scaling
exponents associated with correlation and structure functions, indicating a
rich phenomenology of anomalous scaling. We argue that traditional models of
fracture fail to reproduce this rich phenomenology and new ideas and concepts
are called for. We present some recent models that introduce the effects of
deviations from homogeneous linear elasticity theory on the morphology of
fracture surfaces, succeeding to reproduce the multiscaling phenomenology at
least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel
methods of analysis based on projecting the data on the irreducible
representations of the SO(2) symmetry group. It appears that this approach
organizes effectively the rich scaling properties. We end up with the
proposition of new experiments in which the rotational symmetry is not broken,
such that the scaling properties should be particularly simple.Comment: A review paper submitted to J. Stat. Phy