1,913 research outputs found
Ridge Network in Crumpled Paper
The network formed by ridges in a straightened sheet of crumpled paper is
studied using a laser profilometer. Square sheets of paper were crumpled into
balls, unfolded and their height profile measured. From these profiles the
imposed ridges were extracted as networks. Nodes were defined as intersections
between ridges, and links as the various ridges connecting the nodes. Many
network and spatial properties have been investigated. The tail of the ridge
length distribution was found to follow a power-law whereas the shorter ridges
followed a log-normal distribution. The degree distribution was found to have
an exponentially decaying tail, and the degree correlation was found to be
disassortative. The facets created by the ridges and the Voronoi diagram formed
by the nodes have also been investigated.Comment: 8 pages, 10 figure, 2 tables Replaced due to wrong formating of
author name
Self-Affinity in the Gradient Percolation Problem
We study the scaling properties of the solid-on-solid front of the infinite
cluster in two-dimensional gradient percolation. We show that such an object is
self affine with a Hurst exponent equal to 2/3 up to a cutoff-length
proportional to the gradient to the power (-4/7). Beyond this length scale, the
front position has the character of uncorrelated noise. Importantly, the
self-affine behavior is robust even after removing local jumps of the front.
The previously observed multi affinity, is due to the dominance of overhangs at
small distances in the structure function. This is a crossover effect.Comment: 4 pages, 4 figure
Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution
Presence of lower cutoff in fiber threshold distribution may affect the
failure properties of a bundle of fibers subjected to external load. We
investigate this possibility both in a equal load sharing (ELS) fiber bundle
model and in local load sharing (LLS) one. We show analytically that in ELS
model, the critical strength gets modified due to the presence of lower cutoff
and it becomes bounded by an upper limit. Although the dynamic exponents for
the susceptibility and relaxation time remain unchanged, the avalanche size
distribution shows a permanent deviation from the mean-fiels power law. In the
LLS model, we analytically estimate the upper limit of the lower cutoff above
which the bundle fails at one instant. Also the system size variation of
bundle's strength and the avalanche statistics show strong dependence on the
lower cutoff level.Comment: 7 pages and 7 figure
Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion
We study a non-linear convective-diffusive equation, local in space and time,
which has its background in the dynamics of the thickness of a wetting film.
The presence of a non-linear diffusion predicts the existence of fronts as well
as shock fronts. Despite the absence of memory effects, solutions in the case
of pure non-linear diffusion exhibit an anomalous sub-diffusive scaling. Due to
a balance between non-linear diffusion and convection we, in particular, show
that solitary waves appear. For large times they merge into a single solitary
wave exhibiting a topological stability. Even though our results concern a
specific equation, numerical simulations supports the view that anomalous
diffusion and the solitary waves disclosed will be general features in such
non-linear convective-diffusive dynamics.Comment: Corrected typos, added 3 references and 2 figure
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
Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Correlated Percolation in the Damage Zone
We suggest that the observed large-scale universal roughness of brittle
fracture surfaces is due to the fracture process being a correlated percolation
process in a self-generated quadratic damage gradient. We use the quasi-static
two-dimensional fuse model as a paradigm of a fracture model. We measure for
this model, that exhibits a correlated percolation process, the correlation
length exponent nu approximately equal to 1.35 and conjecture it to be equal to
that of uncorrelated percolation, 4/3. We then show that the roughness exponent
in the fuse model is zeta = 2 nu/(1+2 nu)= 8/11. This is in accordance with the
numerical value zeta=0.75. As for three-dimensional brittle fractures, a
mean-field theory gives nu=2, leading to zeta=4/5 in full accordance with the
universally observed value zeta =0.80.Comment: 4 pages RevTeX
Diamagnetic Susceptibility and Current Distributions in Granular Superconductors at Percolation
Comments: 4 pages RevTeX, 4 Postscript figures. References added. We study a
two-dimensional granular superconducting network at the percolation threshold
under the influence of an external perpendicular magnetic field. By numerical
simulations on the full nonlinear problem, we determine the scaling exponent
for the magnetic susceptibility. Further, we report on the scaling properties
of the current distribution. The scaling of the current is found to be
independent of the value of the magnetic field. Our results are in
contradiction with previous numerical results based on linearized equations. We
find a value for the susceptibility exponent which does not agree with existing
theoretical suggestions, but agrees perfectly with renormalization group
calculations
Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone
We show that the roughness exponent zeta of an in-plane crack front slowly
propagating along a heterogeneous interface embeded in a elastic body, is in
full agreement with a correlated percolation problem in a linear gradient. We
obtain zeta=nu/(1+nu) where nu is the correlation length critical exponent. We
develop an elastic brittle model based on both the 3D Green function in an
elastic half-space and a discrete interface of brittle fibers and find
numerically that nu=1.5, We conjecture it to be 3/2. This yields zeta=3/5. We
also obtain by direct numerical simulations zeta=0.6 in excellent agreement
with our prediction. This modelling is for the first time in close agreement
with experimental observations.Comment: 4 pages RevTeX
Band Formation during Gaseous Diffusion in Aerogels
We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides
of and react in silica aerogel rods with porosity of 92 % and average pore size
of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin
sheet-like structures. We present a numerical study of the phenomenon. Due to
the difference in boundary conditions between this system and those usually
studied, we find the sheet-like structures in the aerogel to differ
significantly from older studies. The influence of random nucleation centers
and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on
request from author
Failure Processes in Elastic Fiber Bundles
The fiber bundle model describes a collection of elastic fibers under load.
the fibers fail successively and for each failure, the load distribution among
the surviving fibers change. Even though very simple, the model captures the
essentials of failure processes in a large number of materials and settings. We
present here a review of fiber bundle model with different load redistribution
mechanism from the point of view of statistics and statistical physics rather
than materials science, with a focus on concepts such as criticality,
universality and fluctuations. We discuss the fiber bundle model as a tool for
understanding phenomena such as creep, and fatigue, how it is used to describe
the behavior of fiber reinforced composites as well as modelling e.g. network
failure, traffic jams and earthquake dynamics.Comment: This article has been Editorially approved for publication in Reviews
of Modern Physic
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