160 research outputs found
Crack roughness and avalanche precursors in the random fuse model
We analyze the scaling of the crack roughness and of avalanche precursors in
the two dimensional random fuse model by numerical simulations, employing large
system sizes and extensive sample averaging. We find that the crack roughness
exhibits anomalous scaling, as recently observed in experiments. The roughness
exponents (, ) and the global width distributions are found
to be universal with respect to the lattice geometry. Failure is preceded by
avalanche precursors whose distribution follows a power law up to a cutoff
size. While the characteristic avalanche size scales as , with a
universal fractal dimension , the distribution exponent differs
slightly for triangular and diamond lattices and, in both cases, it is larger
than the mean-field (fiber bundle) value
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
Statistical properties of fracture in a random spring model
Using large scale numerical simulations we analyze the statistical properties
of fracture in the two dimensional random spring model and compare it with its
scalar counterpart: the random fuse model. We first consider the process of
crack localization measuring the evolution of damage as the external load is
raised. We find that, as in the fuse model, damage is initially uniform and
localizes at peak load. Scaling laws for the damage density, fracture strength
and avalanche distributions follow with slight variations the behavior observed
in the random fuse model. We thus conclude that scalar models provide a
faithful representation of the fracture properties of disordered systems.Comment: 12 pages, 17 figures, 1 gif figur
Effect of Disorder and Notches on Crack Roughness
We analyze the effect of disorder and notches on crack roughness in two
dimensions. Our simulation results based on large system sizes and extensive
statistical sampling indicate that the crack surface exhibits a universal local
roughness of and is independent of the initial notch size
and disorder in breaking thresholds. The global roughness exponent scales as
and is also independent of material disorder. Furthermore, we
note that the statistical distribution of crack profile height fluctuations is
also independent of material disorder and is described by a Gaussian
distribution, albeit deviations are observed in the tails.Comment: 6 pages, 6 figure
Avalanches in self-organized critical neural networks: A minimal model for the neural SOC universality class
The brain keeps its overall dynamics in a corridor of intermediate activity
and it has been a long standing question what possible mechanism could achieve
this task. Mechanisms from the field of statistical physics have long been
suggesting that this homeostasis of brain activity could occur even without a
central regulator, via self-organization on the level of neurons and their
interactions, alone. Such physical mechanisms from the class of self-organized
criticality exhibit characteristic dynamical signatures, similar to seismic
activity related to earthquakes. Measurements of cortex rest activity showed
first signs of dynamical signatures potentially pointing to self-organized
critical dynamics in the brain. Indeed, recent more accurate measurements
allowed for a detailed comparison with scaling theory of non-equilibrium
critical phenomena, proving the existence of criticality in cortex dynamics. We
here compare this new evaluation of cortex activity data to the predictions of
the earliest physics spin model of self-organized critical neural networks. We
find that the model matches with the recent experimental data and its
interpretation in terms of dynamical signatures for criticality in the brain.
The combination of signatures for criticality, power law distributions of
avalanche sizes and durations, as well as a specific scaling relationship
between anomalous exponents, defines a universality class characteristic of the
particular critical phenomenon observed in the neural experiments. The spin
model is a candidate for a minimal model of a self-organized critical adaptive
network for the universality class of neural criticality. As a prototype model,
it provides the background for models that include more biological details, yet
share the same universality class characteristic of the homeostasis of activity
in the brain.Comment: 17 pages, 5 figure
Multifractal Behaviour of n-Simplex Lattice
We study the asymptotic behaviour of resistance scaling and fluctuation of
resistance that give rise to flicker noise in an {\em n}-simplex lattice. We
propose a simple method to calculate the resistance scaling and give a
closed-form formula to calculate the exponent, , associated with
resistance scaling, for any n. Using current cumulant method we calculate the
exact noise exponent for n-simplex lattices.Comment: Latex, 9 pages including one figur
An Efficient Block Circulant Preconditioner For Simulating Fracture Using Large Fuse Networks
{\it Critical slowing down} associated with the iterative solvers close to
the critical point often hinders large-scale numerical simulation of fracture
using discrete lattice networks. This paper presents a block circlant
preconditioner for iterative solvers for the simulation of progressive fracture
in disordered, quasi-brittle materials using large discrete lattice networks.
The average computational cost of the present alorithm per iteration is , where the stiffness matrix is partioned into
-by- blocks such that each block is an -by- matrix, and
represents the operational count associated with solving a block-diagonal
matrix with -by- dense matrix blocks. This algorithm using the block
circulant preconditioner is faster than the Fourier accelerated preconditioned
conjugate gradient (PCG) algorithm, and alleviates the {\it critical slowing
down} that is especially severe close to the critical point. Numerical results
using random resistor networks substantiate the efficiency of the present
algorithm.Comment: 16 pages including 2 figure
Size effects in statistical fracture
We review statistical theories and numerical methods employed to consider the
sample size dependence of the failure strength distribution of disordered
materials. We first overview the analytical predictions of extreme value
statistics and fiber bundle models and discuss their limitations. Next, we
review energetic and geometric approaches to fracture size effects for
specimens with a flaw. Finally, we overview the numerical simulations of
lattice models and compare with theoretical models.Comment: review article 19 pages, 5 figure
Scale free networks by preferential depletion
We show that not only preferential attachment but also preferential depletion
leads to scale-free networks. The resulting degree distribution exponents is
typically less than two (5/3) as opposed to the case of the growth models
studied before where the exponents are larger. Our approach applies in
particular to biological networks where in fact we find interesting agreement
with experimental measurements. We investigate the most important properties
characterizing these networks, as the cluster size distribution, the average
shortest path and the clustering coefficient.Comment: 8 pages, 4 figure
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