287 research outputs found
Elastic lines on splayed columnar defects studied numerically
We investigate by exact optimization method properties of two- and
three-dimensional systems of elastic lines in presence of splayed columnar
disorder. The ground state of many lines is separable both in 2d and 3d leading
to a random walk -like roughening in 2d and ballistic behavior in 3d.
Furthermore, we find that in the case of pure splayed columnar disorder in
contrast to point disorder there is no entanglement transition in 3d.
Entanglement can be triggered by perturbing the pure splay system with point
defects.Comment: 9 pages, 11 figures. Accepted for publication in PR
Surface criticality in random field magnets
The boundary-induced scaling of three-dimensional random field Ising magnets
is investigated close to the bulk critical point by exact combinatorial
optimization methods. We measure several exponents describing surface
criticality: for the surface layer magnetization and the surface
excess exponents for the magnetization and the specific heat, and
. The latter ones are related to the bulk phase transition by the
same scaling laws as in pure systems, but only with the same violation of
hyperscaling exponent as in the bulk. The boundary disorders faster
than the bulk, and the experimental and theoretical implications are discussed.Comment: 6 pages, 9 figures, to appear in Phys. Rev.
Ground-States of Two Directed Polymers
Joint ground states of two directed polymers in a random medium are
investigated. Using exact min-cost flow optimization the true two-line
ground-state is compared with the single line ground state plus its first
excited state. It is found that these two-line configurations are (for almost
all disorder configurations) distinct implying that the true two-line
ground-state is non-separable, even with 'worst-possible' initial conditions.
The effective interaction energy between the two lines scales with the system
size with the scaling exponents 0.39 and 0.21 in 2D and 3D, respectively.Comment: 19 pages RevTeX, figures include
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
Scaling of interfaces in brittle fracture and perfect plasticity
The roughness properties of two-dimensional fracture surfaces as created by
the slow failure of random fuse networks are considered and compared to yield
surfaces of perfect plasticity with similar disorder. By studying systems up to
a linear size L=350 it is found that in the cases studied the fracture surfaces
exhibit self-affine scaling with a roughness exponent close to 2/3, which is
asymptotically exactly true for plasticity though finite-size effects are
evident for both. The overlap of yield or minimum energy and fracture surfaces
with exactly the same disorder configuration is shown to be a decreasing
function of the system size and to be of a rather large magnitude for all cases
studied. The typical ``overlap cluster'' length between pairs of such
interfaces converges to a constant with increasing.Comment: Accepted for publication in Phys. Rev.
Role of disorder in the size-scaling of material strength
We study the sample size dependence of the strength of disordered materials
with a flaw, by numerical simulations of lattice models for fracture. We find a
crossover between a regime controlled by the fluctuations due to disorder and
another controlled by stress-concentrations, ruled by continuum fracture
mechanics. The results are formulated in terms of a scaling law involving a
statistical fracture process zone. Its existence and scaling properties are
only revealed by sampling over many configurations of the disorder. The scaling
law is in good agreement with experimental results obtained from notched paper
samples.Comment: 4 pages 5 figure
Is demagnetization an efficient optimization method?
Demagnetization, commonly employed to study ferromagnets, has been proposed
as the basis for an optimization tool, a method to find the ground state of a
disordered system. Here we present a detailed comparison between the ground
state and the demagnetized state in the random field Ising model, combing exact
results in and numerical solutions in . We show that there are
important differences between the two states that persist in the thermodynamic
limit and thus conclude that AC demagnetization is not an efficient
optimization method.Comment: 2 pages, 1 figur
Role of the sample thickness in planar crack propagation
We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multiscaling to self-affine with exponents, in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches, which is shown to depend on the thickness and the loading mode.Peer reviewe
Fracture of three-dimensional fuse networks with quenched disorder
We study a fracture on a quasistatic time scale in a three-dimensional (3D) fuse network model with âstrongâ and âweakâ disorder. These two cases differ noticeably in the development of the fracture. For strong disorder the damage scaling is very close to volumelike [number of broken bonds NbâźL3/(lnL)0.3] unlike for weak disorder [NbâźL2.4/(lnL)0.3]. With strong disorder global load sharing is only approximately valid. The size distribution of âavalanchesâ of broken fuses in the failure follows roughly a power-law scaling. The power-law exponent Ď has a value close to 2, close to but differing from the exponent â5/2 expected of global load sharing. For weak disorder Ď is about 1.5 which means that the decay of the size distribution is much slower than expected. These exponent values that characterize the development of damage prior to catastrophic failure are comparable to experimental ones. For the final fracture surfaces we observe a roughness exponent Îśâ0.4 for weak disorder. For strong disorder, severe finite size effects are seen, but the exponent seems to converge to the same value as for weak disorder, which is close to the one for the 3D random bond Ising domain wall universality class.Peer reviewe
Quasi-static cracks and minimal energy surfaces
We compare the roughness of minimal energy(ME) surfaces and scalar
``quasi-static'' fracture surfaces(SQF). Two dimensional ME and SQF surfaces
have the same roughness scaling, w sim L^zeta (L is system size) with zeta =
2/3. The 3-d ME and SQF results at strong disorder are consistent with the
random-bond Ising exponent zeta (d >= 3) approx 0.21(5-d) (d is bulk
dimension). However 3-d SQF surfaces are rougher than ME ones due to a larger
prefactor. ME surfaces undergo a ``weakly rough'' to ``algebraically rough''
transition in 3-d, suggesting a similar behavior in fracture.Comment: 7 pages, aps.sty-latex, 7 figure
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