124 research outputs found
Failure Probabilities and Tough-Brittle Crossover of Heterogeneous Materials with Continuous Disorder
The failure probabilities or the strength distributions of heterogeneous 1D
systems with continuous local strength distribution and local load sharing have
been studied using a simple, exact, recursive method. The fracture behavior
depends on the local bond-strength distribution, the system size, and the
applied stress, and crossovers occur as system size or stress changes. In the
brittle region, systems with continuous disorders have a failure probability of
the modified-Gumbel form, similar to that for systems with percolation
disorder. The modified-Gumbel form is of special significance in weak-stress
situations. This new recursive method has also been generalized to calculate
exactly the failure probabilities under various boundary conditions, thereby
illustrating the important effect of surfaces in the fracture process.Comment: 9 pages, revtex, 7 figure
Bounds for the time to failure of hierarchical systems of fracture
For years limited Monte Carlo simulations have led to the suspicion that the
time to failure of hierarchically organized load-transfer models of fracture is
non-zero for sets of infinite size. This fact could have a profound
significance in engineering practice and also in geophysics. Here, we develop
an exact algebraic iterative method to compute the successive time intervals
for individual breaking in systems of height in terms of the information
calculated in the previous height . As a byproduct of this method,
rigorous lower and higher bounds for the time to failure of very large systems
are easily obtained. The asymptotic behavior of the resulting lower bound leads
to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199
Current-voltage characteristics of diluted Josephson-junction arrays: scaling behavior at current and percolation threshold
Dynamical simulations and scaling arguments are used to study the
current-voltage (IV) characteristics of a two-dimensional model of resistively
shunted Josephson-junction arrays in presence of percolative disorder, at zero
external field. Two different limits of the Josephson-coupling concentration
are considered, where is the percolation threshold. For
and zero temperature, the IV curves show power-law behavior above a disorder
dependent critical current. The power-law behavior and critical exponents are
consistent with a simple scaling analysis. At and finite temperature ,
the results show the scaling behavior of a T=0 superconducting transition. The
resistance is linear but vanishes for decreasing with an apparent
exponential behavior. Crossover to non-linearity appears at currents
proportional to , with a thermal-correlation length exponent
consistent with the corresponding value for the diluted XY model at
.Comment: Revtex, 9 postscript pages, to appear in Phys. Rev.
Towards a first principles description of phonons in NiPt disordered alloys: the role of relaxation
Using a combination of density-functional perturbation theory and the
itinerant coherent potential approximation, we study the effects of atomic
relaxation on the inelastic incoherent neutron scattering cross sections of
disordered NiPt alloys. We build on previous work, where
empirical force constants were adjusted {\it ad hoc} to agree with experiment.
After first relaxing all structural parameters within the local-density
approximation for ordered NiPt compounds, density-functional perturbation
theory is then used to compute phonon spectra, densities of states, and the
force constants. The resulting nearest-neighbor force constants are first
compared to those of other ordered structures of different stoichiometry, and
then used to generate the inelastic scattering cross sections within the
itinerant coherent potential approximation. We find that structural relaxation
substantially affects the computed force constants and resulting inelastic
cross sections, and that the effect is much more pronounced in random alloys
than in ordered alloys.Comment: 8 pages, 3 eps figures, uses revtex
Scaling in the time-dependent failure of a fiber bundle with local load sharing
We study the scaling behaviors of a time-dependent fiber-bundle model with
local load sharing. Upon approaching the complete failure of the bundle, the
breaking rate of fibers diverges according to ,
where is the lifetime of the bundle, and is a quite
universal scaling exponent. The average lifetime of the bundle scales
with the system size as , where depends on the
distribution of individual fiber as well as the breakdown rule.Comment: 5 pages, 4 eps figures; to appear in Phys. Rev.
Thermodynamics of Mesoscopic Vortex Systems in 1+1 Dimensions
The thermodynamics of a disordered planar vortex array is studied numerically
using a new polynomial algorithm which circumvents slow glassy dynamics. Close
to the glass transition, the anomalous vortex displacement is found to agree
well with the prediction of the renormalization-group theory. Interesting
behaviors such as the universal statistics of magnetic susceptibility
variations are observed in both the dense and dilute regimes of this mesoscopic
vortex system.Comment: 4 pages, REVTEX, 6 figures included. Comments and suggestions can be
sent to [email protected]
Phonons in random alloys: the itinerant coherent-potential approximation
We present the itinerant coherent-potential approximation(ICPA), an analytic,
translationally invariant and tractable form of augmented-space-based,
multiple-scattering theory in a single-site approximation for harmonic phonons
in realistic random binary alloys with mass and force-constant disorder.
We provide expressions for quantities needed for comparison with experimental
structure factors such as partial and average spectral functions and derive the
sum rules associated with them. Numerical results are presented for Ni_{55}
Pd_{45} and Ni_{50} Pt_{50} alloys which serve as test cases, the former for
weak force-constant disorder and the latter for strong. We present results on
dispersion curves and disorder-induced widths. Direct comparisons with the
single-site coherent potential approximation(CPA) and experiment are made which
provide insight into the physics of force-constant changes in random alloys.
The CPA accounts well for the weak force-constant disorder case but fails for
strong force-constant disorder where the ICPA succeeds.Comment: 19 pages, 12 eps figures, uses RevTex
Absence of Two-Dimensional Bragg Glasses
The stability to dislocations of the elastic phase, or ``Bragg glass'', of a
randomly pinned elastic medium in two dimensions is studied using the
minimum-cost-flow algorithm for a disordered fully-packed loop model. The
elastic phase is found to be unstable to dislocations due to the quenched
disorder. The energetics of dislocations are discussed within the framework of
renormalization group predictions as well as in terms of a domain wall picture.Comment: 5 pages, REVTEX, 3 figures included. Further information can be
obtained from [email protected]
Bursts in a fiber bundle model with continuous damage
We study the constitutive behaviour, the damage process, and the properties
of bursts in the continuous damage fiber bundle model introduced recently.
Depending on its two parameters, the model provides various types of
constitutive behaviours including also macroscopic plasticity. Analytic results
are obtained to characterize the damage process along the plastic plateau under
strain controlled loading, furthermore, for stress controlled experiments we
develop a simulation technique and explore numerically the distribution of
bursts of fiber breaks assuming infinite range of interaction. Simulations
revealed that under certain conditions power law distribution of bursts arises
with an exponent significantly different from the mean field exponent 5/2. A
phase diagram of the model characterizing the possible burst distributions is
constructed.Comment: 9 pages, 11 figures, APS style, submitted for publicatio
Gradient Clogging in Depth Filtration
We investigate clogging in depth filtration, in which a dirty fluid is
``cleaned'' by the trapping of dirt particles within the pore space during flow
through a porous medium. This leads to a gradient percolation process which
exhibits a power law distribution for the density of trapped particles at
downstream distance x from the input. To achieve a non-pathological clogging
(percolation) threshold, the system length L should scale no faster than a
power of ln w, where w is the width. Non-trivial behavior for the permeability
arises only in this extreme anisotropic geometry.Comment: 4 pages, 3 figures, RevTe
- …