144 research outputs found
Reply to the comment by Jacobs and Thorpe
Reply to a comment on "Infinite-Cluster geometry in central-force networks",
PRL 78 (1997), 1480. A discussion about the order of the rigidity percolation
transition.Comment: 1 page revTe
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
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.
Infinite-cluster geometry in central-force networks
We show that the infinite percolating cluster (with density P_inf) of
central-force networks is composed of: a fractal stress-bearing backbone (Pb)
and; rigid but unstressed ``dangling ends'' which occupy a finite
volume-fraction of the lattice (Pd). Near the rigidity threshold pc, there is
then a first-order transition in P_inf = Pd + Pb, while Pb is second-order with
exponent Beta'. A new mean field theory shows Beta'(mf)=1/2, while simulations
of triangular lattices give Beta'_tr = 0.255 +/- 0.03.Comment: 6 pages, 4 figures, uses epsfig. Accepted for publication in Physical
Review Letter
Probability Distribution of the Shortest Path on the Percolation Cluster, its Backbone and Skeleton
We consider the mean distribution functions Phi(r|l), Phi(B)(r|l), and
Phi(S)(r|l), giving the probability that two sites on the incipient percolation
cluster, on its backbone and on its skeleton, respectively, connected by a
shortest path of length l are separated by an Euclidean distance r. Following a
scaling argument due to de Gennes for self-avoiding walks, we derive analytical
expressions for the exponents g1=df+dmin-d and g1B=g1S-3dmin-d, which determine
the scaling behavior of the distribution functions in the limit x=r/l^(nu) much
less than 1, i.e., Phi(r|l) proportional to l^(-(nu)d)x^(g1), Phi(B)(r|l)
proportional to l^(-(nu)d)x^(g1B), and Phi(S)(r|l) proportional to
l^(-(nu)d)x^(g1S), with nu=1/dmin, where df and dmin are the fractal dimensions
of the percolation cluster and the shortest path, respectively. The theoretical
predictions for g1, g1B, and g1S are in very good agreement with our numerical
results.Comment: 10 pages, 3 figure
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]
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.
Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices
Extensive Monte-Carlo simulations were performed to study bond percolation on
the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic
(b.c.c.) lattices, using an epidemic kind of approach. These simulations
provide very precise values of the critical thresholds for each of the
lattices: pc(s.c.) = 0.248 812 6(5), pc(f.c.c.) = 0.120 163 5(10), and
pc(b.c.c.) = 0.180 287 5(10). For p close to pc, the results follow the
expected finite-size and scaling behavior, with values for the Fisher exponent
(2.189(2)), the finite-size correction exponent (0.64(2)), and
the scaling function exponent (0.445(1)) confirmed to be universal.Comment: 16 pgs, 7 figures, LaTeX, to be published 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
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
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