231 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
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
Incidence of Bipolaris and Exserohilum Species in Corn Leaves in North Carolina
Samples of 42–60 corn leaves were collected without regard to disease symptoms at 2-m intervals in each of eight cornfields in western and two in eastern North Carolina in 1985. Sampling dates for the 10 fields ranged from 16 July to 8 August. The leaves were surface-sterilized and incubated in moist chambers for isolation of large-spored species of Bipolaris and Exserohilum. Incidence of B. zeicola infection was high (41–81%) in leaves from nine of the 10 fields. B. maydis and E. turcicum, which are more aggressive pathogens of hybrid corn than B. zeicola, occurred at lower incidences of 0–48% and 0–50%, respectively, in leaves from these fields at the time of sampling. This indicated that initial population densities of these aggressive pathogens were much lower than that of B. zeicola. Forty-five isolates of E. turcicum collected before 28 August were all race 1. Three isolates of race 2 were obtained later from fields of hybrids with the Ht 1 gene for resistance to race 1. All 75 isolates of B. maydis obtained from the 10 extensively sampled fields were race O; they were equally virulent on inbred line B73 with normal cytoplasm or B73 with C, S, or T male sterile cytoplasm. Frequencies of mating types of B. maydis and B. zeicola varied from field to field, with no correlation between the frequencies in the two species. Races 2 and 3 of B. zeicola, however, had similar mating type frequencies in these fields. B. sorokiniana was isolated from leaves from six of the 10 fields; the greatest incidence was 37%. E. rostratum was found in leaves from five fields at incidences up to 18%, and E. holmii occurred in leaves in one field at 11% incidence. These data indicate that a variety of species of Bipolaris and Exserohilum are able to infect green leaves of mature corn plants in the field. Thus, corn may contribute to the survival of species that are primarily pathogenic on other gramineous hosts
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.
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.
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
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.
Strength Reduction in Electrical and Elastic Networks
Particular aspects of problems ranging from dielectric breakdown to metal
insu- lator transition can be studied using electrical o elastic networks. We
present an expression for the mean breakdown strength of such networks.First,
we intro- duce a method to evaluate the redistribution of current due to the
removal of a finite number of elements from a hyper-cubic network of
conducatances.It is used to determine the reduction of breakdown strength due
to a fracture of size .Numerical analysis is used to show that the
analogous reduction due to random removal of elements from electrical and
elastic networks follow a similar form.One possible application, namely the use
of bone density as a diagnostic tools for osteorosporosis,is discussed.Comment: one compressed file includes: 9 PostScrpt figures and a text fil
Using Nonlinear Response to Estimate the Strength of an Elastic Network
Disordered networks of fragile elastic elements have been proposed as a model
of inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221,
http://xyz.lanl.gov]. It is shown that the ratio of responses of such
a network to static and periodic strain can be used to estimate its ultimate
(or breaking) stress. Since bone fracture in older adults results from the
weakening of porous bone, we discuss the possibility of using as a
non-invasive diagnostic of osteoporotic bone.Comment: 4 pages, 4 figure
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