2 research outputs found
Statistics of Largest Loops in a Random Walk
We report further findings on the size distribution of the largest neutral
segments in a sequence of N randomly charged monomers [D. Ertas and Y. Kantor,
Phys. Rev. E53, 846 (1996); cond-mat/9507005]. Upon mapping to one--dimensional
random walks (RWs), this corresponds to finding the probability distribution
for the size L of the largest segment that returns to its starting position in
an N--step RW. We primarily focus on the large N, \ell = L/N << 1 limit, which
exhibits an essential singularity. We establish analytical upper and lower
bounds on the probability distribution, and numerically probe the distribution
down to \ell \approx 0.04 (corresponding to probabilities as low as 10^{-15})
using a recursive Monte Carlo algorithm. We also investigate the possibility of
singularities at \ell=1/k for integer k.Comment: 5 pages and 4 eps figures, requires RevTeX, epsf and multicol.
Postscript file also available at
http://cmtw.harvard.edu/~deniz/publications.htm
Pinning/depinning of crack fronts in heterogeneous materials
The fatigue fracture surfaces of a metallic alloy, and the stress corrosion
fracture surfaces of glass are investigated as a function of crack velocity. It
is shown that in both cases, there are two fracture regimes, which have a well
defined self-affine signature. At high enough length scales, the universal
roughness index 0.78 is recovered. At smaller length scales, the roughness
exponent is close to 0.50. The crossover length separating these two
regimes strongly depends on the material, and exhibits a power-law decrease
with the measured crack velocity , with . The exponents and characterising the dependence of
and upon the pulling force are shown to be close to and
.Comment: 4 pages, latex, and 4 encapsulated postscript figure