847 research outputs found
A periodic elastic medium in which periodicity is relevant
We analyze, in both (1+1)- and (2+1)- dimensions, a periodic elastic medium
in which the periodicity is such that at long distances the behavior is always
in the random-substrate universality class. This contrasts with the models with
an additive periodic potential in which, according to the field theoretic
analysis of Bouchaud and Georges and more recently of Emig and Nattermann, the
random manifold class dominates at long distances in (1+1)- and
(2+1)-dimensions. The models we use are random-bond Ising interfaces in
hypercubic lattices. The exchange constants are random in a slab of size
and these coupling constants are periodically repeated
along either {10} or {11} (in (1+1)-dimensions) and {100} or {111} (in
(2+1)-dimensions). Exact ground-state calculations confirm scaling arguments
which predict that the surface roughness behaves as: and , with in
-dimensions and; and , with in -dimensions.Comment: Submitted to Phys. Rev.
Intermittence and roughening of periodic elastic media
We analyze intermittence and roughening of an elastic interface or domain
wall pinned in a periodic potential, in the presence of random-bond disorder in
(1+1) and (2+1) dimensions. Though the ensemble average behavior is smooth, the
typical behavior of a large sample is intermittent, and does not self-average
to a smooth behavior. Instead, large fluctuations occur in the mean location of
the interface and the onset of interface roughening is via an extensive
fluctuation which leads to a jump in the roughness of order , the
period of the potential. Analytical arguments based on extreme statistics are
given for the number of the minima of the periodicity visited by the interface
and for the roughening cross-over, which is confirmed by extensive exact ground
state calculations.Comment: Accepted for publication in Phys. Rev.
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
Disorder-induced roughening in the three-dimensional Ising model
Using an exact method, we numerically study the zero-temperature roughness of interfaces in the random bond, cubic lattice, Ising model (of size L3, with L<~80). Interfaces oriented along the {100} direction undergo a roughening transition from a weak disorder phase, which is almost flat, to a strong disorder phase with interface width w∼cL0.42 (c is a function of the disorder). For random dilution we find the roughening threshold p∗=0.89±0.01 and c∼p∗−p for p<~p∗ (p is the volume fraction of present bonds). In contrast {111} interfaces are algebraically rough for all disorder.Peer reviewe
Structural compliance, misfit strain and stripe nanostructures in cuprate superconductors
Structural compliance is the ability of a crystal structure to accommodate
variations in local atomic bond-lengths without incurring large strain
energies. We show that the structural compliance of cuprates is relatively
small, so that short, highly doped, Cu-O-Cu bonds in stripes are subject to a
tensile misfit strain. We develop a model to describe the effect of misfit
strain on charge ordering in the copper oxygen planes of oxide materials and
illustrate some of the low energy stripe nanostructures that can result.Comment: 4 pages 5 figure
Self-Attracting Walk on Lattices
We have studied a model of self-attracting walk proposed by Sapozhnikov using
Monte Carlo method. The mean square displacement
and the mean number of visited sites are calculated for
one-, two- and three-dimensional lattice. In one dimension, the walk shows
diffusive behaviour with . However, in two and three dimension, we
observed a non-universal behaviour, i.e., the exponent varies
continuously with the strength of the attracting interaction.Comment: 6 pages, latex, 6 postscript figures, Submitted J.Phys.
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
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