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 $L^{d-1} \times \lambda$ 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 $w$ behaves as: $w \sim L^{2/3}, L \ll L_c$ and $w \sim L^{1/2}, L \gg L_c$, with $L_c \sim \lambda^{3/2}$ in $(1+1)$-dimensions and; $w \sim L^{0.42}, L \ll L_c$ and $w \sim \ln(L), L \gg L_c$, with $L_c \sim \lambda^{2.38}$ in $(2+1)$-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 $\lambda$, 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

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