The acoustic emission of fracture precursors is measured in heterogeneous materials. The statistical behaviour of these precursors is studied as a function of the load features and the geometry. We find that the time interval δt between events (precursors) and events energies ε are power law distributed and that the exponents of these power laws depend on the load history and on the material. I...

2014 Two-dimensional Ising-like cellular automata are simulated in zero field for 24 x 24 to 1600 x 1600 systems. We find that the mass fractal dimensionality at the onset of "chaos" (instability of "damage spreading") is 1.9, and dt = 1.3 for the time. These values are indistinguishable from those recently reported for the Kauffman cellular automata and close to those observed for percolation....

has no solution if Ω ⊂ R , N ≥ 3, is bounded and starshaped with respect to some point, and 2∗ = 2N/(N − 2). In (P0) the nonlinear term is a power of u with the critical exponent (N + 2)/(N − 2). This terminology comes from the fact that the continuous Sobolev imbeddings H 0 (Ω) ⊂ L(Ω), for p ≤ 2∗ and Ω bounded, are also compact except when p = 2∗. This loss of compactness reflects in that the ...

We compute the critical behaviour of three-dimensional scalar theories using a new exact non-perturbative evolution equation. Our values for the critical exponents agree well with previous precision estimates.

The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension x̃. We consider the case when the boundary is a random fractal, specifically a self-avoiding walk or the frontier of a Brownian walk, in two dimensions, and show that the boundary scaling behaviour of the...

We formulate the Wolff algorithm as a site-bond percolation problem, apply it to the ferromagnetic and antiferromagnetic planar triangular spin models, and study the percolation critical behavior using Anite-size scaling. In the former case the Wold' algorithm is successful as an accelerating algorithm, whereas in the latter case it is not. We found the percolation temperatures and the cluster ...

We analyze a controversial question about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both analytical and numerical studies performed so far support an extended Harris criterion (A. Weinrib, B. I. Halperin, Phys. Rev. B 27 (1983) 413) and bring about the new universality class, the numerical values of the critical exponents found so f...

We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the state-of-the-art exponents for directed percolation, dynamical percolation, and other universality classes. This collection of results should help to elucidate ...