We investigate topologically biased failure in scale-free networks with degree distribution P(k) ∝ k^−γ . The probability p that an edge remains intact is assumed to depend on the degree k of adjacent nodes i and j through p_ij ∝ (k_i k_j)^−α . By varying the exponent α, we interpolate...

We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals 1/λn in generation n, in terms of a rescaling factor λ. Without interactions between the blocks, this model is described by a logarithmic fractal, studied...

Sequential wetting, i.e., a sequence of two wetting transitions, in which the first one consists of a discontinuous jump from a microscopically thin to a mesoscopically thick film, followed by a divergence of the thickness of this film as the second, critical transition temperature is...

We study geometrical objects on the borderline between standard Euclidean forms and fractals. The length (or area) increases with an additive rather than multiplicative constant, upon reducing the ruler length by a fixed rescaling factor. This leads to a logarithmic law instead of the usual...

We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-\gamma}$ . The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$ through $p_{ij} \propto (k_i k_j)^{-\alpha}$ . By varying...