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The evolution and spatial structure of displacement fronts in fractures with self-affine rough walls are studied by numerical simulations. The fractures are open and the two faces are identical but shifted along their mean plane, either parallel or perpendicular to the flow. An initially flat front advected by the flow is progressively distorted into a self-affine front with Hurst exponent equal to that of the fracture walls. The lower cutoff of the self-affine regime depends on the aperture and lateral shift, while the upper cutoff grows linearly with the width of the front.
We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar and some
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analy
We consider the binary fragmentation problem in which, at any breakup event, one of the daughter segments either survives with probability $p$ or disappears with probability $1!-!p$. It describes a stochastic dyadic Cantor set that evolves in time, a
We introduce fractal liquids by generalizing classical liquids of integer dimensions $d = 1, 2, 3$ to a fractal dimension $d_f$. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-i
It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in non-fractal netwo