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In this paper we present an efficient numerical approach based on the Renor-malization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlin-ear parabolic partial differential equations. We illustrate the approach with the verification of a conjecture about the… (More)

- G. A. Braga, A. Procacci, R. Sanchis
- 2002

We derive an Ornstein-Zernike asymptotic formula for the decay of the two point finite connectivity function τ f x,y (p) of the Bernoulli bond percolation process on Z d , along the principal directions, for d ≥ 3, and for supercritical values of p sufficiently near to p = 1. y| = 1} (nearest neighbors) where Z is the set of all integers and |x − y| is the… (More)

- Gastão A. Braga, Leandro M. Ciolleti, Rémy Sanchis
- 2008

In this short note we consider mixed short-long range independent bond per-colation models on Z k+d. Let p uv be the probability that the edge (u, v) will be open. Allowing a x, y-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connec-tivity τ xy is governed by the… (More)

We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal is to understand the interplay between anomalous diffusion and nonlinearity in determining the long-time behavior of… (More)

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