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Anti-red bonds distribution law in 3D percolation

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  • Gouyet, J.-F.

Abstract

Combining two independent approaches the power law structure of the anti-red bonds distribution in d=3 percolation can be derived. This result is important to understand the dynamical behaviour of fluctuating fronts during diffusion and invasion processes, but also in problems of fragmentation-aggregation of percolation clusters. In d=2, it allows to calculate the fractal dimension of the hull, Dh=1+1ʋ, a known result not easy to prove. In d>2 dimensions, it gives an anti-red bonds equal to Danti-red=2D−1ʋ−d.

Suggested Citation

  • Gouyet, J.-F., 1992. "Anti-red bonds distribution law in 3D percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 301-308.
    • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:301-308
    DOI: 10.1016/0378-4371(92)90542-X
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    References listed on IDEAS

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    1. Marina Colonna, 1986. "Book Reviews," Contributions to Political Economy, Oxford University Press, vol. 5(1), pages 127-129.
    2. Bunde, Armin & Gouyet, Jean-François, 1985. "Brownian motion in the bistable potential at intermediate and high friction: Relaxation from the instability point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 357-374.
    3. Gouyet, J.F. & Sapoval, B. & Boughaleb, Y. & Rosso, M., 1989. "Structure of noise generated on diffusion fronts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 620-624.
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