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Article Dans Une Revue Journal de Physique I Année : 1996

Sintering of Mass Fractals by Surface Diffusion or by Viscous Flow: Numerical and Scaling Approaches in d = 2

Nathalie Olivi-Tran
Romain Thouy
Rémi Jullien
  • Fonction : Auteur

Résumé

Numerical methods are used to model two kinds of sintering processes, by Surface Diffusion (SD) or by Viscous Flow (VF), and are applied to deterministic and random two-dimensional “mass fractals” with various fractal dimensions. In the SD case the relevant partial differential equation is discretized and the evolution of the contour is numerically studied. In the case of viscous flow, a recently introduced approximate “dressing” method is used. In both cases it is shown that the geometrical characteristics which are the perimeter length L, the size ξ and the lower cut-off a, vary as some powers of time t(L∼t-α,ξ∼t-β,a∼tγ). The exponents α, β, γ, and their dependence on the fractal dimension D, are estimated from scaling arguments and are found to be different in the SD and VF cases. The SD case is particular in the sense that β≃0 (no shrinkage) and that, if the initial fractal is too large, it breaks into separate pieces.

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jpa-00247202 , version 1 (04-02-2008)

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Nathalie Olivi-Tran, Romain Thouy, Rémi Jullien. Sintering of Mass Fractals by Surface Diffusion or by Viscous Flow: Numerical and Scaling Approaches in d = 2. Journal de Physique I, 1996, 6 (4), pp.557-574. ⟨10.1051/jp1:1996229⟩. ⟨jpa-00247202⟩

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