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Breakdown of Dynamical Scale Invariance in the Coarsening of Fractal Clusters

Massimo Conti·Baruch Meerson·Pavel V. Sasorov
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Abstract

We extend a previous analysis [PRL {\bf 80}, 4693 (1998)] of breakdown of dynamical scale invariance in the coarsening of two-dimensional DLAs (diffusion-limited aggregates) as described by the Cahn-Hilliard equation. Existence of a second dynamical length scale, predicted earlier, is established. Having measured the "solute mass" outside the cluster versus time, we obtain a third dynamical exponent. An auxiliary problem of the dynamics of a slender bar (that acquires a dumbbell shape) is considered. A simple scenario of coarsening of fractal clusters with branching structure is suggested that employs the dumbbell dynamics results. This scenario involves two dynamical length scales: the characteristic width and length of the cluster branches. The predicted dynamical exponents depend on the (presumably invariant) fractal dimension of the cluster skeleton. In addition, a robust theoretical estimate for the third dynamical exponent is obtained. Exponents found numerically are in reasonable agreement with these predictions.

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Massimo Conti, Baruch Meerson, Pavel V. Sasorov. 2000-05-19. Breakdown of Dynamical Scale Invariance in the Coarsening of Fractal Clusters. https://arxiv.org/abs/cond-mat/9912426

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