1999/12/23 by Massimo Conti, M. Conti, Baruch Meerson +5
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Pattern Formation and Solitons (nlin.PS) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #nlin.PS
paper · pdf · doi:10.48550/arxiv.cond-mat/9912426
11 pages, 10 figures
openalex publication_date 1999/12/23 · arxiv created 2000/05/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.