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Abstract: The growth of ballistic aggregates on deterministic fractal substrates isstudied by means of numerical simulations. First, we attempt the description ofthe evolving interface of the aggregates by applying the well-establishedFamily-Vicsek dynamic scaling approach. Systematic deviations from thatstandard scaling law are observed, suggesting that significant scalingcorrections have to be introduced in order to achieve a more accurateunderstanding of the behavior of the interface. Subsequently, we study theinternal structure of the growing aggregates that can be rationalized in termsof the scaling behavior of frozen trees, i.e., structures inhibited for furthergrowth, lying below the growing interface. It is shown that the rms height$h {s}$ and width $w {s}$ of the trees of size $s$ obey power laws of theform $h {s} \propto s^{ u {\parallel}}$ and $w {s} \propto s^{ u {\perp}}$,respectively. Also, the tree-size distribution $n {s}$ behaves according to$n {s}\sim s^{-\tau}$. Here, $ u {\parallel}$ and $ u {\perp}$ are thecorrelation length exponents in the directions parallel and perpendicular tothe interface, respectively. Also, $\tau$ is a critical exponent. However, dueto the interplay between the discrete scale invariance of the underlyingfractal substrates and the dynamics of the growing process, all these powerlaws are modulated by logarithmic periodic oscillations. The fundamentalscaling ratios, characteristic of these oscillations, can be linked to thespatial fundamental scaling ratio of the underlying fractal by means ofrelationships involving critical exponents.



Autor: Claudio M. Horowitz, Federico Roma, Ezequiel V. Albano

Fuente: https://arxiv.org/



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