Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes

M. K. Hassan; J. Kurths

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arXiv · cond-mat/0407715

Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes

M. K. Hassan·J. Kurths

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Abstract

We propose a stochastic counterpart of the classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) model to describe the nucleation-and-growth phenomena of a stable phase (S-phase). We report that for growth velocity of S-phase $v=s(t)/t$ where $s(t)$ is the mean value of the interval size $x$ of metastable phase (M-phase) and for $v=x/τ(x)$ where $τ(x)$ is the mean nucleation time, the system exhibits a power law decay of M-phase. We also find that the resulting structure exhibits self-similarity and can be best described as a fractal. Interestingly, the fractal dimension $d_f$ helps generalising the exponent $(1+d_f)$ of the power-law decay. However, when either $v=v_0$ (constant) or $v=σ/t$ ($σ$ is a constant) the decay is exponential and it is accompanied by the violation of scaling.

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M. K. Hassan, J. Kurths. 2004-07-28. Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes. https://arxiv.org/abs/cond-mat/0407715

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