Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes
| dc.creator | Hassan, M. K. | |
| dc.creator | Kurths, J. | |
| dc.date | 2004-07-28 | |
| dc.date.accessioned | 2026-07-07T02:59:26Z | |
| dc.date.available | 2026-07-07T02:59:26Z | |
| dc.description | 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. | |
| dc.description | 4 pages, no figure, Submitted to publication | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0407715 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0407715 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/24508 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes | |
| dc.type | text |