Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-11-19
Phys.Rev. E72 (2005) 031103
Physics
Condensed Matter
Statistical Mechanics
(28 pages, 6 figures, v2+v3 minor corrections)
Scientific paper
10.1103/PhysRevE.72.031103
We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as $\exp(-x^{3/2})$ for large $x$-values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full non-linear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay, $\exp(-x)$, for large $x$, and observe a crossover from the Bessel function for intermediate values of $x$. These findings are checked by numerical simulations and we find perfect agreement between the theoretical predictions and numerical results.
Ferkinghoff-Borg Jesper
Jensen Mogens H.
Mathiesen Joachim
Olesen Poul
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