Scaling Theory for Migration-Driven Aggregate Growth

Details Scaling Theory for Migration-Driven Aggregate Growth Scaling Theory for Migration-Driven Aggregate Growth

2001-08-18

arxiv.org/abs/cond-mat/0108289v2

Phys. Rev. Lett. 88 068301 (2002).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2-column revtex format. Revision to appear in PRL. Various changes in response to referee comments. Figure from versi

Scientific paper

10.1103/PhysRevLett.88.068301

We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j, that is, K(ai;aj) ~ a^{lambda} K(i,j), the mean aggregate size grows with time as t^{1/(2-lambda)} for lambda<2. The aggregate size distribution exhibits distinct regimes of behavior which are controlled by the scaling properties of the migration rate from the smallest to the largest aggregates. Our theory applies to diverse phenomena, such as the distribution of city populations, late stage coarsening of non-symmetric binary systems, and models for wealth exchange.

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