Exact solution of the one-dimensional ballistic aggregation

Details Exact solution of the one-dimensional ballistic aggregation Exact solution of the one-dimensional ballistic aggregation

1998-08-07

arxiv.org/abs/cond-mat/9808077v1

Physics

Condensed Matter

11 pages, 2 Postscript figures

Scientific paper

10.1103/PhysRevLett.82.1502

An exact expression for the mass distribution $\rho(M,t)$ of the ballistic
aggregation model in one dimension is derived in the long time regime. It is
shown that it obeys scaling $\rho(M,t)=t^{-4/3}F(M/t^{2/3})$ with a scaling
function $F(z)\sim z^{-1/2}$ for $z\ll 1$ and $F(z)\sim \exp(-z^3/12)$ for
$z\gg 1$. Relevance of these results to Burgers turbulence is discussed.

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