Non-Universal Decay Kinetics in Ballistic Annihilation,
E. Ben-Naim and S. Redner F. Leyvraz
We study the kinetics of ballistic annihilation, A+A--> 0, with
continuous initial particle velocity distributions. The concentration
and the rms velocity are found to decay as $c\sim t^{-\alpha}$ and
$v\sim t^{-\beta}$ respectively, with the relation $\alpha+\beta=1$
holding in any spatial dimension. A ``mean-field'' Boltzmann equation
for the evolution of the velocity distribution predicts that $\alpha$
and $\beta$ depend strongly on the initial condition. This
non-universal behavior is confirmed numerically in one and two
dimensions.
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