Asymptotic results for the random sequential addition of unoriented objects

Abstract

Asymptotic kinetics for random sequential addition of unoriented nonspherical objects is characterized by an algebraic time dependence. By studying 1D systems, we show that the exponents describing the random sequential addition of objects with and without proper area are not simply related: Whereas the asymptotic behavior for rectangles follows the expected ${\mathit{t}}^{\mathrm{-}1/2}$ law, the long-time kinetics for infinitely thin line segments is governed by a nontrivial, irrational, exponent (${\mathit{t}}^{\mathrm{\surd }2\mathrm{-}1}$) which results from a competition between creation and destruction of targets in the asymptotic regime.