Jammed state characterization of the random sequential adsorption of segments of two lengths on a line
arXiv:1002.0166 · doi:10.1088/1742-5468/2010/02/P02019
Abstract
We characterize the jammed state structure of the random sequential adsorption of segments of two different sizes on a line. To this end, we define the size ratio as a dimensionless quantity measuring the length of the large segments in terms of the smaller ones. We introduce a truncated exponential as an {\it ansatz} for the probability distribution function of the interparticle distance at the jammed state and use it to reckon the first four cumulants of the probability distribution function. The sole free parameter present in the various analytical expressions is tied to the mean interparticle distance from Monte Carlo simulations, while the remaining three cumulants are computed without any free parameter and compared to Monte Carlo results. We find that the proposed {\it ansatz} provides results in good qualitative agreement with Monte Carlo ones.
9 pages, 3 figures, accepted for publication in JSTAT
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