On the car parking problem

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Abstract
The radial distribution functions of randomly distributed one-dimensional spheres are studied. The differences between equilibrium fluids and sequentially constructed systems are discussed in terms of the corresponding configuration spaces and numerical simulations. It is shown that for the sequentially constructed systems, which correspond to the car parking problem, a 'memory effect' occurs, such that the sequential spheres are temporally distinguishable. Exact solutions for some simple cases and numerical simulations for large systems are shown, discussed and compared with the equilibrium fluid results.

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