Let n random intervals I 1 ; : : : ; I n be chosen by selecting end-points independently from the uniform distribution on 0; 1]. A packing is a pairwise disjoint subset of the intervals; its wasted space is the Lebesgue measure of the points of 0; 1] not covered by the packing. In any set of intervals the packing with least wasted space is computa-tionally easy to nd; but its expected wasted sp...

The random sequential adsorption of various particle shapes is studied in order to determine the influence of particle anisotropy on the saturated random packing. For all tested particles there is an optimal level of anisotropy which maximizes the saturated packing fraction. It is found that a concave shape derived from a dimer of disks gives a packing fraction of 0.5833, which is comparable to...

We conduct numerical simulations of random packings of frictionless particles at T = 0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows, and its peak approaches random close packing as the system size increases. For packing fractions within the pe...

The behaviour of the random greedy algorithm for constructing a maximal packing of edgedisjoint triangles on n points (a maximal partial triple system) is analysed with particular emphasis on the final number of unused edges. It is shown that this number is at most n, “halfway” from the previous best-known upper bound o(n) to the conjectured value n. The more general problem of random greedy pa...

The dense packing of hard objects is a recurrent paradigm in physics, for example in early models of crystallinity, and also in theories of granular materials which are under active debate today [1, 2]. Generally speaking the objects are taken to be spheres, leading to the formulation of the Kepler Problem (what is their closest packing?) and the investigations begun by Bernal on disordered pac...