Random close pack crystal lattices have maximum densities equal to this upper limit. Random close packing does not have a precise geometric definition. It is defined statistically, and results are empirical. A container is randomly filled with objects, and then the container is shaken or tapped until the objects do not compact any further, at this point the packing state is RCP. The definition of packing fraction can be given as: "the volume taken by number of particles in a given space of volume". In other words, packing fraction defines the packing density. It has been shown that the filling fraction increases with
Packing in a hypergraph a distinct real "birthtime" formula_16. The edges are taken one by one in the order of their birthtimes. The edge formula_17 is accepted and included in formula_1 if it does not overlap any previously accepted edges. Obviously, the subset formula_1 is a packing and it can be shown that its size is formula_20 almost surely. To show that, let stop the process of adding new edges at time formula_21. For an arbitrary formula_22, pick formula_23 such that for any formula_24-good hypergraph formula_25 where formula_26 denotes the probability of vertex formula_27 survival (a vertex survives if it is not in any