 Jamming in random sequential adsorption

Jamming in random sequential adsorption occurs when previously accepted objects leave no permitted position for another object. The placement rule is irreversible: an object that would overlap an accepted object is rejected, and accepted objects are not rearranged. A jammed configuration need not have the greatest possible covered fraction.

For a one-dimensional example in which touching endpoints is allowed but overlapping interiors are forbidden, place unit intervals $[0.5,1.5]$ and $[1.6,2.6]$ inside $[0,3]$. The uncovered gaps have lengths $0.5$, $0.1$ and $0.4$. No gap can contain another unit interval, so the configuration is jammed even though only $2/3$ of the containing interval is covered. Three unit intervals could cover it completely under a different placement history. This is the geometric obstruction modeled by irreversible parking in random sequential adsorption; the final coverage depends on the proposal rule and object geometry, rather than on a universal packing fraction.