We study the asymptotic coverage of a lattice to which particles are randomly and irreversibly attached, under the constraint of nearest neighbor exclusion. After reviewing the case of a one-dimensional lattice, we extend the treatment first to a triangular ladder and then to a square ladder. The former maps onto a previously solved one-dimensional case, the latter does not. We also determine the time-dependent coverage of the square ladder. Implications as to the process on a full 2-dimensional square lattice are discussed.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics