Random sequential packing in square cellular structures

The problem of random sequential packing has been studied in statistical physics, chemical physics and biophysics. The problem has been treated mainly in the continuum or lattice space, while little attention has been paid to the packing problem in a cellular structure. As a first step to random filling in cellular structures, here the author treats the problem in the square cellular structure, where squares with integer length a are inserted at random without any overlap into the cells of a square divided into square unit cells. In such packing problem, two methods A and B, which are not distinguished in the continuum space, are applied to filling squares. In A any contact among the packed squares is permitted, and forbidden in B. The author calculates the packing fractions of A and B against a by computer simulation, and clearly shows that the packing fraction of A is much larger than that of B when a is small. As a becomes large, the two packing fractions approach that of the continuum space, respectively, from the upper and lower side.