| Abstract: | By means of Monte Carlo simulations we study the irreversible, random, sequential filling of small clusters (e.g., pairs, triples,...) on linear, square, and cubic lattices. In particular, we are interested in the fraction of sites filled at saturation (the point at which further filling is not possible without rearrangement of the filled and empty sites). The results obtained show good agreement with those of previously developed analytic techniques. We present the first extensive results for filling linear strings of lattice sites by use of the end-on mechanism (where the ends of the string are chosen sequentially rather than simultaneously as in conventional filling). For end-on filling we find that the saturation coverage increases, relative to conventional filling, for short strings, but decreases as we go to the limit of infinitely long strings (the car-parking problem). An examination of the Palasti conjecture (and its extension to discrete lattices) is also made. |
