Continuous onehyphen;dimensional average unsaturated coverage as the limit of a lattice model

摘要

When particles occupying more than one compartment (bgr;) are randomly placed on a onehyphen;dimensional array ofNcompartments we are simultaneously creating sequences of vacant compartments. Clearly, after a long period of time, a saturation situation arises in which the probability of placing an additional particle on such an array becomes zero even though the coverage has not attained the value of one. In the continuous version, particles of unit length are placed in a random manner on an interval of total lengthx. It is shown that with the interval lengthxappropriately defined (x=N/bgr;), the average unsaturated coverage of the lattice model tends to that of the continuous one when the mesh of the lattice becomes infinitely fine (Nthinsp;rarr;thinsp;infin;), keeping the ratioN/bgr; constant.