Gelation: the diagonal case revisited

We study the dynamics of a system of polymers of length j = 1, 2, 3, interacting through the reaction (j) + (j) rj/dj (2j). We give criteria on the reaction rates r(j), d(j) for gelation to occur. In the pure coagulation case (d(j) = 0) we find that gelation occurs if r(j)>= c(j)(log j)(alpha), alpha > 2 and does not occur if r(j) <= c(j) log j. The effect of the fragmentation reaction is also investigated.