Generalized Smoluchovski equation with gelation

We have considered coagulation processes containing n-polymer interactions and studied the sole processes of n-polymer coalescence by means of a generalized Smoluchovski equation, which is solved as an initial-value problem for the product kernel: R($i_1$,$i_2$,...,$i_n$) =(${\mathrm{i}}_1$ ${\mathrm{i}}_2$...${\mathrm{i}}_{\mathit{n}}$ ${)}^{\mathrm{\omega }}$ with 0<ω<1. A variety of novel critical behaviors and new critical exponents are found which are different from those obtained from the Smoluchovski equation. Our results can be regarded as higher-order approximations to the two-polymer collision processes and thus contribute towards our understanding of general coagulation processes.