Scaling theory for gelling systems: Work in progress

Gelation as it arises in the kinetic equations describing irreversible aggregation-the so-called Smoluchowski equations-is briefly reviewed. The scaling theory near the gel point, immediately before the transition, is presented. The equations presented earlier for the scaling function and the exponent τ are cast in a form more amenable to numerical study. An algorithm to solve them is described and applied to the kernels of the form K(x,y)=x^μy^ν+x^νy^μ. A theory for the behaviour immediately after the gel transition is also presented and is found to be verified in one special exactly solved case (product kernel with power-law initial conditions).