Scaling theory for gelling systems: work in progress
It is known that systems evolving through a process of irreversible aggregation and obeying the so-called Smoluchowski equation may exhibit the phenomenon of gelation. This means that a finite amount of mass can be swallowed by ``giant'' clusters. This paper points out some accident in which gelation theory has incurred and how a fresh restart proposed by the same author [Scaling theory and exactly solved models in the kinetics of irreversible aggregation, Phys. Rep. 383, 95 (2003); Rigorous results in the scaling theory of irreversible aggregation kinetics, J. Non-linear Math. Phys. 12 (Suppl. 1) 449--465 (2005); \url{arXiv:math-ph/0602007}] can lead, case by case, to the correct results. The basic tool is to introduce a suitable scalings in order to describe the behaviour of the second moment of the mass distribution function. The scaling function is identified with the solution of a nonlinear integro-differential equation of a very peculiar type. Numerical examples are given.
scientific article; zbMATH DE number 5073054