GEL, SELF-SIMILARITY AND UNIVERSALITY IN THE DISCRETE SMOLUCHOWSKI EQUATION WITH FINITE MASS

We approximately solve the Smoluchowski equation (discrete version), for gelling and non-gelling systems with finite mass and arbitrary initial conditions for various kernels (additive and multiplicative). We obtain that the approximate scaling form does not depend on the details of the kernel in contrast with already known results. Numerical simulations are presented which show that the predicted form is valid over a large range of the scaling variable n/s. The critical exponent related to the power law dependence of the distribution is shown to scale rapidly, even with low masses. This could clarify the recent difficulties of the standard theory with both experiments and numerical calculations.