Gelation in Input-Driven Aggregation

We investigate irreversible aggregation processes driven by a source of smallmass clusters. In the spatially homogeneous situation, a well-mixed system isconsists of clusters of various masses whose concentrations evolve according toan infinite system of nonlinear ordinary differential equations. We focus onthe cluster mass distribution in the long time limit. An input-drivenaggregation with rates proportional to the product of merging partnersundergoes a percolation transition. We examine this process analytically andnumerically. There are two theoretical schemes and two natural ways ofnumerical integration on the level of a truncated system with a finite numberof equations. After the percolation transition, the behavior depends on theadopted approach: The giant component quickly engulfs the entire system (Floryapproach), or a non-trivial stationary mass distribution emerges (Stockmayerapproach). We also outline generalization to ternary aggregation.