Migration-driven aggregate growth — general symmetry analysis and scaling theory

Abstract:
The general models for the aggregate growth by migration of components between aggregates are considered. Their general group analysis is performed, and symmetries of the governing equations are identified. The comprehensive description of some classical and new models is proposed, their reduced equations are generated and solved, and the comprehensive scaling theory is given. The results obtained are compared with the Lifshitz-Slyozov-Wagner theory of coarsening, Ispolatov-Krapivsky-Redner theory of asset exchanges, Leyvraz-Redner scaling theory of aggregate growth, etc.