Random hypergraphs and topological gelation criterion for crosslinked polymer systems
A class of hypergraphs, named polygraphs, especially suitable for modelling polymer systems, is defined and we discuss in detail the conditions which give rise to the Giant Component in the polygraph. This problem is analogous to gel formation in a crosslinked polymer system. To this end an equivalence class of polygraphs with given connectivity is defined and characterized by a specially introduced probabilistic representation. Our Topological Gelation Criterion is applicable to systems that may be far from thermodynamic equilibrium and need not necessarily be random. The criterion applies to polymers, superpolymers, cell aggregates, immunocytochemical systems and other systems.
scientific article; zbMATH DE number 4029624
scientific article