Aggregation, polymerisation, cluster formation

Many studies in different disciplines deal with kinetic phenomena where elementary units (e.g. monomers) of a population interact to form greater structures. Cell aggregation, polymerisation showing gelation and an abstract growth model formulated in terms of chemical kinetics, will be presented here as characteristic examples. 

It means that an increase in c is due to the formation of groups of k ft-cells by merging a group of / -cells with a group of j fe-cells and a decrease is given due to the formation of aggregates of size k j (where y = 1, 2,. ..). 

Equation (7.28) has no known closed form solution. In the particular case of Oij = A = constant, introducing the transformed time x = At/2, and writing n, (T) instead of q(0 we get 

Reversible polymerisation is the combined process of formation and breakage of chemical bonds in a system of reaction polymers (see, for example van Dongen Ernst (1984)). 

Particular theories of polymerisation make different structural assumptions that result in different Kjj and F. According to the detailed balance condition 

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