Asymptotic solutions of the Becker-Doring equations

We describe the solution of various Becker-Doring models. First, we analyse equilibrium and steady-state solutions, together with the large-time behaviour of solutions for the case of constant monomer concentration. Then we solve a weak fragmentation, constant mass, case by using matched asymptotic expansions. The methods are applied both to the full Becker-Doring equations and to a coarse-grained, or contracted, system. Comparison of the results show good qualitative agreement; all the phenomena present in the full model are reproduced in the contracted system and no anomalous effects are introduced. However, the quantitative agreement depends strongly on the choice of parameter values in the contracted system.