Metastability in the classical, truncated Becker-Döring equations

Dugald B. Duncan, Rachel M. Dunwell

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We show that in the classical (fixed-monomer-concentration) Becker-Döring equations truncated at finite cluster size, the slow evolution (metastability) of solutions can be explained in terms of the eigensystem of this linear ordinary differential equation (ODE) system. In particular, for a common choice of coagulation-fragmentation rate constants there is an extremely small non-zero eigenvalue which is isolated from the rest of the spectrum. We give estimates and bounds on the size of this eigenvalue, the gap between it and the second smallest, and the size of the largest eigenvalue. The bounds on the smallest eigenvalue are very sharp when the system size and/or monomer concentration are large enough.

Original languageEnglish
Pages (from-to)701-716
Number of pages16
JournalProceedings of the Edinburgh Mathematical Society
Volume45
Issue number3
DOIs
Publication statusPublished - Oct 2002

Keywords

  • Asymptotic behaviour of solution
  • Coagulation-fragmentation
  • Eigenvalue estimates
  • Metastability

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