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METASTABILITY IN THE CLASSICAL, TRUNCATED BECKER–DÖRING EQUATIONS
Published online by Cambridge University Press: 14 October 2002
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.
AMS 2000 Mathematics subject classification: Primary 34A30; 15A18; 65F15
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 3 , October 2002 , pp. 701 - 716
- Copyright
- Copyright © Edinburgh Mathematical Society 2002
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