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METASTABILITY IN THE CLASSICAL, TRUNCATED BECKER–DÖRING EQUATIONS

Published online by Cambridge University Press:  14 October 2002

Dugald B. Duncan  and
Rachel M. Dunwell
Dugald B. Duncan
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK ([email protected])
Rachel M. Dunwell
Affiliation:
Bindura University College, Post Bag 1020, Bindura, Zimbabwe
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Abstract

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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

Keywords

coagulation–fragmentationmetastabilityeigenvalue estimatesasymptotic behaviour of solution
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