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Experimental and theoretical investigation of an equation of dendritic crystal growth

Published online by Cambridge University Press:  16 July 2009

J. N. Dewynne  and
F. N. H. Robinson
J. N. Dewynne
Affiliation:
Mathematics Faculty, Southampton University, Southampton SO9 5NH, UK
F. N. H. Robinson
Affiliation:
Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
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Abstract

An experimental study using an analogue electronic model of the equation x‴ + x′ = є sin x, modified by the addition of small terms ax″ and βx with 0 < β < α ≫ є shows that these dissipative terms have a profound effect on the solutions for large time. If ∈ is not too large, experimental solutions tend to a simple periodic form, unlike the case α=β = 0. The existence of this limiting periodic form suggests the possibility of a simple analytic treatment using the method of harmonic balance, and this treatment leads to excellent agreement with the experimental results for a wide range of initial conditions and values of the parameters. The approach towards attracting limiting periodic solutions is analysed by using the method of multiple scales.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 2 , Issue 3 , September 1991 , pp. 199 - 222
Copyright
Copyright © Cambridge University Press 1991

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