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Interface closure in the root region of steady deep-cellular growth in directional solidification

Published online by Cambridge University Press:  06 March 2015

J.-J. XU  and
Y.-Q. CHEN
J.-J. XU
Affiliation:
School of Material Science and Engineering, USTB, Beijing, 100083, China email: xu@math.mcgill.ca Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 0B9, Canada
Y.-Q. CHEN
Affiliation:
School of Science, Tianjin Chengjian University, Tianjin, 300384, China email: yonqiang@gmail.com
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Abstract

The present paper investigates the mechanism of interface closure in the root region of the solutions for steady deep-cellular growth. This phenomenon is determined by a transcendentally small factor beyond all orders. It is found that the root region comprises three inner-inner regions; the inner system in the root region has a simple turning point, whose presence generates the so-called trapped-waves mechanism, which is responsible for the interface closure at the bottom of root. The quantization condition derived from the trapped-waves mechanism yields the eigenvalue that determines the location of interface closure and its dependence on the interfacial energy and other physical parameters.

Keywords

Asymptotics beyond all ordersMultiple variables expansionQuantization conditionSteady deep-cellular growthInterface closure
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 3 , June 2015 , pp. 355 - 382
Copyright
Copyright © Cambridge University Press 2015 

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