Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Thermal grooving by surface diffusion: Mullins revisited and extended to multiple grooves

Author: P. A. Martin
Journal: Quart. Appl. Math. 67 (2009), 125-136
MSC (2000): Primary 35R35
DOI: https://doi.org/10.1090/S0033-569X-09-01086-4
Published electronically: January 7, 2009
MathSciNet review: 2497600
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Abstract: We extend the original Mullins theory of surface grooving due to a single interface to multiple interacting grooves formed due to closely spaced flat interfaces. First, we show that Mullins' analysis for one groove can be simplified by using Fourier cosine transforms instead of Laplace transforms. Second, we solve the corresponding problem for an infinite periodic row of grooves. For both of these problems, symmetry considerations ensure that the interface conditions reduce to boundary conditions. Third, we solve the problem for two interacting grooves. Continuity requirements at the groove roots require sliding at the interfaces or tilting of the groove roots. We adopt the latter model. We find that the groove roots tilt until the surface curvature of the semi-infinite profiles is eliminated.

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Additional Information

P. A. Martin
Affiliation: Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401-1887
Email: pamartin@mines.edu

DOI: https://doi.org/10.1090/S0033-569X-09-01086-4
Received by editor(s): July 25, 2007
Published electronically: January 7, 2009
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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