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Grooving of a Bicrystal by Surface Diffusion

Conclusions

A search for point symmetries on the function derived by Katoanga and Lisle was successful in finding only one symmetry generator to each function pair. While the constitutive equations derived from the second set of functions appeared useful, the inability to reduce the non-linear evolution equation below third order was disappointing. Furthermore, the boundary conditions for the symmetric groove remained unable to be reduced.

It is possible that further symmetry analysis utilising contact symmetries; returning to the original PDE, or considering a larger set of ODEs may provide more generators and permit further reductions of the evolution equation. It may also be possible to find other boundary conditions which do uncouple under the transformations used here and which may model other processes.

 

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Abstract

Introduction

Derivation of the Evolution Equation

Isotropic Materials

New Constitutive Functions

Symmetry Reductions

The Symmetric Grain Boundary Groove Problem

Conclusions

Bibliography

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