| Abstract: |
| Delaunay surfaces were introduced by Delaunay in 1841, and the motions known as mean curvature flow and surface diffusion were introduced by Mullins in 1956 and 1957, respectively, in modelling materials science processes. Quite recently has it been noted that the Delaunay surfaces may be successfully combined to describe various materials science phenomena, such as hillock and hole formation, and line grating structures.
We review some of these constructions and their implications, indicating open questions and future directions.
[1] K. Golubkov, A. Novick-Cohen, Y. Vaknin, Coupled surface diffusion and mean curvature motion: an axisymmetric system with two grains and a hole. Quart. Appl. Math. 83 (2025) 97-134.
[2] A. Zigelman & A. Novick-Cohen, Critical effective radius for holes in thin films: energetic and dynamic considerations. J. Appl. Phys. 134 (2023) 135302.
[3] D. Goldberg & A. Novick-Cohen, Rayleigh type stability criteria for certain coupled surface diffusion and mean curvature flows, in preparation. |
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