A Morphological Scheme for Mean Curvature Motion and Applications to Anisotropic Diffusion and Motion of Level Sets

1995 ◽  
Vol 32 (6) ◽  
pp. 1895-1909 ◽  
Author(s):  
Francine Catté ◽  
Françoise Dibos ◽  
Georges Koepfler
Keyword(s):  
Mean Curvature ◽  
Level Sets ◽  
Anisotropic Diffusion ◽  
Mean Curvature Motion ◽  
Curvature Motion

The Influence of the Exterior Surface on Grain Boundary Mobility Measurements

2014 ◽  
Vol 95 ◽  
pp. 56-65
Author(s):  
Amy Novick-Cohen ◽  
Anna Zigelman ◽  
Arkady Vilenkin
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Mean Curvature ◽  
Boundary Energy ◽  
Polycrystalline Materials ◽  
Normal Velocity ◽  
Exterior Surface ◽  
Mean Curvature Motion ◽  
Curvature Motion ◽  
Half Loop

Polycrystalline materials typically contain a very large number of grains whose surrounding grain boundaries evolve over time to reducethe overall energy of the microstructure. The evolution of the microstructure is influencedby the motion of the exterior surface since the grain boundaries couple to the exterior surface of the specimen; these effects can be appreciable especially in thin specimens. We model these effects using the classical framework of Mullins, in whichgrain boundaries move by mean curvature motion, Vn =A κ, and the exterior surface evolves by surface diffusion, Vn = -BΔs κ. Here Vn and κ denote the normal velocity and the mean curvature of the respective evolving surfaces, and Δs is the surface Laplacian. A classical way to determine A, the ``reduced mobility," is to make measurements based on the half-loop bicrystalline geometry. In this geometry one of the two grains, which embedded within the other, recedes at a roughly constant rate which can provide an estimate for A. In this note, we report on findings concerning the effects of the exterior surface on grain boundary motion and mobility measurements in the context of the half-loop bicrystalline geometry. We assume that the ratio of grain boundary energy to the exterior surface energy is small, and suitable assumptions are made of the specimen aspect ratio.

A Representation Formula for the Mean Curvature Motion

2001 ◽  
Vol 33 (4) ◽  
pp. 827-846 ◽  
Author(s):  
R. Buckdahn ◽  
P. Cardaliaguet ◽  
M. Quincampoix
Keyword(s):  
Mean Curvature ◽  
Representation Formula ◽  
Mean Curvature Motion ◽  
Curvature Motion ◽  
The Mean
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