next up previous
Next: About this document Up: Variational Methods for Microstructural Previous: Discussion

References

1
J.E. Taylor and J.W. Cahn. Surface motion by surface diffusion. Acta Met., 42:1045-63, 1994.

2
J.E. Taylor and J.W. Cahn. Linking anisotropic sharp and diffuse surface motion laws via gradient flows. J. Stat. Phys., 77:183-97, 1994.

3
Z. Suo. Motions of microscopic surfaces in materials. Advances in Appl. Mechs., 33:193-294, 1997.

4
J.W. Cahn and W.C. Carter. Crystal shapes and phase equilibria: A common mathematical basis. Met. Trans., 27A:1431-1440, 1996.

5
I.M. Gelfand and S.V. Fomin. Calculus of Variations. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1963.

6
J.E. Taylor. Mean curvature and weighted mean curvature, overview 98(ii). Acta Met., 40(7):1475-1485, 1992.

7
Conyers Herring. Some theorems on the free energies of crystal surfaces. Phys. Rev., 82(1):87-93, 1951.

8
J. W. Cahn and D. W. Hoffman. A vector thermodynamics for anisotropic surfaces. ii. curved and facetted surfaces. Acta Met., 22:1205-1214, 1974.

9
David W. Hoffman and John W. Cahn. A vector thermodynamics for anisotropic surfaces. i. fundamentals and applications to plane surface junctions. Surface Science, 31:368-388, 1972.

10
W. W. Mullins. Solid surface morphologies governed by capillarity. In Metal Surfaces: Structure, Energetics and Kinetics, pages 17-66. American Society for Metals, 1962.

11
J. Willard Gibbs. On the equilibrium of heterogeneous substances (1876). In Collected Works, volume 1. Longmans, Green, and Co., 1928.

12
F.J. Almgren, J.E. Taylor, and L. Wang. Curvature driven flows: A variational approach. SIAM Journal of Control and Optimization, 31:386-437, 1993.

13
D. Caraballo. A Variational Scheme for the Evolution of Polycrystals by Curvature. PhD thesis, Department of Mathematics, Princeton University, 1997.

14
F.J. Almgren and J.E. Taylor. Curvature driven flows: A variational approach. SIAM Journal of Control and Optimization, 31:386-437, 1993.

15
W.C. Carter, A.R. Roosen, J.W. Cahn, and J.E. Taylor. Shape evolution by surface diffusion and surface attachment limited kinetics on completely facetted surfaces. Acta Met., 43:4309-23, 1995.


W. Craig Carter
Tue Sep 30 16:07:27 EDT 1997