References on Surface Diffusion (for AMSC 698V) - B. Li

AMSC 698V: Advanced Topics in Applied Mathematics, Fall, 2003

MATHEMATICAL AND COMPUTATIONAL PROBLEMS
IN MATERIALS SCIENCE

Instructor: Bo Li

References on Surface Diffusion

  1. S. A. Alvarez and C. Liu, Motion of a closed curve by minus the surface Laplacian of Curvature, Diff. Integral Eqns, 13(10-12):1583--1594, 1997.
  2. S. Asvadurov, B. D. Coleman, R.S. Falk, and M. Moakher, Similarity solutions inthe theory of curvature driven diffusion along planar curves: I. Symmetric curves expanding in time, Physica D, 121:263-274, 1998.
  3. A. J. Bernoff and A. L. Bertozzi and T. P. Witelski, Axisymmetric surface diffusion: Dynamics and stability of self-similar pinch-off, J. Stat. Phys., 93(314):725-776, 1998,
  4. E. Bänsch, P. Morin, and R. H. Nochetto, Finite element methods for surface diffusion, Proceedings of the International Conference on "Free Boundary Problems, Th eory and Applications", Trento, Italy, June 2002.
  5. E. Bänsch, P. Morin, and R. H. Nochetto, Surface diffusion of graphs: variational formulation, error analysis and simulation, SIAM J. Numer. Anal., 2003 (accepted for publication).
  6. P. Baras, J. Duchon, and R. Robert, Evolution d'une interface par diffusion de surface, Comm. PDEs, 9:313-335, 1984.
  7. J. W. Cahn, C. M. Elliott, and A. Novick-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature, Euro. J. Appl. Math., 7:287-301, 1996.
  8. J. W. Cahn and J. E. Taylor, Surface motion by surface diffusion, Acta. Metall. Meter., 42:1045-1063, 1994.
  9. W. C. Carter, A. R. Roosen, J. W. Cahn, and J. Taylor, Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces, Acta Metal. Mater. 43:4309-4323, 1995.
  10. D. L. Chopp and J. A. Sethian, Motion by intrinsic Laplacian of curvature, Interface and Free Boundries, 1:107-123, 1999.
  11. B. D. Coleman, R.S. Falk, and M. Moakher, Stability of cylindrical bodies in the theory of surface diffusion, Physica D, 89:123-135, 1995.
  12. B. D. Coleman, R.S. Falk, and M. Moakher, Space-time finite element methods for surface diffusion with applications to the theory of the stability of cylinders, SIAM J. Sci. Comp., 17:1434-1448, 1996.
  13. F. Davi and M. E. Gurtin, On the motion of a phase interface by surface diffusion, J. Appl. Math. Phys., 41:782-811, 1990.
  14. K. Deckelnick, G. Dziuk, and C. M. Elliott, Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces, Preprint, 2002.
  15. C. M. Elliott, and H. Garcke, Existence results for diffusive surface motion laws, Adv. Math. Sci. Appl., 7(1):467-490, 1997.
  16. J. Escher, U. F. Mayer, and G. Simonett, The Surface Diffusion Flow for Immersed Hypersurfaces, SIAM J. Math. Anal., 29(6):1419-1433, 1998.
  17. Y. Giga and K. Ito, On pinching of curves moved by surface diffusion, Comm. Appl. Anal., 2(3):393-405, 1998.
  18. C. Herring, Surface tension as a motivation for sintering, in The Physics of Powder Metallurgy, Editor: W. E. Kingston, McGraw-Hill, New York, pp. 143-179, 1951.
  19. W. W. Mullins, Theory of thermal grooving, J. Appl. Phys., 28:333-339, 1957.
  20. F. A. Nichols and W. W. Mullins, Surface- (interface-) and volume-diffusion contributions to morphological changes driven by capillarity, Trans. Metall. Soc. AIME, 233:1840-1848, 1965.
  21. P. Smereka, Semi-implicit level set methods for curvature and surface diffusion motion, J. Sci. Comput., 19(1):439-456, 2003.
  22. B. Sun and Z. Suo, A finite element method for simulating interface motion: II. large shape change due to surface diffusion, Acta mater., 45:4953-4962, 1997.
  23. J. Taylor and J. W. Cahn, Linking anisotropic sharp and diffuse surface motion laws via gradient flows, J. Stat. Phys. 77:183-197, 1994.