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
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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.
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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.
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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,
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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.
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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).
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P. Baras, J. Duchon, and R. Robert,
Evolution d'une interface par diffusion de surface,
Comm. PDEs, 9:313-335, 1984.
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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.
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J. W. Cahn and J. E. Taylor, Surface motion by surface diffusion, Acta.
Metall. Meter., 42:1045-1063, 1994.
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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.
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D. L. Chopp and J. A. Sethian, Motion by intrinsic Laplacian of curvature,
Interface and Free Boundries, 1:107-123, 1999.
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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.
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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.
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F. Davi and M. E. Gurtin, On the motion of a phase interface by surface
diffusion, J. Appl. Math. Phys., 41:782-811, 1990.
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K. Deckelnick, G. Dziuk, and C. M. Elliott,
Error analysis of a semidiscrete numerical scheme for diffusion in
axially symmetric surfaces, Preprint, 2002.
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C. M. Elliott, and H. Garcke, Existence results for diffusive surface
motion laws, Adv. Math. Sci. Appl., 7(1):467-490, 1997.
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J. Escher, U. F. Mayer, and G. Simonett,
The Surface Diffusion Flow for Immersed Hypersurfaces,
SIAM J. Math. Anal., 29(6):1419-1433, 1998.
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Y. Giga and K. Ito, On pinching of curves moved by surface diffusion,
Comm. Appl. Anal., 2(3):393-405, 1998.
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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.
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W. W. Mullins, Theory of thermal grooving, J. Appl. Phys., 28:333-339, 1957.
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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.
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P. Smereka, Semi-implicit level set methods for curvature and
surface diffusion motion, J. Sci. Comput., 19(1):439-456, 2003.
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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.
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J. Taylor and J. W. Cahn, Linking anisotropic sharp and diffuse surface
motion laws via gradient flows, J. Stat. Phys. 77:183-197, 1994.