A computational approach to fractures in crystal growth

Matteo Novaga; Emanuele Paolini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1999)

  • Volume: 10, Issue: 1, page 47-56
  • ISSN: 1120-6330

Abstract

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In the present paper, we motivate and describe a numerical approach in order to detect the creation of fractures in a facet of a crystal evolving by anisotropic mean curvature. The result appears to be in accordance with the known examples of facet-breaking. Graphical simulations are included.

How to cite

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Novaga, Matteo, and Paolini, Emanuele. "A computational approach to fractures in crystal growth." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 10.1 (1999): 47-56. <http://eudml.org/doc/252288>.

@article{Novaga1999,
abstract = {In the present paper, we motivate and describe a numerical approach in order to detect the creation of fractures in a facet of a crystal evolving by anisotropic mean curvature. The result appears to be in accordance with the known examples of facet-breaking. Graphical simulations are included.},
author = {Novaga, Matteo, Paolini, Emanuele},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Nonlinear partial differential equations of parabolic type; Crystal growth; Non-smooth analysis},
language = {eng},
month = {3},
number = {1},
pages = {47-56},
publisher = {Accademia Nazionale dei Lincei},
title = {A computational approach to fractures in crystal growth},
url = {http://eudml.org/doc/252288},
volume = {10},
year = {1999},
}

TY - JOUR
AU - Novaga, Matteo
AU - Paolini, Emanuele
TI - A computational approach to fractures in crystal growth
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1999/3//
PB - Accademia Nazionale dei Lincei
VL - 10
IS - 1
SP - 47
EP - 56
AB - In the present paper, we motivate and describe a numerical approach in order to detect the creation of fractures in a facet of a crystal evolving by anisotropic mean curvature. The result appears to be in accordance with the known examples of facet-breaking. Graphical simulations are included.
LA - eng
KW - Nonlinear partial differential equations of parabolic type; Crystal growth; Non-smooth analysis
UR - http://eudml.org/doc/252288
ER -

References

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  1. Almgren, F. J. - Taylor, J., Flat flow is motion by crystalline curvature for curves with crystalline energies. J. Diff. Geom., 42, 1995, 1-22. Zbl0867.58020MR1350693
  2. Almgren, F. J. - Taylor, J. E. - Wang, L., Curvature-driven flows: a variational approach. SIAM J. Control Optim., 31, 1993, 387-437. Zbl0783.35002MR1205983DOI10.1137/0331020
  3. Bellettini, G. - Novaga, M., Approximation and comparison for non-smooth anisotropic motion by mean curvature in R N . Math. Mod. Meth. Appl. Sc., to appear. Zbl1016.53048MR1749692DOI10.1142/S0218202500000021
  4. Bellettini, G. - Novaga, M. - Paolini, M., Facet-breaking for three-dimensional crystals evolving by mean curvature. Interfaces and Free Boundaries, to appear. Zbl0934.49023MR1865105DOI10.4171/IFB/3
  5. Bellettini, G. - Paolini, M. - Venturini, S., Some results on surface measures in Calculus of Variations. Ann. Mat. Pura Appl., 170, 1996, 329-359. Zbl0890.49020MR1441625DOI10.1007/BF01758994
  6. Brezis, H., Operateurs Maximaux Monotones. North-Holland, Amsterdam1973. 
  7. Cahn, J. W. - Handwerker, C. A. - Taylor, J. E., Geometric models of crystal growth. Acta Metall. Mater., 40, 1992, 1443-1474. 
  8. Giga, M.-H. - Giga, Y., A subdifferential interpretation of crystalline motion under nonuniform driving force. Dynamical Systems and Differential Equations, 1, 1998, 276-287. MR1720610
  9. Giga, Y. - Gurtin, M. E. - Matias, J., On the dynamics of crystalline motion. Japan Journal of Industrial and Applied Mathematics, 15, 1998, 7-50. MR1610305DOI10.1007/BF03167395
  10. Taylor, J. E., Crystalline variational problems. Bull. Amer. Math. Soc. (N.S.), 84, 1978, 568-588. Zbl0392.49022MR493671
  11. Taylor, J. E., Geometric crystal growth in 3D via facetted interfaces. In: Computational Crystal Growers Workshop. Selected Lectures in Mathematics, Amer. Math. Soc., 1992, 111-113. Zbl0776.65002MR1224451
  12. Taylor, J. E., Mean curvature and weighted mean curvature. Acta Metall. Mater., 40, 1992, 1475-1485. 
  13. Yunger, J., Facet Stepping and Motion By Crystalline Curvature. Ph. D. Thesis, 1998. MR2698605

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