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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  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
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  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
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