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Computational studies of conserved mean-curvature flow

Miroslav Kolář; Michal Beneš; Daniel Ševčovič

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 4, page 677-684
  • ISSN: 0862-7959

Abstract

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The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are presented as well.

How to cite

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Kolář, Miroslav, Beneš, Michal, and Ševčovič, Daniel. "Computational studies of conserved mean-curvature flow." Mathematica Bohemica 139.4 (2014): 677-684. <http://eudml.org/doc/269861>.

@article{Kolář2014,
abstract = {The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are presented as well.},
author = {Kolář, Miroslav, Beneš, Michal, Ševčovič, Daniel},
journal = {Mathematica Bohemica},
keywords = {phase transitions; area-preserving mean-curvature flow; parametric method; phase transitions; area-preserving mean-curvature flow; parametric method},
language = {eng},
number = {4},
pages = {677-684},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Computational studies of conserved mean-curvature flow},
url = {http://eudml.org/doc/269861},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Kolář, Miroslav
AU - Beneš, Michal
AU - Ševčovič, Daniel
TI - Computational studies of conserved mean-curvature flow
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 4
SP - 677
EP - 684
AB - The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are presented as well.
LA - eng
KW - phase transitions; area-preserving mean-curvature flow; parametric method; phase transitions; area-preserving mean-curvature flow; parametric method
UR - http://eudml.org/doc/269861
ER -

References

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