Global minimizers for axisymmetric multiphase membranes

Rustum Choksi; Marco Morandotti; Marco Veneroni

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 4, page 1014-1029
  • ISSN: 1292-8119

Abstract

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We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase [R. Choksi and M. Veneroni, Calc. Var. Partial Differ. Equ. (2012). DOI:10.1007/s00526-012-0553-9] and prove existence of a global minimizer.

How to cite

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Choksi, Rustum, Morandotti, Marco, and Veneroni, Marco. "Global minimizers for axisymmetric multiphase membranes." ESAIM: Control, Optimisation and Calculus of Variations 19.4 (2013): 1014-1029. <http://eudml.org/doc/272804>.

@article{Choksi2013,
abstract = {We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase [R. Choksi and M. Veneroni, Calc. Var. Partial Differ. Equ. (2012). DOI:10.1007/s00526-012-0553-9] and prove existence of a global minimizer.},
author = {Choksi, Rustum, Morandotti, Marco, Veneroni, Marco},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {helfrich functional; biomembranes; global minimizers; axisymmetric surfaces; multicomponent vesicle; Helfrich functional},
language = {eng},
number = {4},
pages = {1014-1029},
publisher = {EDP-Sciences},
title = {Global minimizers for axisymmetric multiphase membranes},
url = {http://eudml.org/doc/272804},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Choksi, Rustum
AU - Morandotti, Marco
AU - Veneroni, Marco
TI - Global minimizers for axisymmetric multiphase membranes
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 4
SP - 1014
EP - 1029
AB - We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase [R. Choksi and M. Veneroni, Calc. Var. Partial Differ. Equ. (2012). DOI:10.1007/s00526-012-0553-9] and prove existence of a global minimizer.
LA - eng
KW - helfrich functional; biomembranes; global minimizers; axisymmetric surfaces; multicomponent vesicle; Helfrich functional
UR - http://eudml.org/doc/272804
ER -

References

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