Stresses in curved nematic membranes
Ordering configurations of a director field on a curved membrane induce stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motio...
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ftdatacite:10.48550/arxiv.1802.10428 2023-05-15T17:39:42+02:00 Stresses in curved nematic membranes Santiago, J. A. 2018 https://dx.doi.org/10.48550/arxiv.1802.10428 https://arxiv.org/abs/1802.10428 unknown arXiv https://dx.doi.org/10.1103/physreve.97.052706 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Soft Condensed Matter cond-mat.soft FOS Physical sciences article-journal Article ScholarlyArticle Text 2018 ftdatacite https://doi.org/10.48550/arxiv.1802.10428 https://doi.org/10.1103/physreve.97.052706 2022-04-01T09:51:42Z Ordering configurations of a director field on a curved membrane induce stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in gaussian curvature. These forces are mediated by the Green function of Laplace-Beltrami operator of the surface. In addition, we find non-isotropic forces that involve derivatives of the Green function and the gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive respect to the north pole, indicating that it is an unstable equilibrium point. : To appear in PRE Text North Pole DataCite Metadata Store (German National Library of Science and Technology) North Pole Laplace ENVELOPE(141.467,141.467,-66.782,-66.782) Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
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DataCite Metadata Store (German National Library of Science and Technology) |
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topic |
Soft Condensed Matter cond-mat.soft FOS Physical sciences |
spellingShingle |
Soft Condensed Matter cond-mat.soft FOS Physical sciences Santiago, J. A. Stresses in curved nematic membranes |
topic_facet |
Soft Condensed Matter cond-mat.soft FOS Physical sciences |
description |
Ordering configurations of a director field on a curved membrane induce stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in gaussian curvature. These forces are mediated by the Green function of Laplace-Beltrami operator of the surface. In addition, we find non-isotropic forces that involve derivatives of the Green function and the gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive respect to the north pole, indicating that it is an unstable equilibrium point. : To appear in PRE |
format |
Text |
author |
Santiago, J. A. |
author_facet |
Santiago, J. A. |
author_sort |
Santiago, J. A. |
title |
Stresses in curved nematic membranes |
title_short |
Stresses in curved nematic membranes |
title_full |
Stresses in curved nematic membranes |
title_fullStr |
Stresses in curved nematic membranes |
title_full_unstemmed |
Stresses in curved nematic membranes |
title_sort |
stresses in curved nematic membranes |
publisher |
arXiv |
publishDate |
2018 |
url |
https://dx.doi.org/10.48550/arxiv.1802.10428 https://arxiv.org/abs/1802.10428 |
long_lat |
ENVELOPE(141.467,141.467,-66.782,-66.782) ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
geographic |
North Pole Laplace Lagrange |
geographic_facet |
North Pole Laplace Lagrange |
genre |
North Pole |
genre_facet |
North Pole |
op_relation |
https://dx.doi.org/10.1103/physreve.97.052706 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1802.10428 https://doi.org/10.1103/physreve.97.052706 |
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1766140484054417408 |