@article{AIHPC_2008__25_1_77_0,
author = {Majumdar, A. and Robbins, J. M. and Zyskin, M.},
title = {Energies of ${S}^{2}$-valued harmonic maps on polyhedra with tangent boundary conditions},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {77--103},
year = {2008},
publisher = {Elsevier},
volume = {25},
number = {1},
doi = {10.1016/j.anihpc.2006.11.003},
mrnumber = {2383079},
zbl = {1141.35005},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2006.11.003/}
}
TY - JOUR
AU - Majumdar, A.
AU - Robbins, J. M.
AU - Zyskin, M.
TI - Energies of ${S}^{2}$-valued harmonic maps on polyhedra with tangent boundary conditions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
SP - 77
EP - 103
VL - 25
IS - 1
PB - Elsevier
UR - https://www.numdam.org/articles/10.1016/j.anihpc.2006.11.003/
DO - 10.1016/j.anihpc.2006.11.003
LA - en
ID - AIHPC_2008__25_1_77_0
ER -
%0 Journal Article
%A Majumdar, A.
%A Robbins, J. M.
%A Zyskin, M.
%T Energies of ${S}^{2}$-valued harmonic maps on polyhedra with tangent boundary conditions
%J Annales de l'I.H.P. Analyse non linéaire
%D 2008
%P 77-103
%V 25
%N 1
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2006.11.003/
%R 10.1016/j.anihpc.2006.11.003
%G en
%F AIHPC_2008__25_1_77_0
Majumdar, A.; Robbins, J. M.; Zyskin, M. Energies of ${S}^{2}$-valued harmonic maps on polyhedra with tangent boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 1, pp. 77-103. doi: 10.1016/j.anihpc.2006.11.003
[1] , , Handbook of Mathematical Functions, Dover Publications, 1965.
[2] , Tres observaciones sobre el algebra lineal, Univ. Nac. Tacumán Rev. Ser. A 5 (1946) 147-151. | Zbl | MR
[3] , The interplay between analysis and topology in some nonlinear PDE problems, Bull. Amer. Math. Soc. 40 (2006) 179-201. | Zbl | MR
[4] , , , Harmonic maps with defects, Comm. Math. Phys. 107 (1986) 649-705. | Zbl | MR
[5] , , Flexoelectric switching in a bistable nematic device, Phys. Rev. E 65 (2002) 051710.
[6] , , The Physics of Liquid Crystals, second ed., Oxford University Press, 1995.
[7] , , Flexoelectric surface switching of bistable nematic devices, Phys. Rev. Lett. 87 (2001) 275505.
[8] , , Harmonic Maps Between Riemannian Polyhedra, Cambridge Tracts in Mathematics, vol. 142, Cambridge University Press, 2001. | Zbl | MR
[9] , , Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. IHES 76 (1992) 165-246. | Zbl | MR | Numdam
[10] , Singularities of harmonic maps, Bull. Amer. Math. Soc. 34 (1997) 15-34. | Zbl | MR
[11] J.C. Jones, J.R. Hughes, A. Graham, P. Brett, G.P. Bryan-Brown, E.L. Wood, Zenithal bistable devices: Towards the electronic book with a simple LCD, In: Proc IDW, 2000, pp. 301-304.
[12] , , Controllable alignment of nematic liquid crystals around microscopic posts: Stabilization of multiple states, Appl. Phys. Lett. 80 (2002) 3635-3637.
[13] , Points, Lines and Walls, John Wiley and Sons, Chichester, 1983. | MR
[14] , , Soft Condensed Matter, Springer, 2002.
[15] , Topological defects in dispersed liquid crystals, or words and worlds around liquid crystal drops, Liquid Crystals 24 (1998) 117-125.
[16] , , On nematic liquid crystal droplets, in: Elliptic and Parabolic Methods in Geometry, A.K. Peters, 1996, pp. 91-121. | Zbl | MR
[17] A. Majumdar, Liquid crystals and tangent unit-vector fields in polyhedral geometries, PhD thesis, University of Bristol, 2006.
[18] , , , Elastic energy of liquid crystals in convex polyhedra, J. Phys. A 37 (2004) L573-L580, J. Phys. A 38 (2005) 7595. | Zbl | MR
[19] , , , Lower bound for energies of harmonic tangent unit-vector fields on convex polyhedra, Lett. Math. Phys. 70 (2004) 169-183. | Zbl | MR
[20] , , , Elastic energy for reflection-symmetric topologies, J. Phys. A 39 (2006) 2673-2687. | Zbl | MR
[21] , , , Topology and bistability in liquid crystal devices, math-ph/0611016.
[22] , The topological theory of defects in ordered media, Rev. Mod. Phys. 51 (C) (1979) 591-651. | Zbl | MR
[23] C.J.P. Newton, T.P. Spiller, Bistable nematic liquid crystal device modelling, In: Proc. 17th IDRC (SID), 1997, p. 13.
[24] , , Classification of unit-vector fields in convex polyhedra with tangent boundary conditions, J. Phys. A 37 (2004) 10609-10623. | Zbl | MR
[25] , The Static and Dynamic Continuum Theory of Liquid Crystals, Taylor and Francis, London, 2004.
[26] , Variational Theories for Liquid Crystals, Chapman and Hall, 1994. | Zbl | MR
[27] , , Topological dynamics of defects - boojums in nematic drops, Sov. Phys. JETP 58 (1983) 1159.
[28] M. Zyskin, Homotopy classification of director fields on polyhedral domains with tangent and periodic boundary conditions, Preprint, 2005.
Cité par Sources :





