@article{AIHPA_1997__66_4_411_0,
author = {Alouges, F. and Ghidaglia, Jean-Michel},
title = {Minimizing Oseen-Frank energy for nematic liquid crystals : algorithms and numerical results},
journal = {Annales de l'I.H.P. Physique th\'eorique},
volume = {67},
year = {1997},
pages = {411-447},
mrnumber = {1459514},
zbl = {0911.35007},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1997__66_4_411_0}
}
Alouges, F.; Ghidaglia, J. M. Minimizing Oseen-Frank energy for nematic liquid crystals : algorithms and numerical results. Annales de l'I.H.P. Physique théorique, Tome 67 (1997) pp. 411-447. http://gdmltest.u-ga.fr/item/AIHPA_1997__66_4_411_0/
[1] ,, Un algorithme qui décroît sûrement l'énergie des cristaux liquides, thèse de doctorat, Université d'Orsay, 1990.
[2] , A new algorithm for computing liquid crystal stable configurations: The harmonic mapping case, to appear in SIAM Journal on Numer. Anal. and prépublication du CMLA # 9515, Cachan, 1995. | MR 1472192
[3] and , Computation of stable equilibrium states of nematic phases between cylinders, in preparation.
[4] , and , Relaxed energies for harmonie maps, Variational methods, H. Berestycki, J.-M. Coron and I. Ekeland Eds, Birkhäuser, Boston, Basel, Berlin, 1990, pp. 37-52. | MR 1205144 | Zbl 0793.58011
[5] , and , Harmonic maps with defects, Comm. Math. Phys., Vol. 107, 1986, pp. 649-705. | MR 868739 | Zbl 0608.58016
[6] and , Weak stability of the map x/|x| for liquid crystal, Comm. Partial Differential Equations, Vol. 15, 1990, pp. 675-692. | MR 1070842 | Zbl 0716.49001
[7] , Perturbation techniques for liquid crystal functionals, lectures given at the Ecole Normale Supérieure de Cachan.
[8] , Fractional step methods for liquid crystals problems, PhD thesis, University of Minnesota, Minneapolis, 1988.
[9] and , Field-induced instabilities in Nematic liquid crystals, in Nematics: Mathematical and physical aspects, 1991, pp. 261-278. | MR 1178100 | Zbl 0727.76015
[10] , , , and , Minimum energy configurations for liquid crystals: computational results, in Theory and application of liquid crystals, IMA 5, Springer-Verlag, New-York, 1987, pp. 99-122. | MR 900831
[11] , and Eds, Nematics: Mathematical and physical aspects, Kluwer, Dordrecht, 1991. | MR 1178081 | Zbl 0722.00043
[12] and , A report on harmonic maps, Bull. London Math. Soc., Vol. 10, 1978, pp. 1-68. | MR 495450 | Zbl 0401.58003
[13] , Liquid crystals with variable degree of orientation, IMA preprint # 559, Minneapolis, 1989. | MR 1079183
[14] , The physics of liquid crystals, Clarendon Press, Oxford, 1974,
see also and , The physics of liquid crystals, 2nd edition, International series of monographs (Physics) 83, Oxford Sci. Pub., Oxford, 1993.
[15] , Multiple integrals in the calculus ofvariations and nonlinear elliptic systems, Annals of mathematics studies, Princeton University Press, Princeton, 1983. | MR 717034 | Zbl 0516.49003
[16] , Mathematical models of liquid crystals with variable degree of orientation, PhD thesis, Pennsylvania State University, 1994.
[17] , Harmonic mappings, symmetry and computer graphics, preprint CMA-R- 52-88. | MR 1081330
[18] , Fiber evolution in the Heat flow of harmonie maps, in Nematics: Mathematical and physical aspects, J.-M. Coron et al. eds (1991). | MR 1178092 | Zbl 0738.58013
[19] , and , Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys., Vol. 105, 1986, pp. 547-570. | MR 852090 | Zbl 0611.35077
[20] , and , Stable defects of minimizers of constrained variational principles, Ann. Inst. Henri Poincaré, Vol. 5, 1988, pp. 297-322. | Numdam | MR 963102 | Zbl 0657.49018
[21] , and , Remarks about the mathematical theory of liquid crystals, Proc. CIRM, Trento, IMA, preprint 276. | MR 974607
[22] and , A remark on H1 mappings, Manuscripta Math., Vol. 56, 1986, pp. 1-10. | MR 846982 | Zbl 0618.58015
[23] and , Mathematical questions of liquid crystal theory, in Theory and applications of liquid crystals, IMA Vol. 5, Springer-Verlag, New-York, 1987, pp. 161-166. | MR 900833
[24] , Minima de la fonctionnelle énergie libre des cristaux liquides, C. R. Acad. Sci. Paris, Série I, t. 305, 1987, pp. 565-568. | MR 916336 | Zbl 0641.49003
[25] and , Quadratic variation of liquid crystal energy at x/|x|, Proc. R. Soc. London A, Vol. 437, 1992, pp. 475-487. | MR 1163558 | Zbl 0761.49012
[26] , and , The elementary defects of the Oseen-Frank energy for a liquid crystal, C. R. Acad. Sci. Paris, Série I, Vol. 316, 1993, pp. 465-470. | MR 1209268 | Zbl 0784.35085
[27] , Points, Lines and Walls, John Wiley, 1983. | MR 734901
[28] , On nematic liquid crystals with variable degree of orientation, C. P. A. M., Vol. XLIV, 1991, pp. 453-468. | MR 1100811 | Zbl 0733.49005
[29] , Une remarque sur l'application x/|x|, C. R. Acad. Sci. Paris, Série I, t. 305, 1987, pp. 529-531. | Zbl 0652.58022
[30] , Numerical analysis for liquid crystal problems, PhD thesis, University of Minnesota, Minneapolis, 1987.
[31] , Equations différentielles opérationnelles et problèmes aux limites, Springer Verlag, 1961. | MR 153974 | Zbl 0098.31101
[32] , A minimization algorithm for a relaxed energy connected with the theory of liquid crystal, to appear in Mathematical models and methods in applied sciences, and Prépublication du CMLA # 9420, Cachan, 1994. | MR 1316191
[33] , Everywhere discontinuous harmonic maps, Prépublication du CMLA # 9302, Cachan, 1993. See also C. R. Acad. Sci. Paris, Série I, t. 314, 1992, pp. 719-723. | MR 1163864 | Zbl 0780.49030
[34] and , A regularity theory for harmonic maps, J. Diff. Geom., Vol. 17, 1982, pp. 307-335. | MR 664498 | Zbl 0521.58021
[35] , Variational Theories for liquid crystals, Chapman & Hall London, New York, 1994. | Zbl 0814.49002