@article{AIHPA_1997__66_4_411_0, author = {Alouges, F. and Ghidaglia, J. M.}, title = {Minimizing {Oseen-Frank} energy for nematic liquid crystals : algorithms and numerical results}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {411--447}, publisher = {Gauthier-Villars}, volume = {66}, number = {4}, year = {1997}, mrnumber = {1459514}, zbl = {0911.35007}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1997__66_4_411_0/} }
TY - JOUR AU - Alouges, F. AU - Ghidaglia, J. M. TI - Minimizing Oseen-Frank energy for nematic liquid crystals : algorithms and numerical results JO - Annales de l'I.H.P. Physique théorique PY - 1997 SP - 411 EP - 447 VL - 66 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1997__66_4_411_0/ LA - en ID - AIHPA_1997__66_4_411_0 ER -
%0 Journal Article %A Alouges, F. %A Ghidaglia, J. M. %T Minimizing Oseen-Frank energy for nematic liquid crystals : algorithms and numerical results %J Annales de l'I.H.P. Physique théorique %D 1997 %P 411-447 %V 66 %N 4 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1997__66_4_411_0/ %G en %F 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 66 (1997) no. 4, pp. 411-447. http://www.numdam.org/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
,[3] Computation of stable equilibrium states of nematic phases between cylinders, in preparation.
and ,[4] 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 | Zbl
, and ,[5] Harmonic maps with defects, Comm. Math. Phys., Vol. 107, 1986, pp. 649-705. | MR | Zbl
, and ,[6] Weak stability of the map x/|x| for liquid crystal, Comm. Partial Differential Equations, Vol. 15, 1990, pp. 675-692. | MR | Zbl
and ,[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] Field-induced instabilities in Nematic liquid crystals, in Nematics: Mathematical and physical aspects, 1991, pp. 261-278. | MR | Zbl
and ,[10] 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
, , , and ,[11] Nematics: Mathematical and physical aspects, Kluwer, Dordrecht, 1991. | MR | Zbl
, and Eds,[12] A report on harmonic maps, Bull. London Math. Soc., Vol. 10, 1978, pp. 1-68. | MR | Zbl
and ,[13] Liquid crystals with variable degree of orientation, IMA preprint # 559, Minneapolis, 1989. | MR
,[14] The physics of liquid crystals, Clarendon Press, Oxford, 1974,
,see also The physics of liquid crystals, 2nd edition, International series of monographs (Physics) 83, Oxford Sci. Pub., Oxford, 1993.
and ,[15] Multiple integrals in the calculus ofvariations and nonlinear elliptic systems, Annals of mathematics studies, Princeton University Press, Princeton, 1983. | MR | Zbl
,[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
,[18] Fiber evolution in the Heat flow of harmonie maps, in Nematics: Mathematical and physical aspects, J.-M. Coron et al. eds (1991). | MR | Zbl
,[19] Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys., Vol. 105, 1986, pp. 547-570. | MR | Zbl
, and ,[20] Stable defects of minimizers of constrained variational principles, Ann. Inst. Henri Poincaré, Vol. 5, 1988, pp. 297-322. | Numdam | MR | Zbl
, and ,[21] Remarks about the mathematical theory of liquid crystals, Proc. CIRM, Trento, IMA, preprint 276. | MR
, and ,[22] A remark on H1 mappings, Manuscripta Math., Vol. 56, 1986, pp. 1-10. | MR | Zbl
and ,[23] 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
and ,[24] Minima de la fonctionnelle énergie libre des cristaux liquides, C. R. Acad. Sci. Paris, Série I, t. 305, 1987, pp. 565-568. | MR | Zbl
,[25] Quadratic variation of liquid crystal energy at x/|x|, Proc. R. Soc. London A, Vol. 437, 1992, pp. 475-487. | MR | Zbl
and ,[26] 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 | Zbl
, and ,[27] Points, Lines and Walls, John Wiley, 1983. | MR
,[28] On nematic liquid crystals with variable degree of orientation, C. P. A. M., Vol. XLIV, 1991, pp. 453-468. | MR | Zbl
,[29] Une remarque sur l'application x/|x|, C. R. Acad. Sci. Paris, Série I, t. 305, 1987, pp. 529-531. | Zbl
,[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 | Zbl
,[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
,[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 | Zbl
,[34] A regularity theory for harmonic maps, J. Diff. Geom., Vol. 17, 1982, pp. 307-335. | MR | Zbl
and ,[35] Variational Theories for liquid crystals, Chapman & Hall London, New York, 1994. | Zbl
,