Local stability of biaxial nematic phases between two cylinders

International Journal of Non-Linear Mechanics

Volumn 32, Issue 2, 1997, Pages 337-351

  Biscari, Paolo ^a   Virga, Epifanio G ^b  

^a POLITECNICO DI MILANO   (Italy)

^b Dipartimento di Matematica   (Italy)

Author keywords

Biaxiality; Nematic liquid crystals; Stability

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); CRYSTAL SYMMETRY; EIGENVALUES AND EIGENFUNCTIONS; FREE ENERGY; MATHEMATICAL MODELS; MOLECULAR ORIENTATION; NUMERICAL ANALYSIS; PHASE EQUILIBRIA; PROBABILITY DENSITY FUNCTION; SURFACES; TENSORS;

BIAXIALITY; INTERNAL POTENTIAL; LATERAL SURFACES;

NEMATIC LIQUID CRYSTALS;

EID: 0031103692     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-7462(97)81142-0     Document Type: Article

References (18)

1. P. G. de Gennes, Phenomenology of short-range-order effects in the isotropic phase of nematics materials. Phys. Lett. 30A, 454 (1969).
2. J. L. Ericksen, Liquid crystals with variable degree of orientation. Arch. Rat. Mech. Anal. 113, 97 (1991).
3. E. G. Virga, Variational Theories for Liquid Crystals. Chapman & Hall, London (1994).
4. P. Biscari and G. Guidone, A hierarchy of defects in biaxial nematics. Quad. Dip. Mat. Pisa, 811, 1 (1994).
5. P. Biscari and G. Capriz, Optical and statistical anisotropy in nematics. Rend. Mat. Appl. Acc. Lincei 4, 307 (1993).
6. L. Longa, D. Monselesan and H.-R. Trebin, An extension of the Landau-Ginsburg-de Gennes theory for liquid crystals. Liquid Crystals 2, 769 (1987).
7. L. Longa and H.-R. Trebin, Integrity basis approach to the elastic free energy functional of liquid crystals- 1. Classification of basic elastic modes. Liquid Crystals 5, 617 (1989).
8. P. Palffy-Muhoray, E. C. Gartland and J. R. Kelly, A new configurational transition in inhomogeneous nematics. Liquid Crystals 16, 713 (1994).
9. F. Bethuel, H. Brezis, B. D. Coleman and F. Hélein, Bifurcation analysis of minimizing harmonic maps describing the equilibrium of nematic phases between cylinders. Arch. Rat. Mech. Anal. 118, 149 (1992).
10. P. Palffy-Muhoray, A. Sparavigna and A. Strigazzi, Saddle-splay and mechanical instability in nematics confined to a cylindrical annular geometry. Liquid Crystals 14, 1143 (1993).
11. E. Sandier, Symétrie des applications harmoniques minimisantes d'une couronne vers la sphère. C.R. Acad. Sci. Paris 313, 435 (1991).
12. P. Cladis and M. Kléman, Non-singular disclinations of strength S= +1 in nematics. J. Phys. (Paris) 33, 591 (1972).
13. R. B. Meyer, On the existence of even indexed disclinations in nematic liquid crystals. Phil. Mag. 77, 405 (1973).
14. G. Fubini, Su un teorema di confronto per le equazioni del secondo ordine alle derivate ordinarie. Ann. R. Scuola Norm. Sup. Pisa II (1933). Reprinted in Opere Scelte, Vol. III. Cremonese, pp. 212-213. Roma (1962).
15. G. Fubini, Su un teorema di confronto per le equazioni del secondo ordine alle derivate ordinarie. Ann. R. Scuola Norm. Sup. Pisa II (1933). Reprinted in Opere Scelte, Vol. III. Cremonese, pp. 212-213. Roma (1962).
16. P. Biscari. G Capriz and E. G. Virga, On surface biaxiality. Liquid Crystals 16, 479 (1994).
17. P. Biscari, G. Capriz and E. G. Virga, Biaxial nematic liquid crystals. In Boundary-Value Problems for Partial Differential Equations and Applications (edited by C. Baiocchi and J. L. Lions), pp. 313-318. Masson, Paris, (1993).
18. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Corrected and enlarged edition. Academic Press, New York (1980).