Ericksen's bar and modeling of the smectic a-nematic phase transition

SIAM Journal on Applied Mathematics

Volumn 60, Issue 3, 2000, Pages 1073-1098

  Calderer, M Carme ^a   Palffy Muhoray, Peter ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b KENT STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DISLOCATIONS (CRYSTALS); ELASTICITY; FREE ENERGY; NEMATIC LIQUID CRYSTALS; NUCLEATION; PHASE TRANSITIONS; PLATES (STRUCTURAL COMPONENTS); SMECTIC LIQUID CRYSTALS; SUPERCONDUCTIVITY;

FREE ENERGY DENSITY FUNCTION; GINZBURG-LANDAU MODEL; NEMATIC DEFECTS; NONLINEAR ELASTIC BAR;

MATHEMATICAL MODELS;

EID: 0033723884     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139997327563     Document Type: Article

References (21)

1. F. BETHUEL, H. BREZIS, AND J.M. HELEIN, Ginzburg-Landau Vortices, Birkhauser, Boston, 1994.
2. M.C. CALDERER, C. LIU, AND K. VOSS, Radial configurations of smectic A materials and focal conics, Phys. D, 124 (1997), pp. 11-22.
3. S. CHANDRASEKHAR, Liquid Crystals, 2nd ed., Cambridge University Press, Cambridge, 1992.
4. N.A. CLARK AND R.B. MEYER, Strain-induced instability of monodomain smectic A and cholesteric, Appl. Phys. Lett., 22 (1973), pp. 493-499.
5. J.L. ERICKSEN, Equilibrium of bars, J. Elasticity, 5 (1975), pp. 191-202.
6. P.G. DE GENNES, An analogy between superconductors and smectics A, Solid State Commun., 10 (1972), pp. 753-756.
7. P.G. DE GENNES AND J. PROST, The Physics of Liquid Crystals, 2nd ed., Oxford University Press, London, 1993.
8. C.J. GARCIA-CERVERA AND E WEINAN, Dupin Cyclades, NYU, New York, 1996, preprint.
9. W. HELFRICH, Bending instabilities of smectic A layer structures, Phys. Rev. Lett., 23 (1969). pp. 372-334.
10. D. KINDERLEHRER AND C. LIU, Revisiting the focal conic structures in smectic A, in Proceedings of the Symposium on Elasticity to honor Professor J.L. Ericksen, Contemporary Research in the Mechanics and Mathematics of Materials, CIMNE, Barcelona, 1996, pp. 217-225.
11. S. KRALJ AND T.J. SLUCKIN, Landau-de Gennes theory of the chevron structure in a smectic-A liquid crystal, Phys. Rev. E, 50 (1969), pp. 2940-2951.
12. L. LIMAT AND J. PROST, A model for the chevron structure obtained by cooling a smectic-A liquid crystal in a cell of finite thickness, Liquid Crystals, 13 (1993), pp. 101-113.
13. T.C. LUBENSKY, The nematic to smectic-A transition: A theoretical overview, Journal de Chimie Physique, 80 (1983), pp. 31-43.
14. T.C. LUBENSKY AND J.H. CHEN, Landau-Ginzburg mean-field theory for the nematic to smectic-C and nematic to smectic-A phase transitions, Phys. Rev. A, 14 (1976), pp. 1202-1207.
15. T.C. LUBENSKY AND S.R. RENN, Abrikosov dislocation in a model of the cholesteric-to-smectic-A transition, Phys. Rev. A, 38 (1988), pp. 2132-2147.
16. T.C. LUBENSKY AND S.R. RENN, Twist-grain-boundary phases near the nematic-smectic A-smectic-C point in liquid crystals, Phys. Rev. A, 41 (1990), pp. 4392-4401.
17. D. NELSON AND J.V. SELIGER, Theory of hexatic-to-hexatic transitions, Phys. Rev. Lett., 61 (1988), pp. 416-419.
18. D. NELSON AND J. TONER, Bond-orientational order, dislocation loops, and melting of solids and smectic-A liquid crystals, Phys. Rev. B, 24 (1981), pp. 363-387.
19. M. RENARDY AND R.C. ROGERS, An Introduction to Partial Differential Equations, Springer-Verlag, New York, 1993.
20. L. TRUSKINOVSKY AND G. ZANZOTTO, Ericksen's bar revisited: Energy wiggles, J. Mech. Phys. Solids, 44 (1996), pp. 1371-1408.
21. E. VIRGA, Variational Theories of Liquid Crystals, Chapman and Hall, London, 1994.