Abstract
The interplay between two possibly incommensurate lengths can lead to complex spatial patterns. A series of experimets by Lowe and Gollub (1,2) on nematic liquid crystal convection cells with spatially periodic forcing fields provide visual images of a number of such patterns. This paper will use the Lowe-Gollub experiments to discuss general aspects of spatial structure in systems with competing incommensurate lengths. Particular applications to polar liquid crystals (3,4) and icosahedral quasi-crystals (5,6) will be considered. Spatial structure in these systems is microscopic (on a scale of tens of Angstroms) rather than macroscopic (on a scale of hundreds of microns) as in the Lowe-Gollub experiments. Nevertheless, the general mechanisms for pattern formation to be discussed in this paper apply to both cases.
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References
Lowe M., Gollub J. and Lubensky T.C. : Phys. Rev. Lett. 51, 786, 1983.
Lowe M. and Gollub J.P. : Phys. Rev. A31, 3893, 1985; Lowe M. and Gollub J.P. : (submitted to J. Fluid Mech.).
Hardouin F., Levelut A.M., Archard M.F. and Sigaud G. : J. Chim. Phys. 80, 53, 1983.
Prost J. and Barois P. : J. Chim. Phys., 80, 65, 1983.
Shechtman D., Blech I., Gratias D. and Cahn J.W. : Phys. Rev. Lett. 53, 1951, 1984.
Levine D.I. and Steinhardt P.J. : Phys. Rev. Lett. 53, 2477, 1984.
Dubois-Violette E., Durand G., Guyon E., Manneville P. and Pieranski P. : in Liquid Crystals, Solid State Phys. Suppl. No. 14, edited by Liebert L., p.147 (Academic, New York, 1978)4. Hardouin F., Levelut A.M., Archard M.F. and Sigaud G. : J. Chim. Phys. 80, 53, 1983.
Ratna B.R., Shashidahr R. and Raja N.J. : Phys. Rev. Lett. 55, 1476, 1985.
Levine D., Lubensky T.C., Ostlund S., Ramaswamy S., Steinhardt P.J. and Toner J. : Phys. Rev. Lett. 54, 1524, 1985.
Mermin N.C. and Troian S. : Phys. Rev. Lett. 54, 1524, 1985.
Bak P. : Phys. Rev. Lett. 54:, 1517, 1985.
Frenkel Y.I. and Kontorowa T. : Zh. Eksp. Teor. Fiz. 8, 1340, 1938.
Frank F.C. and Van der Merwe J.H. : Proc. R. Soc. Lond. A198, 205, 1949.
Bak P. : Rep. Prog. Phys. 45, 587, 1982.
Pokrovsky V.L. and Talapov A.L. : Theory of Incommensurate Crystals, Soviet Science Reviews (Switzerland: Harwood Academic Pub. 1985).
Aubry S. : in Solitons and Condensed Matter Physics, edited by Bishop A. and Schneider T. (Springer, Berlin, 1978), p. 264; Physica D 7, 240, 1983; J. Phys. C 16, 2497, 1983.
Swift J. and Hohenberg P.C. : Phys. Rev. A15, 319, 1977.
Cross M.C. : Phys. Rev. A27, 490, 1983.
Socolar J., Lubensky T.C. and Steinhardt P.J. (Submitted to Phys. Rev.).
Lubensky T.C., Socolar J., Steinhardt P.J., Bancel P. and Heiney P. (Submitted to Phys. Rev. Lett.)
Hiraga K., Hirabayashi M., Inoue A. and Masumoto T. : Sci. Rep. RITU. A-Vol. 32, n°2, 309, 1985.
Penrose R. : Bull. Inst. Math, and Its Appl. 10, 266, 1974.
Gardner M., Sci. Am. 236, 110, 1977.
Dov Levine and Steinhardt P.J., to be published in Phys. Rev. B; Socolar Josh and Steinhardt P.J., to be published in Phys. Rev. B.
Coullet P. : Phys. Rev. Lett. 56, 724, 1986.
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© 1987 Martinus Nijhoff Publishers, Dordrecht
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Lubensky, T.C., Ingersent, K. (1987). Patterns in Systems with Competing Incommensurate Lengths. In: Walgraef, D. (eds) Patterns, Defects and Microstructures in Nonequilibrium Systems. NATO ASI Series, vol 121. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3559-4_4
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DOI: https://doi.org/10.1007/978-94-009-3559-4_4
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