Asymptotic Director Fields of Moving Defects in Nematic Liquid Crystals

Paolo Biscari; Stefano Turzi

Bollettino dell'Unione Matematica Italiana (2012)

  • Volume: 5, Issue: 1, page 81-91
  • ISSN: 0392-4041

Abstract

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This paper deals with the detailed structure of the order-parameter field both close and far from a moving singularity in nematic liquid crystals. We put forward asymptotic expansions that allow to extract from the exact solution the necessary analytical details, at any prescribed order. We also present a simple uniform approximation, which captures the qualitative features of the exact solution in all the domain. This paper is dedicated to the memory of Carlo Cercignani, a master who will be never praised enough for both his scientific achievements and the way he taught how research is to be conducted.

How to cite

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Biscari, Paolo, and Turzi, Stefano. "Asymptotic Director Fields of Moving Defects in Nematic Liquid Crystals." Bollettino dell'Unione Matematica Italiana 5.1 (2012): 81-91. <http://eudml.org/doc/290965>.

@article{Biscari2012,
abstract = {This paper deals with the detailed structure of the order-parameter field both close and far from a moving singularity in nematic liquid crystals. We put forward asymptotic expansions that allow to extract from the exact solution the necessary analytical details, at any prescribed order. We also present a simple uniform approximation, which captures the qualitative features of the exact solution in all the domain. This paper is dedicated to the memory of Carlo Cercignani, a master who will be never praised enough for both his scientific achievements and the way he taught how research is to be conducted.},
author = {Biscari, Paolo, Turzi, Stefano},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {81-91},
publisher = {Unione Matematica Italiana},
title = {Asymptotic Director Fields of Moving Defects in Nematic Liquid Crystals},
url = {http://eudml.org/doc/290965},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Biscari, Paolo
AU - Turzi, Stefano
TI - Asymptotic Director Fields of Moving Defects in Nematic Liquid Crystals
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/2//
PB - Unione Matematica Italiana
VL - 5
IS - 1
SP - 81
EP - 91
AB - This paper deals with the detailed structure of the order-parameter field both close and far from a moving singularity in nematic liquid crystals. We put forward asymptotic expansions that allow to extract from the exact solution the necessary analytical details, at any prescribed order. We also present a simple uniform approximation, which captures the qualitative features of the exact solution in all the domain. This paper is dedicated to the memory of Carlo Cercignani, a master who will be never praised enough for both his scientific achievements and the way he taught how research is to be conducted.
LA - eng
UR - http://eudml.org/doc/290965
ER -

References

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  1. MERMIN, N. D., The topological theory of defects in ordered media, Rev. Mod. Phys., 51 (1979), 591-648. MR541885DOI10.1103/RevModPhys.51.591
  2. KLÉMAN, M., Defects in liquid crystals, Rep. Prog. Phys., 52 (1989), 555-654. MR1000548
  3. BISCARI, P. - GUIDONE-PEROLI, G., A hierarchy of defects in biaxial nematics, Commun. Math. Phys., 186 (1997), 381-392. Zbl0880.76006MR1462769DOI10.1007/s002200050113
  4. GUIDONE-PEROLI, G. - VIRGA, E. G., Annihilation of point defects in nematic liquid crystals, Phys. Rev. E, 54 (1996), 5235-5241. MR1601519DOI10.1016/S0167-2789(97)80021-8
  5. BISCARI, P. - GUIDONE-PEROLI, G. - VIRGA, E. G., A statistical study for evolving arrays of nematic point defects, Liquid Crystals, 26 (1999), 1825-1832. MR1601519DOI10.1016/S0167-2789(97)80021-8
  6. GUIDONE-PEROLI, G. - VIRGA, E. G., Nucleation of topological dipoles in nematic liquid crystals, Commun. Math. Phys., 200 (1999), 195-210. Zbl0917.76005MR1671924DOI10.1007/s002200050527
  7. RYSKIN, G. - KREMENETSKY, M., Drag force on a line defect moving through an otherwise undisturbed field: Disclination line in a nematic liquid crystal, Phys. Rev. Lett., 67 (1991), 1574-1577. 
  8. KATS, E. I. - LEBEDEV, V. V. - MALININ, S. V., Disclination motion in liquid crystalline films, J. Exp. Theor. Phys., 95 (2002), 714-727. 
  9. BISCARI, P. - SLUCKIN, T. J., Field-induced motion of nematic disclinations, SIAM J. Appl. Math., 65 (2005), 2141-2157. Zbl1086.76002MR2177743DOI10.1137/040618898
  10. SVENŠEK, D. - ŽUMER, S., Hydrodynamics of pair-annihilating disclination lines in nematic liquid crystals, Phys. Rev. E, 66 (2002), 021712. 
  11. BLANC, C. - SVENŠEK, D. - ŽUMER, S. - NOBILI, M., Dynamics of nematic liquid crystal disclinations: The role of the backflow, Phys. Rev. Lett., 95 (2005), 097802. 
  12. BISCARI, P. - SLUCKIN, T. J., A perturbative approach to the backflow dynamics of nematic defects, Euro. J. Appl. Math.23 (2012), 181-200. Zbl1235.76009MR2873031DOI10.1017/S0956792510000343
  13. BISCARI, P. - GUIDONE-PEROLI, G. - SLUCKIN, T. J., The topological microstructure of defects in nematic liquid crystals, Mol. Cryst. Liq. Cryst., 292 (1997), 91-101. 
  14. BENDER, C. - ORSZAG, S., Advanced Mathematical Methods for Scientists and Engineers, Springer-Verlag, New York (1999). Zbl0938.34001MR538168
  15. BREZIS, H. - CORON, J. M. - LIEB, E., Harmonic maps with defects, Comm. Math. Phys., 107 (1986), 649-705. Zbl0608.58016MR868739
  16. ABRAMOWITZ, M. - STEGUN, I., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications (1965). MR1225604

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