Anomalous coupling between topological defects and curvature

Physical Review Letters

Volumn 93, Issue 21, 2004, Pages

  Vitelli, Vincenzo ^a   Turner, Ari M ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOND ANGLE; CRYSTALLINE PHASE; GAUSSIAN CURVATURE; TOPOLOGICAL DEFECTS;

CHEMICAL BONDS; DEFECTS; DEGREES OF FREEDOM (MECHANICS); ELASTIC MODULI; FREE ENERGY; LIQUID CRYSTALS; MATHEMATICAL MODELS; POISSON EQUATION; SUPERCONDUCTING MATERIALS; SURFACE TREATMENT; TOPOLOGY; VECTORS;

SUPERFLUID HELIUM;

ARTICLE; SURFACE PROPERTY; THEORETICAL MODEL; VIRAL PHENOMENA AND FUNCTIONS;

MODELS, THEORETICAL; SURFACE PROPERTIES; VIRAL PHYSIOLOGY;

EID: 42749105028     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.93.215301     Document Type: Article

References (25)

1. R. D. Kamien, Science 299, 1671 (2003).
2. D. R. Nelson, Nano Lett. 2, 1125 (2002).
3. A. R. Bausch et al., Science 299, 1716 (2003).
4. D. Caspar and A. Klug, Principles in the Construction of Regular Viruses, Cold Spring Harbor Symposium on Quantitative Biology, (Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, 1962), Vol. 27, p. 1.
5. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993), pp. 98-108.
6. D. R. Nelson and R. A. Pelcovits, Phys. Rev. B 16, 2191 (1977).
7. D. R. Nelson and J. M. Kosterlitz, Phys. Rev. Lett. 39, 1201 (1977).
8. F. David, in Statistical Mechanics of Membranes and Surfaces, edited by D. R. Nelson et al. (World Scientific, Singapore, 2004).
9. D.R. Nelson and L. Peliti, J. Physique 48, 1085 (1987).
10. M. Bowick, D. R. Nelson, and A. Travesset, Phys. Rev. B 62, 8738 (2000); Phys. Rev. E 69, 041102 (2004).
11. M. Bowick, D. R. Nelson, and A. Travesset, Phys. Rev. B 62, 8738 (2000); Phys. Rev. E 69, 041102 (2004).
12. V. Vitelli and D.R. Nelson, cond-mat/0406328 [Phys. Rev. E (to be published)].
13. We assume that a is much smaller than the radius of curvature and hence independent of the defect position.
14. A. M. Polyakov, Phys. Lett. B 103, 207 (1981).
15. j) is given by the Green's function of the covariant Laplacian that is not translationally invariant and depends on the shape of the surface [11].
16. This identification is possible only for deformed planes. The details of the analysis valid for deformed spheres and tori will be presented elsewhere.
17. Additional couplings resulting from other terms in a Landau expansion introduce negligible corrections inversely proportional to the area of the surface.
18. J. M. Park and T.C. Lubensky, Phys. Rev. E 53, 2648 (1996) and references therein.
19. The symmetry around q = 2π is reflected in the pattern of field lines around a defect. There are |q-2π/π| lobes.
20. B.I. Halperin (private communication).
21. The sum of the defects' charges on a surface of genus γ is equal to 4π(1-γ) for a vector field and to 0 for a scalar [8].
22. T.C. Lubensky and J. Prost, J. Phys. II 2, 371 (1992).
23. αβ [11].
24. D. R. Nelson (private communication).
25. E. J. Yarmchuk and R. E. Packard, J. Low Temp. Phys. 46, 4790 (1982).