Geometric Constant Defining Shape Transitions of Carbon Nanotubes under Pressure

Physical Review Letters

Volumn 92, Issue 10, 2004, Pages

  Zang, Ji ^a   Treibergs, Andrejs ^b   Han, Y ^a   Liu, Feng ^a  

^a UNIVERSITY OF UTAH   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ELECTROMECHANICAL DEVICES; HYDROSTATIC PRESSURE; LAGRANGE MULTIPLIERS; MOLECULAR DYNAMICS; PHASE TRANSITIONS; PRESSURE EFFECTS; THEOREM PROVING; VAN DER WAALS FORCES; VARIATIONAL TECHNIQUES;

GEOMETRIC CONSTANTS; MECHANICAL LOADINGS; SHAPE TRANSITIONS; VERTEX THEOREM;

CARBON NANOTUBES;

EID: 2142754514     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.92.105501     Document Type: Article

References (23)

1. P. Beckmann, A History of π (St Martin's Press, New York, 1971).
2. For a review of geometry of carbon nanotubes, see M. S. Dresselhaus, G. Dresselhaus, and R. Saito, Carbon 33, 883 (1995).
3. U. D. Venkateswaran et al., Phys. Rev. B 59, 10928 (1999).
4. J. Tang et al., Phys. Rev. Lett. 85, 1887 (2000); M. J. Lopez et al., Ibid. 86, 3056 (2001).
5. J. Tang et al., Phys. Rev. Lett. 85, 1887 (2000); M. J. Lopez et al., Ibid. 86, 3056 (2001).
6. M. J. Peters et al., Phys. Rev. B 61, 5939 (2000).
7. S. M. Sharma et al., Phys. Rev. B 63, 205417 (2001).
8. S. Rols, Phys. Rev. B 64, 153401 (2001).
9. S. Reich, C. Thomsen, and P. Ordejón, Phys. Rev. B 65, 153407 (2002).
10. J. Sandler et al., Phys. Rev. B 67, 035417 (2003).
11. T. W. Tombler et al., Nature (London) 405, 769 (2000).
12. J.-Q. Lu et al., Phys. Rev. Lett. 90, 156601 (2003).
13. J. Wu, J. Zang, B. Larade, H. Guo, X. G. Gong, and Feng Liu (to be published).
14. D. Y. Sun and X. G. Gong, J. Phys. Condens. Matter 14, L487 (2002).
15. M. Levy, J. Math. Ser. 3, 7 (1884).
16. G. F. Carrier, J. Math. Phys. 26, 94 (1947).
17. J. Chaskalovic, Z. Angew. Math. Phys. 46, 149 (1995), and references therein.
18. Here, we present only the main idea of solution process. The detailed mathematical derivation will be published elsewhere.
19. M. Do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, NJ, 1976), p. 37.
20. P. Canham, J. Theor. Biol. 26, 61 (1970).
21. H. Deuling and W. Helfisch, Biophys. J. 16, 861 (1976).
22. H. Deuling and W. Helfisch, J. Phys. (France) 37, 1335 (1976).
23. J. Opea, American Mathematical Student Mathematical Library 10, Providence, 147 (2000).