Minimal resonances in annular non-Euclidean strips

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 5, 2010, Pages

  Chen, Bryan Gin Ge ^a   Santangelo, Christian D ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEAD-SPRING MODELS; BENDING ENERGIES; BIOLOGICAL TISSUES; DIFFERENTIAL GROWTHS; ELASTIC STRIPS; METRIC TENSOR; MINIMAL ENERGY; NON-EUCLIDEAN; NUMERICAL CALCULATION; RESONANCE CONDITION; STRIP SHAPE;

RESONANCE;

EID: 78651295146     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.056601     Document Type: Article

References (29)

1. D. Drasdo, Phys. Rev. Lett. 84, 4244 (2000). 10.1103/PhysRevLett.84.4244
2. H. Liang and L. Mahadevan, Proc. Natl. Acad. Sci. U.S.A. 106, 22049 (2009). 10.1073/pnas.0911954106
3. M. Marder, Found. Phys. 33, 1743 (2003). 10.1023/A:1026229605010
4. E. Sharon, B. Roman, and H. L. Swinney, Phys. Rev. E 75, 046211 (2007). 10.1103/PhysRevE.75.046211 (Pubitemid 46652829)
5. U. Nath, B. C. W. Crawford, R. Carpenter, and E. Coen, Science 299, 1404 (2003). 10.1126/science.1079354 (Pubitemid 36254655)
6. A. Goriely and M. Ben Amar, Phys. Rev. Lett. 94, 198103 (2005). 10.1103/PhysRevLett.94.198103 (Pubitemid 41493013)
7. E. Sharon, B. Roman, M. Marder, G. S. Shin, and H. L. Swinney, Nature (London) 419, 579 (2002). 10.1038/419579a
8. T. Mora and A. Boudaoud, Eur. Phys. J. E 20, 119 (2006). 10.1140/epje/i2005-10124-5 (Pubitemid 43996760)
9. Y. Klein, E. Efrati, and E. Sharon, Science 315, 1116 (2007). 10.1126/science.1135994 (Pubitemid 46328020)
10. L. D. Landau and E. M. Lifschitz, Theory of Elasticity, 3rd ed. (Pergamon, London, 1959).
11. J. Dervaux and M. Ben Amar, Phys. Rev. Lett. 101, 068101 (2008). 10.1103/PhysRevLett.101.068101
12. S. Nechaev and R. Voituriez, J. Phys. A 34, 11069 (2001). 10.1088/0305-4470/34/49/322 (Pubitemid 33577312)
13. B. Audoly and A. Boudaoud, C. R. Mec. 330, 831 (2002). 10.1016/S1631-0721(02)01545-0 (Pubitemid 36077181)
14. B. Audoly and A. Boudaoud, Phys. Rev. Lett. 91, 086105 (2003). 10.1103/PhysRevLett.91.086105
15. M. Marder, E. Sharon, S. Smith, and B. Roman, EPL 62, 498 (2003). 10.1209/epl/i2003-00334-5 (Pubitemid 36630143)
16. M. Marder and N. Papaniolaou, J. Stat. Phys. 125, 1065 (2006). 10.1007/s10955-006-9087-x
17. E. Efrati, E. Sharon, and R. Kupferman, J. Mech. Phys. Solids 57, 762 (2009). 10.1016/j.jmps.2008.12.004
18. C. D. Santangelo, EPL 86, 34003 (2009). 10.1209/0295-5075/86/34003
19. Q. Han and J.-X. Hong, Isometric Embedding of Riemannian Manifolds in Euclidean Spaces, Mathematical Surveys and Monographs (American Mathematical Society, Providence, RI, 2006), Vol. 130.
20. E. G. Poznyak and E. V. Shikin, J. Math. Sci. 74, 1078 (1995). 10.1007/BF02362833
21. J. Gemmer and S. Venkataramani, e-print arXiv:1005.4442.
22. B. G. Chen and C. D. Santangelo (unpublished).
23. P. G. Ciarlet, J. Elast. 78-79, 1 (2005). 10.1007/s10659-005-4738-8 (Pubitemid 43014128)
24. M. P. Do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, NJ, 1976).
25. D. J. Struick, Lectures on Classical Differential Geometry, 2nd ed. (Addison-Wesley, Reading, Mass, 1961).
26. E. Efrati, E. Sharon, and R. Kupferman, private communication.
27. M. Sadowsky, Sitzungsber. K. Preuss. Akad. Wiss. 22, 412 (1930).
28. M. Marder, R. D. Deegan, and E. Sharon, Phys. Today 60 (2), 33 (2007). 10.1063/1.2711634
29. E. Sharon, private communication.