Hidden symmetry of global solutions in twisted elastic rings

Journal of Nonlinear Science

Volumn 11, Issue 1, 2001, Pages 47-67

  Domokos, G ^a,b   Healey, T ^b  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042872746     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003320010008     Document Type: Article

References (24)

1. E. L. Allgower and K. Georg. Numerical Continuation Methods: An Introduction. Springer-Verlag, Berlin, 1990.
2. S. S. Antman. Nonlinear Problems of Elasticity. Springer-Verlag, New York, 1995.
3. B. D. Coleman, D. Swigon, and I. Tobias. Elastic stability of DNA configurations: II. Supercoiled plasmids with self-contact. Phys. Rev. E, 61:759-770, 2000.
4. B. D. Coleman and D. Tobias, and I. Swigon. Theory of the influence of end conditions on self-contact in DNA loops. J. Chem. Phys, 103:9101-9109, 1995.
5. E. Doedel, H. B. Keller, and J. P. Kernevez. Numerical analysis and control of bifurcation problems (I) Bifurcation in finite dimensions. Int. J. Bifurcation Chaos, 1(3):493-520, 1991.
6. G. Domokos. Global description of elastic bars. Z. Angew. Math. Mech., 74(4):T289-T291, 1994.
7. G. Domokos. A group-theoretic approach to the geometry of elastic rings. J. Nonlin. Sci., 5:453-478, 1995.
8. G. Domokos and Zs. Gáspár. A global, direct algorithm for path-following and active static control of elastic bar structures, Int J. Structures Machines, 23 (4):549-571, 1995.
9. G. Domokos and P. Holmes. Euler's problem and Euler's method, or the discrete charm of buckling. J. Nonlin. Sci., 3:109-151, 1993.
10. G. Domokos and R. Paffenroth. A case study on visualization tool for boundary value problems. In IEEE Computer Society Visualization '94 Conference Proceedings, pages 345-350. IEEE Comp. Soc. Press, 1995.
11. Zs. Gáspár. The form of an ideally elastic bar with a space curve axis. Acta Technica Hung. Acad. Sci., 84:293-306, 1977.
12. Zs. Gáspár. Large deflection analysis of bar structures. Acta Technica Hung. Acad. Sci., 87:49-58, 1978.
13. Zs. Gáspár. An exact analysis of elastic bar-structures. Z. Angew. Math. Mech., 59:T179-T180, 1979.
14. Zs. Gáspár, G. Domokos, and I. Szeberényi. A parallel algorithm for the global computation of elastic bar structures. Comp. Assist. Mech. Eng. Sci., 4:55-68, 1997.
15. B. Gidas, W. N. Ni, and L. Nirenberg. Symmetry and related properties via the maximum principle. Comm. Math. Phys., 68:209-243, 1979.
16. M. Golubitsky, I. Stewart, and D. G. Schaeffer. Singularities and Groups in Bifurcation Theory, Vol II. Springer-Verlag, New York, 1988.
17. Y. Li and J. Maddocks. On the computation of equilibria of elastic rods, Part i: Integrals, symmetry and a Hamiltonian formulation. J. Comput. Phys., Submitted.
18. E. Riks. An incremental approach to the solution of snapping and buckling problems. Int. J. Solids Structures, 15:529-551, 1979.
19. Y. Shi and J. E. Hearst. The Kirchhoff elastic rod, the nonlinear Schrodinger equation, and DNA supercoiling. J. Chem. Phys., 101:5186-5200, 1994.
20. D. Swigon. Doctoral Dissertation, Rutgers University, 1999.
21. D. Swigon, B. D. Coleman, and I. Tobias. The elastic rod model for DNA and its application to tertiary structure of DNA minicircles in mononucleosomes. Biophys. J., 74:2515-2530, 1998.
22. I. Tobias, B. D. Coleman, and W. Olson. The dependence of DNA tertiary structure on end conditions: Theory and implications for topological transitions. J. Chem. Phys, 101:10990-10996, 1994.
23. I. Tobias. D. Swigon, and B. D Coleman. Elastic stability of DNA configurations: I. General theory. Phys. Rev. E, 61:747-758, 2000.
24. J. C. Wohlever and T. J. Healey. A group-theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell. Comp. Meth. Appl. Mech. Eng., 122:315-349, 1995.