Towards a classification of Euler-Kirchhoff filaments

Journal of Mathematical Physics

Volumn 40, Issue 6, 1999, Pages 2830-2866

  Nizette, Michel ^a   Goriely, Alain ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF ARIZONA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033242309     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532731     Document Type: Article

References (41)

1. J. Coyne, "Analysis of the formation and elimination of loops in twisted cable," IEEE J. Ocean Eng. 15, 72-83 (1990).
2. Z. Tan and J. A. Witz, Loop Formation of Marine Cables and Umbilicals during Installation, edited by M. H. Patel and R. Gibbins (BBP Technical Services, London, 1992), Vol. 92, pp. 1270-1285.
3. E. E. Zajac, "Stability of two loop elasticas," Trans. ASME (March), 136-142 (1962).
4. M. D. Barkley and B. H. Zimm, "Theory of twisting and bending of chain macromolecules: Analysis of the fluorescence depolarization of DNA," J. Chem. Phys. 70, 2991-3006 (1979).
5. R. E. Goldstein and S. A. Langer, "Nonlinear dynamics of stiff polymers," Phys. Rev. Lett. 75, 1094-1097 (1995).
6. W. Helfrich, "Elastic theory of helical fibers," Langmuir 7, 567-568 (1991).
7. J. V. Selinger, F. C. MacKintosh, and J. M. Schnur, "Theory of cylindrical tubules and helical ribbons of chiral lipid membranes," Phys. Rev. E 53, 3804-3818 (1996).
8. W. R. Bauer, R. A. Lund, and J. H. White, "Twist and writhe of a DNA loop containing intrinsic bends," Proc. Natl. Acad. Sci. USA 90, 833-837 (1993).
9. D. Bensimon, A. J. Simon, V. Croquette, and A. Bensimon, "Stretching DNA with a receding meniscus: Experiments and models," Phys. Rev. Lett. 74, 4754-4757 (1995).
10. Ph. Cluzel, A. Lebrun, Ch. Heller, R. Lavery, J.-L. Viovy, D. Chatenay, and F. Caron, "DNA: An extensible molecule," Science 271, 792-794 (1996).
11. N. G. Hunt and J. E. Hearst, "Elastic model of DNA supercoiling in the infinite length limit," J. Chem. Phys. 12, 9329-9336 (1991).
12. T. Schlick and W. K. Olson, "Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA," Science 257, 1110-1114 (1992).
13. S. B. Smith, Y. Cui, and C. Bustamante, "Overstretching B-DNA: The elastic response of individual double-stranded and single-stranded DNA molecules," Science 271, 795-799 (1996).
14. T. R. Strick, J.-F. Allemand, D. Bensimon, and V. Croquette, "The elasticity of a single supercoiled DNA molecule," Science 271, 1835-1837 (1996).
15. Y. Yang, I. Tobias, and W. K. Olson, "Finite element analysis of DNA supercoiling," J. Chem. Phys. 98, 1673-1686 (1993).
16. A. Goriely and M. Tabor, Nonlinear dynamics of filaments, nonlinear dynamics (to be published).
17. N. H. Mendelson, "Bacterial microfibers: The morphogenesis of complex multicellular bacterial forms," Sci. Prog. 74, 425-441 (1990).
18. J. J. Thwaites and N. H. Mendelson, "Mechanical behavior of bacterial cell walls," Adv. Microbial. Physiol. 32, 174-222 (1991).
19. R. L. Ricca and M. A. Berger, "Topological ideas and fluid mechanics," Phys. Today (12), 28-34 (1996).
20. J. J. Tyson and S. H. Strogatz, "The differential geometry of scroll waves," Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 723-744 (1991).
21. J. P. Keener, "Knotted vortex filament in an ideal fluid," J. Fluid Mech. 211, 629-651 (1990).
22. S. Da Silva and A. R. Chouduri, "A theoretical model for tilts of bipolar magnetic regions," Astron. Astrophys. 272, 621 (1993).
23. H. C. Spruit, "Motion of magnetic flux tubes in the solar convection zone and chromosphere," Astron. Astrophys. 98, 155 (1981).
24. G. Kirchhoff, "Über das gleichgewicht und die bewegung eines unendlich dünnen elastischen stabes," J. Reine Anglew. Math. 56, 285-313 (1859).
25. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th ed. (Dover, New York, 1944).
26. S. S. Antman, A Nonlinear Problems of Elasticity (Springer, Berlin, 1995).
27. A. Goriely and M. Tabor, "Nonlinear dynamics of filaments III: Instabilities of helical rods," Proc. R. Soc. London, Ser. A 453, 2583-2601 (1997).
28. A. Goriely and M. Tabor, "Nonlinear dynamics of filaments I: Dynamical instabilities," Physica D 105, 20-24 (1997).
29. A. Goriely and M. Tabor, "Nonlinear dynamics of filaments IV: Spontaneous looping of elastic rods," Proc. R. Soc. London, Ser. A 454, 3183-3202 (1998).
30. R. L. Ricca, "The energy spectrum of a twisted flexible string under elastic relaxation," J. Phys. A 28, 2335-2352 (1995).
31. C, J. Benham, "An elastic model of the large-scale structure of duplex DNA," Biopolymers 18, 609-623 (1979).
32. S. Kehrbaum and J. H. Maddocks, "Elastic rods, rigid bodies, quaternions, and the last quadrature," Philos. Trans. 355, 2117-2136 (1997).
33. G. Domokos, "A group-theoretic approach to the geometry of elastic rings," J. Nonlinear Sci. 5, 453-478 (1995).
34. Y. Shi and J. E. Hearst, "The Kirchhoff elastic rod, the nonlinear Schrödinger equation and DNA supercoiling," J. Chem. Phys. 101, 5186-5200 (1994).
35. B. D. Coleman, E. H. Dill, M. Lembo, Z. Lu, and I. Tobias, "On the dynamics of rods in the theory of Kirchoff and Clebsch," Arch. Ration. Mech. Anal. 121, 339-359 (1993).
36. J. L. Lagrange, Mécanique Analytique (Chez la Veuve Desaint, Paris, 1788).
37. W. D. MacMillan, Dynamics of Rigid Bodies (McGraw-Hill, New York, 1936).
38. E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4th ed. (Cambridge University Press, London, 1965).
39. A. Goriely, M. Nizette, and M. Tabor, "Nonlinear dynamics of strips" (preprint, 1999).
40. C. J. Benham, "Theoretical analysis of conformational equilibria in superhelical DNA," Annu. Rev. Biophys. Chem. 14, 23-45 (1985).
41. W. F. Pohl, "DNA and differential geometry," Math. Intelligencer 3, 20-27 (1980).