Nonlinear dynamics of filaments I. Dynamical instabilities

Physica D: Nonlinear Phenomena

Volumn 105, Issue 1-3, 1997, Pages 20-44

  Goriely, Alain ^a   Tabor, Michael ^a  

^a UNIVERSITY OF ARIZONA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002803267     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00290-4     Document Type: Article

References (43)

1. E.E. Zajac, Stability of two loop elasticas, Trans. ASME (1962) 136-142.
2. 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 (1979) 2991-3006.
3. C.J. Benham, Theoretical analysis of conformational equilibria in superhelical DNA, Ann. Rev. Biophys. Chem. (1985) 23-45.
4. N.H. Mendelson, Bacterial macrofibers: The morphogenesis of complex multicellular bacterial forms, Sci. Progress Oxford 74 (1990) 425-441.
5. J.J. Thwaites and N.H. Mendelson, Mechanical behavior of bacterial cell walls, Adv. Microbiol. Physiol. 32 (1991) 174-222.
6. N.G. Hunt and J.E Hearst, Elastic model of DNA supercoiling in the infinite length limit, J. Chem. Phys. 12 (1991) 9329-9336.
7. T. Schlick and W.K. Olson, Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA, Science 257 (1992) 1110-1114.
8. Y. Yang, I. Tobias and W.K. Olson, Finite element analysis of DNA supercoiling, J. Chem. Phys. 98 (1993) 1673-1686.
9. W.R. Bauer, R.A. Lund and J.H. White, Twist and writhe of a DNA loop containing intrinsic bends, Proc. Natl. Acad. Sci. 90 (1993) 833-837.
10. Y. Shi and J.E. Hearst, The Kirchhoff elastic rod, the nonlinear Schrödinger equation and DNA supercoiling, J. Chem. Phys. 101 (1994) 5186-5200.
11. J.P. Keener, Knotted vortex filament in an ideal fluid, J. Fluid Mech. 211 (1990) 629-651.
12. H.C. Spruit, Motion of magnetic flux tubes in the solar convection zone and chromosphere, Astron. Astrophys. 98 (1981) 155.
13. S. Da Silva and A.R. Chouduri, A theoretical model for tilts of bipolar magnetic regions, Astron. Astrophys. 272 (1993) 621.
14. R.E. Goldstein and S.A. Langer, Nonlinear dynamics of stiff polymers, Phys. Rev. Lett. 75 (1995) 1094.
15. M.J. Shelley and T. Ueda, The nonlocal dynamics of stretching buckling filaments, in: Multi-Fluid Flows and Instabilities (AMS/SIAM, Providence, RI/Pheladelphia, PA, 1996), to appear.
16. G.L. Lamb, Jr., Solitons on moving space curves, J. Math. Phys. 18 (1977) 1654-1661.
17. R.E. Goldstein and D.M. Petrich, The Korteweg-de Vries hierarchy as dynamics of closed curves in the plane, Phys. Rev. Lett. 67 (1991) 3203-3206.
18. J. Langer and R. Perline, Poisson geometry of the filament equation, J. Nonlinear Sci. 1 (1991) 71-93.
19. K. Nakayama, H. Segur and M. Wadati, Integrability and the motion of curves, Phys. Rev. Lett. 69 (1992) 2603-2606.
20. L.H. Kauffman, Knots and Physics (World Scientific, Singapore, 1993).
21. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity (Cambridge University Press, Cambridge, 1892).
22. L.D. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon Press, Oxford, 1959).
23. S.P. Timoshenko and J.M. Gere, Theory of Elastic Stability (McGraw-Hill, New York, 1961).
24. C.J. Benham, An elastic model of the larger structure of duplex DNA, Bioploymers 18 (1979) 609-623.
25. Y. Ichikawa, K. Konno and M. Wadati, Nonlinear transverse oscillation of elastic beams under tension, J. Phys. Soc. Jpn. 50 (1981) 1799-1802.
26. C.J. Benham, Geometry and Mechanics of DNA superhelicity, Biopolymers 22 (1983) 2477-2495.
27. M. Wadati and H. Tsuru, Elastic model of looped DNA, Physica D 21 (1986) 213-226.
28. F. Tanaka and H. Takahashi, Elastic theory of supercoiled DNA, J. Chem. Phys. 11 (1985) 6017-6026.
29. H. Tsuru, Equilibrium shapes and vibrations of thin elastic rod, J. Phys. Soc. Jpn. 56 (1987) 2309-2324.
30. B.D. Coleman and E.H. Dill, Flexure waves in elastic rods, J. Acoust. Soc. Amer. 91 (1992) 2663.
31. E.H. Dill, Kirchhoff's theory of rods, Arch. Hist. Exact. Sci. 44 (1992) 2-23.
32. R.L. Bishop, There is more than one way to frame a curve, Amer. Math. Month. 82 (1975) 246-251.
33. B.D. Coleman, E.H. Dill, M. Lembo, Z. Lu and I. Tobias, On the dynamics of rods in the theory of Kirchhoff and Clebsch, Arch. Rational Mech. Anal. 121 (1993) 339-359.
34. J.H. Maddocks and D.J. Dichmann, Conservation laws in the dynamics of rods, Journal of Elasticity 34 (1994) 83-96.
35. M. Le Bret, Catastrophic variation of twist and writhing of circular DNA with constraint?, Biopolymers 18 (1979) 1709-1725.
36. C.J. Benham, Onset of writhing in circular elastic polymers, Phys. Rev. A 39 (1989) 2582-2586.
37. I. Klapper, Biological applications of the dynamics of twisted elastic rods, J. Comput. Phys. 125 (1996) 325-337.
38. I. Klapper and M. Tabor, Dynamics of twist and writhe and the modeling of bacterial fibers, in: Mathematical Approaches to Bimolecular Structure and Dynamics, eds. J. Mesirov, K. Schuiten and De Witt Summers (Springer, Berlin, 1996) pp. 139-159.
39. D.J. Dichmann, Y. Li and J.H. Maddocks, Hamiltonian formulations and symmetries in rod mechanics, preprint (1995).
40. 3, J. London Math. Soc. 30 (1984) 512-520.
41. J.M.T. Thompson and A.R. Champneys, From helix to localized writhing in the torsional post-buckling of elastic rods, Proc. Roy. Soc. 452 (1996) 117-138.
42. A. Goriely and M. Tabor, Nonlinear dynamics of filaments II: Nonlinear analysis, Physica D 105 (1997) 45.
43. A. Goriely and M. Tabor, New amplitude equations for thin elastic rods, Phys. Rev. Lett. 77 (1996) 3537-3540.