Nonlinear dynamics of filaments

Nonlinear Dynamics

Volumn 21, Issue 1, 2000, Pages 101-133

  Goriely, Alain ^a   Tabor, Michael ^a  

^a The University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUCKLING; ELASTICITY; EQUATIONS OF MOTION; FIBERS; PERTURBATION TECHNIQUES;

KIRCHHOFF EQUATION;

DYNAMICS;

EID: 0033874539     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008366526875     Document Type: Article

References (48)

1. Zajac, E. E., 'Stability of two planar loop elasticas', Transactions of the ASME, March, 1962, 136-142.
2. Coyne, J., 'Analysis of the formation and elimination of loops in twisted cable', IEE Journal of Oceanic Engineering 15, 1990, 72-83.
3. Barkley, M. D. and Zimm, B. H., 'Theory of twisting and bending of chain macromolecules; Analysis of the fluorescence depolorization of DNA', Journal of Chemical Physics 70, 1979, 2991-3006.
4. Benham, C. J., 'Theoretical analysis of conformational equilibria in superhelical DNA', Annual Review of Biophysical Chemistry 14, 1985, 23-45.
5. Mendelson, N. H., 'Bacterial macrofibers: The morphogenesis of complex multicellular bacterial forms', Scientific Progress Oxford 74, 1990, 425-441.
6. Thwaites, J. J. and Mendelson, N. H., 'Mechanical behavior of bacterial cell walls', Advances in Microbiological Physiology 32, 1991, 174-222.
7. Hunt, N. G. and Hearst, J. E., 'Elastic model of DNA supercoiling in the infinite length limit', Journal of Chemical Physics 12, 1991, 9329-9336.
8. Schlick, T. and Olson, W. K., 'Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA', Science 257, 1992, 1110-1114.
9. Yang, Y., Tobias, I., and Olson, W. K., 'Finite element analysis of DNA supercoiling', Journal of Chemical Physics 98, 1993, 1673-1686.
10. Bauer, W. R., Lund, R. A., and White, J. H., 'Twist and writhe of a DNA loop containing intrinsic bends', Proceedings of the National Academy of Science (USA) 90, 1993, 833-837.
11. Shi, Y. and Hearst, J. E., 'The Kirchhoff elastic rod, the nonlinear Schrödinger equation and DNA supercoiling', Journal of Chemical Physics 101, 1994, 5186-5200.
12. Goldstein, R. E. and Langer, S. A., 'Nonlinear dynamics of stiff polymers', Physical Review Letters 75, 1995, 1094.
13. Shelley, M. J. and Ueda, T., 'The nonlocal dynamics of stretching, buckling filaments', in Advances in Multi-Fluid Flows, D. Papageorgiou and Y. Renardi (eds.), SIAM, Philadelphia, PA, 1996, pp. 415-425.
14. Keener, J. P., 'Knotted vortex filament in an ideal fluid', Journal of Fluid Mechanics 211, 1990, 629-651.
15. Spruit, H. C., 'Motion of magnetic flux tubes in the solar convection zone and chromosphere', Astronomy and Astrophysics 98, 1981, 155.
16. Da Silva, S. and Chouduri, A. R., 'A theoretical model for tilts of bipolar magnetic regions', Astronomy and Astrophysics 272, 1993, 621.
17. Thompson, J. M. T. and Champneys, A. R., 'From helix to localized writhing in the torsional post-buckling of elastic rods', Proceedings of Royal Society of London Series A 452, 1996, 117-138.
18. Schlick, T., 'Modeling superhelical DNA: Recent analytical and dynamical approaches', Current Opinions in Structural Biology 5, 1995, 245-262.
19. Dill, E. H., 'Kirchhoff's theory of rods', Archives of the History of Exact Science 44, 1992, 2-23.
20. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, Cambridge, 1892.
21. Landau, L. D. and Lifshitz, E. M., Theory of Elasticity, Pergamon Press, Oxford, 1959.
22. Timoshenko, S. P. and Gere, J. M., Theory of Elastic Stability, McGraw-Hill, New York, 1961.
23. Coleman, B. D. and Dill, E. H., 'Flexure waves in elastic rods', Journal of Acoustical Society of America 91, 1992, 2663.
24. Tanaka, F. and Takahashi, H., 'Elastic theory of supercoiled DNA', Journal of Chemical Physics 11, 1985, 6017-6026.
25. Tsuru, H., 'Equilibrium shapes and vibrations of thin elastic rod', Journal of the Physical Society of Japan 56, 1987, 2309-2324.
26. Maddocks, J. H. and Dichmann, D. J., 'Conservation laws in the dynamics of rods', Journal of Elasticity 34, 1994, 83-96.
27. Klapper, I. and Tabor, M., 'Dynamics of twist and writhe and the modeling of bacterial fibers', Mathematical Approaches to Biomolecular Structure and Dynamics, J. Mesirov, K. Schuiten, and D. W. Summers (eds.), Springer-Verlag, New York, 1996, pp. 139-159.
28. Klapper, I., 'Biological applications of the dynamics of twisted elastic rods', Journal of Computational Physics 125, 1996, 325-337.
29. Goriely, A. and Tabor, M., 'New amplitude equations for thin elastic rods', Physical Review Letters 77, 1996, 3537-3540.
30. Goriely, A. and Tabor, M., 'Nonlinear dynamics of filaments I: Dynamical instabilities', Physica D 105, 1997, 20-44.
31. Goriely, A. and Tabor, M., 'Nonlinear dynamics of filaments II: Nonlinear analysis', Physica D 105, 1997, 45-61.
32. Goriely, A. and Tabor, M., 'Nonlinear dynamics of filaments III: Instabilities of helical rods', Proceedings of the Royal Society of London Series A 453, 1997, 2583-2601.
33. Goriely, A. and Tabor, M., 'Nonlinear dynamics of filaments IV: Spontaneous looping', Proceedings of the Royal Society of London Series A 455, 1998, 3183-3202.
34. Goriely, A., Nizette, M., and Tabor, M., 'On the dynamics of elastic strips', Journal of Nonlinear Science, 1999, submitted.
35. Coleman, B. D., Dill, E. H., Lembo, M., Lu, Z., and Tobias, I., 'On the dynamics of rods in the theory of Kirchhoff and Clebsch', Archives for Rational Mechanics and Analysis 121, 1993, 339-359.
36. Goriely, A., Mendelson, N., and Tabor, M., 'Dynamical buckling of Bacillus subtilis', Preprint, 1998.
37. Goriely, A. and Tabor, M., 'Spontaneous helix-hand reversal and tendril perversion in climbing plants', Physical Review Letters 80, 1998, 1564-1567.
38. Newell, A., Envelope Equations, Lectures in Applied Mathematics, Vol. 15, American Mathematical Society, Providence, RI, 1974.
39. Rogers, K. A., 'Stability exchange in parameter dependent constrained variational principles with applications to elastic rod models os DNA minicircles', University of Maryland, Ph.D. Thesis, 1997.
40. Kehrbaum, S. and Maddocks, J. H., 'Effective properties of elastic rods with high intrinsic twist', Preprint, 1997.
41. Goriely, A. and Lega, J., 'Pulses, fronts and oscillations of an elastic rod', Physica D, 1998, to be published.
42. Weiss, J., Tabor, M. and Carnevale, G., 'The Painlevé property for partial differential equations', Journal of Mathematical Physics 24, 1983, 3.
43. Champneys, A. R., van der Heiden, G. H. M., and Thompson, J. M. T., 'Spatially complex localisation after one-twist-per-wave equilibria in twisted rod circular rods with initial curvature', Philosophical Transactions of the Royal Society of London Series A 355, 1988, 2151-2174.
44. Darwin, Ch., The Movements and Habits of Climbing Plants, Appleton, New York, 1888.
45. Hearle, J. W. S., Thwaites, J. J., and Amirbayat, J. (eds.), Mechanics of Flexible Fibre Assemblies, Sijthoff & Noordhoff, Germantown, 1980.
46. Tilby, M. J., 'Helical shape and wall synthesis in bacterium', Nature 266, 1977, 450-452.
47. Galloway, J. W., 'Macromolecular asymmetry', in Biological Asymmetry and Handedness, G. R. Bock and J. Marsh (eds.), Wiley-Interscience, New York, 1991, pp. 16-35.
48. Goldstein, R. E., Powers, T. R., and Wiggins, C. H., 'Viscous nonlinear dynamics of twist and writhe', Physical Review Letters 80, 1998, 5232-5235.