| 摘要(英) |
Motivated by the rare studies of the dynamical problems and the common characteristic in biophysics: twirling filaments, which includes the diverse bacterial filaments
motion. We consider a simple dynamical system which one end is clamped to a motor and the other is free to study the
dynamical behaviors of a slender elastic rod at different motor rotation rate. There are three main parts in this thesis. First, we derive the general equations of motion for a slender elastic rod subjected to the external force (gravity). The axial rotation dynamics and geometry constraint about the torsion rate and spinning rate are considered in detail. Second, analytical and numerical methods reveal that a critical twirling rate (we term it the first critical twirling rate) exists, which controls the bifurcation behavior of axial rotation (i.e., twirling) and the steady whirling. Above the first critical twirling rate, the governing nonlinear equation for the rod shape at different whirling rate is solved by numerical method and the results agree with experimental measurements. Our theory also shows that when the motor rotation rate is higher than the second critical twirling rate, the rod would be bent back. We find the relation between the first (the second) critical twirling rate and the material parameters, that agrees well with results observed in experiments. Third, in experiments rods with long length, the whirling rate would remain almost constant as we increase the motor rotation rate. Whereas rods with short length, the whirling rate would be the same with the motor rotation rate. Thus we develop the linear stability analysis to study dynamical stability of a twirling rod at different whirling rate.
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| 參考文獻 |
Bibliography
[1] M. J. Kim, J. C. Bird, A. J. Van Parys, K. S. Breuer, and T. R. Powers, Proc.
Natl. Acad. Sci. 100, 15481 (2003).
[2] Stephan A. Koehler, Thomas R. Powers, Phys. Rev. Lett. 86, 4827 (2000).
[3] Bian Qian, Thomas R. Powers, Kenneth S. Breuer, Phys. Rev. Lett. 100, 078101
(2008).
[4] Alain Goriely and Sébastien Neukirch, Phys. Rev. Lett. 97, 194302 (2006).
[5] Leif E. Becker and Michael J. Shelley, Phys. Rev. Lett. 87, 198301 (2001).
[6] Zicong Zhou, Pik-Yin Lai, Béla Joós, Phys. Rev. E. 71, 052801 (2005).
[7] Raymond E. Goldstein and Alain Goriely, Phys. Rev. E. 74, 010901 (2006).
[8] Charles W. Wolgemuth, Thomas R. Powers, and Raymond E. Goldstein, Phys.
Rev. Lett. 84, 1623 (2000).
[9] Alain Goriely, J. Elasticity 84, 281 (2006).
[10] A. E. H. Love, A treatise on the mathematical theory of elasticity (Dover, New
York, 1994).
[11] Alain Goriely and Patrick Shipman, Phys. Rev. E. 61, 4508 (2000).
[12] Alain Goriely and M. Tabor, Physica D 105, 20 (1997).
43
[13] David A. Kessler and Yitzhak Rabin, Phys. Rev. Lett. 90, 024301 (2003).
[14] L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon Press, Oxford,
1986), 3rd ed..
[15] F Tisseur and K Meerbergen, SIAM Review 43, 235 (2001).
[16] Yi-Ting Wang, and Peling Chen, Experiment of Dynamic Rotating Rod in Air,
M.S.Thesis, NCU, Taiwan (2009).
[17] Raymond E. Goldstein, Thomas R. Powers, and Chris H. Wiggins, Phys. Rev.
Lett. 80, 5232 (1998).
[18] Alain Goriely and Michael Tabor, Phys. Rev. Lett. 77, 3537 (1996).
[19] Raymond E. Goldstein and Alain Goriely, Phys. Rev. E. 74, 010901 (2006).
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