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The Kirchhoff thin elastic rod models and related systems are always the important basis to research the topology and stability of the flexible structures in not only the macroscopic but also microscopic scale. Firstly the initial Kirchhoff equations are rebuilt in a complex style to suit the character of obvious asymmetry embodied on the cross section by considering the mathematical background of DNA double helix. Then we introduce a complex form variable solution of the torque, and extend the knowledge of effective bending coefficients as well as its facility in the high dimensional system by using the complicated system. As the result, a simplified second order ordinary differential equation with single variable is obtained. Furthermore the periodically varying bending coefficients of the DNA molecular are considered as the appended components to the effective bending coefficients. The whole reduction process makes the numerical simulation become not solely the exclusively eligible approach, and produces adaptable channel to quantitative analysis.
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Keywords:
- thin elastic rod /
- Kirchhoff equation /
- DNA molecular
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[33] 杨斌 2008 青岛大学学报 21 3]
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[39] 青岛大学学报 20 10]
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[46] [47] Guo J G,Zhou L J,Zhao Y P 2008 Surf.Rev.Lett.15 599
[48] [49] [50] [51] -
[1] Kirchhoff G 1859 J.Reine.Angew.Math.56 285
[2] Benham C J 1977 Proc.Natl.Acad.Sci.USA 74 2397
[3] [4] [5] Le Bret M 1978 Biopolymers 17 1939
[6] Liu Y Z 2006 Nonlinear Mechanics of Thin Elastic Rod (Beijing:Tsinghua University) p15 (in Chinese) [刘延柱 2006\弹性细杆的非线性力学 (北京: 清华大学出版社) 第15页]
[7] [8] Liu Y Z,Zu J W 2004 Acta Mech.24 206
[9] [10] Xue Y,Liu Y Z,Chen L Q 2004 Acta Phys.Sin.53 4029 (in Chinese) [薛纭,刘延柱,陈立群 2004 物理学报 53 4029]
[11] [12] [13] Shi Y M,Hearst J E 1994 J.Chem.Phys.101 5186
[14] Xue Y,Liu Y Z,Chen L Q 2004 Chin.Phys.13 794
[15] [16] [17] Balaeff A,Mahadevan L,Schulten K 2006 Phys.Rev.E 73 031919
[18] Da Fonseca Alexandre F,Malta C P,De AguiarMAM2005 Physica A 352 547
[19] [20] [21] Davies M A,Moon F C 1993 Chaos 3 93
[22] [23] Westcott T P,Tobias I,Olson W K 1997 J.Chem.Phys.107 3967
[24] [25] Nitiss J L 1998 Biochim.Biophys.Acta 1400 63
[26] Zhao W J,Zhang G H 2008 Chin.J.Comput.Mech.25 265 (in Chinese) [赵维加,张光辉 2008 计算力学学报 25 265]
[27] [28] Huang J F,Zhao W J,Jia M J,Yang B 2008 J.Qingdao Technol.Univ.21 3 (in Chinese) [黄健飞,赵维加,贾美娟,
[29] [30] [31] Jiang G H,Zhao W J,Jiang Y M 2007 J.Qingdao Technol.Univ.20 10 (in Chinese) [张光辉,赵维加,姜咏梅 2007 \
[32] Nayfeh A H 1993 Method of Normal Forms (New York:John Wiley Sons) p14
[33] 杨斌 2008 青岛大学学报 21 3]
[34] [35] Gore J,Bryant Z,Nollmann M,Le M U,Cozzarelli N R,Bustamante C 2006 Nature 442 836
[36] [37] Balaeff A,Koudella C R,Mahadevan L,Schulten K 2004 Phil.Trans.R.Soc.Lond.A 362 1355
[38] Hoffman K A,Manning R S,Maddocks J H 2003 Biopolymers 70 145
[39] 青岛大学学报 20 10]
[40] Kehrbaum S,Maddocks J H 2000 Proceedings of the 16th IMACS World Congress Lausanne,Switzerland,August 21-25 2000,ISBN 3-9522075-1-9
[41] [42] Eslami-Mossallam B,Ejthadi M R 2009 Phys.Rev.E 80 011919
[43] [44] [45] Zhang Q C,Wang W,He X J 2008 Acta Phys.Sin.57 5384 (in Chinese) [张琪昌,王炜,何学军 2008 物理学报 57 5384]
[46] [47] Guo J G,Zhou L J,Zhao Y P 2008 Surf.Rev.Lett.15 599
[48] [49] [50] [51]
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