非对称截面Kirchhoff弹性细杆模型简化方法研究

王炜; 张琪昌; 靳刚

doi:10.7498/aps.61.064602

摘要

研究弹性细杆Kirchhoff模型及其相关演化系统, 是深入考察宏观、微观柔性体拓扑结构与稳定性问题的重要依据. 以DNA弹性细杆数学模型为背景, 考虑截面非对称性特征的影响, 构造新的复数形式Kirchhoff系统. 在此基础上, 结合复变量扭矩设解形式, 获得了非对称截面系统的有效抗弯刚度; 并通过相关理论在高维系统简化过程中的应用, 得到了对应于原有系统的单变量二阶常微分方程. 此外, 将DNA分子具备的抗弯刚度周期变化特征转化为针对有效抗弯刚度的周期摄动形式, 以期从总体上减少理论分析对于数值积分的依赖, 为后续定量分析工作提供新的思路.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
天津大学机械学院力学系, 内燃机燃烧学国家重点实验室, 天津 300072

通信作者: 王炜, wangweifrancis@yahoo.com.cn

基金项目: 国家自然科学基金(批准号:10872141,11072168)和高等学校博士学科点专项科研基金(批准号:20100032120006)资助的课题.

Authors and contacts

1.
State Key Laboratory of Engines, Department of Mechanics, School of Engineering, Tianjin University, Tianjin 300072, China

Corresponding author: Wang Wei, wangweifrancis@yahoo.com.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.10872141,11072168) and Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20100032120006).

参考文献

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施引文献

[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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