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Mathematical Problems in Engineering
Volume 2015, Article ID 351362, 7 pages
http://dx.doi.org/10.1155/2015/351362
Research Article

Equilibrium Configurations of the Noncircular Cross-Section Elastic Rod Model with the Elliptic KB Method

1Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
2School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China

Received 3 November 2014; Accepted 21 February 2015

Academic Editor: Lakshmanan Shanmugam

Copyright © 2015 Yongzhao Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The mechanical deformation of DNA is very important in many biological processes. In this paper, we consider the reduced Kirchhoff equations of the noncircular cross-section elastic rod characterized by the inequality of the bending rigidities. One family of exact solutions is obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behavior of the system in response to changes in physical parameters that concern asymmetry. The effects of the factor on the DNA conformation are discussed. A qualitative analysis is also conducted to provide valuable insight into the topological configuration of DNA segments.