The Schrödinger equation for a Kirchhoff elastic rod with noncircular cross section

Yun Xue; Yan Zhu Liu; Li Qun Chen

doi:10.1088/1009-1963/13/6/002

The Schrödinger equation for a Kirchhoff elastic rod with noncircular cross section

Yun Xue^*
, Yan Zhu Liu
, Li Qun Chen

^*Corresponding author for this work

Shanghai University
Shanghai Institute of Technology
Shanghai Jiao Tong University

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

The extended Schrödinger equation for the Kirchhoff elastic rod with noncircular cross section is derived using the concept of complex rigidity. As a mathematical model of supercoiled DNA, the Schrödinger equation for the rod with circular cross section is a special case of the equation derived in this paper. In the twistless case of the rod when the principal axes of the cross section are coincident with the Frenet coordinates of the centreline, the Schrödinger equation is transformed to the Duffing equation. The equilibrium and stability of the twistless rod are discussed, and a bifurcation phenomenon is presented.

Original language	English
Pages (from-to)	794-797
Number of pages	4
Journal	Chinese Physics
Volume	13
Issue number	6
DOIs	https://doi.org/10.1088/1009-1963/13/6/002
State	Published - 1 Jun 2004
Externally published	Yes

Keywords

DNA model
Kirchhoff elastic rod
Schrödinger equation

Access to Document

10.1088/1009-1963/13/6/002

Cite this

@article{f549b217a4f74b899d90eaaae21a6ae2,

title = "The Schr{\"o}dinger equation for a Kirchhoff elastic rod with noncircular cross section",

abstract = "The extended Schr{\"o}dinger equation for the Kirchhoff elastic rod with noncircular cross section is derived using the concept of complex rigidity. As a mathematical model of supercoiled DNA, the Schr{\"o}dinger equation for the rod with circular cross section is a special case of the equation derived in this paper. In the twistless case of the rod when the principal axes of the cross section are coincident with the Frenet coordinates of the centreline, the Schr{\"o}dinger equation is transformed to the Duffing equation. The equilibrium and stability of the twistless rod are discussed, and a bifurcation phenomenon is presented.",

keywords = "DNA model, Kirchhoff elastic rod, Schr{\"o}dinger equation",

author = "Yun Xue and Liu, \{Yan Zhu\} and Chen, \{Li Qun\}",

year = "2004",

month = jun,

day = "1",

doi = "10.1088/1009-1963/13/6/002",

language = "英语",

volume = "13",

pages = "794--797",

journal = "Chinese Physics",

issn = "1009-1963",

publisher = "Chinese Physical Society",

number = "6",

}

TY - JOUR

T1 - The Schrödinger equation for a Kirchhoff elastic rod with noncircular cross section

AU - Xue, Yun

AU - Liu, Yan Zhu

AU - Chen, Li Qun

PY - 2004/6/1

Y1 - 2004/6/1

N2 - The extended Schrödinger equation for the Kirchhoff elastic rod with noncircular cross section is derived using the concept of complex rigidity. As a mathematical model of supercoiled DNA, the Schrödinger equation for the rod with circular cross section is a special case of the equation derived in this paper. In the twistless case of the rod when the principal axes of the cross section are coincident with the Frenet coordinates of the centreline, the Schrödinger equation is transformed to the Duffing equation. The equilibrium and stability of the twistless rod are discussed, and a bifurcation phenomenon is presented.

AB - The extended Schrödinger equation for the Kirchhoff elastic rod with noncircular cross section is derived using the concept of complex rigidity. As a mathematical model of supercoiled DNA, the Schrödinger equation for the rod with circular cross section is a special case of the equation derived in this paper. In the twistless case of the rod when the principal axes of the cross section are coincident with the Frenet coordinates of the centreline, the Schrödinger equation is transformed to the Duffing equation. The equilibrium and stability of the twistless rod are discussed, and a bifurcation phenomenon is presented.

KW - DNA model

KW - Kirchhoff elastic rod

KW - Schrödinger equation

UR - https://www.scopus.com/pages/publications/23244466264

U2 - 10.1088/1009-1963/13/6/002

DO - 10.1088/1009-1963/13/6/002

M3 - 文章

AN - SCOPUS:23244466264

SN - 1009-1963

VL - 13

SP - 794

EP - 797

JO - Chinese Physics

JF - Chinese Physics

IS - 6

ER -

The Schrödinger equation for a Kirchhoff elastic rod with noncircular cross section

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this