Quasi-static manipulation of a Kirchhoff elastic rod based on a geometric analysis of equilibrium configurations

2013 ◽  
Vol 33 (1) ◽  
pp. 48-68 ◽  
Author(s):  
Timothy Bretl ◽  
Zoe McCarthy
Keyword(s):  
Geometric Analysis ◽  
Elastic Rod ◽  
Equilibrium Configurations

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

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Yongzhao Wang ◽  
Qichang Zhang ◽  
Wei Wang
Keyword(s):  
Cross Section ◽  
Dynamical Behavior ◽  
Elliptic Functions ◽  
Physical Parameters ◽  
Valuable Insight ◽  
Elastic Rod ◽  
Noncircular Cross Section ◽  
Equilibrium Configurations ◽  
Rational Expressions ◽  
Elastic Rod Model

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.

scholarly journals GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS

2012 ◽  
Vol 88 (1) ◽  
pp. 70-80 ◽  
Author(s):  
SATOSHI KAWAKUBO
Keyword(s):  
Space Form ◽  
Global Solutions ◽  
Infinite Length ◽  
Elastic Rods ◽  
Elastic Rod ◽  
Lagrange Equations ◽  
Initial Value ◽  
Space Forms ◽  
Equilibrium Configurations ◽  
Rod Of Finite Length

AbstractThe Kirchhoff elastic rod is one of the mathematical models of equilibrium configurations of thin elastic rods, and is defined to be a solution of the Euler–Lagrange equations associated to the energy with the effect of bending and twisting. In this paper, we consider Kirchhoff elastic rods in a space form. In particular, we give the existence and uniqueness of global solutions of the initial-value problem for the Euler–Lagrange equations. This implies that an arbitrary Kirchhoff elastic rod of finite length extends to that of infinite length.

Free Rotation of an Elastic Rod With an End Mass

1986 ◽  
Vol 53 (4) ◽  
pp. 864-868 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Angular Momentum ◽  
Large Deformations ◽  
Free Rotation ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Elastic Rod ◽  
Critical Rotation ◽  
Minimum Total Energy ◽  
Equilibrium Configurations ◽  
Flexible Antenna

This paper models a rotating space satellite with a long flexible antenna. Large deformations of the elastic rod are caused by the centrifugal forces. Bifurcation analysis shows the effect of end mass on the critical rotation speeds above which sinuous equilibrium configurations occur. The nonlinear governing equations are then integrated numerically. We find a class of solutions with a looped configuration whose existence requires a certain minimum total energy and minimum angular momentum. Catastrophic changes are possible.

Elastic response of DNA molecules under the action of interfacial traction and stretching: An elastic thin rod model

2015 ◽  
Vol 29 (31) ◽  
pp. 1550193 ◽  
Author(s):  
Ye Xiao ◽  
Zaixing Huang ◽  
Lei Qiang ◽  
Jun Gao
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Shooting Method ◽  
Elastic Strain Energy ◽  
Elastic Response ◽  
Elastic Rod ◽  
Equilibrium Configurations ◽  
End Distance ◽  
Condensed Dna ◽  
Interfacial Traction

In a multivalent salt solution, a segment of DNA is modeled as an elastic rod subjected to the interfacial traction. The shooting method is used to calculate the equilibrium configurations of condensed DNA under the action of the longitudinal end-force and interfacial traction simultaneously. The results show that the shapes of DNA are mainly determined by the competition between the interfacial energy and elastic strain energy of stretching. The change of end-to-end distance with the longitudinal end-force is consistent with the worm-like chain (WLC) model. The higher the concentration is, the stronger the condensation of DNA.

Dynamics of an electrostatically charged elastic rod in fluid

2010 ◽  
Vol 467 (2126) ◽  
pp. 569-590 ◽  
Author(s):  
Sookkyung Lim ◽  
Yongsam Kim ◽  
David Swigon
Keyword(s):  
Immersed Boundary Method ◽  
Stable Equilibrium ◽  
Equations Of Motion ◽  
Initial Perturbation ◽  
Hard Core ◽  
Unstable Equilibrium ◽  
Immersed Boundary ◽  
Governing Equations ◽  
Elastic Rod ◽  
Equilibrium Configurations

We investigate the effects of electrostatic and steric repulsion on the dynamics of a pre-twisted charged elastic rod immersed in a viscous incompressible fluid. Equations of motion of the rod include the fluid–structure interaction, rod elasticity and a combination of two interactions that prevent self-contact, namely the electrostatic interaction and hard-core repulsion. The governing equations are solved using the generalized immersed-boundary method. We find that after perturbation, a pre-twisted minicircle collapses into a compact supercoiled configuration. The collapse proceeds along a complex trajectory that may pass near several unstable equilibrium configurations, before it settles in a locally stable equilibrium. The dwell time near an unstable equilibrium can be up to several microseconds. Both the final configuration and the transition path are sensitive to the initial excess link, ionic strength of the solvent and the initial perturbation.

Liquid crystalline ordering of paired helical filaments in neurofibrillary tangles of Alzheimer's disease

1986 ◽  
Vol 44 ◽  
pp. 348-349
Author(s):  
D.F. Clapin ◽  
V.J.A. Montpetit
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Neurofibrillary Tangles ◽  
Liquid Crystalline ◽  
Amyloid Fibrils ◽  
Geometric Analysis ◽  
Paired Helical Filaments ◽  
Microscopic Level ◽  
Light Microscopic Level ◽  
Regular Spacing

Alzheimer's disease is characterized by the accumulation of abnormal filamentous proteins. The most important of these are amyloid fibrils and paired helical filaments (PHF). PHF are located intraneuronally forming bundles called neurofibrillary tangles. The designation of these structures as "tangles" is appropriate at the light microscopic level. However, localized domains within individual tangles appear to demonstrate a regular spacing which may indicate a liquid crystalline phase. The purpose of this paper is to present a statistical geometric analysis of PHF packing.

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