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 Branching and Stability of Elasic Rod Equilibrium Forms

2021 ◽  
Author(s):  
Dmitrii Skubov ◽  
Dmitry Yu. Kopnin
Keyword(s):  
Differential Equation ◽  
Boundary Problem ◽  
Cross Section ◽  
Compressive Load ◽  
Elliptic Functions ◽  
Vertical Position ◽  
Loss Of Stability ◽  
Elastic Rod ◽  
Turn Angle ◽  
Thin Elastic Rod

Abstract In our article from the positions of branching theory the classical Euler task about stability of thin elastic rod under action of vertical compressive load is considered. With using of turn-tensor and accompanying vector the deformation of rod is described. In result the conditions of equilibrium in a case of linear determining equation are reduced to boundary problem relatively turn angle of cross section, described by the differential equation of pendulum. With help elliptic functions the diagrams of branching are constructed and are received the exact formulas of rod deformation at the loss of stability of vertical position. Analogy the task of stability of rod at turned force on end of rod is considered. Also, the oscillating loss of rod stability at tracking load is studied.

Approximate Calculation of Pressure Drop in Laminar Flow of Generalized Newtonian Liquid Through Channel of Noncircular Cross Section

1994 ◽  
Vol 59 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Václav Dolejš ◽  
Ivan Machač ◽  
Petr Doleček
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Numerical Solution ◽  
Cross Section ◽  
Approximate Calculation ◽  
Newtonian Liquid ◽  
Straight Channel ◽  
Suggested Procedure ◽  
Noncircular Cross Section ◽  
Calculation Results

The paper presents a modification of the equations of Rabinowitsch-Mooney type for an approximate calculation of pressure drop in laminar flow of generalized Newtonian liquid through a straight channel whose cross section forms a simple continuous area. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with both the published and original results of numerical solution and experiments.

Calculation of hydraulic resistivity coefficients for turbulent fluid flow in channels of noncircular cross section

1967 ◽  
Vol 23 (4) ◽  
pp. 1042-1047 ◽  
Author(s):  
M. Kh. Ibragimov ◽  
I. A. Isupov ◽  
L. L. Kobzar' ◽  
V. I. Subbotin
Keyword(s):  
Fluid Flow ◽  
Cross Section ◽  
Turbulent Fluid Flow ◽  
Turbulent Fluid ◽  
Noncircular Cross Section

Acoustic intensity for a long vessel with noncircular cross section

2004 ◽  
Vol 51 (5) ◽  
pp. 566-575 ◽  
Author(s):  
R.S. Thompson ◽  
C. Macaskill ◽  
V.B. Fraser ◽  
L. Farnell
Keyword(s):  
Cross Section ◽  
Acoustic Intensity ◽  
Noncircular Cross Section
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