scholarly journals Infinitesimal bending of DNA helices

2021 ◽  
Keyword(s):  
Infinitesimal Bending

scholarly journals CURVES ON RULED SURFACES UNDER INFINITESIMAL BENDING

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marija Najdanović ◽  
Miroslav Maksimović ◽  
Ljubica Velimirović
Keyword(s):  
Euclidean Space ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
Hyperbolic Paraboloid ◽  
3 Dimensional ◽  
Infinitesimal Bending

Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the bending of curves on the cylinder, the hyperbolic paraboloid and the helicoid are considered and appropriate bending fields are found. Some examples are graphically presented.

scholarly journals Higher order infinitesimal bending of a class of toroids

2010 ◽  
Vol 31 (4) ◽  
pp. 1136-1147 ◽  
Author(s):  
Ljubica S. Velimirović ◽  
Svetozar R. Rančić
Keyword(s):  
Higher Order ◽  
Infinitesimal Bending

Infinitesimal bending of knots and energy change

2019 ◽  
Vol 28 (11) ◽  
pp. 1940009
Author(s):  
Louis H. Kauffman ◽  
Ljubica S. Velimirović ◽  
Marija S. Najdanović ◽  
Svetozar R. Rančić
Keyword(s):  
Visual Representation ◽  
Energy Change ◽  
Visualization Tool ◽  
Infinitesimal Bending ◽  
Willmore Energy

We discuss the infinitesimal bending of curves and knots in [Formula: see text]. A brief overview of the results on the infinitesimal bending of curves is outlined. Change of the Willmore energy, as well as of the Möbius energy under infinitesimal bending of knots is considered. Our visualization tool devoted to visual representation of infinitesimal bending of knots is presented.

Visualization of Infinitesimal Bending of Curves

2010 ◽  
pp. 469-480
Author(s):  
Ljubica S. Velimirović ◽  
Svetozar R. Rančić ◽  
Milan Lj. Zlatanović
Keyword(s):  
Infinitesimal Bending

scholarly journals Second order infinitesimal bending of curves

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4127-4137 ◽  
Author(s):  
Marija Najdanovic ◽  
Ljubica Velimirovic
Keyword(s):  
Vector Fields ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Second Order ◽  
Dimensional Euclidean Space ◽  
Second Variation ◽  
Explicit Formulas ◽  
Infinitesimal Bending ◽  
Necessary And Sufficient ◽  
The Second Variation

We investigate a second order infinitesimal bending of curves in a three-dimensional Euclidean space in this paper. We give the necessary and sufficient conditions for the vector fields to be infinitesimal bending fields of the corresponding order, as well as explicit formulas which determine these fields. We examine the first and the second variation of some geometric magnitudes which describe a curve, specially a change of the curvature. Two illustrative examples (a circle and a helix) are studied not only analytically but also by drawing curves using computer program Mathematica.

scholarly journals On the Willmore energy of curves under second order infinitesimal bending

2017 ◽  
Vol 17 (2) ◽  
pp. 979 ◽  
Author(s):  
Marija S. Najdanovic ◽  
Ljubica S. Velimirovic
Keyword(s):  
Second Order ◽  
Infinitesimal Bending ◽  
Willmore Energy
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