Total Curvature and Total Torsion of a Freely Jointed Circular Polymer withn≫ 1 Segments

2008 ◽  
Vol 41 (12) ◽  
pp. 4524-4527 ◽  
Author(s):  
Alexander Y. Grosberg
Keyword(s):  
Total Curvature ◽  
Total Torsion

scholarly journals Total Curvature and Total Torsion of Knotted Polymers

2007 ◽  
Vol 40 (10) ◽  
pp. 3860-3867 ◽  
Author(s):  
Patrick Plunkett ◽  
Michael Piatek ◽  
Akos Dobay ◽  
John C. Kern ◽  
Kenneth C. Millett ◽  
...  
Keyword(s):  
Total Curvature ◽  
Total Torsion

SPACE CURVES WITH NONZERO TORSION

1990 ◽  
Vol 01 (01) ◽  
pp. 109-117 ◽  
Author(s):  
BURT TOTARO
Keyword(s):  
Total Curvature ◽  
Closed Curve ◽  
Space Curves ◽  
Curvature And Torsion ◽  
Total Torsion ◽  
Nonzero Torsion

For a closed curve in R3 with curvature and torsion everywhere nonzero, the sum of the total curvature and the total torsion is greater than 4π.

scholarly journals On torus knots and unknots

2016 ◽  
Vol 25 (06) ◽  
pp. 1650036 ◽  
Author(s):  
Chiara Oberti ◽  
Renzo L. Ricca
Keyword(s):  
Total Curvature ◽  
Topological Information ◽  
Torus Knots ◽  
Space Curves ◽  
Global Properties ◽  
Inflection Points ◽  
Total Squared Curvature ◽  
Curvature And Torsion ◽  
Total Torsion ◽  
Comprehensive Study

A comprehensive study of geometric and topological properties of torus knots and unknots is presented. Torus knots/unknots are particularly symmetric, closed, space curves, that wrap the surface of a mathematical torus a number of times in the longitudinal and meridian direction. By using a standard parametrization, new results on local and global properties are found. In particular, we demonstrate the existence of inflection points for a given critical aspect ratio, determine the location and prescribe the regularization condition to remove the local singularity associated with torsion. Since to first approximation total length grows linearly with the number of coils, its nondimensional counterpart is proportional to the topological crossing number of the knot type. We analyze several global geometric quantities, such as total curvature, writhing number, total torsion, and geometric ‘energies’ given by total squared curvature and torsion, in relation to knot complexity measured by the winding number. We conclude with a brief presentation of research topics, where geometric and topological information on torus knots/unknots finds useful application.

Total curvature and total torsion of knotted random polygons in confinement

2018 ◽  
Vol 51 (15) ◽  
pp. 154002 ◽  
Author(s):  
Yuanan Diao ◽  
Claus Ernst ◽  
Eric J Rawdon ◽  
Uta Ziegler
Keyword(s):  
Total Curvature ◽  
Random Polygons ◽  
Total Torsion

The focusing of radiation by a random surface when the source is at a finite distance

1960 ◽  
Vol 56 (1) ◽  
pp. 27-40 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Mean Curvature ◽  
Joint Distribution ◽  
Total Curvature ◽  
Statistical Distribution ◽  
Constant Parameter ◽  
Random Surface ◽  
Second Derivatives ◽  
Finite Distance ◽  
The Mean ◽  
Image Position

Imagine a nearly horizontal, statistically uniform, random surface ζ(x, y), Gaussian in the sense that the second derivatives , , have a normal joint distribution. The problem considered is the statistical distribution of the quantitywhere J and Ω denote the mean curvature and total curvature of the surface, respectively, and ν is a constant parameter.

Curvature-dependent energies: a geometric and analytical approach

2017 ◽  
Vol 147 (3) ◽  
pp. 449-503 ◽  
Author(s):  
Emilio Acerbi ◽  
Domenico Mucci
Keyword(s):  
Bounded Variation ◽  
Analytical Approach ◽  
Total Curvature ◽  
Representation Formula ◽  
Energy Functional ◽  
Continuous Functions ◽  
Explicit Representation ◽  
Functions Of Bounded Variation ◽  
One Dimensional ◽  
Relaxed Energy

We consider the total curvature of graphs of curves in high-codimension Euclidean space. We introduce the corresponding relaxed energy functional and prove an explicit representation formula. In the case of continuous Cartesian curves, i.e. of graphs cu of continuous functions u on an interval, we show that the relaxed energy is finite if and only if the curve cu has bounded variation and finite total curvature. In this case, moreover, the total curvature does not depend on the Cantor part of the derivative of u. We treat the wider class of graphs of one-dimensional functions of bounded variation, and we prove that the relaxed energy is given by the sum of the length and total curvature of the new curve obtained by closing the holes in cu generated by jumps of u with vertical segments.

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