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

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.

2017 ◽  
Vol 17 (2) ◽  
pp. 979 ◽  
Author(s):  
Marija S. Najdanovic ◽  
Ljubica S. Velimirovic

2010 ◽  
Vol 59 (12) ◽  
pp. 3679-3686 ◽  
Author(s):  
Ljubica S. Velimirović ◽  
Marija S. Ćirić ◽  
Milica D. Cvetković

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2411-2419 ◽  
Author(s):  
Marija Najdanovic

In this paper we study the change of the Willmore energy of curves, as a special case of so-called Helfrich energy, under infinitesimal bending determined by the stationarity of arc length. We examine the variation of the unit tangent, principal normal and binormal vector fields, the curvature and the torsion of the curve. We obtain an explicit formula for calculating the variation of the Willmore energy, as well as the Euler-Lagrange equations describing equilibrium. We find an infinitesimal bending field for a helix and compute the variation of its Willmore energy under such infinitesimal bending.


EDIS ◽  
2017 ◽  
Vol 2017 (6) ◽  
Author(s):  
Brian J. Estevez ◽  
Chad Carr ◽  
Larry F. Eubanks

  A visual representation of the beef retail cuts along with suggested cooking methods.


2020 ◽  
Vol 2 ◽  
pp. 1-18
Author(s):  
Tuncay Şur ◽  
Betül Yarar

This paper seeks to understand why there has been an increase in photographic images exposing military violence or displaying bodies killed by military forces and how they can freely circulate in the public without being censored or kept hidden. In other words, it aims to analyze this particular issue as a symptom of the emergence of new wars and a new regime of their visual representation. Within this framework, it attempts to relate two kinds of literature that are namely the history of war and war photography with the bridge of theoretical discussions on the real, its photographic representation, power, and violence.  Rather than systematic empirical analysis, the paper is based on a theoretical attempt which is reflected on some socio-political observations in the Middle East where there has been ongoing wars or new wars. The core discussion of the paper is supported by a brief analysis of some illustrative photographic images that are served through the social media under the circumstances of war for instance in Turkey between Turkish military troops and the Kurdish militants. The paper concludes that in line with the process of dissolution/transformation of the old nation-state formations and globalization, the mechanism and mode of power have also transformed to the extent that it resulted in the emergence of new wars. This is one dynamic that we need to recognize in relation to the above-mentioned question, the other is the impact of social media in not only delivering but also receiving war photographies. Today these changes have led the emergence of new machinery of power in which the old modern visual/photographic techniques of representing wars without human beings, torture, and violence through censorship began to be employed alongside medieval power techniques of a visual exhibition of tortures and violence.


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