Геометрија, образовање и визуализација са применама, 5. децембар 2018.

Наредни састанак Семинара биће одржан у среду, 5. децембра 2018. у сали 301ф Математичког института САНУ са почетком у 14 часова.

Предавач: Љубица Велимировић, Faculty of Sciences and Mathematics, Niš, Serbia

Наслов предавања: ON KNOTS AND ENERGIES

Apstrakt: This is talk based on the joint research with Louis Kauffman, Marija Najdanović and Svetozar Rančić. Knot theory is the study of mathematical models of knotting phenomena, often motivated by considerations from biology, chemistry, and physics (Kauffman 1991). Physical knot theory is used to study how geometric and topological characteristics of filamentary structures, such as magnetic flux tubes, vortex filaments, polymers, DNA's, influence their physical properties and functions. It has applications in various fields of science, including topological fluid dynamics, structural complexity analysis and DNA biology (Kauffman 1991 , Ricca 1998,). Traditional knot theory models a knot as a simple closed loop in three-dimensional space. Such a knot has no thickness or physical properties such as tension or friction. Physical knot theory incorporates more realistic models.

The talk is devoted to the shape descriptors of knots during infinitesimal bending. The problem of infinitesimal bending of knots is a special part of the theory of deformation. Bending theory considers bending of manifolds, isometric deformations as well as infinitesimal bending. It requires use of differential geometry, mechanics, physics and has applications in modern computer graphics. Infinitesimal bending is "almost" an isometric deformation, or it is an isometric deformation in a precise approximation. Arc length is stationary under infinitesimal bending with a given precision.

We will discussed here: Mobius energy, Willmore energy, Total curvature, Total torsion, Total normalcy. Some examples are visualised developed by Svetozar Rančić and coauthors. Instead of using existing software capable to do symbolic and numeric calculations, we decided to develop our own software tool in Visual C++.

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