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Energies on Deformed Planar Lattices: Geometric Consideration

ISEF · 2024 Physics and Astronomy

Gaydarov, Stefan · Model High School of Mathematics "Akademik Kiril Popov"

Overview

The discovery of graphenes and fullerenes sparked a surge of interest in the understanding of their structures and properties. One approach, proposed by Friedrich, Seitz and Stefanelli stems from geometrical considerations with elements of potential theory, or as they present it - molecular mechanics. Our motivation is similar to that of Friedrich, Seitz and Stefanelli, but in some sense, inversed. We want to know what kind of constraints will generate certain "nice" geometrical configurations and whether the original constraints can be somewhat relaxed and altered. We alter their approach to energy by introducing an external field instead of the area element and study what constraints for the functions can yield certain geometrically "nice" configurations. We also consider relaxing some of the conditions of Friedrich, Seitz and Stefanelli and what changes that will introduce in the geometry of optimal configurations.

Competition history

  • ISEF 2024 Physics and Astronomy · Entry PHYS009 · Los Angeles, California, United States Affiliated fair in Bulgaria, Bulgaria

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Source: Regeneron International Science and Engineering Fair

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