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math.DG2022
Complex asymptotics of the Möbius energy gradient of symmetric helix pairs
Max Lipton
The Möbius energy is a well-studied knot energy with nice regularity and self-repulsive properties. Stationary curves under the Möbius energy gradient are of significant theoretica…
math.DG2022
Stationary curves under the Möbius-Plateau energy
Max Lipton, Gokul Nair
Plateau problems with elastic boundary energies have been of recent theoretical and applied interest. However, strong assumptions have to be made to avoid self-intersections of the…
math.DS2022
Exploring the electric field around a loop of static charge: Rectangles, stadiums, ellipses, and knots
Max Lipton, Steven H Strogatz, Alex Townsend
We study the electric field around a continuous one-dimensional loop of static charge, under the assumption that the charge is distributed uniformly along the loop. For rectangular…