Curve-shortening flow of open, elastic curves in $\mathbb{R}^2$ with repelling endpoints: A minimizing movement approach
Rufat Badal
TL;DR
This paper investigates the evolution of open elastic curves in the plane with repelling endpoints using a gradient flow approach, establishing long-term existence and supporting findings with numerical experiments.
Contribution
It introduces a novel gradient flow model for elastic curves with Coulomb repulsion and proves its long-time existence via a minimizing movement scheme.
Findings
Long-time existence of the flow is proven.
Numerical experiments support theoretical results.
The model captures the behavior of elastic curves with endpoint repulsion.
Abstract
We study an -type gradient flow of an immersed elastic curve in whose endpoints repel each other via a Coulomb potential. By De Giorgi's minimizing movements scheme we prove long-time existence of the flow. The work is complemented by several numerical experiments.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Fluid Dynamics and Turbulent Flows · Geometric Analysis and Curvature Flows