9 citations · 13 across the 8 of their papers we have counts for
9 papers
Complex methods in the asymptotics of Möbius energy integrals of helix curves
Max Lipton
The Möbius energy of a curve is a topic of interest to physical knot theorists, harmonic analysts, and geometric analysts. In particular, there are many open questions regarding th…
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…
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…
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…
Topological approaches to knotted electric charge distributions
Max Lipton
Consider a knot in with uniformly distributed electric charge. Whilst solutions to the Laplace equation in terms of Dirichlet integrals are readily available, it is still…
A lower bound on critical points of the electric potential of a knot
Max Lipton
Given a knot parametrized by , we can define the electric potential on its complement by . Physicis…
The Kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry
Max Lipton, Renato Mirollo, Steven H. Strogatz
We study a system of interacting particles moving on the unit sphere in -dimensional space. The particles are self-propelled and coupled all to all, and their motion is heav…
Conformal Group Actions on Generalized Kuramoto Oscillators
Max Lipton
This paper unifies the recent results on generalized Kuramoto Model reductions. Lohe took a coupled system of bodies on governed by the Kuramoto equations $\dot{x_i} = Ωx…
Six variations on a theme: almost planar graphs
Max Lipton, Eoin Mackall, Thomas W. Mattman +4
A graph is apex if it can be made planar by deleting a vertex, that is, such that is planar. We define the related notions of edge apex, such that $G-…