9 citations · 13 across the 8 of their papers we have counts for
5 papers · 1 filter
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…