- Spherical equilibrium arrangements of four point particles which interact pairwise with repulsive power law forces
- Project Year:
2020
- REU Student (s):
Joy Hamlin | Stony Brook University NY
- Student 1 Institution:
Stony Brook University
- Project Mentor:
Michael Kiessling
- Project Mentor Area:
Mathematics
- Project Abstract:
I surveyd equilibrium arrangements, proper as well as pseudo, of four point particles on the unit circle which interact pairwise with a repulsive power law force. The bifurcation diagram which jointly exhibits all these equilibrium arrangements as functions of s features four obvious "universal" equilibria, which do not depend on s, and many more continuous families of s-dependent non-universal equilibria, some of which were known before but many were not. All equilibria are also planar special cases of the analogous four-particle equilibrium problem on the 2-sphere, some of which are also studied.
