Bradford Taylor | Searcharxiv

arXiv2009

On the Stability of Electrostatic Orbits

We analyze the stability of two charged conducting spheres orbiting each other. Due to charge polarization, the electrostatic force between the two spheres deviates significantly from $1/r^2$ as they come close to each other. As a consequence, there exists a critical angular momentum, $L_c$, with a corresponding critical radius $r_c$. For $L > L_c$ two circular orbits are possible: one at $r > r_c$ that is stable and the other at $r < r_c$ that is unstable. This critical behavior is analyzed as a function of the charge and the size ratios of the two spheres.

physics.class-ph↗

arXiv2009

Classifying closed 2-orbifolds with Euler characteristics

We determine the extent to which the collection of $Γ$-Euler-Satake characteristics classify closed 2-orbifolds. In particular, we show that the closed, connected, effective, orientable 2-orbifolds are classified by the collection of $Γ$-Euler-Satake characteristics corresponding to free or free abelian $Γ$ and are not classified by those corresponding to any finite collection of finitely generated discrete groups. Similarly, we show that such a classification is not possible for non-orientable 2-orbifolds and any collection of $Γ$, nor for noneffective 2-orbifolds. As a corollary, we generate families of orbifolds with the same $Γ$-Euler-Satake characteristics in arbitrary dimensions for any finite collection of $Γ$; this is used to demonstrate that the $Γ$-Euler-Satake characteristics each constitute new invariants of orbifolds.

math.DG↗