In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations and in particular at the relative strengths of the toroidal and poloidal components. Both toroidal and poloidal fields are unstable on their own, and stability is achieved by adding the two together in some ratio. I use Tayler’s (1973) stability conditions for tor...

1 We investigate the toroidal expanse of an embedded graph G, that is, the size of the largest 2 toroidal grid contained in G as a minor. In the course of this work we introduce a new embedding 3 density parameter, the stretch of an embedded graph G, and use it to bound the toroidal 4 expanse from above and from below within a constant factor depending only on the genus and 5 the maximum degree...

An experimental investigation into the detailed mixing, combustion and ignition processes occurring in a flow field under the influence of resonant acoustic perturbations has been performed. These acoustic perturbations were created by a pulse combustor of the "Helmholtz" type. Cycle-resolved ensemble-averaged measurements of the velocity field, combined with instantaneous images of chemilumine...

Toroidal droplets are inherently unstable due to surface tension. They can break up, similar to cylindrical jets, but also exhibit a shrinking instability, which is inherent to the toroidal shape. We investigate the evolution of shrinking toroidal droplets using particle image velocimetry. We obtain the flow field inside the droplets and show that as the torus evolves, its cross-section signifi...

The gyrokinetic toroidal code (GTC) capability has been extended for simulating internal kink instability with kinetic effects in toroidal geometry. The global simulation domain covers the magnetic axis, which is necessary for simulating current-driven instabilities. GTC simulation in the fluid limit of the kink modes in cylindrical geometry is verified by benchmarking with a magnetohydrodynami...