A geometric approach to scalar field theories on the supersphere

Following a strictly geometric approach we construct globally supersymmetric scalar field theories on the supersphere, defined as the quotient space $S^{2|2} = UOSp(1|2)/\mathcal{U}(1)$. We analyze the superspace geometry of the supersphere, in particular deriving the invariant vielbein and spin connection from a generalization of the left-invariant Maurer-Cartan form for Lie groups. Using this information we proceed to construct a superscalar field action on $S^{2|2}$, which can be decomposed in terms of the component fields, yielding a supersymmetric action on the ordinary two-sphere. We are able to derive Lagrange equations and Noether's theorem for the superscalar field itself.Comment: 38 pages, 1 figur

Curvature blow up in Bianchi VIII and IX vacuum spacetimes

The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum initial data and of non-NUT Bianchi VIII vacuum initial data is C2 inextendible. Furthermore, a curvature invariant is unbounded in the incomplete directions of inextendible causal geodesics.Comment: 20 pages, no figures. Submitted to Classical and Quantum Gravit

Impact pressure probe reponse characteristics in high speed flows with transition knudsen numbers

Impact pressure probe response characteristics in high speed flows with transition Knudsen number

Impact pressure probe response characteristics in high speed flows, with transition Knudsen numbers

Impact pressure probe response characteristics in free-molecular and continuum flows with transition Knudsen number