  We use a gradient-decent method to compute 3D ground states of dipolar
Bose-Einstein conden- sates. We discover that in highly-prolate traps, whose
long axis is parallel to the dipoles, can give rise to candlestick ground
states. Direct numerical simulations of the dipolar Gross-Pitaevskii equation
reveal that the nucleus of the candlestick mode undergoes collapse, while
obtaining a highly flat pancake shape. The rate of this anisotropic collapse
scales differently from what occurs in isotropic collapse. Stability analysis
reveals a surprising cusp point in the mass vs. chemical potential curve, which
may serve as a signature for this dynamics.
