  With a series of conformal arrays it is possible to create asymmetric
substrates, and it was previously shown that when an ac drive is applied
parallel to the asymmetry direction, a pronounced ratchet effect occurs with a
net dc flow of vortices in the same direction as the ac drive. Here we show
that when the ac drive is applied perpendicular to the substrate asymmetry
direction, it is possible to realize a transverse ratchet effect where a net dc
flow of vortices is generated perpendicular to the ac drive. The conformal
transverse ratchet effect is distinct from previous versions of transverse
ratchets in that it occurs due to the generation of non-Gaussian transverse
vortex velocity fluctuations by the plastic motion of vortices, so that the
system behaves as a noise correlation ratchet. The transverse ratchet effect is
much more pronounced in the conformal arrays than in random gradient arrays,
and is absent in square gradient arrays due the different nature of the vortex
flow in each geometry. We show that a series of reversals can occur in the
transverse ratchet effect due to changes in the vortex flow across the pinning
gradient as a function of vortex filling, pinning strength, and ac amplitude.
We also consider the case where a dc drive applied perpendicular to the
substrate asymmetry direction generates a net flow of vortices perpendicular to
the dc drive, producing a geometric or drift ratchet that arises due to
non-Gaussian dynamically generated fluctuations. The drift ratchet is more
efficient than the ac driven ratchet and also exhibits a series of reversals
for varied parameters. Our results should be general to a wide class of systems
undergoing nonequilibrium dynamics on conformal substrates, such as colloidal
particles on optical traps.
