  Anomalous transport in a circular comb is considered. The circular motion
takes place for a fixed radius, while radii are continuously distributed along
the circle. Two scenarios of the anomalous transport, related to the reflecting
and periodic angular boundary conditions, are studied. The first scenario with
the reflection boundary conditions for the circular diffusion corresponds to
the conformal mapping of a 2D comb Fokker-Planck equation on the circular comb.
This topologically constraint motion is named umbrella comb model. In this
case, the reflecting boundary conditions are imposed on the circular (rotator)
motion, while the radial motion corresponds to geometric Brownian motion with
vanishing to zero boundary conditions on infinity. The radial diffusion is
described by the log-normal distribution, which corresponds to exponentially
fast motion with the mean squared displacement (MSD) of the order of $e^t$. The
second scenario corresponds to the circular diffusion with periodic boundary
conditions and the outward radial diffusion with vanishing to zero boundary
conditions at infinity. In this case the radial motion corresponds to normal
diffusion. The circular motion in both scenarios is a superposition of cosine
functions that results in the stationary Bernoulli polynomials for the
probability distributions.
