Anomalous diffusion in umbrella comb

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