Anomalous subdiffusion in angular and radial direction on a circular comb-like structure with nonisotropic relaxation

This paper presents a research for the anomalous diffusion on a circular comb-like structure with nonisotropic relaxation in angular and radial direction. The nonlinear governing equation is formulated and solved by finite volume method (FVM), which is verified with the analytical one in a particular case. The effects of involved parameters on mean squared displacements (MSD) are discussed and a particular characteristic of two periods of time are found: in a long period and a relatively short period. We find that MSD converges to a constant as the particles saturate the circular comb structure (because of the finite region) for a long period, but it has a growth form of tα on τ ≪ t ≪ 1 for a relatively short period, where τ is the maximum of two relaxation parameters in radial τr and angular τθ respectively. Moreover, the influence of the nonisotropic relaxation parameters on exponent α is also analyzed. From these, we may assert that there exists an invariant for α ( ≈ 1/2), which is independent of relaxation parameters.