Fig. 1: Schematic illustration of our hybrid comb model.

This model is defined by Eq. (4) and simultaneously accounts for the medium’s heterogeneity and trapping mechanisms. The Dirac delta that multiplies the second term of Eq. (4) is responsible for trapping particles along the x-direction each time they leave the line y = 0. Consequently, diffusive motion in the x-direction only occurs when y = 0, and diffusion along the y-direction is restricted to the current x-position, requiring particles to return to the line y = 0 to resume movement along the x-direction. As a result, we observe the emergence of a structure characterized by a backbone along the line y = 0 and perpendicular branches extending in the y-direction. In turn, the term \({D}_{x}(x)={{{{{{{\mathcal{D}}}}}}}}| x{| }^{-\eta }\) inside the first spatial derivative of the second term of Eq. (4) accounts for the medium’s heterogeneity by modifying the diffusion coefficient along the backbone. a When η < 0, the diffusion coefficient increases as particles move away from the origin (x = 0). b On the other hand, for η > 0, the diffusion coefficient decreases with the distance from the origin. In both panels, blue arrows depict possible particle trajectories, vertical dashed lines indicate the branch-like structure, and the color bar along the x-axis illustrates the variation of the diffusion coefficient with respect to the position along the backbone.