Structural similarity between the magnetic-flux profile in superconductors and the surface of a 2d rice pile

We analyze the magnetic-flux profile in the critical state of an $\chem{YBa_2Cu_3O}$ $_{7-x}$ thin film. It is found that the profile forms a self-affine structure in both space and time. Furthermore, the surface of a pile of rice is studied, which also shows a self-affine structure. These experimental results are compared to simulations of a two-dimensional version of the Oslo model for sandpiles. The exponents characterizing the roughness and dynamics of the profiles for both experimental systems agree with each other, the values being $\alpha = 0.39(3)$ for the roughness exponents and $\beta = 0.50(3)$ for the growth exponents. These values are reproduced in the simulations as well. This shows that a simple sandpile model can be used to describe the shape and dynamics of the vortex landscape in the critical state. Conversely, superconductors may be used as a model granular system.