Pattern formation due to non-linear vortex diffusion

Penetration of magnetic flux in YBa2Cu3O7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A va riety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those obse rved in burning paper including two distinct regimes where respectively spa tial disorder and temporal disorder dominate. In the latter regime Kardar-P arisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdor ff dimension depending on the critical current anisotropy. (3) Penetration as 'flux-rivers'. (4) The occurrence of commensurate and incommensurate cha nnels in films with anti-dots as predicted in numerical simulations by Reic hhardt, Olson and Nori. It is shown that most of the observed behavior is r elated to the non-linear diffusion of vortices by comparison with simulatio ns of the non-linear diffusion equation appropiate for vortices.