A superconductor, when in the Meissner state, expels magnetic fields from its interior. Very near its surface, there is an exponential decay in field strength that is predicted by the London equation, a special limit of the Ginzburg-Landau equations, provided the surface is flat. In the superconductivity literature, the assumption of a flat interface was taken for granted, but due to experimental measurements of a non-exponential decay in field strength near the surface of a superconductor, experimentalists asked the question of whether small-amplitude perturbations could have an effect on the field profile. With colleagues, I studied these effects through idealized mathematical models of sinusoidal surfaces with the use of asymptotics and numerical methods; then, we further expanded the work by using experimental data measuring the roughness of the surfaces to more accurately describe the magnetic field perturbations.
