  Interface dynamics in two-dimensional systems with a maximal number of
conservation laws gives an accurate theoretical model for many physical
processes, from the hydrodynamics of immiscible, viscous flows (zero
surface-tension limit of Hele-Shaw flows, [1]), to the granular dynamics of
hard spheres [2], and even diffusion-limited aggregation [3]. Although a
complete solution for the continuum case exists [4, 5], efficient
approximations of the boundary evolution are very useful due to their practical
applications [6]. In this article, the approximation scheme based on orthogonal
polynomials with a deformed Gaussian kernel [7] is discussed, as well as
relations to potential theory.
