PATTERN-FORMATION IN SCREENED ELECTROSTATIC FIELDS

It is shown that screening greatly diversifies the type of patterns that can grow in an electrostatic field. Screening introduces a new length scale and a nontrivial dependence on the boundary conditions. Growing patterns can either have a fractal character (diffusion-limited-aggregation-like) at scales shorter than the screening length, be similar to the Eden model, or even be dense. A transition from dense to multibranched growth occurs at a point which depends on the potentials at the boundaries, the distance between them, and the screening length.