Mark Bradley - Surface Dynamics of a Current-Carrying Metal Thin Film: A Novel Free Boundary Problem

Surface Dynamics of a Current-Carrying Metal Thin Film: A Novel Free Boundary Problem

R. Mark Bradley
Department of Physics
Colorado State University

When an electrical current passes through a piece of solid metal, collisions between the conduction electrons and the metal atoms at the surface lead to drift of these atoms. The free surface of a metal therefore moves and deforms in response to the electrical current flowing through it, in much the same way that flow in the bulk of a fluid affects the motion of its surface.

Just as solitary waves can propagate over the surface of a shallow body of water, solitons can propagate over the free surface of a current-carrying metal thin film. The equation of motion for one-dimensional small-amplitude long waves is the KdV equation. The generalization of this equation to two-dimensional disturbances differs from previously-studied generalizations of the KdV equation, and shows that the 1D solitons are unstable against perturbations with small transverse wave vector. The motion of a packet of finite-amplitude surface waves will also be discussed.