Nucleation Far from Equilibrium

(Received 23 May 1995, revised 6 May 1995, accepted 6 July 1995)

Abstract
Nucleation in phase transition is a classical problem. Close to the transition point, the critical radius is known to be much larger than the diffusion length. In this paper, we focus on the case far from the critical point, as it is the case in a supercooled liquid, or in the related context of excitable media. We show that the physics of nucleation is different from the classical case. The critical radius is of the order of the diffusion length (in 2-dimensions), and smaller than the diffusion length (in 1-dimension). As a result, diffusion first leads to a decrease in amplitude of the initial seed, before a propagating pulse (or front) is initiated. This results in different laws for the critical radius. The relevance of these effects to stimulation in biological tissues, such as cardiac muscle, is discussed.