The effective velocity of the domain wall motion in the quasi-one-dimensional nanosystem at a multiple nucleation of domains of the new phase

The process of switching a metastable state into an energetically preferable state in extended quasione- dimensional systems often occurs through the motion of domains walls of new phase. Usually considered limit cases are the propagation of the edge domains over the whole system or multiple nucleation and coalescence of domains in the volume of the material. This paper deals with the more general situation of front propagation of the switching state from the sample edge at a multiple nucleation of domains of a new phase on randomly located defects in the volume. The corresponding statistically-kinetic problem is solved with the calculation of the average magnitude and dispersion of path lengths, as well as the full generating function for finding higher moments of distribution of “the relay” run lengths of the boundary of the edge domain.