Action minimization and macroscopic interface motion under forced displacement
Mathematical Physics
2017-03-07 v2 Analysis of PDEs
math.MP
Abstract
We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be quantified by obtaining the large deviations cost functional from the underlying stochastic process. For such a functional, derived in a companion paper, we investigate the optimal way for a macroscopic interface to move from an initial to a final position distant by R within fixed time T. We find that for small values of R/T the interface moves with a constant speed, while for larger values there appear nucleations of the other phase ahead of the front.
Cite
@article{arxiv.1610.00605,
title = {Action minimization and macroscopic interface motion under forced displacement},
author = {P. Birmpa and D. Tsagkarogiannis},
journal= {arXiv preprint arXiv:1610.00605},
year = {2017}
}