Volume 24, Number 2, April–June 2018
|Page(s)||765 - 792|
|Published online||13 June 2018|
Action minimization and macroscopic interface motion under forced displacement
Department of Mathematics, University of Sussex,
a Corresponding author: P.Birmpa@sussex.ac.uk
Revised: 22 February 2017
Accepted: 3 March 2017
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.
Mathematics Subject Classification: 82C24 / 49J
Key words: Action minimization / large deviations functional / sharp-interface limit / non-local Allen−Cahn equation / nucleation
© EDP Sciences, SMAI 2018
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