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.
Accepté le :
DOI : 10.1051/cocv/2017021
Keywords: Action minimization, large deviations functional, sharp-interface limit, non-local Allen−Cahn equation, nucleation
Birmpa, Panagiota 1 ; Tsagkarogiannis, Dimitrios 1
@article{COCV_2018__24_2_765_0,
author = {Birmpa, Panagiota and Tsagkarogiannis, Dimitrios},
title = {Action minimization and macroscopic interface motion under forced displacement},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {765--792},
year = {2018},
publisher = {EDP Sciences},
volume = {24},
number = {2},
doi = {10.1051/cocv/2017021},
zbl = {1404.82043},
mrnumber = {3816414},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2017021/}
}
TY - JOUR AU - Birmpa, Panagiota AU - Tsagkarogiannis, Dimitrios TI - Action minimization and macroscopic interface motion under forced displacement JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 765 EP - 792 VL - 24 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2017021/ DO - 10.1051/cocv/2017021 LA - en ID - COCV_2018__24_2_765_0 ER -
%0 Journal Article %A Birmpa, Panagiota %A Tsagkarogiannis, Dimitrios %T Action minimization and macroscopic interface motion under forced displacement %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 765-792 %V 24 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2017021/ %R 10.1051/cocv/2017021 %G en %F COCV_2018__24_2_765_0
Birmpa, Panagiota; Tsagkarogiannis, Dimitrios. Action minimization and macroscopic interface motion under forced displacement. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 765-792. doi: 10.1051/cocv/2017021
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