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.
Accepted:
DOI: 10.1051/cocv/2017021
Keywords: Action minimization, large deviations functional, sharp-interface limit, non-local Allen−Cahn equation, nucleation
@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}, publisher = {EDP-Sciences}, volume = {24}, number = {2}, year = {2018}, doi = {10.1051/cocv/2017021}, zbl = {1404.82043}, mrnumber = {3816414}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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, Volume 24 (2018) no. 2, pp. 765-792. doi : 10.1051/cocv/2017021. http://archive.numdam.org/articles/10.1051/cocv/2017021/
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