Sharp-interface limit of a Ginzburg-Landau functional with a random external field

Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367 and Orlandi, Enza 2009. Sharp-interface limit of a Ginzburg-Landau functional with a random external field. SIAM Journal on Mathematical Analysis 41 (2) , pp. 781-824. 10.1137/070684100

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Abstract

We add a random bulk term, modeling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double-well potential. For the resulting functional we study the asymptotic properties of minimizers and minimal energy under a rescaling in space, i.e., on the macroscopic scale. By bounding the energy from below by a coarse-grained, discrete functional, we show that for a suitable strength of the random field the random energy functional has two types of random global minimizers, corresponding to two phases. Then we derive the macroscopic cost of low energy “excited” states that correspond to a bubble of one phase surrounded by the opposite phase.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0036-1410/ (accessed 28/02/2014).
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0036-1410
Date of First Compliant Deposit:	30 March 2016
Last Modified:	10 May 2023 13:14
URI:	https://orca.cardiff.ac.uk/id/eprint/13064

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