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Sharp-Interface Limit of a Ginzburg–Landau Functional with a Random External Field


Reference:

Dirr, N. and Orlandi, E., 2009. Sharp-Interface Limit of a Ginzburg–Landau Functional with a Random External Field. SIAM Journal on Mathematical Analysis (SIMA), 41 (2), pp. 781-824.

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Official URL:

http://dx.doi.org/10.1137/070684100

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.

Details

Item Type Articles
CreatorsDirr, N.and Orlandi, E.
DOI10.1137/070684100
Uncontrolled Keywordsrandom functionals, phase segregation in disordered materials, gamma-convergence
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code14983

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