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

Nicolas Dirr, E Orlandi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)781-824
Number of pages44
JournalSIAM Journal on Mathematical Analysis (SIMA)
Volume41
Issue number2
DOIs
Publication statusPublished - 2009

Keywords

  • random functionals
  • phase segregation in disordered materials
  • Gamma-convergence

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