Ginzburg-Landau model of a liquid crystal with random inclusions

L. Berlyand; E. Khruslov

doi:10.1063/1.2013127

Ginzburg-Landau model of a liquid crystal with random inclusions

L. Berlyand, E. Khruslov

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Abstract

We consider a Ginzburg-Landau three-dimensional functional with a surface energy term to model a nematic liquid crystal with inclusions. The locations and radii of the inclusions are randomly distributed and described by a set of finite dimensional distribution functions. We show that the presence of inclusions can be accounted for by an effective potential. Our main objectives are (a) to derive the sufficient conditions on the distribution functions such that the solutions converge in probability to a solution of a homogenized deterministic problem and (b) to compute the effective potential.

Original language	English (US)
Article number	095107
Journal	Journal of Mathematical Physics
Volume	46
Issue number	9
DOIs	https://doi.org/10.1063/1.2013127
State	Published - Sep 2005

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.2013127

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title = "Ginzburg-Landau model of a liquid crystal with random inclusions",

abstract = "We consider a Ginzburg-Landau three-dimensional functional with a surface energy term to model a nematic liquid crystal with inclusions. The locations and radii of the inclusions are randomly distributed and described by a set of finite dimensional distribution functions. We show that the presence of inclusions can be accounted for by an effective potential. Our main objectives are (a) to derive the sufficient conditions on the distribution functions such that the solutions converge in probability to a solution of a homogenized deterministic problem and (b) to compute the effective potential.",

author = "L. Berlyand and E. Khruslov",

note = "Funding Information: The first author (L.B.) was supported in part by NSF Grant No. DMS-0204637. This work started when both authors were visiting the Department of Mathematics and Computer Science, University of Akron in the academic year 1999∕2000. They are grateful for the support and hospitality received during this visit. The authors wish to thank D. Golovaty for careful reading of the paper and very useful suggestions.",

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AU - Khruslov, E.

N1 - Funding Information: The first author (L.B.) was supported in part by NSF Grant No. DMS-0204637. This work started when both authors were visiting the Department of Mathematics and Computer Science, University of Akron in the academic year 1999∕2000. They are grateful for the support and hospitality received during this visit. The authors wish to thank D. Golovaty for careful reading of the paper and very useful suggestions.

PY - 2005/9

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N2 - We consider a Ginzburg-Landau three-dimensional functional with a surface energy term to model a nematic liquid crystal with inclusions. The locations and radii of the inclusions are randomly distributed and described by a set of finite dimensional distribution functions. We show that the presence of inclusions can be accounted for by an effective potential. Our main objectives are (a) to derive the sufficient conditions on the distribution functions such that the solutions converge in probability to a solution of a homogenized deterministic problem and (b) to compute the effective potential.

AB - We consider a Ginzburg-Landau three-dimensional functional with a surface energy term to model a nematic liquid crystal with inclusions. The locations and radii of the inclusions are randomly distributed and described by a set of finite dimensional distribution functions. We show that the presence of inclusions can be accounted for by an effective potential. Our main objectives are (a) to derive the sufficient conditions on the distribution functions such that the solutions converge in probability to a solution of a homogenized deterministic problem and (b) to compute the effective potential.

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ER -

Ginzburg-Landau model of a liquid crystal with random inclusions

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