### 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 | |

State | Published - Sep 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*46*(9), [095107]. https://doi.org/10.1063/1.2013127

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*Journal of Mathematical Physics*, vol. 46, no. 9, 095107. https://doi.org/10.1063/1.2013127

**Ginzburg-Landau model of a liquid crystal with random inclusions.** / Berlyand, L.; Khruslov, E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Ginzburg-Landau model of a liquid crystal with random inclusions

AU - Berlyand, L.

AU - Khruslov, E.

PY - 2005/9/1

Y1 - 2005/9/1

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.

UR - http://www.scopus.com/inward/record.url?scp=26444516550&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26444516550&partnerID=8YFLogxK

U2 - 10.1063/1.2013127

DO - 10.1063/1.2013127

M3 - Article

AN - SCOPUS:26444516550

VL - 46

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

M1 - 095107

ER -