### 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) |
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Article number | 095107 |

Journal | Journal of Mathematical Physics |

Volume | 46 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2005 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Berlyand, L., & Khruslov, E. (2005). Ginzburg-Landau model of a liquid crystal with random inclusions.

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