### Satisfaction of the eigenvalue constraints on the $Q$-tensor

**Ball, J ***(University of Oxford)*

Monday 18 March 2013, 09:00-09:50

Seminar Room 1, Newton Institute

#### Abstract

We discuss how Onsager theory with the Maier-Saupe interaction leads naturally to a bulk free energy depending on the $Q$-tensor that blows up as the minimum eigenvalue $\lambda_{\rm min}(Q)\rightarrow -1/3$, using methods closely related to those of Katriel, Kventsel, Luckhurst and Sluckin (1986). With this bulk energy, and in the one constant approximation for the elastic energy, it is shown that for suitable boundary conditions, minimizers $Q$ of the total free energy for a nematic liquid crystal filling a region $\Omega$ satisfy the physical requirement that $\inf_{x\in\Omega}\lambda_{\rm min}(Q(x))>-1/3$.

#### Presentation

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