### include sentences about Landau and de Gennes

still no mention of the Nobel prize!
parent 26ee66e9
 ... ... @@ -141,10 +141,15 @@ The director field minimizes the \enquote{Frank-Oseen energy}. \end{figure} The Frank-Oseen model is simple but has shortcomings. We address one of them, namely that These were addressed in 1974 by \textcite{q48-original-de-gennes}. He formulated another model of so-called \newTerm{$Q$-tensors} that are described in \cref{sec:qtensor}. It is based on the solid-liquid phase transition theory of Lev Landau \parencite%[Section 4] {q45-LCD} and is therefore called Landau-de Gennes model. We address only one of the shortcomings, namely that % The paper of \textcite{q4-Ball2011} and this thesis address one of the shortcomings: % die haben sich das ja nicht ausgedacht the two ends of the rod-like molecules are equal so that the opposite orientation is actually the same. Therefore it is more appropriate to use a \newTerm{line field} instead of a unit vector field. \cref{sec:fs-vs-ldg} describes in which way line fields are a special case of $Q$-tensors. \begin{figure}[htbp] \centering \includegraphics[width=0.8\textwidth,height=5cm,keepaspectratio]{.maindir/zeichnungen/unorientable-line-field} ... ... @@ -155,8 +160,8 @@ Therefore it is more appropriate to use a \newTerm{line field} instead of a unit \label{fig:unorientable_line_field} \end{figure} \cref{fig:unorientable_line_field} illustrates how we can picture a line field on a flat domain. Mathematically the codomain of the line field is the real projective space. Since unit vector fields are easier and more common to handle mathematically the question is: Mathematically the codomain of a line field is the real projective space. Since unit vector fields are easier and more common to handle mathematically than maps into a projective space the question is: \begin{quote} Do we get a correct result if we work with unit vector fields or do we have to use line fields? \end{quote} ... ...
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