Commit 55a6a0ee authored by Felix Hilsky's avatar Felix Hilsky
Browse files

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]
[162]{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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