Minor updates.

Author: jvdoorn

chapters/appendices/q_factors.tex

@@ -48,7 +48,7 @@ \section{Decay time}
 We now see that the definition of the Q-factor in terms of the decay time is equivalent to the definition in terms of the FWHM in the power spectrum.
 
 \section{Summary}
-In summary, calculating a Q-factor can be done in four ways: by looking at the decay time of the energy, the decay time of the amplitude, the FWHM in the power spectrum or the FWHM in the Fourier spectrum. The table below provides a overview on how to calculate the Q-factor based on your observations.
+In summary, calculating a Q-factor can be done in four ways: by looking at the decay time of the energy, the decay time of the amplitude, the FWHM in the power spectrum or the FWHM in the Fourier spectrum. The table below provides a overview on how to calculate the Q-factor based on your observations. The resulting Q-factor is the same for all methods, thus it can be used to convert between different observations.
 
 \begin{table}[h]
     \centering

chapters/conventions.tex

@@ -1,9 +1,9 @@
 \chapter*{Conventions}
 \label{chap:conventions}
-In this thesis we regularly have to project 3D structures onto a 2D plane. To clarify the x-, y- and z-directions they have been color coded. This is done consistently throughout the thesis and matches with the colors assigned to the axes by COMSOL. The x-direction is colored in \textcolor{x_axis_color}{red}, the y-direction in \textcolor{y_axis_color}{green} and the z-direction in \textcolor{blue}{blue}. Additionally an attempt has been made to optimize figures for colorblind readers based on Paul Tol's color schemes\cite{paul_tol}.
+In this thesis we regularly have to project 3D structures onto a 2D plane. To clarify the x-, y- and z-directions, they have been color coded. This is done consistently throughout the thesis and matches with the colors assigned to the axes by COMSOL. The x-direction is colored in \textcolor{x_axis_color}{red}, the y-direction in \textcolor{y_axis_color}{green} and the z-direction in \textcolor{blue}{blue}. Additionally an attempt has been made to optimize figures for colorblind readers based on Paul Tol's color schemes\cite{paul_tol}.
 
-Furthermore, when a damping rate or Q-factor is given, we use the following definition:
+Furthermore, when a damping rate ($\gamma$) or Q-factor is given, we use the following definition:
 \begin{equation*}
-    Q = \frac{\text{energy stored}}{\text{energy dissipated per cycle}}
+    Q = \omega_0 \frac{\text{energy stored}}{\text{dissipation}} = \frac{\omega_0}{\gamma}
 \end{equation*}
-Another common way of expressing the Q-factor is in terms of the oscillations amplitude. This Q-factor is a factor $???$ higher than the Q-factor defined above.
+where $\omega_0$ is the resonance frequency. More information on the definition and conversion of Q-factors can be found in Appendix~\ref{app:q_factors}.

chapters/results.tex

@@ -57,7 +57,7 @@ \section{Measurements at atmospheric pressure}
 
 \section{Measurements at low pressure}
 \label{sec:measurements-at-low-pressure}
-At \qty{1}{\milli\bar} the readout was performed using the Thorcam and analysed using our custom object tracking algorithm. The reason to no longer use laser readout is due to the heating of the particle. By equating the power of the laser to Stefan-Boltzmann law we find that, in equillibrium assuming no heat dissipation through air, the temperature of the particle could reach \qty{2500}{\kelvin}. Even if only a fraction of the laser power would reach the particle this would be enough to reach its Curie temperature. Lower laser powers lead to an insufficient signal-to-noise ratio. We will return to this in the discussion.
+At \qty{1}{\milli\bar} the readout was performed using the Thorcam and analysed using our custom object tracking algorithm. The reason to no longer use laser readout is due to the heating of the particle. By equating the power of the laser to Stefan-Boltzmann law we find that, in equillibrium assuming no heat dissipation through air, the temperature of the particle could reach \qty{2500}{\kelvin}. Even if only a fraction of the laser power would reach the particle this would be enough to reach its Curie temperature. Lower laser powers lead to an insufficient signal-to-noise ratio. We will return to this in the discussion. For a more thorough analysis of heating refer to \cite{millen}.
 
 \begin{SCfigure}
     \centering