Moved by.eps.

Revisions requested, small errors fixed.

Signed-off-by: Paul Ganssle <pganssle@berkeley.edu>

.gitignore

@@ -2,3 +2,11 @@
 *.pyc
 Thumbs.db
 /figures/scripts/analyzedata/load_hist.pkl
+*.aux
+*.bbl
+*.brf
+*.synctex.gz
+*.out
+*.log
+*.toc
+*.blg

PaulGanssle-Thesis.tex

@@ -116,8 +116,7 @@
 \usepackage{styles/aasmacros,amsmath,amssymb}
 \usepackage{styles/mydeluxetable} % deluxetable customized to play well with ucthesis
 
-\usepackage{tipa}
-%\usepackage{algc}
+\usepackage[safe]{tipa}
 \usepackage{listings}
 \usepackage{textcomp}
 \lstset{basicstyle=\ttfamily\scriptsize,
@@ -157,7 +156,6 @@
 \maketitle
 
 \copyrightpage
-%\approvalpage
 
 \begin{abstract}
 The availability of high-sensitivity magnetic sensors such as alkali vapor-cell magnetometers has fueled a growing body of literature on the development of inexpensive, portable and robust magnetic resonance systems which operate in ultra-low magnetic fields. This work covers the design, construction and operation of such a magnetometer, and its use as a high-sensitivity low-field detector of in nuclear magnetic resonance (NMR) experiments, including zero-field J-spectroscopy, relaxometry and diffusometry. In particular, we have attempted to demonstrate the utility of these devices for 1- and 2-dimensional relaxometry and diffusometry measurements, which are currently a significant commercial application of low-field NMR.

acknowledgements.tex

@@ -1,5 +1,4 @@
 \documentclass[PaulGanssle-Thesis.tex]{subfiles}
-
 \begin{document}
 
 \begin{acknowledgements}

console.tex

@@ -774,7 +774,7 @@ \subsubsection{Pulse Program (.pp) Files}
 \label{Section:NDPCHeader}
 This section concerns the variation components of the pulse program and is only present if at least one instruction is varied either along an indirect dimension or a phase cycle. These are a set of various arrays used to determine the parameters of the program and how indexing proceeds. Phase cycling and multidimensional experiments both represent modifications to a base program which replace one or more of the instructions from the original set; as such, the two features are implemented using a common core set of functions. 
 
-The ``variation space'' has dimensionality $nd+nc$ where $nd$ is the number of dimensions and $nc$ is the number of phase cycles. The size of the sampling grid (which can be subsampled using the Skip functionality described in Section \ref{Section:Console-Subsampling}) is defined as $[sd_1, sd_2, ... sd_{nd}, sc_{1}, ... , sc_{nc}]$ where $sd_{n}$ is the number of points in the $n^{\mathrm{th}}$ indirect dimension, and $sc_{n}$ is the number of points in the $n^{\mathrm{th}}$ phase cycle. The size of the \textit{entire} grid as stored is $[sd_{1}, ... , sd_{nd}, sc_{1}, ..., sc_{nc}, nr]$ where $nr$ is the number of times the full phase set of phase cycles is repeated, given by:
+The ``variation space'' has dimensionality $nd+nc$ where $nd$ is the number of dimensions and $nc$ is the number of phase cycles. The size of the sampling grid (which can be subsampled using the Skip functionality described in Section \ref{Section:Console-Subsampling}) is defined as $[sd_1,$ $sd_2,$ $...$ $sd_{nd},$ $sc_{1},$ $...$ $, sc_{nc}]$ where $sd_{n}$ is the number of points in the $n^{\mathrm{th}}$ indirect dimension, and $sc_{n}$ is the number of points in the $n^{\mathrm{th}}$ phase cycle. The size of the \textit{entire} grid as stored is $[sd_{1},$ $...$ $, sd_{nd},$ $sc_{1},$ $...,$ $sc_{nc},$ $nr]$ where $nr$ is the number of times the full phase set of phase cycles is repeated, given by:
 
 \begin{equation*}
 nr= \frac{nt}{\prod_{i=0}^{nc}sd_{i}},

design.tex

@@ -128,7 +128,7 @@ \subsection{NMR Pulses}
 
 \begin{equation}
 \label{eqn:SpinTipAngle}
-\theta_p = \int_0^{t_p}\!\gamma B_1(t)t\textrm{d}t
+\theta_p = \int_0^{t_p}\!\gamma B_1(t)t\mathrm{d}t
 \end{equation}
 
 For a stationary pulse applied to spins at zero field, $B_1$ is constant, and so $\theta_p = \gamma B_1 t$, but in the presence of a bias offset field $B_0 \gg B_1$ along $\vec{\mathbf{z}}$, spins tipped transverse to the field will precess at frequency $\omega_0$, and so the transverse amplitude varies as a function of time. The natural coordinate system for analyzing the spin evolution of such a system is not the laboratory frame but a rotating frame of reference in which unperturbed spins are stationary. This can be achieved by defining time-dependent axes $\vec{\mathbf{x'}}$ and $\vec{\mathbf{y'}}$:

nmrexperiments.tex

@@ -114,7 +114,7 @@ \subsection{Application}
 
 For the case of carbon-hydrogen pairs, $\gamma_H \approx 4\gamma_C$, so $P_{\uparrow\downarrow} = \sfrac{3}{8}$, while $P_{\uparrow\uparrow} = \sfrac{5}{8}$, and so the signal can be increased if the spins can be pulsed out of phase of one another. This has the additional advantage of allowing the ``start point'' of the experiment to be determined by the pulse, ensuring a consistent phase between transients. In the case of carbon and hydrogen, the simple 4:1 ratio allows $I_{z} + S_{z}$ terms to be easily transformed into $I_{z} - S_{z}$ terms (and vice-versa) by applying a $4\pi_{x}$ pulse to the hydrogens, which corresponds to a $\pi$ pulse to the carbons. This is particularly convenient because it starts the spins aligned along the $z$ axis, which is the sensitive direction of the magnetometer. 
 
-In the more general case, for a pulse about the $y$ axis of angle $\theta_{I} = \theta + \frac{\Delta}{2}$ on spins $I_{z}$ and angle $\theta_{S} = \theta + \frac{\Delta}{2}$ $^{[}$\footnote{From this definition $\Delta = \frac{\theta_{I}\gamma_{S}}{2\gamma_{I}}$.}$^{]}$ on the $S_z$ spins applied to spins initially aligned along $I_{z} + S_{z}$, the density matrix evolves in Eqn \ref{eqn:ISPulseEvolution}\footnote{A full proof for this assertion is found in Sec. \label{proofs.qm.jcoupling.pulseapplied}}:
+In the more general case, for a pulse about the $y$ axis of angle $\theta_{I} = \theta + \frac{\Delta}{2}$ on spins $I_{z}$ and angle $\theta_{S} = \theta + \frac{\Delta}{2}$ $^{[}$\footnote{From this definition $\Delta = \frac{\theta_{I}\gamma_{S}}{2\gamma_{I}}$.}$^{]}$ on the $S_z$ spins applied to spins initially aligned along $I_{z} + S_{z}$, the density matrix evolves in Eqn \ref{eqn:ISPulseEvolution}\footnote{A full proof for this assertion is found in Sec. \ref{proofs.qm.jcoupling.pulseapplied}}:
 
 \begin{align}
 \label{eqn:ISPulseEvolution}
@@ -123,7 +123,6 @@ \subsection{Application}
 \end{align}
 
 Both $I_{z} - S_{z}$ and $I_{x} - S_{x}$ represent evolving, singlet polarization, along different spatial axes under the zero-quantum coherences evolving under the J-coupling Hamiltonian, and they are maximized when $\Delta = n\pi$ for  $n \in \mathbbm{Z}$, and so the optimal pulse length on the $\mathbf{I}$ spins is:
-%\mathbb{Z}
 
 \begin{align}
 \theta_{I,op} & = \theta_{S,op} - n\pi \nonumber\\ 

ucthesis.cls

@@ -441,7 +441,7 @@ by\par
 Some rights reserved\par 
 \begin{figure*}[b]
 \centering
-\includegraphics[width=0.4\textwidth]{by.eps}\par
+\includegraphics[width=0.4\textwidth]{figures/general/by.eps}\par
 This work is licensed under a Creative Commons Attribution 4.0 International License (CC-BY 4.0)
 \end{figure*}}
 \end{center}