From: W. Trevor King <wking@drexel.edu>
Date: Thu, 11 Mar 2010 18:34:16 +0000 (-0500)
Subject: Fixed typos Mom found in the appenidicies + switched cantilver-calib to cref
X-Git-Tag: v1.0~429
X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=853ba96ff94fe3e53877904e8783c6357eb103fe;p=thesis.git

Fixed typos Mom found in the appenidicies + switched cantilver-calib to cref

Use - instead of _ in labels (I think it looks nicer :).

Note that using multiple references in \cref in appendicies
  \cref{eq:res-thm,eq:res-simple}
breaks with cleveref v0.14.2 (but works with v0.15.3).  The errors were:
  ! Missing number, treated as zero.
  <to be read again>
                     {
  l.94 Applying \cref{eq:res_thm,eq:res_simple}
Caused by \@results like
  {2147483647}\@result
rather than the newer
  2147483647,\@result
---

diff --git a/tex/src/cantilever-calib/contour_integration.tex b/tex/src/cantilever-calib/contour_integration.tex
index 1bcb399..7ef39f9 100644
--- a/tex/src/cantilever-calib/contour_integration.tex
+++ b/tex/src/cantilever-calib/contour_integration.tex
@@ -1,39 +1,43 @@
 \section{Contour integration}
 
+As a brief review, some definite integrals from $-\infty$ to $\infty$
+can be evaluated by integrating along the contour \C\ 
+shown in \cref{fig:UHP-contour}.
+
 \begin{figure}
   \asyfig{figures/contour/contour}
-  \caption{Integral contour \C\ enclosing the upper half plane.
-    \label{f.UHP_contour}}
+  \caption{Integral contour \C\ enclosing the upper half of the
+    complex plane.  If the integrand $f(z)$ goes to zero ``quickly
+    enough'' as the radius of \C\ approaches
+    infinity\nomenclature{$\infty$}{Infinity}, then the only
+    contribution comes from integration along the real axis (see text
+    for details).\label{fig:UHP-contour}}
 \end{figure}
 
-As a brief review, some definite integrals from $-\infty$ to $\infty$
-can be evaluated by integrating along the contour \C\ 
-shown in Figure \ref{f.UHP_contour}.
-
 A sufficient condition on the function $f(z)$ to be integrated, is
 that $\lim_{|z|\rightarrow\infty}|f(z)|$ falls off at least as fast as
 $\frac{1}{z^2}$.
 When this is the case, the integral around the outer semicircle of \C\ is 0,
 so the $\iC{f(z)} = \iInfInf{z}{f(z)}$.
 
-We can evaluate the integral using residue theorem
+We can evaluate the integral using the residue theorem\index{residue theorem},
 \begin{equation}
   \iC{f(x)} = \sum_{z_p \in \text{poles in \C}} 2\pi i \Res{z_p}{f(z)},
-                                        \label{eq.res_thm}
+                                        \label{eq:res-thm}
 \end{equation}
 where for simple poles (single roots)
 \begin{equation}
-  \Res{z_p}{f(z)} = \limZp(z-z_p) f(z), \label{eq.res_simple}
+  \Res{z_p}{f(z)} = \limZp(z-z_p) f(z), \label{eq:res-simple}
 \end{equation}
 and in general for a pole of order $n$
 \begin{equation}
   \Res{z_p}{f(z)} = \frac{1}{(n-1)!} \cdot\limZp
                        \nderiv{n-1}{z}{}\left[ (z-z_p)^n \cdot f(z) \right]
-                                        \label{eq.res_general}
+                                        \label{eq:res-general}
 \end{equation}
 
 %We also use the following theorem
-%\begin{thm} \label{thm.res_even_fn}
+%\begin{thm} \label{thm:res-even-fn}
 %If $f(z) = f(-z)$, then $\Res{z_p}{f(z)} = \Res{-z_p}{f(z)}$.\\
 %\end{thm}
 %\begin{proof}
diff --git a/tex/src/cantilever-calib/integrals.tex b/tex/src/cantilever-calib/integrals.tex
index d9b6752..3d41a35 100644
--- a/tex/src/cantilever-calib/integrals.tex
+++ b/tex/src/cantilever-calib/integrals.tex
@@ -1,5 +1,5 @@
 \section{Integrals}
-\label{sec.integrals}
+\label{sec:integrals}
 
 \subsection{Highly damped integral}
 
@@ -30,10 +30,10 @@ and that $f(z)$ is even, so
 \begin{equation}
   I = \iC{\frac{1}{(a^2-z^2)^2 + b^2 z^2}},
 \end{equation}
-where \C\ is the contour shown in Figure \ref{f.UHP_contour}.
+where \C\ is the contour shown in \cref{fig:UHP-contour}.
 
 Because the denominator is of the form $A^2 + B^2$, we can factor it
-into $(A+iB)(A-iB)$ like so % thanks Prof. Yuan
+into $(A+iB)(A-iB)$. % thanks Prof. Yuan
 \begin{equation}
   (a^2-z^2)^2 + b^2 z^2
       = (a^2-z^2 \colA{+} ibz)(a^2-z^2 \colA{-} ibz)
@@ -91,7 +91,7 @@ Our factored function $f(z)$ is
   f(z) = \frac{1}{(z-z_{r+})(z+z_{r+})(z+z_{r-})(z-z_{r-})}
 \end{equation}
 
-Applying eq. \ref{eq.res_thm} and \ref{eq.res_simple} we have
+Applying \cref{eq:res-thm,eq:res-simple} we have
 \begin{align}
   I &= 2\pi i \left( \Res{z_{r+}}{f(z)} + \Res{z_{r-}}{f(z)} \right) \\
     &= 2\pi i \left(
@@ -118,7 +118,7 @@ Applying eq. \ref{eq.res_thm} and \ref{eq.res_simple} we have
     &= \frac{ 4\pi }{ b^3 (1 - S^2)} \\
     &= \frac{ 4\pi }{ b^3 [1 - (1-4\frac{a^2}{b^2})]} \\
     &= \frac{ 4\pi }{ b^3 \cdot 4\frac{a^2}{b^2}} \\
-                         &= \frac{ \pi }{ b a^2 } \label{eq.gen_int_noncrit}
+                         &= \frac{ \pi }{ b a^2 } \label{eq:gen-int-noncrit}
 \end{align}
 Hooray!
 
@@ -129,7 +129,7 @@ Our factored function $f(z)$ is
   f(z) = \frac{1}{(z-z_{r+})^2(z-z_{r-})^2}
 \end{equation}
 
-Applying eq. \ref{eq.res_thm} and \ref{eq.res_general} we have
+Applying \cref{eq:res-thm,eq:res-general} we have
 \begin{align}
   I &= 2\pi i \Res{z_{r+}}{f(z)} \\
     &= \colA{2}\pi i \left( \colA{\frac{1}{2!}}
@@ -140,6 +140,6 @@ Applying eq. \ref{eq.res_thm} and \ref{eq.res_general} we have
     &= - 2 \pi i \frac{1}{z_{r+}^3} \\
     &= \colA{-} 2 \pi \colA{i} \frac{1}{(\frac{\colA{i}b}{2})^3} \\
     &= \frac{\pi}{b (\frac{b}{2})^2} \\
-    &= \frac{\pi}{b a^2}, \label{eq.gen_int_crit}
+    &= \frac{\pi}{b a^2}, \label{eq:gen_int_crit}
 \end{align}
-which matches eq. \ref{eq.gen_int_noncrit}
+which matches \cref{eq:gen-int-noncrit}
diff --git a/tex/src/cantilever-calib/overview.tex b/tex/src/cantilever-calib/overview.tex
index 2948376..5144afe 100644
--- a/tex/src/cantilever-calib/overview.tex
+++ b/tex/src/cantilever-calib/overview.tex
@@ -7,7 +7,7 @@ via Hooke's law $F = -kx$.
 
 The basic idea is to use the equipartition theorem\cite{hutter93},
 \begin{equation}
-  \frac{1}{2} k \avg{x^2} = \frac{1}{2} k_BT \label{eq.equipart},
+  \frac{1}{2} k \avg{x^2} = \frac{1}{2} k_BT \label{eq:equipart},
 \end{equation}
 where $k_B$ is Boltzmann's constant, 
  $T$ is the absolute temperature, and
@@ -18,7 +18,7 @@ where $k_B$ is Boltzmann's constant,
 \end{equation}
 Solving the equipartition theorem for $k$ yields
 \begin{equation}
-  k = \frac{k_BT}{\avg{x^2}}, \label{eq.equipart_k}
+  k = \frac{k_BT}{\avg{x^2}}, \label{eq:equipart_k}
 \end{equation}
 so we need to measure (or estimate) the temperature $T$ and variance
 of the cantilever position $\avg{x^2}$ in order to estimate $k$.
@@ -40,7 +40,7 @@ power spectral density\cite{roters96}. %,
 
 \emph{WARNING}: It is popular to refer to the power spectral density
 as a ``Lorentzian''\cite{hutter93,roters96,levy02,florin95} even
-though eq.~\ref{eq.model_psd} differs from the classic
+though \cref{eq:model-psd} differs from the classic
 Lorentzian\cite{mathworld_lorentzian}.
 \begin{equation}
   L(x) = \frac{1}{\pi}\frac{\frac{1}{2}\Gamma}
@@ -48,8 +48,8 @@ Lorentzian\cite{mathworld_lorentzian}.
 \end{equation}
 It is unclear whether the references are due to uncertainty about the
 definition of the Lorentzian or to the fact that
-eq.~\ref{eq.model_psd} is also peaked.  In order to avoid any
-uncertainty, we will leave eq.~\ref{eq.model_psd} unnamed.
+\cref{eq:model-psd} is also peaked.  In order to avoid any
+uncertainty, we will leave \cref{eq:model-psd} unnamed.
 
 \section{Methods}
 
@@ -63,26 +63,26 @@ while the tip is in contact with the surface) via
 Rather than computing the variance of $x(t)$ directly, we attempt to
 filter out noise by fitting the spectral power density (\PSD) of
 $x(t)$ to the theoretically predicted \PSD\ for a damped harmonic
-oscillator (eq.~\ref{eq.model_psd})
+oscillator (\cref{eq:model-psd})
 \begin{align}
   \ddt{x} + \beta\dt{x} + \omega_0^2 x &= \frac{F_\text{thermal}}{m} \\
   \PSD(x, \omega) &= \frac{G_1}{(\omega_0^2-\omega^2)^2 + \beta^2\omega^2},
 \end{align}
 where $G_1\equiv G_0/m^2$, $\omega_0$, and $\beta$ are used as the
-fitting parameters (see eqn.s \ref{eq.model_psd}).  The variance of
-$x(t)$ is then given by eq.~\ref{eq.DHO_var}
+fitting parameters (see \cref{eq:model-psd}).  The variance of $x(t)$
+is then given by \cref{eq:DHO-var}
 \begin{equation}
   \avg{x(t)^2} = \frac{\pi G_1}{2\beta\omega_0^2},
 \end{equation}
 which we can plug into the equipartition theorem
-(eqn.~\ref{eq.equipart}) yielding
+(\cref{eq:equipart}) yielding
 \begin{align}
   k = \frac{2 \beta \omega_0^2 k_BT}{\pi G_1}.
 \end{align}
 
-From eqn. \ref{eq.GO}, we find the expected value of $G_1$ to be
+From \cref{eq:GO}, we find the expected value of $G_1$ to be
 \begin{equation}
-  G_1 \equiv G_0/m^2 = \frac{2}{\pi m} k_BT \beta.  \label{eq.Gone}
+  G_1 \equiv G_0/m^2 = \frac{2}{\pi m} k_BT \beta.  \label{eq:Gone}
 \end{equation}
 
 
@@ -111,17 +111,17 @@ Plugging into the equipartition theorem yeilds
     = \frac{2 \beta\omega_0^2 \sigma_p^2 k_BT}{\pi G_{1p}}.
 \end{align}
 
-From eqn. \ref{eq.Gone}, we find the expected value of $G_{1p}$ to be
+From \cref{eq:Gone}, we find the expected value of $G_{1p}$ to be
 \begin{equation}
   G_{1p} \equiv \sigma_p^2 G_1 = \frac{2}{\pi m} \sigma_p^2 k_BT \beta.
-    \label{eq.Gone-p}
+    \label{eq:Gone-p}
 \end{equation}
 
 
 \subsection{Fitting deflection voltage in frequency space}
 
 Note: the math in this section depends on some definitions from
-section \ref{sec.setup}.
+section \cref{sec:setup}.
 
 As yet another alternative, you could fit in frequency
 $f\equiv\omega/2\pi$ instead of angular frequency $\omega$.  But we
@@ -142,7 +142,7 @@ from which we can translate the \PSD
     = 2\pi \PSD(x, \omega=2\pi f).
 \end{align}
 The variance of the function $x(t)$ is then given by plugging into
-eqn.~\ref{eq.parseval_var} (our corollary to Parseval's theorem)
+\cref{eq:parseval-var} (our corollary to Parseval's theorem)
 \begin{align}
   \avg{x(t)^2} &= \iOInf{\omega}{\PSD(x,\omega)}
      = \iOInf{f}{\frac{1}{2\pi}\PSD_f(x,f)2\pi\cdot}
@@ -166,11 +166,11 @@ $G_{1f}\equiv G_{1p}/8\pi^3$.  Finally
     = \frac{2 \beta_f f_0^2 \sigma_p^2 k_BT}{\pi G_{1f}}.
 \end{align}
 
-From eqn. \ref{eq.Gone}, we expect $G_{1f}$ to be
+From \cref{eq:Gone}, we expect $G_{1f}$ to be
 \begin{equation}
   G_{1f} = \frac{G_{1p}}{8\pi^3}
     = \frac{\sigma_p^2 G_1}{8\pi^3}
     = \frac{\frac{2}{\pi m} \sigma_p^2 k_BT \beta}{8\pi^3}
     = \frac{\sigma_p^2 k_BT \beta}{4\pi^4 m}.
-    \label{eq.Gone-f}
+    \label{eq:Gone-f}
 \end{equation}
diff --git a/tex/src/cantilever-calib/setup_general.tex b/tex/src/cantilever-calib/setup_general.tex
index d391a05..0961638 100644
--- a/tex/src/cantilever-calib/setup_general.tex
+++ b/tex/src/cantilever-calib/setup_general.tex
@@ -1,9 +1,9 @@
 \section{Theoretical power spectral density for a damped harmonic oscillator}
-\label{sec.setup}
+\label{sec:setup}
 
 Our cantilever can be approximated as a damped harmonic oscillator
 \begin{equation}
-  m\ddt{x} + \gamma \dt{x} + k x = F(t), \label{eq.DHO}
+  m\ddt{x} + \gamma \dt{x} + k x = F(t), \label{eq:DHO}
   % DHO for Damped Harmonic Oscillator
 \end{equation}
 where $x$ is the displacement from equilibrium,
@@ -22,13 +22,13 @@ In the following analysis, we use the unitary, angular frequency Fourier transfo
 We also use the following theorems (proved elsewhere):
 \begin{align}
   \cos\left(\frac{\theta}{2}\right) &= \pm\sqrt{\frac{1}{2}[1+\cos(\theta)]}
-     &\text{\cite{cos_halfangle},} \label{eq.cos_halfangle} \\
+     &\text{\cite{cos_halfangle},} \label{eq:cos_halfangle} \\
   \Four{\nderiv{n}{t}{x(t)}} &= (i \omega)^n x(\omega)
-     &\text{\cite{four_deriv},} \label{eq.four_deriv} \\
-%  \Four{x*y} &= x(\omega) y(\omega),  \label{eq.four_conv}
+     &\text{\cite{four-deriv},} \label{eq:four-deriv} \\
+%  \Four{x*y} &= x(\omega) y(\omega),  \label{eq:four_conv}
 %     & \text{and} \\
   \iInfInf{t}{\magSq{x(t)}} &= \iInfInf{\omega}{\magSq{x(w)}}
-     &\text{(Parseval's)\cite{parseval}.} \label{eq.parseval}
+     &\text{(Parseval's)\cite{parseval}.} \label{eq:parseval}
 \end{align}
 %where $x*y$ denotes the convolution of $x$ and $y$,
 %\begin{equation}
@@ -37,14 +37,14 @@ We also use the following theorems (proved elsewhere):
 As a corollary to Parseval's theorem, we note that the one sided power spectral density per unit time (\PSD) defined by
 \begin{align}
   \PSD(x, \omega) &\equiv \normLimT 2 \left| x(\omega) \right|^2 
-     &\text{\cite{PSD}} \label{eq.psd_def}
+     &\text{\cite{PSD}} \label{eq:psd-def}
 \end{align}
 relates to the variance by
 \begin{align}
   \avg{x(t)^2}
      &= \iLimT{\magSq{x(t)}}
      = \normLimT \iInfInf{\omega}{\magSq{x(\omega)}}
-     = \iOInf{\omega}{\PSD(x,\omega)}, \label{eq.parseval_var}
+     = \iOInf{\omega}{\PSD(x,\omega)}, \label{eq:parseval-var}
 \end{align}
 where $t_T$ is the total time over which data has been aquired.
 
@@ -54,7 +54,7 @@ which relates the two sided power spectral density $S_{xx}(\omega)$
 to the autocorrelation function $r_{xx}(t)$ via
 \begin{align}
   S_{xx}(\omega) &= \Four{ r_{xx}(t) }
-       &\text{(Wiener-Khinchin)\cite{wiener_khinchin},} \label{eq.wiener_khinchin}
+       &\text{(Wiener-Khinchin)\cite{wiener_khinchin},} \label{eq:wiener_khinchin}
 \end{align}
 where $r_{xx}(t)$ is defined in terms of the expectation value
 \begin{align}
diff --git a/tex/src/cantilever-calib/solve_general.tex b/tex/src/cantilever-calib/solve_general.tex
index bb4076d..05d296d 100644
--- a/tex/src/cantilever-calib/solve_general.tex
+++ b/tex/src/cantilever-calib/solve_general.tex
@@ -1,32 +1,33 @@
 \subsection{General form}
 
-The procedure here is exactly the same as the previous section.
-The integral normalizing $G_0$ just become a little more complicated\ldots
+The procedure here is exactly the same as the previous section.  The
+integral normalizing $G_0$, however, becomes a little more
+complicated.
 
-Fourier transforming eq. \ref{eq.DHO} and applying \ref{eq.four_deriv} we have
+Fourier transforming \cref{eq:DHO} and applying \cref{eq:four-deriv} we have
 \begin{align}
   (-m\omega^2 + i \gamma \omega + k) x(\omega) &= F(\omega)
-                                              \label{eq.DHO_freq} \\
+                                              \label{eq:DHO-freq} \\
   (\omega_0^2-\omega^2 + i \beta \omega) x(\omega) &= \frac{F(\omega)}{m} \\
   |x(\omega)|^2 &= \frac{|F(\omega)|^2/m^2}
                         {(\omega_0^2-\omega^2)^2 + \beta^2\omega^2}
-                                              \label{eq.DHO_xmag},
+                                              \label{eq:DHO-xmag},
 \end{align}
 where $\omega_0 \equiv \sqrt{k/m}$ is the resonant angular frequency
  and $\beta \equiv \gamma / m$ is the drag-acceleration coefficient.
 
-We compute the \PSD\ by plugging eq. \ref{eq.DHO_xmag} into \ref{eq.psd_def}
+We compute the \PSD\ by plugging \cref{eq:DHO-xmag} into \cref{eq:psd-def}
 \begin{equation}
   \PSD(x, \omega)
         = \normLimT \frac{2 |F(\omega)|^2/m^2}
                          {(\omega_0^2-\omega^2)^2 + \beta^2\omega^2}.
-                                               \label{eq.DHO_psd}
+                                               \label{eq:DHO-psd}
 \end{equation}
 
-Plugging eq. \ref {eq.GOdef} into \ref{eq.DHO_psd} we have
+Plugging \cref{eq:GOdef} into \cref{eq:DHO-psd} we have
 \begin{equation}
   \PSD(x, \omega) = \frac{G_0/m^2}{(\omega_0^2-\omega^2)^2 + \beta^2\omega^2}.
-                                       \label{eq.model_psd}
+                                       \label{eq:model-psd}
 \end{equation}
 Integrating over positive $\omega$ to find the total power per unit time yields
 \begin{align}
@@ -38,17 +39,17 @@ Integrating over positive $\omega$ to find the total power per unit time yields
      &= \frac{G_0 \pi}{2m^2\beta \frac{k}{m}} \\
      &= \frac{G_0 \pi}{2m \beta k}
 \end{align}
-The integration is detailed in Section \ref{sec.integrals}.
-By our corollary to Parseval's theorem (eq. \ref{eq.parseval_var}), we have
+The integration is detailed in \cref{sec:integrals}.
+By our corollary to Parseval's theorem (\cref{eq:parseval-var}), we have
 \begin{equation}
-  \avg{x(t)^2} = \frac{G_0 \pi}{2m^2\beta\omega_0^2} \label{eq.DHO_var}
+  \avg{x(t)^2} = \frac{G_0 \pi}{2m^2\beta\omega_0^2} \label{eq:DHO-var}
 \end{equation}
 
-Plugging eq. \ref{eq.DHO_var} into the equipartition theorem
-(eqn. \ref{eq.equipart}) we have
+Plugging \cref{eq:DHO-var} into the equipartition theorem
+(\cref{eq:equipart}) we have
 \begin{align}
   k \frac{G_0 \pi}{2m \beta k} &= k_BT \\
-  G_0 &= \frac{2}{\pi} k_BT m \beta.  \label{eq.GO}
+  G_0 &= \frac{2}{\pi} k_BT m \beta.  \label{eq:GO}
 \end{align}
 
 So we expect $x(t)$ to have a power spectral density per unit time given by
diff --git a/tex/src/cantilever-calib/solve_highly_damped.tex b/tex/src/cantilever-calib/solve_highly_damped.tex
index 2855b14..1c8ea69 100644
--- a/tex/src/cantilever-calib/solve_highly_damped.tex
+++ b/tex/src/cantilever-calib/solve_highly_damped.tex
@@ -5,30 +5,33 @@ For highly damped systems, the inertial term becomes insignificant
 This model is commonly used for optically trapped beads. % \cite{}
 Because it is simpler and solutions are more easily available,
  %cite{grossman05}{}{}{}
-we'll use it outline the general approach before diving into the general case.
+it will server to outline the general approach before we dive into the
+general case.
 
-Fourier transforming eq. \ref{eq.DHO} with $m=0$ and applying \ref{eq.four_deriv} we have
+Fourier transforming \cref{eq:DHO} with $m=0$ and applying
+\cref{eq:four-deriv} we have
 % ODHO stands for very Over Damped Harmonic oscillator
 \begin{align}
-  (i \gamma \omega + k) x(\omega) &= F(\omega) \label{eq.ODHO_freq} \\
+  (i \gamma \omega + k) x(\omega) &= F(\omega) \label{eq:ODHO-freq} \\
   |x(\omega)|^2 &= \frac{|F(\omega)|^2}{k^2 + \gamma^2 \omega^2}.
-                                               \label{eq.ODHO_xmag}
+                                               \label{eq:ODHO-xmag}
 \end{align}
-We compute the \PSD\ by plugging eq. \ref{eq.ODHO_xmag} into \ref{eq.psd_def}
+We compute the \PSD\ by plugging \cref{eq:ODHO-xmag} into
+\cref{eq:psd-def}
 \begin{equation}
   \PSD(x, \omega)
         = \normLimT \frac{2\magSq{F(\omega)}}{k^2 + \gamma^2\omega^2}.
-                                               \label{eq.ODHO_psd}
+                                               \label{eq:ODHO-psd}
 \end{equation}
 
 Because thermal noise is white (not autocorrelated + Wiener-Khinchin Theorem),
 we can denote the one sided thermal power spectral density per unit time by
 \begin{equation}
   \PSD(F, \omega) = G_0
-     = \normLimT 2 \magSq{F(\omega)} \label{eq.GOdef} % label O != zero
+     = \normLimT 2 \magSq{F(\omega)} \label{eq:GOdef} % label O != zero
 \end{equation}
 
-Plugging eq. \ref {eq.GOdef} into \ref{eq.ODHO_psd} we have
+Plugging \cref{eq:GOdef} into \cref{eq:ODHO-psd} we have
 \begin{equation}
   \PSD(x, \omega) = \frac{G_0}{k^2 + \gamma^2\omega^2}.
 \end{equation}
@@ -43,14 +46,14 @@ Integrating over positive $\omega$ to find the total power per unit time yields
      &= \frac{G_0}{\gamma}\iOInf{z}{\frac{1}{k^2 + z^2}} \\
      &= \frac{G_0 \pi}{2 \gamma k},
 \end{align}
-where the integral is solved in Section \ref{sec.integrals}.
+where the integral is solved in \cref{sec:integrals}.
 
-Plugging into our corollary to Parseval's theorem (eq. \ref{eq.parseval_var}), 
+Plugging into our corollary to Parseval's theorem (\cref{eq:parseval-var}), 
 \begin{equation}
-  \avg{x(t)^2} = \frac{G_0 \pi}{2 \gamma k} \label{eq.ODHO_var}
+  \avg{x(t)^2} = \frac{G_0 \pi}{2 \gamma k} \label{eq:ODHO-var}
 \end{equation}
 
-Plugging eq. \ref{eq.ODHO_var} into eqn. \ref{eq.equipart} we have
+Plugging \cref{eq:ODHO-var} into \cref{eq:equipart} we have
 \begin{align}
   k \frac{G_0 \pi}{2 \gamma k} &= k_BT \\
   G_0 &= \frac{2 \gamma k_BT}{\pi}.
diff --git a/tex/src/packages/cleveref.sty b/tex/src/packages/cleveref.sty
index 7775250..8a119ef 100644
--- a/tex/src/packages/cleveref.sty
+++ b/tex/src/packages/cleveref.sty
@@ -22,7 +22,7 @@
 %% version 1999/12/01 or later.
 \NeedsTeXFormat{LaTeX2e}[1999/12/01]
 \ProvidesPackage{cleveref}
- [2009/09/22 v0.14.2 Intelligent cross-referencing]
+ [2009/12/11 v0.15.3 Intelligent cross-referencing]
 %% \CharacterTable
 %%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
 %%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
@@ -112,7 +112,11 @@
     \gdef\refstepcounter@noarg##1{%
       \cref@old@refstepcounter{##1}%
       \cref@constructprefix{##1}{\@result}%
-      \edef\@result{{2147483647}\@result}%
+      \ifx\@result\@empty%
+        \def\@result{2147483647}%
+      \else%
+        \edef\@result{2147483647,\@result}%
+      \fi%
       \def\@tmpa{##1}%
       \def\@tmpb{section}%
       \ifx\@tmpa\@tmpb%
@@ -141,7 +145,11 @@
     \def\refstepcounter@noarg##1{%
       \cref@old@refstepcounter{##1}%
       \cref@constructprefix{##1}{\@result}%
-      \edef\@result{{2147483647}\@result}%
+      \ifx\@result\@empty%
+        \def\@result{2147483647}%
+      \else%
+        \edef\@result{2147483647,\@result}%
+      \fi%
       \def\@tmpa{##1}%
       \def\@tmpb{chapter}%
       \ifx\@tmpa\@tmpb%
@@ -286,8 +294,7 @@
       \else%
         \cref@stack@pop{\@tmpstack}%
         \cref@isstackfull{\@tmpstack}%
-      \fi
-    }%
+      \fi}%
   \expandafter\endgroup%
   \if@notthere\cref@stack@push{#1}{#2}\fi}
 \newif\if@cref@stackempty
@@ -776,7 +783,10 @@
 \DeclareRobustCommand{\Cref}[1]{\@cref{Cref}{#1}}
 \DeclareRobustCommand{\crefrange}[2]{\@setcrefrange{#1}{#2}{cref}{}}
 \DeclareRobustCommand{\Crefrange}[2]{\@setcrefrange{#1}{#2}{Cref}{}}
+\@ifpackageloaded{hyperref}{\newif\if@crefstarred}{%
+  \@ifpackageloaded{varioref}{\newif\if@crefstarred}{}}
 \def\@cref#1#2{%
+  \leavevmode%
   \begingroup%
   \countdef\count@consecutive=0%
   \countdef\count@group=1%
@@ -1488,7 +1498,11 @@
       \def\H@refstepcounter##1{%
         \stepcounter{##1}%
         \cref@constructprefix{##1}{\@result}%
-        \edef\@result{{2147483647}\@result}%
+        \ifx\@result\@empty%
+          \def\@result{2147483647}%
+        \else%
+          \edef\@result{2147483647,\@result}%
+        \fi%
         \def\@tmpa{##1}%
         \def\@tmpb{section}%
         \ifx\@tmpa\@tmpb%
@@ -1520,7 +1534,11 @@
       \def\H@refstepcounter##1{%
         \stepcounter{##1}%
         \cref@constructprefix{##1}{\@result}%
-        \edef\@result{{2147483647}\@result}%
+        \ifx\@result\@empty%
+          \def\@result{2147483647}%
+        \else%
+          \edef\@result{2147483647,\@result}%
+        \fi%
         \def\@tmpa{##1}%
         \def\@tmpb{chapter}%
         \ifx\@tmpa\@tmpb%
@@ -1558,7 +1576,6 @@
         \fi}%
     }%
   }
-  \newif\if@crefstarred
   \DeclareRobustCommand{\cref}{%
     \@ifstar{\@crefstar{cref}}{\@crefnostar{cref}}}
   \DeclareRobustCommand{\Cref}{%
@@ -1632,7 +1649,52 @@
     \advance\@totalleftmargin \theorem@indent%
     \parshape \@ne \@totalleftmargin \linewidth%
     \@ifnextchar[{\@ythm{#1}{#2}{#3}}{\@xthm{#1}{#2}{#3}}%]
-  }}{}%  end of \@ifpackageloaded
+  }
+  }{}%  end of \@ifpackageloaded
+  \@ifpackageloaded{amsthm}{%
+  \PackageInfo{cleveref}{`amsthm' support loaded}
+\let\@thmnoarg\@thm
+\def\@thm{\@ifnextchar[{\@thmoptarg}{\@thmnoarg}}%]
+\def\@thmoptarg[#1]#2#3#4{%
+  \ifhmode\unskip\unskip\par\fi%
+  \normalfont%
+  \trivlist%
+  \let\thmheadnl\relax%
+  \let\thm@swap\@gobble%
+  \thm@notefont{\fontseries\mddefault\upshape}%
+  \thm@headpunct{.}% add period after heading
+  \thm@headsep 5\p@ plus\p@ minus\p@\relax%
+  \thm@space@setup%
+  #2% style overrides
+  \@topsep \thm@preskip%   used by thm head
+  \@topsepadd \thm@postskip%   used by \@endparenv
+  \def\@tempa{#3}\ifx\@empty\@tempa%
+    \def\@tempa{\@oparg{\@begintheorem{#4}{}}[]}%
+  \else%
+    \refstepcounter[#1]{#3}%
+    \def\@tempa{\@oparg{\@begintheorem{#4}{\csname the#3\endcsname}}[]}%
+  \fi%
+  \@tempa}
+\def\@ynthm#1[#2]#3{%
+  \ifx\relax#2\relax%
+    \def\@tempa{\@oparg{\@xthm{#1}{#3}}[]}%
+  \else%
+    \@ifundefined{c@#2}{%
+      \def\@tempa{\@nocounterr{#2}}%
+    }{%
+      \@xp\xdef\csname the#1\endcsname{\@xp\@nx\csname the#2\endcsname}%
+      \toks@{#3}%
+      \@xp\xdef\csname#1\endcsname{%
+        \@nx\@thm[#1]{% <<<<< new optional argument for theorem name
+          \let\@nx\thm@swap%
+            \if S\thm@swap\@nx\@firstoftwo\else\@nx\@gobble\fi%
+          \@xp\@nx\csname th@\the\thm@style\endcsname}%
+            {#2}{\the\toks@}}%
+      \let\@tempa\relax%
+    }%
+  \fi%
+  \@tempa}
+  }{}%  end of \@ifpackageloaded
 \@ifpackageloaded{varioref}{%
     \PackageInfo{cleveref}{`varioref' support loaded}
     \PackageInfo{cleveref}{`cleveref' supersedes `varioref's %
@@ -1640,21 +1702,24 @@
   \AtBeginDocument{%
     \def\cref@vref#1#2{%
       \if@cref@legacyvarioref%
-        \leavevmode\unskip\vref@space
+        \leavevmode\unskip\vref@space%
       \fi%
       \@cref{#1}{#2} % space here is deliberate
       \begingroup%
         \def\@tmpstack{#2,\@nil}%
         \cref@stack@topandbottom{\@tmpstack}{\@firstref}{\@lastref}%
         \ifx\@lastref\@empty%
-          \vpageref{#2}%
+          \vpageref[\unskip]{#2}%
         \else%
           \edef\@tmpa{{\@firstref}{\@lastref}}%
+          \expandafter\def\expandafter\@tmpa\expandafter{%
+            \expandafter[\expandafter\unskip\expandafter]%
+            \@tmpa}%
           \expandafter\vpagerefrange\@tmpa%
         \fi%
       \endgroup}
     \def\cref@vrefrange#1#2#3{%
-      \@setcrefrange{#2}{#3}{#1}{} \vpagerefrange{#2}{#3}}
+      \@setcrefrange{#2}{#3}{#1}{} \vpagerefrange[\unskip]{#2}{#3}}
     \def\cref@fullref#1#2{%
       \@cref{#1}{#2} % space here is deliberate
       \begingroup%
@@ -1667,9 +1732,9 @@
             \@tmpa\expandafter{\@firstref}%
           \expandafter\vrefpagenum\expandafter%
             \@tmpb\expandafter{\@lastref}%
-          \ifx\@tmpa\@tmpb
+          \ifx\@tmpa\@tmpb%
             \expandafter\reftextfaraway\expandafter{\@firstref}%
-          \else
+          \else%
             \edef\@tmpa{{\@firstref}{\@lastref}}%
             \expandafter\reftextpagerange\@tmpa%
           \fi%
@@ -1679,7 +1744,7 @@
       \def\vr@f#1{\cref@vref{cref}{#1}}
       \def\Vr@f#1{\cref@vref{Cref}{#1}}
       \renewcommand\vrefrange[3][\reftextcurrent]{%
-        \crefrange{#2}{#3} \vpagerefrange{#2}{#3}}
+        \crefrange{#2}{#3} \vpagerefrange[\unskip]{#2}{#3}}
       \def\fullref#1{\cref@fullref{cref}{#1}}
     \else%
       \@ifpackageloaded{hyperref}{%
@@ -1696,17 +1761,11 @@
         \DeclareRobustCommand{\Fullref}{%
           \@ifstar{\cref@fullrefstar{Cref}}{\cref@fullref{Cref}}}
         \def\cref@vrefstar#1#2{%
-          \@crefstarredtrue%
-          \cref@vref{#1}{#2}%
-          \@crefstarredfalse}
+          \@crefstarredtrue\cref@vref{#1}{#2}\@crefstarredfalse}
         \def\cref@vrefrangestar#1#2#3{%
-          \@crefstarredtrue%
-          \cref@vrefrange{#1}{#2}{#3}%
-          \@crefstarredfalse}
+          \@crefstarredtrue\cref@vrefrange{#1}{#2}{#3}\@crefstarredfalse}
         \def\cref@fullrefstar#1#2{%
-          \@crefstarredtrue%
-          \cref@fullref{#1}{#2}%
-          \@crefstarredfalse}
+          \@crefstarredtrue\cref@fullref{#1}{#2}\@crefstarredfalse}
       }{%
         \DeclareRobustCommand{\vref}{\cref@vref{cref}}
         \DeclareRobustCommand{\Vref}{\cref@vref{Cref}}
@@ -1757,47 +1816,47 @@
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \crefrangeconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\crefrangeconjunction}}
+        \expandafter{\@address}{\string\crefrangeconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \crefrangepreconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\crefrangepreconjunction}}
+        \expandafter{\@address}{\string\crefrangepreconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \crefrangepostconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\crefrangepostconjunction}}
+        \expandafter{\@address}{\string\crefrangepostconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \crefpairconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\crefpairconjunction}}
+        \expandafter{\@address}{\string\crefpairconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \crefmiddleconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\crefmiddleconjunction}}
+        \expandafter{\@address}{\string\crefmiddleconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \creflastconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\creflastconjunction}}
+        \expandafter{\@address}{\string\creflastconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \crefpairgroupconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\crefpairgroupconjunction}}
+        \expandafter{\@address}{\string\crefpairgroupconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \crefmiddlegroupconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\crefmiddlegroupconjunction}}
+        \expandafter{\@address}{\string\crefmiddlegroupconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \expandafter\def\expandafter\cref@poorman@text\expandafter{%
         \creflastgroupconjunction}%
       \expandafter\def\expandafter\@tmpa\expandafter{%
-        \expandafter{\@address}{\string\creflastgroupconjunction}}
+        \expandafter{\@address}{\string\creflastgroupconjunction}}%
       \expandafter\cref@writescript\@tmpa%
       \let\@tmpstack\cref@label@types%
       \cref@isstackfull{\@tmpstack}%
@@ -1814,7 +1873,7 @@
         \expandafter\expandafter\expandafter{%
           \expandafter\expandafter\expandafter{%
             \expandafter\@address\expandafter}%
-          \expandafter{\@tmpa}}
+          \expandafter{\@tmpa}}%
         \expandafter\cref@writescript\@tmpa%
         \edef\@tmpa{\cref@stack@top{\@tmpstack}}%
         \expandafter\expandafter\expandafter\def%
@@ -1829,7 +1888,7 @@
         \expandafter\expandafter\expandafter{%
           \expandafter\expandafter\expandafter{%
             \expandafter\@address\expandafter}%
-          \expandafter{\@tmpa}}
+          \expandafter{\@tmpa}}%
         \expandafter\cref@writescript\@tmpa%
         \edef\@tmpa{\cref@stack@top{\@tmpstack}}%
         \expandafter\expandafter\expandafter\def%
@@ -1843,7 +1902,7 @@
         \expandafter\expandafter\expandafter{%
           \expandafter\expandafter\expandafter%
           {\expandafter\@address\expandafter}%
-          \expandafter{\@tmpa}}
+          \expandafter{\@tmpa}}%
         \expandafter\cref@writescript\@tmpa%
         \edef\@tmpa{\cref@stack@top{\@tmpstack}}%
         \expandafter\expandafter\expandafter\def%
@@ -1858,7 +1917,7 @@
         \expandafter\expandafter\expandafter{%
           \expandafter\expandafter\expandafter%
           {\expandafter\@address\expandafter}%
-          \expandafter{\@tmpa}}
+          \expandafter{\@tmpa}}%
         \expandafter\cref@writescript\@tmpa%
         \cref@stack@pop{\@tmpstack}%
         \cref@isstackfull{\@tmpstack}}%
@@ -1911,7 +1970,7 @@
           s/||label|[[^]]*|]/||label/g}}
       \expandafter\g@addto@macro\expandafter%
         \cref@poorman@text\expandafter{\@tmpa^^J}%
-      \lowercase{\edef\@tmpa{s/||usepackage|(|[.*|]|)|?<cleveref>//g}}%
+      \lowercase{\edef\@tmpa{s/||usepackage|(|[.*|]|)|<0,1|><cleveref>//g}}%
       \expandafter\g@addto@macro\expandafter%
         \cref@poorman@text\expandafter{\@tmpa^^J}%
       \lowercase{\edef\@tmpa{s/||[cC]refformat<.*><.*>//g}}%
@@ -1974,7 +2033,7 @@
     \immediate\openout\@crefscript=\jobname.sed%
     \immediate\write\@crefscript{\cref@poorman@text}%
     \immediate\closeout\@crefscript%
-  }
+  }%  end of \AtEndDocument
   \def\cref@getmeaning#1{\expandafter\@cref@getmeaning\meaning#1\@nil}
   \def\@cref@getmeaning#1->#2\@nil{#2}
   \def\cref@writescript#1#2{%
@@ -1984,31 +2043,47 @@
     \def\@crefnostar#1#2{%
       \gdef\cref@poorman@text{}%
       \@cref{#1}{#2}%
-      \begingroup%
-        \lccode`|=92 \lccode`<=123 \lccode`>=125 \lccode`C=67
-        \lowercase{\cref@writescript{}{|#1<#2>}}%
-      \endgroup}
+      \def\@tmpa##1##2\@nil{%
+        \if##1c%
+          \cref@writescript{}{\string\cref\string{#2\string}}%
+        \else%
+          \cref@writescript{}{\string\Cref\string{#2\string}}%
+        \fi}%
+      \@tmpa#1\@nil}
     \def\@crefstar#1#2{%
       \gdef\cref@poorman@text{}%
       \@crefstarredtrue\@cref{#1}{#2}\@crefstarredfalse%
-      \begingroup%
-        \lccode`|=92 \lccode`<=123 \lccode`>=125 \lccode`C=67
-        \lowercase{\cref@writescript{}{|#1*<#2>}}%
-      \endgroup}
+      \def\@tmpa##1##2\@nil{%
+        \if##1c%
+          \cref@writescript{}{\string\cref*\string{#2\string}}%
+        \else%
+          \cref@writescript{}{\string\Cref*\string{#2\string}}%
+        \fi}%
+      \@tmpa#1\@nil}
     \def\@crefrangenostar#1#2#3{%
       \gdef\cref@poorman@text{}%
       \@setcrefrange{#2}{#3}{#1}{}%
-      \begingroup%
-        \lccode`|=92 \lccode`<=123 \lccode`>=125 \lccode`C=67
-        \lowercase{\cref@writescript{}{|#1range<#2><#3>}}%
-      \endgroup}
+      \def\@tmpa##1##2\@nil{%
+        \if##1c%
+          \cref@writescript{}{%
+            \string\crefrange\string{#2\string}\string{#3\string}}%
+        \else%
+          \cref@writescript{}{%
+            \string\Crefrange\string{#2\string}\string{#3\string}}%
+        \fi}%
+      \@tmpa#1\@nil}
     \def\@crefrangestar#1#2#3{%
       \gdef\cref@poorman@text{}%
       \@crefstarredtrue\@setcrefrange{#2}{#3}{#1}{}\@crefstarredfalse%
-      \begingroup%
-        \lccode`|=92 \lccode`<=123 \lccode`>=125 \lccode`C=67
-        \lowercase{\cref@writescript{}{|#1range*<#2><#3>}}%
-      \endgroup}
+      \def\@tmpa##1##2\@nil{%
+        \if##1c%
+          \cref@writescript{}{%
+            \string\crefrange*\string{#2\string}\string{#3\string}}%
+        \else%
+          \cref@writescript{}{%
+            \string\Crefrange*\string{#2\string}\string{#3\string}}%
+        \fi}%
+      \@tmpa#1\@nil}
   }{%
     \DeclareRobustCommand{\cref}[1]{%
       \edef\cref@poorman@text{}%
@@ -2036,11 +2111,11 @@
           \@ifstar{\cref@vrefstar{cref}}{\cref@vref{cref}}}
         \def\cref@vrefstar#1#2{%
           \@crefstarredtrue\cref@vref{#1}{#2}\@crefstarredfalse}
-      \fi
+      \fi%
       \def\cref@vref#1#2{%
         \gdef\cref@poorman@text{}%
         \if@cref@legacyvarioref%
-          \leavevmode\unskip\vref@space
+          \leavevmode\unskip\vref@space%
         \fi%
         \begingroup%
           \let\if@tmp\if@crefstarred%
@@ -2050,11 +2125,14 @@
           \def\@tmpstack{#2,\@nil}%
           \cref@stack@topandbottom{\@tmpstack}{\@firstref}{\@lastref}%
           \ifx\@lastref\@empty%
-            \vpageref{#2}%
-            \g@addto@macro\cref@poorman@text{ \vpageref{#2}}%
+            \vpageref[\unskip]{#2}%
+            \g@addto@macro\cref@poorman@text{ \vpageref[\unskip]{#2}}%
           \else%
             \g@addto@macro\cref@poorman@text{ }%
             \edef\@tmpa{{\@firstref}{\@lastref}}%
+            \expandafter\def\expandafter\@tmpa\expandafter{%
+              \expandafter[\expandafter\unskip\expandafter]%
+              \@tmpa}%
             \expandafter\vpagerefrange\@tmpa%
             \expandafter\g@addto@macro\expandafter\cref@poorman@text%
               \expandafter{\expandafter\vpagerefrange\@tmpa}%
@@ -2077,8 +2155,8 @@
         \endgroup}
       \def\cref@vrefrange#1#2#3{%
         \gdef\cref@poorman@text{}%
-        \@setcrefrange{#2}{#3}{#1}{} \vpagerefrange{#2}{#3}%
-        \g@addto@macro\cref@poorman@text{ \vpagerefrange{#2}{#3}}%
+        \@setcrefrange{#2}{#3}{#1}{} \vpagerefrange[\unskip]{#2}{#3}%
+        \g@addto@macro\cref@poorman@text{ \vpagerefrange[\unskip]{#2}{#3}}%
         \def\@tmpa##1##2\@nil{%
           \if##1c%
             \if@crefstarred%
@@ -2112,11 +2190,11 @@
               \@tmpa\expandafter{\@firstref}%
             \expandafter\vrefpagenum\expandafter%
               \@tmpb\expandafter{\@lastref}%
-            \ifx\@tmpa\@tmpb
+            \ifx\@tmpa\@tmpb%
               \expandafter\reftextfaraway\expandafter{\@firstref}%
               \expandafter\def\expandafter\@pageref\expandafter{%
                 \expandafter\reftextfaraway\expandafter{\@firstref}}%
-            \else
+            \else%
               \edef\@tmpa{{\@firstref}{\@lastref}}%
               \expandafter\reftextpagerange\@tmpa%
               \expandafter\def\expandafter\@pageref\expandafter{%
@@ -2140,7 +2218,7 @@
                 \cref@writescript{}{\string\Fullref\string{#2\string}}%
               \fi%
             \fi}%
-          \@tmpa#1\@nil
+          \@tmpa#1\@nil%
         \endgroup}
     }% end of \AtBeginDocument
   }{}% end of \@ifpackageloaded
@@ -2187,6 +2265,8 @@
           \expandafter{#1{\ref{#2}}{\ref{#3}}{}{}{}{}}%
       \fi}
   }{%
+    \let\old@@setcref\@@setcref%
+    \let\old@@setcrefrange\@@setcrefrange%
     \def\@@setcref#1#2{%
       \old@@setcref{#1}{#2}%
       \expandafter\g@addto@macro\expandafter{%
@@ -2231,12 +2311,12 @@
 \creflabelformat{equation}{\textup{(#2#1#3)}}
 \def\cref@addto#1#2{%
   \@temptokena{#2}%
-  \ifx#1\undefined
+  \ifx#1\undefined%
     \edef#1{\the\@temptokena}%
-  \else
+  \else%
     \toks@\expandafter{#1}%
     \edef#1{\the\toks@\the\@temptokena}%
-  \fi
+  \fi%
   \@temptokena{}\toks@\@temptokena%
 }
 \@onlypreamble\cref@addto
@@ -2258,6 +2338,7 @@
     \Crefname@preamble{appendix}{Appendix}{Appendices}%
     \Crefname@preamble{figure}{Figure}{Figures}%
     \Crefname@preamble{table}{Table}{Tables}%
+    \Crefname@preamble{theorem}{Theorem}{Theorems}%
     \Crefname@preamble{enumi}{Item}{Items}%
     \Crefname@preamble{lemma}{Lemma}{Lemmas}%
     \Crefname@preamble{corollary}{Corollary}{Corollaries}%
@@ -2657,6 +2738,143 @@
         \crefname{note}{Anmerkung}{Anmerkungen}%
       \fi%
     }}}
+\DeclareOption{dutch}{%
+  \PackageInfo{cleveref}{loaded `dutch' language definitions}
+  \AtBeginDocument{%
+    \def\crefrangeconjunction@preamble{ tot~}%
+    \def\crefrangepreconjunction@preamble{}%
+    \def\crefrangepostconjunction@preamble{}%
+    \def\crefpairconjunction@preamble{ en~}%
+    \def\crefmiddleconjunction@preamble{, }%
+    \def\creflastconjunction@preamble{ en~}%
+    \def\crefpairgroupconjunction@preamble{ en~}%
+    \def\crefmiddlegroupconjunction@preamble{, }%
+    \def\creflastgroupconjunction@preamble{ en~}%
+    \Crefname@preamble{equation}%
+      {Ver\-ge\-l\ij{}k\-ing}{Ver\-ge\-l\ij{}k\-ing\-en}%
+    \Crefname@preamble{chapter}{Hoofdstuk}{Hoofdstuken}%
+    \Crefname@preamble{section}{Paragraaf}{Paragrafen}%
+    \Crefname@preamble{appendix}{Appendix}{Appendices}%
+    \Crefname@preamble{figure}{Figuur}{Figuren}%
+    \Crefname@preamble{table}{Tabel}{Tabellen}%
+    \Crefname@preamble{enumi}{Punt}{Punten}%
+    \Crefname@preamble{lemma}{Lemma}{Lemma's}%
+    \Crefname@preamble{corollary}{Corollarium}{Corollaria}%
+    \Crefname@preamble{proposition}{Bewering}{Beweringen}%
+    \Crefname@preamble{definition}{Definitie}{Definities}%
+    \Crefname@preamble{result}{Resultaat}{Resultaten}%
+    \Crefname@preamble{example}{Voorbeeld}{Voorbeelden}%
+    \Crefname@preamble{remark}{Opmerking}{Opmerkingen}%
+    \Crefname@preamble{note}{Aantekening}{Aantekeningen}%
+    \if@cref@capitalise%
+      \crefname@preamble{equation}{Verg.}{Verg's.}%
+      \crefname@preamble{chapter}{Hoofdstuk}{Hoofdstukken}%
+      \crefname@preamble{section}{Paragraaf}{Paragrafen}%
+      \crefname@preamble{appendix}{Appendix}{Appendices}%
+      \crefname@preamble{figure}{Fig.}{Fig's.}%
+      \crefname@preamble{table}{Tabel}{Tabellen}%
+      \crefname@preamble{theorem}{Theorema}{Theorema's}%
+      \crefname@preamble{enumi}{Punt}{Punten}%
+      \crefname@preamble{lemma}{Lemma}{Lemma's}%
+      \crefname@preamble{corollary}{Corollarium}{Corollaria}%
+      \crefname@preamble{proposition}{Bewering}{Beweringen}%
+      \crefname@preamble{definition}{Definitie}{Definities}%
+      \crefname@preamble{result}{Resultaat}{Resultaten}%
+      \crefname@preamble{example}{Voorbeeld}{Voorbeelden}%
+      \crefname@preamble{remark}{Opmerking}{Opmerkingen}%
+      \crefname@preamble{note}{Aantekening}{Aantekeningen}%
+    \else%
+      \crefname@preamble{equation}{verg.}{verg's.}%
+      \crefname@preamble{chapter}{hoofdstuk}{hoofdstukken}%
+      \crefname@preamble{section}{paragraaf}{paragrafen}%
+      \crefname@preamble{appendix}{appendix}{appendices}%
+      \crefname@preamble{figure}{fig.}{fig's.}%
+      \crefname@preamble{table}{tabel}{tabellen}%
+      \crefname@preamble{theorem}{theorema}{theorema's}%
+      \crefname@preamble{enumi}{punt}{punten}%
+      \crefname@preamble{lemma}{lemma}{lemma's}%
+      \crefname@preamble{corollary}{corollarium}{corollaria}%
+      \crefname@preamble{proposition}{bewering}{beweringen}%
+      \crefname@preamble{definition}{definitie}{definities}%
+      \crefname@preamble{result}{resultaat}{resultaten}%
+      \crefname@preamble{example}{voorbeeld}{voorbeelden}%
+      \crefname@preamble{remark}{opmerking}{opmerkingen}%
+      \crefname@preamble{note}{aantekening}{aantekeningen}%
+    \fi%
+    \def\cref@language{dutch}%
+    \cref@addto\extrasdutch{%
+      \renewcommand{\crefrangeconjunction}{ tot~}%
+      \renewcommand\crefrangepreconjunction{}%
+      \renewcommand\crefrangepostconjunction{}%
+      \renewcommand{\crefpairconjunction}{ en~}%
+      \renewcommand{\crefmiddleconjunction}{, }%
+      \renewcommand{\creflastconjunction}{ en~}%
+      \renewcommand{\crefpairgroupconjunction}{ en~}%
+      \renewcommand{\crefmiddlegroupconjunction}{, }%
+      \renewcommand{\creflastgroupconjunction}{ en~}%
+      \Crefname{equation}{Ver\-ge\-l\ij{}k\-ing}{Ver\-ge\-l\ij{}k\-ing\-en}%
+      \Crefname{chapter}{Hoofdstuk}{Hoofdstuken}%
+      \Crefname{section}{Paragraaf}{Paragrafen}%
+      \Crefname{subsection}{Paragraaf}{Paragrafen}%
+      \Crefname{subsubsection}{Paragraaf}{Paragrafen}%
+      \Crefname{appendix}{Appendix}{Appendices}%
+      \Crefname{subappendix}{Appendix}{Appendices}%
+      \Crefname{subsubappendix}{Appendix}{Appendices}%
+      \Crefname{subsubsubappendix}{Appendix}{Appendices}%
+      \Crefname{figure}{Figuur}{Figuren}%
+      \Crefname{subfigure}{Figuur}{Figuren}%
+      \Crefname{table}{Tabel}{Tabellen}%
+      \Crefname{subtable}{Tabel}{Tabellen}%
+      \Crefname{theorem}{Theorema}{Theorema's}%
+      \Crefname{enumi}{Punt}{Punten}%
+      \Crefname{enumii}{Punt}{Punten}%
+      \Crefname{enumiii}{Punt}{Punten}%
+      \Crefname{enumiv}{Punt}{Punten}%
+      \Crefname{enumv}{Punt}{Punten}%
+      \Crefname{lemma}{Lemma}{Lemma's}%
+      \Crefname{corollary}{Corollarium}{Corollaria}%
+      \Crefname{proposition}{Bewering}{Beweringen}%
+      \Crefname{definition}{Definitie}{Definities}%
+      \Crefname{result}{Resultaat}{Resultaten}%
+      \Crefname{example}{Voorbeeld}{Voorbeelden}%
+      \Crefname{remark}{Opmerking}{Opmerkingen}%
+      \Crefname{note}{Aantekening}{Aantekeningen}%
+      \if@cref@capitalise%
+        \crefname{equation}{Verg.}{Verg's.}%
+        \crefname{chapter}{Hoofdstuk}{Hoofdstukken}%
+        \crefname{section}{Paragraaf}{Paragrafen}%
+        \crefname{appendix}{Appendix}{Appendices}%
+        \crefname{figure}{Fig.}{Fig's.}%
+        \crefname{table}{Tabel}{Tabellen}%
+        \crefname{theorem}{Theorema}{Theorema's}%
+        \crefname{enumi}{Punt}{Punten}%
+        \crefname{lemma}{Lemma}{Lemma's}%
+        \crefname{corollary}{Corollarium}{Corollaria}%
+        \crefname{proposition}{Bewering}{Beweringen}%
+        \crefname{definition}{Definitie}{Definities}%
+        \crefname{result}{Resultaat}{Resultaten}%
+        \crefname{example}{Voorbeeld}{Voorbeelden}%
+        \crefname{remark}{Opmerking}{Opmerkingen}%
+        \crefname{note}{Aantekening}{Aantekeningen}%
+      \else%
+        \crefname{equation}{verg.}{verg's.}%
+        \crefname{chapter}{hoofdstuk}{hoofdstukken}%
+        \crefname{section}{paragraaf}{paragrafen}%
+        \crefname{appendix}{appendix}{appendices}%
+        \crefname{figure}{fig.}{fig's.}%
+        \crefname{table}{tabel}{tabellen}%
+        \crefname{theorem}{theorema}{theorema's}%
+        \crefname{enumi}{punt}{punten}%
+        \crefname{lemma}{lemma}{lemma's}%
+        \crefname{corollary}{corollarium}{corollaria}%
+        \crefname{proposition}{bewering}{beweringen}%
+        \crefname{definition}{definitie}{definities}%
+        \crefname{result}{resultaat}{resultaten}%
+        \crefname{example}{voorbeeld}{voorbeelden}%
+        \crefname{remark}{opmerking}{opmerkingen}%
+        \crefname{note}{aantekening}{aantekeningen}%
+      \fi%
+    }}}
 \DeclareOption{french}{%
   \PackageInfo{cleveref}{loaded `french' language definitions}
   \AtBeginDocument{%
@@ -3263,7 +3481,7 @@
         \csname cref@\@tmpa @name@plural\endcsname}%
       \expandafter\def\expandafter\@tmpc\expandafter{%
         \csname cref@\@tmpa @name@plural@preamble\endcsname}%
-      \expandafter\expandafter\expandafter\let\expandafter\@tmpb\@tmpc
+      \expandafter\expandafter\expandafter\let\expandafter\@tmpb\@tmpc%
     }{%
       \edef\@tmpb{%
         \expandafter\noexpand\csname extras\cref@language\endcsname}%
@@ -3292,7 +3510,7 @@
         \csname Cref@\@tmpa @name@plural\endcsname}%
       \expandafter\def\expandafter\@tmpc\expandafter{%
         \csname Cref@\@tmpa @name@plural@preamble\endcsname}%
-      \expandafter\expandafter\expandafter\let\expandafter\@tmpb\@tmpc
+      \expandafter\expandafter\expandafter\let\expandafter\@tmpb\@tmpc%
     }{%
       \edef\@tmpb{%
         \expandafter\noexpand\csname extras\cref@language\endcsname}%
diff --git a/tex/src/viscocity/main.tex b/tex/src/viscocity/main.tex
index 8ec3c4f..7db3c8d 100644
--- a/tex/src/viscocity/main.tex
+++ b/tex/src/viscocity/main.tex
@@ -12,7 +12,7 @@ We had some trouble with their notation, so I'll try and clear some things up...
  M\"uller \Bstrut & Trevor & Meaning \\
  \hline
  $z_{surface}$ \Tstrut & $z_{surface}$ & Distance from the surface to the equilibrium cantilever position (increases on pulling) \\
- $z_{cantilever}$ & $z_{cantilever}$ & Cantilever deflection from it's equilibrium position (downward deflection positive) \\
+ $z_{cantilever}$ & $z_{cantilever}$ & Cantilever deflection from its equilibrium position (downward deflection positive) \\
  $h$ & $h$ & $h = z_{surface} - z_{cantilever}$ the distance between the tip and surface \\
  $v_{tip}$ & $v_{tip,surface}$ & $v_{tip,surface} = dh/dt$, tip velocity relative to the surface \\
   & $v_{eq,surface}$ & $v_{eq,surface} = dz_{surface}/dt$, pulling speed \\