Minor copy edit.

Author: razor-x

tex/_fits.tex

@@ -69,8 +69,8 @@ \section{Fits}
 The lifetime is equivalent to fitting with $R_C → ∞$.
 
 Note that we have used $R_C$ as a fitting parameter.
-In most devices, this quantity can be experimentally determined
-helping further constrain the fitting algorithm.
+In most devices, this quantity can be experimentally determined,
+thus further constraining the fitting algorithm.
 As we will discuss further in the next section, a fact that becomes apparent
 from our analytic result is that the relevant scale is $λ / r$.
 Once $r$ becomes larger than $λ$,

tex/_regimes.tex

@@ -30,19 +30,19 @@ \section{Regimes}
 \begin{equation}
   Δ \rNL = \left( P_Σ^L \right)^2 R_N e^{- L / λ} ,
 \end{equation}
-which agrees with eq. (6) in
+which agrees with equation (6) in
 \cite{PhysRevB.67.052409}.
 
 Let $f_0$ denote $f$ at zero magnetic field,
 \begin{equation}
   f_0 = \left[ 2 \left( 1 + λ / r \right) e^{L / λ} + \left( λ / r \right)^2 \sinh{L / λ} \right]^{-1} ,
 \end{equation}
-which agrees with eq. (3) in
+which agrees with equation (3) in
 \cite{PhysRevB.80.214427}.
 
 To further explore the nature of the Hanle curves,
 we exploit the fact that it only depends on
-the dimensionless ratios $r / λ$, $L / λ$, and $ω τ$.
+the dimensionless ratios $λ / r$, $L / λ$, and $ω τ$.
 The only other parameter of the conducting channel that enters the expression
 is the overall scale $λ$ in $R_N$.
 The expression $f$ contains three terms
@@ -57,7 +57,7 @@ \section{Regimes}
 \cite{Swartz2013}.
 Our result shows that the same is also true
 when the contact resistance is taken into account.
-In numerical simulations, interesting features where observed
+In numerical simulations, interesting features were observed
 when $L / λ ≪ 1$ and $r / λ ≪ 1$
 \cite{PhysRevB.86.235408}.