@@ -3634,7 +3634,7 @@ \subsubsection{Method 1: Free sampling}
36343634\includegraphics [width=\linewidth ]{US-potential}
36353635\caption {Potential $ U$ given in Eq.\, \eqref {eq:U } (a) and force $ F$ given in
36363636Eq.\, \eqref {eq:F } (b) as functions of the coordinate $ x$ . Here,
3637- $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\mathrm {\AA {}}$ , and $ x_0 = 10 ~\mathrm {\AA {}}$ .}
3637+ $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ , and $ x_0 = 10 ~\text {\AA {}}$ .}
36383638\label {fig:potential }
36393639\end {figure }
36403640
@@ -3714,7 +3714,7 @@ \subsubsection{Method 1: Free sampling}
37143714\caption {Evolution of the number of atoms $ n_\text {center}$ in the central
37153715region \lmpcmd {mymes} as a function of time $ t$ during equilibration. The dark line
37163716is $ n_\text {center} = 22 \exp (-t/160 )+5 $ and serves as a guide for the eyes. Here, $ U_0 = 0.36 ~\text {kcal/mol}$ ,
3717- $ \delta = 0.5 ~\mathrm {\AA {}}$ , and $ x_0 = 5 ~\mathrm {\AA {}}$ .}
3717+ $ \delta = 0.5 ~\text {\AA {}}$ , and $ x_0 = 5 ~\text {\AA {}}$ .}
37183718\label {fig:US-density-evolution }
37193719\end {figure }
37203720
@@ -3739,7 +3739,7 @@ \subsubsection{Method 1: Free sampling}
37393739step of \hyperref [umbrella-sampling-label]{Tutorial 7}.
37403740The atoms density is the lowest in the central
37413741part of the box, \lmpcmd {mymes}. Here,
3742- $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\mathrm {\AA {}}$ , and $ x_0 = 10 ~\mathrm {\AA {}}$ .}
3742+ $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ , and $ x_0 = 10 ~\text {\AA {}}$ .}
37433743\label {fig:US-system-unbiased }
37443744\end {figure }
37453745
@@ -3749,7 +3749,7 @@ \subsubsection{Method 1: Free sampling}
37493749\caption {a) Fluid density $ \rho $ along the $ x$ direction.
37503750b) Potential $ U$ as a function of $ x$ measured using free sampling (blue disks)
37513751compared to the imposed potential given in Eq.\, \eqref {eq:U } (dark line).
3752- Here, $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\mathrm {\AA {}}$ , $ x_0 = 10 ~\mathrm {\AA {}}$ ,
3752+ Here, $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ , $ x_0 = 10 ~\text {\AA {}}$ ,
37533753and the measured reference density in the reservoir is $ \rho _\text {bulk} = 0.0009 ~\text {\AA {}}^{-3}$ .} % SG: check units of rho bulk
37543754\label {fig:US-density }
37553755\end {figure }
@@ -3855,7 +3855,7 @@ \subsubsection{Method 2: Umbrella sampling}
38553855step of \hyperref [umbrella-sampling-label]{Tutorial 7}, showing type-1 atoms
38563856in cyan and the type-2 atom in red. Only the type-2 atom explores the central part of the box,
38573857\lmpcmd {mymes}, due to the additional biasing potential $ V$ . Parmaeters are
3858- $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\mathrm {\AA {}}$ , and $ x_0 = 10 ~\mathrm {\AA {}}$ .}
3858+ $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ , and $ x_0 = 10 ~\text {\AA {}}$ .}
38593859\label {fig:US-system-biased }
38603860\end {figure }
38613861
@@ -3882,7 +3882,7 @@ \subsubsection{Method 2: Umbrella sampling}
38823882The \lmpcmd {spring} command imposes the additional harmonic potential $ V$ with
38833883the previously defined spring constant $ k$ . The center of the harmonic
38843884potential, $ x_\text {des}$ , successively takes values
3885- from $ -28 \, \mathrm {\AA }$ to $ 28 \, \mathrm {\AA }$ . For each value of $ x_\text {des}$ ,
3885+ from $ -28 \, \text {\AA }$ to $ 28 \, \text {\AA }$ . For each value of $ x_\text {des}$ ,
38863886an equilibration step of 40\, ps is performed, followed by a step
38873887of 400\, ps during which the position of the particle of
38883888type 2 along the $ x$ -axis, $ x_\text {ave}$ , is saved in data files named \flecmd {umbrella-sampling.i.dat},
@@ -3930,8 +3930,8 @@ \subsubsection{Method 2: Umbrella sampling}
39303930\includegraphics [width=\linewidth ]{US-free-energy}
39313931\caption {The potential $ U$ as a function of $ x$ , measured using umbrella sampling
39323932(blue disks), is compared to the imposed potential given in Eq.\, \eqref {eq:U }
3933- (dark line). Parameters are $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\mathrm {\AA {}}$ ,
3934- and $ x_0 = 10 ~\mathrm {\AA {}}$ .}
3933+ (dark line). Parameters are $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ ,
3934+ and $ x_0 = 10 ~\text {\AA {}}$ .}
39353935\label {fig:US-freenergy }
39363936\end {figure }
39373937
@@ -4181,7 +4181,7 @@ \subsubsection{Simulating the reaction}
41814181}
41824182With the \textit {stabilization } keyword, the \textit {bond/react } command will
41834183try to stabilize the atoms involved in the reaction using the nve/limit
4184- command with a maximum displacement of $ 0.03 \, \mathrm {\AA {}}$ (a command that was
4184+ command with a maximum displacement of $ 0.03 \, \text {\AA {}}$ (a command that was
41854185used, for instance, in \hyperref [sheared-confined-label]{Tutorial 4}). The two
41864186\textit {react } keywords contain specific details about the two reactions
41874187involved here, i.e. a transformation of \textit {mol1 } into \textit {mol2 } based
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