diff --git a/DESCRIPTION.md b/.DESCRIPTION.md
similarity index 91%
rename from DESCRIPTION.md
rename to .DESCRIPTION.md
index 4d35091..30af01e 100644
--- a/DESCRIPTION.md
+++ b/.DESCRIPTION.md
@@ -5,12 +5,6 @@ more accessible to new users.
## Tutorials
-
-
- Tutorial 1: Lennard-Jones fluid
- Tutorial 2: Pulling on a carbon nanotube
- Tutorial 3: Polymer in water
diff --git a/dependencies/.github b/dependencies/.github
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--- a/dependencies/.github
+++ /dev/null
@@ -1 +0,0 @@
-Subproject commit 9931c7cd1dcaa8d248bde41190e1900fb4e58961
diff --git a/figures/GCMC.png b/figures/GCMC.png
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diff --git a/figures/US.png b/figures/US.png
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diff --git a/files.txt b/files.txt
deleted file mode 100644
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--- a/files.txt
+++ /dev/null
@@ -1,4 +0,0 @@
-./dependencies/.github/COMMENT.md
-DESCRIPTION.md
-./dependencies/.github/AUTHORS.md
-./dependencies/.github/ACKNOWLEDGEMENTS.md
diff --git a/generateREADME.sh b/generateREADME.sh
deleted file mode 100755
index fd7b1b6..0000000
--- a/generateREADME.sh
+++ /dev/null
@@ -1,3 +0,0 @@
-#!/bin/bash
-
-./dependencies/.github/generateREADME.sh
diff --git a/lammps-tutorials.tex b/lammps-tutorials.tex
index 072636a..c5f77d3 100644
--- a/lammps-tutorials.tex
+++ b/lammps-tutorials.tex
@@ -177,12 +177,10 @@
suite of tutorials designed to make learning LAMMPS more accessible to
new users. The first four tutorials cover the basics of running
molecular simulations in LAMMPS with systems of varying complexities,
- including a simple fluid and a carbon nanotube. The last three
+ including a simple fluid and a carbon nanotube. The last four
tutorials address more advanced molecular simulation techniques,
- specifically the use of a reactive force field, enhanced sampling, and
- grand canonical Monte Carlo.
- % AK: ideally, there would be an eighth tutorial showcasing both
- % fix bond/react and how to benefit from type labels in its use.
+ specifically the use of a reactive force field, grand canonical Monte Carlo,
+ enhanced sampling, and REACTER protocol.
In addition, we introduce LAMMPS--GUI, an enhanced graphical text
editor with syntax highlighting, command completion, context help,
plus built--in visualization and plotting facilities, and the ability
@@ -433,16 +431,17 @@ \subsection{Tutorial 1: Lennard-Jones fluid}
The objective of this tutorial is to perform a simple MD simulation
using LAMMPS. The system consists of a Lennard-Jones fluid composed of neutral
particles with two different effective diameters, contained within a
-cubic box with periodic boundary conditions (Fig.~\ref{fig:LJ-avarar}). In
-this tutorial, the temperature of the system is maintained using a
-Langevin thermostat~\cite{schneider1978molecular}, and basic quantities,
-including potential and kinetic energies, are calculated from the simulation.
+cubic box with periodic boundary conditions (Fig.~\ref{fig:LJ-avatar}). In
+this tutorial, simple MD simulations in the microcanonical
+(NVE) and canonical (NVT) ensembles are performed, and basic quantities are calculated,
+including the potential and kinetic energies.
\begin{figure}
\centering
\includegraphics[width=0.55\linewidth]{LJ-avatar}
\caption{The binary mixture simulated in \hyperref[lennard-jones-label]{Tutorial 1},
-with the small atoms of type 1 in green and large atoms of type 2 in blue.}
+with the atoms of type 1 represented as small green spheres and lge atoms of type 2
+as large blue spheres.}
\label{fig:LJ-avatar}
\end{figure}
@@ -1073,8 +1072,7 @@ \subsubsection{Improving the script}
coordinated atoms, and the second calculates the average over all type 1
atoms. Add the following lines to \flecmd{improved.md.lmp}:
\begin{lstlisting}
-compute coor12 grp_t1 coord/atom cutoff 2 &
- group grp_t2
+compute coor12 grp_t1 coord/atom cutoff 2 group grp_t2
compute sumcoor12 grp_t1 reduce ave c_coor12
\end{lstlisting}
The \lmpcmd{compute reduce ave} command is used to average the per-atom
@@ -1129,7 +1127,8 @@ \subsubsection{Improving the script}
\includegraphics[width=\linewidth]{LJ-mixing}
\caption{a)~Evolution of the numbers $N_\text{1, in}$ and $N_\text{2, in}$ of atoms
of types 1 and 2, respectively, within the \lmpcmd{cyl\_in} region as functions
-of time $t$. b)~Evolution of the coordination number $C_{1-2}$ between atoms of types 1 and 2.}
+of time $t$. b)~Evolution of the coordination number $C_{1-2}$ (compute \lmpcmd{sumcoor12})
+between atoms of types 1 and 2.}
\label{fig:mixing}
\end{figure}
@@ -1144,14 +1143,14 @@ \subsubsection{Improving the script}
force applied to the atoms is equal to zero.
\begin{note}
-The steps to ensure no initial linear momentum and no net random
+The steps to ensure no initial linear momentum and no net total
force are important to prevent the system from starting to drift or move as a
whole. For a bulk system with periodic boundary conditions, it is
-expected to remain in place. Thus, when computing the temperature from the
+expected to remain in place. Accordingly, when computing the temperature from the
kinetic energy, we use $3N-3$ degrees of freedom since there is no
global translation. In a drifting system, some of the kinetic energy is
due to the drift, which means the system itself cools down. In
-extreme cases, it can freeze and drift very fast. This phenomenon is
+extreme cases, the system can freeze while its center of mass drifts very quickly. This phenomenon is
sometimes referred to as the ``flying ice cube syndrome''~\cite{wong2016good}.
\end{note}
@@ -1176,7 +1175,7 @@ \subsubsection{Improving the script}
\caption{Snapshot of the binary mixture simulated
during \hyperref[lennard-jones-label]{Tutorial 1} with atoms of type 1
colored according to their computed $1-2$ coordination
- number \lmpcmd{c\_coor12}, ranging from turquoise, \lmpcmd{c\_coor12 = 0},
+ number from the compute \lmpcmd{coor12}, ranging from turquoise,\lmpcmd{c\_coor12 = 0},
to yellow, \lmpcmd{c\_coor12 = 1}, and red, \lmpcmd{c\_coor12 = 2}.}
\label{fig:coords-viz}
\end{figure}
@@ -1187,15 +1186,16 @@ \subsubsection{Improving the script}
may lead to additional insights into how different systems are configured
and how various features function:
\begin{itemize}
-\item Use Nos\'e--Hoover thermostat (\lmpcmd{fix nvt}) instead of Langevin
+\item Use the Nos\'e--Hoover thermostat (\lmpcmd{fix nvt}) instead of the Langevin thermostat
(\lmpcmd{fix nve} + \lmpcmd{fix langevin}).
-\item Omit the energy minimization step for both, Nos\'e--Hoover and Langevin.
+\item Omit the energy minimization step before starting the MD simulation using either
+the Nos\'e--Hoover or the Langevin thermostat.
\item Apply the thermostat to only one type of atoms and observe the
temperature for each type separately.
\item Append an NVE run (i.e.~without any thermostat) and observe the energy levels.
\end{itemize}
-Another useful experiment to try is to color the atoms in the \guicmd{Slide Show}
+Another useful experiment is coloring the atoms in the \guicmd{Slide Show}
according to an observable, such as their respective coordination
numbers. To do this, replace the
\lmpcmd{dump} and \lmpcmd{dump\_modify} commands with the following lines:
@@ -1206,7 +1206,7 @@ \subsubsection{Improving the script}
dump_modify viz adiam 1 1 adiam 2 3 backcolor white &
amap -1 2 ca 0.0 4 min royalblue 0 turquoise 1 yellow max red
\end{lstlisting}
-Run LAMMPS again. Now, the atoms of type 1 are colored based on the value
+Run LAMMPS again. Atoms of type 1 are now colored based on the value
of \lmpcmd{c\_coor12}, which is mapped continuously from turquoise to yellow
and red for atoms with the highest coordination (Fig.~\ref{fig:coords-viz}).
In the definition of the variable \lmpcmd{v\_coor12}, atoms of type 2 are
@@ -1217,15 +1217,13 @@ \subsection{Tutorial 2: Pulling on a carbon nanotube}
In this tutorial, the system of interest is a small, single-walled
carbon nanotube (CNT) in an empty box (Fig.~\ref{fig:CNT}). The CNT is
-strained by fixing atoms at one end and moving atoms at the
-other end with constant velocity. To illustrate the difference between
-conventional and reactive force fields, this % SG: I am not sure why typelabel_paper was cited here. Am I wrong to remove it?
+strained by imposing a constant velocity on the edge atoms.
+To illustrate the difference between conventional and reactive force fields, this
tutorial is divided into two parts: in the first part, a conventional molecular force
field (called OPLS-AA~\cite{jorgensenDevelopmentTestingOPLS1996}) is
used and the bonds between the atoms of the CNT are unbreakable. In the
second part, a reactive force field (called AIREBO
-\cite{stuart2000reactive}) is used, allowing for the breaking of
-chemical bonds when the CNT experiences large strain.
+\cite{stuart2000reactive}) is used, which allows chemical bonds to break under large strain.
To set up this tutorial, select \guicmd{Start Tutorial 2} from the
\guicmd{Tutorials} menu of LAMMPS--GUI and follow the instructions. This will
@@ -1463,7 +1461,7 @@ \subsubsection{Unbreakable bonds}
\begin{note}
The \lmpcmdnote{velocity set}
- commands impose the velocity of a group of atoms at the start of a run but do
+ command imposes the velocity of a group of atoms at the start of a run but does
not enforce the velocity during the entire simulation. When \lmpcmdnote{velocity set}
is used in combination with \lmpcmdnote{setforce 0 0 0}, as is the case here, the
atoms won't feel any force during the entire simulation. According to the Newton
@@ -1554,7 +1552,7 @@ \subsubsection{Unbreakable bonds}
Right-click inside the \guicmd{Output} window, and select
\guicmd{Export YAML data to file}. Call the output \flecmd{unbreakable.yaml}, and save
it within the same folder as the input files, where a Python script named
-\href{\filepath tutorial2/yaml-reader.py}{\dwlcmd{yaml-reader.py}} should also
+\href{\filepath tutorial2/unbreakable-yaml-reader.py}{\dwlcmd{unbreakable-yaml-reader.py}} should also
be located. When executed using Python, this .py file first imports
the \flecmd{unbreakable.yaml} file. Then, a certain pattern is
identified and stored as a string character named `docs'. The string is
@@ -1623,7 +1621,7 @@ \subsubsection{Breakable bonds}
required for placing the atoms in the box, but no bond/angle/dihedral information.
Another difference between the \flecmd{unbreakable.data} and \flecmd{breakable.data} files
is that, here, a larger distance of 120~Ångströms was used for the box size along
-the $x$ axis, to allow for larger deformation of the CNT.
+the $x$-axis, to allow for larger deformation of the CNT.
\paragraph{Start the simulation}
@@ -1688,11 +1686,13 @@ \subsubsection{Breakable bonds}
Looking at the evolution of the energy, one can see that the total
energy $E_\text{tot}$ is initially increasing with the deformation. When
-bonds break, the energy relaxes abruptly,
-as can be seen near $t=110~\text{ps}$ and again near $t=130~\text{ps}$ in
-Fig.~\ref{fig:CNT-deformed-breakable}\,a. Using the same script as previously to
-import the data into Python, the stress-strain
-curve can be generated, see Fig.~\ref{fig:CNT-deformed-breakable}\,b.
+bonds break, the energy relaxes abruptly, as can be seen near $t=32~\text{ps}$ in Fig.~\ref{fig:CNT-breakable-energy-stress}\,a.
+Using a similar script as previously,
+i.e.,~\href{\filepath tutorial2/unbreakable-yaml-reader.py}{\dwlcmd{unbreakable-yaml-reader.py}},
+import the data into Python and generate the stress-strain curve (Fig.~\ref{fig:CNT-breakable-energy-stress}\,b). The
+stress-strain curve reveals a linear (elastic) regime where $F_\text{cnt} \propto \Delta L_\text{cnt}$
+for $\Delta L_\text{cnt} < 5\,\%$, and a non-linear (plastic) regime
+for $5\,\% < \Delta L_\text{cnt} < 25\,\%$.
\begin{figure}
\centering
@@ -1742,7 +1742,7 @@ \subsection{Tutorial 3: Polymer in water}
for the PEG, the SPC/Fw model~\cite{wu2006flexible} is used for the water, and the
long-range Coulomb interactions are solved using the PPPM solver~\cite{luty1996calculating}.
This tutorial was inspired by a publication by Liese and coworkers, in which molecular
-dynamics simulations are compared with force spectroscopy experiments~\cite{liese2017hydration}.
+dynamics simulations are compared with force spectroscopy experiments, see Ref.\,~\citenum{liese2017hydration}.
\subsubsection{Preparing the water reservoir}
@@ -1904,9 +1904,9 @@ \subsubsection{Preparing the water reservoir}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{PEG-density}
-\caption{a) Temperature of the water reservoir from
-\hyperref[all-atom-label]{Tutorial 3} with time $t$. The horizontal dashed line is
-the target temperature of 300\,K. b) Evolution of the density $\rho$.}
+\caption{a) Temperature ($T$) of the water reservoir from
+\hyperref[all-atom-label]{Tutorial 3} as a function of the ($t$). The horizontal dashed line is
+the target temperature of 300\,K. b) Evolution of the system density ($\rho$) with $t$.}
\label{fig:PEG-density}
\end{figure}
@@ -1932,7 +1932,7 @@ \subsubsection{Solvating the PEG in water}
to the water. The PEG molecule topology was downloaded from the ATB repository
\cite{malde2011automated, oostenbrink2004biomolecular}. It has a formula
$\text{C}_{16}\text{H}_{34}\text{O}_{9}$, and the parameters are taken from
-the GROMOS 54A7 force field~\cite{schmid2011definition}.
+the GROMOS 54A7 force field~\cite{schmid2011definition} (Fig.~\ref{fig:PEG-in-vacuum}).
\begin{figure}
\centering
@@ -1985,12 +1985,12 @@ \subsubsection{Solvating the PEG in water}
molecules will unnecessarily be deleted.
Let us use the \lmpcmd{fix npt} to control the temperature, as
-well as the pressure by allowing the box size to be rescaled along the $x$ axis:
+well as the pressure by allowing the box size to be rescaled along the $x$-axis:
\begin{lstlisting}
fix mynpt all npt temp 300 300 100 x 1 1 1000
\end{lstlisting}
Let us also use the \lmpcmd{recenter} command to always keep the PEG at
-the position $0 0 0$:
+the position $(0,~0,~0)$:
\begin{lstlisting}
fix myrct PEG recenter 0 0 0 shift all
\end{lstlisting}
@@ -2044,9 +2044,8 @@ \subsubsection{Stretching the PEG molecule}
kspace_style pppm 1e-5
read_restart merge.restart
\end{lstlisting}
-Next, we'll create new atom groups, each containing a single atom: the oxygen
-atoms located at the ends of the chain. The atoms of type \lmpcmd{OAlc}
-correspond to the hydroxy (alcohol) group oxygen atoms located at the ends
+Next, we'll create new atom groups, each containing a single oxygen atom. The atoms of type OAlc
+correspond to the hydroxyl (alcohol) group oxygen atoms located at the ends
of the PEG molecule, which we will use to apply the force. Add the
following lines to \flecmd{pull.lmp}:
\begin{lstlisting}
@@ -2058,10 +2057,10 @@ \subsubsection{Stretching the PEG molecule}
group topull1 variable end1
group topull2 variable end2
\end{lstlisting}
-These lines identify the oxygen atoms (\lmpcmd{OAlc}) at the ends of the PEG
-molecule and calculates their center of mass along the $x$ axis. It then
-divides these atoms into two groups, \lmpcmd{OAlc} (i.e.,~the OAlc atom to
-the right of the center) and \lmpcmd{OAlc} (i.e.,~the OAlc atom to the right
+These lines identify the oxygen atoms (type OAlc) at the ends of the PEG
+molecule and calculates their center of mass along the $x$-axis. It then
+divides these atoms into two groups, \lmpcmd{end1} (i.e.,~the OAlc atom to
+the right of the center) and \lmpcmd{end2} (i.e.,~the OAlc atom to the right
of the center), for applying force during the stretching process.
Add the following \lmpcmd{dump} command to create images of the system:
@@ -2089,7 +2088,7 @@ \subsubsection{Stretching the PEG molecule}
To investigate the stretching of the PEG molecule, let us compute its radius of
gyration~\cite{fixmanRadiusGyrationPolymer1962a} and the angles of its dihedral
-constraints using the following conmmands:
+constraints using the following commands:
\begin{lstlisting}
compute rgyr PEG gyration
compute prop PEG property/local dtype
@@ -2101,9 +2100,9 @@ \subsubsection{Stretching the PEG molecule}
thermo 250
dump mydmp all local 100 pull.dat index c_dphi c_prop
\end{lstlisting}
-Since the dihedral angle $\phi$ is returned as a vector by the compute
-\lmpcmd{dihedral/local} command, it needs to be printed to a file using
-the \lmpcmd{dump} command.
+By contrast with the radius of gyration (compute \lmpcmd{rgyr}), the dihedral angle % SG: why is c_prop not printed?
+$\phi$ (compute \lmpcmd{dphi}) is returned as a vector by the \lmpcmd{compute dihedral/local}
+command and must be written to a file using the \lmpcmd{dump local} command.
Finally, let us simulate 15 picoseconds without any external force:
\begin{lstlisting}
@@ -2111,16 +2110,16 @@ \subsubsection{Stretching the PEG molecule}
\end{lstlisting}
This initial run will serve as a benchmark to quantify the changes caused by
the applied force in later steps. Next, let us apply a force to the two selected
-oxygen atoms using two \lmpcmd{add\_force} commands, and then run the simulation
+oxygen atoms using two \lmpcmd{addforce} commands, and then run the simulation
for an extra 15~ps:
\begin{lstlisting}
fix myaf1 topull1 addforce 10 0 0
fix myaf2 topull2 addforce -10 0 0
run 15000
\end{lstlisting}
-The force magnitude of $10\,\text{kcal/mol/\AA{}}$ corresponds to $0.67\,\text{nN}$
-and was selected to be sufficiently large to overcome both thermal agitation and
-the entropic contributions from both the water and PEG molecules.
+Each applied force has a magnitude of $10\,\text{kcal/mol/\AA{}}$, corresponding to $0.67\,\text{nN}$.
+This value was chosen to be sufficiently large to overcome both the thermal agitation and
+the entropic contributions from the molecules.
Run the \flecmd{pull.lmp} file using LAMMPS. From the generated images of the system,
you should observe that the PEG molecule eventually aligns
@@ -2130,7 +2129,7 @@ \subsubsection{Stretching the PEG molecule}
(Fig.~\ref{fig:PEG-distance}\,a). Additionally, from the values of the dihedral angles
printed in the \flecmd{pull.dat} file, you can create a histogram
of dihedral angles for a specific type. For example, the angle $\phi$ for dihedrals
-of type 1 (C-C-OE-C) is shown in Fig.~\ref{fig:PEG-distance}\,b.
+of type 1 (C-C-OE-C) is shown in Fig.~\ref{fig:PEG-distance}\,b. % SG: is it type 1 or 2?
\begin{figure}
\centering
@@ -2147,7 +2146,7 @@ \subsubsection{Stretching the PEG molecule}
the radius of gyration $R_\text{gyr}$ of the PEG molecule
from \hyperref[all-atom-label]{Tutorial 3}, with the force
applied starting at $t = 15\,\text{ps}$. b) Histograms of the dihedral angles of type 2
-in the absence (orange) and in the presence (blue) of the applied force.}
+in the absence (orange) and in the presence (blue) of the applied force.} % SG: is it type 1 or 2?
\label{fig:PEG-distance}
\end{figure}
@@ -2730,10 +2729,10 @@ \subsubsection{Imposed shearing}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{NANOSHEAR-profiles}
-\caption{a) Water density $\rho$ along the \textit{z} axis as
+\caption{a) Water density $\rho$ along the $z$-axis as
simulated in \hyperref[sheared-confined-label]{Tutorial 4}.
b) Velocity profiles for water (blue) and walls
-(orange) along the $z$ axis.}
+(orange) along the $z$-axis.}
% The line is a linear fit assuming
% that the pore size is $h = 1.8\,\text{nm}$.}
\label{fig:NANOSHEAR-profiles}
@@ -2763,7 +2762,10 @@ \subsection{Tutorial 5: Reactive silicon dioxide}
\centering
\includegraphics[width=0.55\linewidth]{SIO}
\caption{A portion of the silicon dioxide structure as simulated during
-\hyperref[reactive-silicon-dioxide-label]{Tutorial 5}. Atoms are colored by their charges.}
+\hyperref[reactive-silicon-dioxide-label]{Tutorial 5}. Atoms are colored
+by their charges: the hydrogen atoms appear as small greenish spheres, silicon
+atoms as large orange spheres, and oxygen atoms as blue spheres of intermediate
+size.}
\label{fig:SIO}
\end{figure}
@@ -3121,9 +3123,8 @@ \subsubsection{Decorate the surface}
\includegraphics[width=\linewidth]{SIO-decorated}
\caption{Cracked silicon oxide after the addition of hydrogen atoms
during \hyperref[reactive-silicon-dioxide-label]{Tutorial 5}. The atoms
-are colored by their charges. Dangling oxygen groups appear in greenish, bulk
-Si atoms with a charge of about $1.8~\text{e}$ appear in red/orange, and bulk
-O atoms with a charge of about $-0.9 ~ \text{e}$ appear in blue.}
+are colored by their charges, with the newly added hydrogen atoms appearing as small
+greenish spheres.}
\label{fig:SIO-decorated}
\end{figure}
@@ -3132,10 +3133,11 @@ \subsection{Tutorial 6: Water adsorption in silica}
\begin{figure}
\centering
-\includegraphics[width=0.55\linewidth]{GCMC}
-\caption{Water molecules adsorbed in cracked silica (SiO$_2$) material as simulated
-during \hyperref[gcmc-silica-label]{Tutorial 6}. Water molecules are colored in
-cyan and white, oxygen (O) atoms from SiO$_2$ in red, and silicon (Si) atoms in yellow.}
+\includegraphics[width=0.6\linewidth]{GCMC}
+\caption{Water molecules (H$_2$O) adsorbed in cracked silica (SiO$_2$) material as simulated
+during \hyperref[gcmc-silica-label]{Tutorial 6}. The oxygen atoms of the water
+molecules are represented in cyan, the silicon atoms in yellow, and the oxygen
+atoms of the solid in red.}
\label{fig:GCMC}
\end{figure}
@@ -3205,11 +3207,6 @@ \subsubsection{Generation of the silica block}
thermo_style custom step temp etotal vol density
\end{lstlisting}
-% SG
-% FROM . Chem. Phys. 97, 2682–2689 (1992)
-% https://doi.org/10.1063/1.463056
-% 3 steps only. Say that its too fast to be correct. Show density.
-% Show rdf instead of box size?
Finally, let us implement the annealing procedure which
consists of three consecutive runs. This procedure was inspired
by Ref.\,\cite{della1992molecular}. First, to melt the system,
@@ -3252,12 +3249,10 @@ \subsubsection{Generation of the silica block}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{GCMC-dimension}
-\caption{a) Temperature $T$ as a function of time $t$
-during the annealing of the silica system
-from \hyperref[gcmc-silica-label]{Tutorial 6}.
-b) System density $\rho$ during
-annealing. The vertical dashed lines mark the transition between the different
-phases of the simulation.}
+\caption{a) Temperature $T$ as a function of time $t$ during the annealing
+of the silica system from \hyperref[gcmc-silica-label]{Tutorial 6}.
+b) System density $\rho$ during the annealing process. The vertical dashed lines
+mark the transition between the different phases of the simulation.}
\label{fig:GCMC-dimension}
\end{figure}
@@ -3266,7 +3261,7 @@ \subsubsection{Generation of the silica block}
\includegraphics[width=0.9\linewidth]{GCMC-generate}
\caption{Amorphous silica ($\text{SiO}_2$) simulated
during \hyperref[gcmc-silica-label]{Tutorial 6}. Silicon atoms are
-represented in yellow, and the oxygen atoms in red.}
+represented in yellow, and oxygen atoms in red.}
\label{fig:GCMC-snapshot}
\end{figure}
@@ -3310,16 +3305,17 @@ \subsubsection{Cracking the silica}
\end{lstlisting}
The \lmpcmd{fix nvt} command is employed to control the temperature of the system.
As observed from the generated images, the atoms
-progressively adjust to the changing box dimensions. At some point, bonds begin to break,
-leading to the appearance of dislocations (Fig.~\ref{fig:GCMC-cracked}).
+progressively adjust to the changing box dimensions. At some point,
+bonds begin to break, leading to the appearance of
+dislocations (Fig.~\ref{fig:GCMC-cracked}).
\begin{figure}
\centering
\includegraphics[width=\linewidth]{GCMC-cracked}
\caption{Block of silica from \hyperref[gcmc-silica-label]{Tutorial 6}
after deformation. Silicon atoms are represented in yellow,
-and the oxygen atoms in red. The crack was induced by the
-imposed deformation of the box along the $x$-axis.}
+and oxygen atoms in red. The crack was induced by the
+imposed deformation of the box along the $x$-axis (i.e.,~the horizontal axis).}
\label{fig:GCMC-cracked}
\end{figure}
@@ -3329,7 +3325,7 @@ \subsubsection{Adding water}
the Monte Carlo method in the grand canonical ensemble (GCMC). In short, the
system is placed into contact with a virtual reservoir of a given chemical potential
$\mu$, and multiple attempts to insert water molecules at random positions are
-made. Each attempt is either accepted or rejected based on energy considerations.
+made. Each attempt is either accepted or rejected based on energy considerations.
For further details, please refer to classical textbooks like Ref.~\citenum{frenkel2023understanding}.
\paragraph{Using hydrid potentials}
@@ -3536,7 +3532,7 @@ \subsubsection{Adding water}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{GCMC-number}
-\caption{Number of water molecules $N_\text{H2O}$ as a function of the time $t$
+\caption{Number of water molecules, $N_\text{H2O}$, as a function of time, $t$,
as extracted from \hyperref[gcmc-silica-label]{Tutorial 6}.}
\label{fig:GCMC-number}
\end{figure}
@@ -3565,10 +3561,10 @@ \subsection{Tutorial 7: Free energy calculation}
\begin{figure}
\centering
-\includegraphics[width=0.55\linewidth]{US}
-\caption{Atoms as simulated during \hyperref[umbrella-sampling-label]{Tutorial 7}.
-Only the atom colored in pink feels the additional force used for the umbrella
-sampling method.}
+\includegraphics[width=0.7\linewidth]{US}
+\caption{System simulated during \hyperref[umbrella-sampling-label]{Tutorial 7}.
+The pink atom explores the energetically unfavorable central area of the simulation
+box thanks to the additional potential imposed during umbrella sampling.}
\label{fig:US}
\end{figure}
@@ -3716,15 +3712,13 @@ \subsubsection{Method 1: Free sampling}
run 50000
\end{lstlisting}
Run the simulation with LAMMPS. The number of atoms in the
-central region, $n_\mathrm{center}$, reaches
-its equilibrium value after approximately $40\,\text{ps}$
-(Fig.~\ref{fig:US-density-evolution}). A snapshot of the
-equilibrated system is shown in Fig.~\ref{fig:US-system-unbiased}.
+central region, $n_\mathrm{center}$, reaches its equilibrium value after approximately $40\,\text{ps}$
+(Fig.~\ref{fig:US-density-evolution}). A snapshot of the equilibrated system is shown in Fig.~\ref{fig:US-system-unbiased}.
\paragraph{Run and data acquisition}
Once the system is equilibrated, we will record the density profile of
-the atoms along the $x$ axis using the \lmpcmd{ave/chunk} command.
+the atoms along the $x$-axis using the \lmpcmd{ave/chunk} command.
Add the following line to \flecmd{free-energy.lmp}:
\begin{lstlisting}
reset_timestep 0
@@ -3746,8 +3740,8 @@ \subsubsection{Method 1: Free sampling}
\includegraphics[width=\linewidth]{US-density-evolution}
\caption{Evolution of the number of atoms $n_\text{center}$ in the central
region \lmpcmd{mymes} as a function of time $t$ during equilibration. The dark line
-is $n_\text{center} = 22 \exp(-t/160)+5$ and serves as a guide for the eyes. Here, $U_0 = 0.36~\text{kcal/mol}$,
-$\delta = 0.5~\text{\AA{}}$, and $x_0 = 5~\text{\AA{}}$.}
+is $n_\text{center} = 22 \exp(-t/160)+5$ and serves as a guide for the eyes.
+Here, $U_0 = 0.36~\text{kcal/mol}$, $\delta = 1.0~\text{\AA{}}$, and $x_0 = 10~\text{\AA{}}$.}
\label{fig:US-density-evolution}
\end{figure}
@@ -3961,9 +3955,10 @@ \subsubsection{Method 2: Umbrella sampling}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{US-free-energy}
-\caption{The potential $U$ as a function of $x$, measured using umbrella sampling
-(blue disks), is compared to the imposed potential given in Eq.~\eqref{eq:U}
-(dark line). Parameters are $U_0 = 2.38~\text{kcal/mol}$, $\delta = 1.0~\text{\AA{}}$,
+\caption{The potential $U$ as a function of $x$, measured using umbrella
+sampling during \hyperref[umbrella-sampling-label]{Tutorial 7} (blue disks),
+is compared to the imposed potential given in Eq.~\eqref{eq:U}
+(dark line). Parameters are $U_0 = 2.38~\text{kcal/mol}$, $\delta = 1.0~\text{\AA{}}$,
and $x_0 = 10~\text{\AA{}}$.}
\label{fig:US-freenergy}
\end{figure}
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