first range of reviewer comments

Author: Simon Gravelle

docs/sphinx/source/tutorial1/tutorial.rst

@@ -274,7 +274,7 @@ initially positive potential energy is expected, as the atoms are
 created at random positions within the simulation box, with some in very
 close proximity to each other.  This proximity results in a large
 initial potential energy due to the repulsive branch of the
-Lennard-Jones potential [i.e., the term in :math:`1/r^{12}` in
+Lennard-Jones potential [i.e., the term :math:`1/r^{12}` in
 Eq. :eq:`eq_LJ`].  As the energy minimization progresses, the energy
 decreases - first rapidly - then more gradually, before plateauing at a
 negative value.  This indicates that the atoms have moved to reasonable
@@ -311,7 +311,7 @@ command is introduced to specify the thermodynamic information LAMMPS should
 print during ``PART B``.  This adjustment is made because, during
 molecular dynamics, the system exhibits a non-zero temperature :math:`T` (and
 consequently a non-zero kinetic energy :math:`K`, keyword ``ke``), which are useful to monitor.
-The ``pe`` keyword represents the potential energy of the system, :math:`E`, such that
+The ``pe`` keyword represents the potential energy of the system, :math:`U`, such that
 :math:`U + K = E`.
 
 Then, add a second ``Run`` category by including the following

docs/sphinx/source/tutorial2/tutorial.rst

@@ -357,6 +357,7 @@ from the typical dependency of bond energy with bond distance,
     The CNT starts deforming at :math:`t = 5\,\text{ps}`, and :math:`L_\text{cnt-0}` is the  
     CNT initial length.  b) Evolution of the total energy :math:`E` of the system with time :math:`t`.  
     Here, the potential is OPLS-AA, and the CNT is unbreakable.
+    The orange line shows the raw data, and the blue line represents a time-averaged curve.
 
 Importing YAML log file into Python
 -----------------------------------

docs/sphinx/source/tutorial3/tutorial.rst

@@ -35,7 +35,7 @@ angles, and dihedrals used in the simulation, here ``harmonic``.
 With the ``pair_style`` named ``lj/cut/coul/long``, atoms
 interact through both a Lennard-Jones (LJ) potential and Coulomb
 interactions.  The value of :math:`10\,\text{Å}` is the cutoff, and the
-``ewald`` command defines the long-range solver for the Coulomb
+``kspace_style`` command defines the long-range solver for the Coulomb
 interactions :cite:`ewald1921berechnung`.  Finally, the
 ``special_bonds`` command, which was already seen in
 :ref:`carbon-nanotube-label`, sets the LJ and Coulomb
@@ -177,16 +177,16 @@ Let us also extract the volume and density every 500 steps:
     thermo_style custom step temp etotal v_myvol v_rho
 
 Here, several variables are defined and used for converting the units of the
-density in kg/mol:  The variable ``myoxy`` represents the number of
+density in :math:`\text{kg/m}^3`:  The variable ``myoxy`` represents the number of
 atoms divided by 3,  which corresponds to the number of molecules, :math:`N_\text{H2O}`,
-and the variable ``myrho`` is the density in kg/mol:  
+and the variable ``myrho`` is the density in :math:`\text{kg/m}^3`.
 
 .. math::
 
-    \rho = \dfrac{N_\text{H2O}}{V N_\text{A}},
+    \rho = \dfrac{N_\text{H2O} M}{V N_\text{A}},
 
 where :math:`V` is the volume in :math:`\text{m}^3`, :math:`N_\text{A}` the Avogadro number, and
-:math:`M = 0.018`\,kg/mol the molar mass of water.
+:math:`M = 0.018 ~ \text{kg/mol}` the molar mass of water.
 
 Finally, let us set the timestep to 1.0 fs, and run the simulation for 15 ps by
 adding the following lines into **water.lmp**:

docs/sphinx/source/tutorial4/tutorial.rst

@@ -344,7 +344,7 @@ to **equilibrate.lmp**:
     thermo 1
     thermo_style custom step temp etotal press
 
-Let us perform an energy minization by adding the following lines to **equilibrate.lmp**:
+Let us perform an energy minimization by adding the following lines to **equilibrate.lmp**:
 
 .. code-block:: lammps
 
@@ -443,7 +443,8 @@ the end of the simulation.
 
     Figure: a) Pressure, :math:`p`, of the nanosheared electrolyte system as a function
     of the time, :math:`t`.  b) Distance between the walls, :math:`\Delta z`, as a
-    function of :math:`t`.
+    function of :math:`t`. The orange line shows the raw data, and the blue line
+    represents a time-averaged curve.
 
 Imposed shearing
 ----------------