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docs: complete howto review

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Richard Berger
2024-08-18 13:20:00 -06:00
parent b7cf79a7b9
commit 216be2e96f
5 changed files with 35 additions and 25 deletions
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2
doc/src/Howto_bioFF.rst
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@ -73,7 +73,7 @@ with additional switching or shifting functions that ramp the energy
and/or force smoothly to zero between an inner :math:`(a)` and outer
:math:`(b)` cutoff. The older styles with *charmm* (not *charmmfsw* or
*charmmfsh*\ ) in their name compute the LJ and Coulombic interactions
with an energy switching function (esw) S(r) which ramps the energy
with an energy switching function (esw) :math:`S(r)` which ramps the energy
smoothly to zero between the inner and outer cutoff. This can cause
irregularities in pairwise forces (due to the discontinuous second
derivative of energy at the boundaries of the switching region), which

8
doc/src/Howto_diffusion.rst
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@ -1,8 +1,8 @@
Calculate diffusion coefficients
================================
The diffusion coefficient D of a material can be measured in at least
2 ways using various options in LAMMPS. See the examples/DIFFUSE
The diffusion coefficient :math:`D` of a material can be measured in at least
2 ways using various options in LAMMPS. See the ``examples/DIFFUSE``
directory for scripts that implement the 2 methods discussed here for
a simple Lennard-Jones fluid model.
@ -12,7 +12,7 @@ of the MSD versus time is proportional to the diffusion coefficient.
The instantaneous MSD values can be accumulated in a vector via the
:doc:`fix vector <fix_vector>` command, and a line fit to the vector to
compute its slope via the :doc:`variable slope <variable>` function, and
thus extract D.
thus extract :math:`D`.
The second method is to measure the velocity auto-correlation function
(VACF) of the system, via the :doc:`compute vacf <compute_vacf>`
@ -20,4 +20,4 @@ command. The time-integral of the VACF is proportional to the
diffusion coefficient. The instantaneous VACF values can be
accumulated in a vector via the :doc:`fix vector <fix_vector>` command,
and time integrated via the :doc:`variable trap <variable>` function,
and thus extract D.
and thus extract :math:`D`.

16
doc/src/Howto_kappa.rst
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@ -1,20 +1,22 @@
Calculate thermal conductivity
==============================
The thermal conductivity kappa of a material can be measured in at
least 4 ways using various options in LAMMPS. See the examples/KAPPA
The thermal conductivity :math:`\kappa` of a material can be measured in at
least 4 ways using various options in LAMMPS. See the ``examples/KAPPA``
directory for scripts that implement the 4 methods discussed here for
a simple Lennard-Jones fluid model. Also, see the :doc:`Howto viscosity <Howto_viscosity>` page for an analogous discussion
for viscosity.
The thermal conductivity tensor kappa is a measure of the propensity
The thermal conductivity tensor :math:`\mathbf{\kappa}` is a measure of the propensity
of a material to transmit heat energy in a diffusive manner as given
by Fourier's law
J = -kappa grad(T)
.. math::
where J is the heat flux in units of energy per area per time and
grad(T) is the spatial gradient of temperature. The thermal
J = -\kappa \cdot \text{grad}(T)
where :math:`J` is the heat flux in units of energy per area per time and
:math:`\text{grad}(T)` is the spatial gradient of temperature. The thermal
conductivity thus has units of energy per distance per time per degree
K and is often approximated as an isotropic quantity, i.e. as a
scalar.
@ -49,7 +51,7 @@ details.
The fourth method is based on the Green-Kubo (GK) formula which
relates the ensemble average of the auto-correlation of the heat flux
to kappa. The heat flux can be calculated from the fluctuations of
to :math:`\kappa`. The heat flux can be calculated from the fluctuations of
per-atom potential and kinetic energies and per-atom stress tensor in
a steady-state equilibrated simulation. This is in contrast to the
two preceding non-equilibrium methods, where energy flows continuously

10
doc/src/Howto_structured_data.rst
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@ -341,7 +341,12 @@ data files and obtain a list of dictionaries.
.. code-block::
[{'timestep': 0, 'pe': -6.773368053259247, 'ke': 4.498875000000003}, {'timestep': 50, 'pe': -4.80824944183232, 'ke': 2.5257981827119798}, {'timestep': 100, 'pe': -4.787560887558151, 'ke': 2.5062598821985103}, {'timestep': 150, 'pe': -4.747103368600548, 'ke': 2.46609592554545}, {'timestep': 200, 'pe': -4.750905285854413, 'ke': 2.4701136792591694}, {'timestep': 250, 'pe': -4.777432735632181, 'ke': 2.4962152903997175}]
[{'timestep': 0, 'pe': -6.773368053259247, 'ke': 4.498875000000003},
{'timestep': 50, 'pe': -4.80824944183232, 'ke': 2.5257981827119798},
{'timestep': 100, 'pe': -4.787560887558151, 'ke': 2.5062598821985103},
{'timestep': 150, 'pe': -4.747103368600548, 'ke': 2.46609592554545},
{'timestep': 200, 'pe': -4.750905285854413, 'ke': 2.4701136792591694},
{'timestep': 250, 'pe': -4.777432735632181, 'ke': 2.4962152903997175}]
Line Delimited JSON (LD-JSON)
-----------------------------
@ -352,7 +357,8 @@ Each line represents one JSON object.
.. code-block:: LAMMPS
fix extra all print 50 """{"timestep": $(step), "pe": $(pe), "ke": $(ke)}""" title "" file output.json screen no
fix extra all print 50 """{"timestep": $(step), "pe": $(pe), "ke": $(ke)}""" &
title "" file output.json screen no
.. code-block:: json
:caption: output.json

24
doc/src/Howto_viscosity.rst
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@ -1,22 +1,24 @@
Calculate viscosity
===================
The shear viscosity eta of a fluid can be measured in at least 6 ways
using various options in LAMMPS. See the examples/VISCOSITY directory
The shear viscosity :math:`\eta` of a fluid can be measured in at least 6 ways
using various options in LAMMPS. See the ``examples/VISCOSITY`` directory
for scripts that implement the 5 methods discussed here for a simple
Lennard-Jones fluid model and 1 method for SPC/E water model.
Also, see the :doc:`page on calculating thermal conductivity <Howto_kappa>`
for an analogous discussion for thermal conductivity.
Eta is a measure of the propensity of a fluid to transmit momentum in
:math:`\eta` is a measure of the propensity of a fluid to transmit momentum in
a direction perpendicular to the direction of velocity or momentum
flow. Alternatively it is the resistance the fluid has to being
sheared. It is given by
J = -eta grad(Vstream)
.. math::
where J is the momentum flux in units of momentum per area per time.
and grad(Vstream) is the spatial gradient of the velocity of the fluid
J = -\eta \cdot \text{grad}(V_{\text{stream}})
where :math:`J` is the momentum flux in units of momentum per area per time.
and :math:`\text{grad}(V_{\text{stream}})` is the spatial gradient of the velocity of the fluid
moving in another direction, normal to the area through which the
momentum flows. Viscosity thus has units of pressure-time.
@ -38,11 +40,11 @@ velocity to prevent the fluid from heating up.
In both cases, the velocity profile setup in the fluid by this
procedure can be monitored by the :doc:`fix ave/chunk <fix_ave_chunk>`
command, which determines grad(Vstream) in the equation above.
E.g. the derivative in the y-direction of the Vx component of fluid
motion or grad(Vstream) = dVx/dy. The Pxy off-diagonal component of
command, which determines :math:`\text{grad}(V_{\text{stream}})` in the equation above.
E.g. the derivative in the y-direction of the :math:`V_x` component of fluid
motion or :math:`\text{grad}(V_{\text{stream}}) = \frac{\text{d} V_x}{\text{d} y}`. The :math:`P_{xy}` off-diagonal component of
the pressure or stress tensor, as calculated by the :doc:`compute pressure <compute_pressure>` command, can also be monitored, which
is the J term in the equation above. See the :doc:`Howto nemd <Howto_nemd>` page for details on NEMD simulations.
is the :math:`J` term in the equation above. See the :doc:`Howto nemd <Howto_nemd>` page for details on NEMD simulations.
The third method is to perform a reverse non-equilibrium MD simulation
using the :doc:`fix viscosity <fix_viscosity>` command which implements
@ -55,7 +57,7 @@ See the :doc:`fix viscosity <fix_viscosity>` command for details.
The fourth method is based on the Green-Kubo (GK) formula which
relates the ensemble average of the auto-correlation of the
stress/pressure tensor to eta. This can be done in a fully
stress/pressure tensor to :math:`\eta`. This can be done in a fully
equilibrated simulation which is in contrast to the two preceding
non-equilibrium methods, where momentum flows continuously through the
simulation box.