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some more cases where we can use embedded math

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This commit is contained in:
Axel Kohlmeyer
2020-02-29 04:57:44 -05:00
parent e6c9efe6bf
commit 66a0e27edf
3 changed files with 27 additions and 26 deletions
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2
doc/src/Howto_drude2.rst
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@ -181,7 +181,7 @@ include Coulomb interactions, for instance *lj/cut/coul/long* with
As compared to the non-polarizable input file, *pair\_coeff* lines need
to be added for the DPs. Since the DPs have no Lennard-Jones
interactions, their *epsilon* is 0. so the only *pair\_coeff* line
interactions, their :math:`\epsilon` is 0. so the only *pair\_coeff* line
that needs to be added is

15
doc/src/angle_sdk.rst
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@ -35,13 +35,14 @@ The *sdk* angle style is a combination of the harmonic angle potential,
E = K (\theta - \theta_0)^2
where :math:`\theta_0` is the equilibrium value of the angle and :math:`K` a prefactor,
with the *repulsive* part of the non-bonded *lj/sdk* pair style
between the atoms 1 and 3. This angle potential is intended for
coarse grained MD simulations with the CMM parameterization using the
:doc:`pair_style lj/sdk <pair_sdk>`. Relative to the pair\_style
*lj/sdk*\ , however, the energy is shifted by *epsilon*\ , to avoid sudden
jumps. Note that the usual 1/2 factor is included in :math:`K`.
where :math:`\theta_0` is the equilibrium value of the angle and
:math:`K` a prefactor, with the *repulsive* part of the non-bonded
*lj/sdk* pair style between the atoms 1 and 3. This angle potential is
intended for coarse grained MD simulations with the CMM parameterization
using the :doc:`pair_style lj/sdk <pair_sdk>`. Relative to the
pair\_style *lj/sdk*\ , however, the energy is shifted by
:math:`\epsilon`, to avoid sudden jumps. Note that the usual 1/2 factor
is included in :math:`K`.
The following coefficients must be defined for each angle type via the
:doc:`angle_coeff <angle_coeff>` command as in the example above:

36
doc/src/pair_line_lj.rst
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@ -28,13 +28,13 @@ Description
"""""""""""
Style *line/lj* treats particles which are line segments as a set of
small spherical particles that tile the line segment length as
explained below. Interactions between two line segments, each with N1
and N2 spherical particles, are calculated as the pairwise sum of
N1\*N2 Lennard-Jones interactions. Interactions between a line segment
with N spherical particles and a point particle are treated as the
pairwise sum of N Lennard-Jones interactions. See the :doc:`pair_style lj/cut <pair_lj>` doc page for the definition of Lennard-Jones
interactions.
small spherical particles that tile the line segment length as explained
below. Interactions between two line segments, each with N1 and N2
spherical particles, are calculated as the pairwise sum of N1\*N2
Lennard-Jones interactions. Interactions between a line segment with N
spherical particles and a point particle are treated as the pairwise sum
of N Lennard-Jones interactions. See the :doc:`pair_style lj/cut
<pair_lj>` doc page for the definition of Lennard-Jones interactions.
The set of non-overlapping spherical sub-particles that represent a
line segment are generated in the following manner. Their size is a
@ -50,10 +50,10 @@ each pair of points.
The LJ interaction between 2 spheres on different line segments (or a
sphere on a line segment and a point particles) is computed with
sub-particle epsilon, sigma, and cutoff values that are set by the
pair\_coeff command, as described below. If the distance between the 2
spheres is greater than the sub-particle cutoff, there is no
interaction. This means that some pairs of sub-particles on 2 line
sub-particle :math:`\epsilon`, :math:`\sigma`, and *cutoff* values that
are set by the pair\_coeff command, as described below. If the distance
between the 2 spheres is greater than the sub-particle cutoff, there is
no interaction. This means that some pairs of sub-particles on 2 line
segments may interact, but others may not.
For purposes of creating the neighbor list for pairs of interacting
@ -86,8 +86,8 @@ commands:
* sizeI (distance units)
* sizeJ (distance units)
* epsilon (energy units)
* sigma (distance units)
* :math:`\epsilon` (energy units)
* :math:`\sigma` (distance units)
* subcutoff (distance units)
* cutoff (distance units)
@ -102,11 +102,11 @@ sizeI will apply to all segments of type I. If typeI or typeJ refers
to point particles, the corresponding sizeI or sizeJ is ignored; it
can be set to 0.0.
The *epsilon*\ , *sigma*\ , and *subcutoff* coefficients are used to
compute an LJ interactions between a pair of sub-particles on 2 line
segments (of type I and J), or between a sub particle/point particle
pair. As discussed above, the *subcutoff* and *cutoff* params are
different. The latter is only used for building the neighbor list
The :math:`\epsilon`, :math:`\sigma`, and *subcutoff* coefficients are
used to compute an LJ interactions between a pair of sub-particles on 2
line segments (of type I and J), or between a sub particle/point
particle pair. As discussed above, the *subcutoff* and *cutoff* params
are different. The latter is only used for building the neighbor list
when the distance between centers of two line segments or one segment
and a point particle is calculated.