some more formatting and math conversion improvements

This commit is contained in:
Axel Kohlmeyer
2020-02-27 18:18:49 -05:00
parent d242051c8e
commit 03985454ed
14 changed files with 93 additions and 96 deletions

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@ -38,7 +38,7 @@ If an error occurs, carefully go through the steps on the
library and the :doc:`Python\_install <Python_install>` doc page about
insuring Python can find the necessary two files it needs.
**Test LAMMPS and Python in serial:**
Test LAMMPS and Python in serial:
-------------------------------------
To run a LAMMPS test in serial, type these lines into Python
@ -67,7 +67,7 @@ typed something like:
lmp_g++ -in in.lj
**Test LAMMPS and Python in parallel:**
Test LAMMPS and Python in parallel:
---------------------------------------
To run LAMMPS in parallel, assuming you have installed the
@ -128,7 +128,7 @@ described in the PyPar documentation. The last line of your Python
script should be pypar.finalize(), to insure MPI is shut down
correctly.
**Running Python scripts:**
Running Python scripts:
---------------------------
Note that any Python script (not just for LAMMPS) can be invoked in

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@ -155,17 +155,15 @@ simulation domain.
To accomplish this, if :math:`B_{ij} < B_{target}`, the :math:`C_{ij}`
prefactor for bond *ij* is incremented on the current timestep by an
amount proportional to the inverse of the specified *alpha* and the
difference (:math:`B_{ij} - B_{target}`).
Conversely if :math:`B_{ij} > B_{target}`, :math:`C_{ij}` is decremented
by the same amount.
This procedure is termed "boostostatting" in :ref:`(Voter2013) <Voter2013lhd>`.
It drives all of the individual :math:`C_{ij}` to
values such that when :math:`V^{max}_{ij}` is applied as a bias to
bond *ij*, the resulting boost factor :math:`B_{ij}` will be close
to :math:`B_{target}` on average.
Thus the LHD time acceleration factor for the overall system is
effectively *Btarget*\ .
amount proportional to the inverse of the specified :math:`\alpha` and
the difference (:math:`B_{ij} - B_{target}`). Conversely if
:math:`B_{ij} > B_{target}`, :math:`C_{ij}` is decremented by the same
amount. This procedure is termed "boostostatting" in :ref:`(Voter2013)
<Voter2013lhd>`. It drives all of the individual :math:`C_{ij}` to
values such that when :math:`V^{max}_{ij}` is applied as a bias to bond
*ij*, the resulting boost factor :math:`B_{ij}` will be close to
:math:`B_{target}` on average. Thus the LHD time acceleration factor
for the overall system is effectively *Btarget*\ .
Note that in LHD, the boost factor :math:`B_{target}` is specified by the user.
This is in contrast to global hyperdynamics (GHD) where the boost

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@ -125,9 +125,9 @@ functions,
Full details of the lattice-Boltzmann algorithm used can be found in
:ref:`Mackay et al. <fluid-Mackay>`.
The fluid is coupled to the MD particles described by *group-ID*
through a velocity dependent force. The contribution to the fluid
force on a given lattice mesh site j due to MD particle alpha is
The fluid is coupled to the MD particles described by *group-ID* through
a velocity dependent force. The contribution to the fluid force on a
given lattice mesh site j due to MD particle :math:`\alpha` is
calculated as:
.. math::

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@ -45,12 +45,12 @@ Examples
fix 1 all qbmsst z 0.122 q 25 mu 0.9 tscale 0.01 damp 200 seed 35082 f_max 0.3 N_f 100 eta 1 beta 400 T_init 110 (liquid methane modeled with the REAX force field, real units)
fix 2 all qbmsst z 72 q 40 tscale 0.05 damp 1 seed 47508 f_max 120.0 N_f 100 eta 1.0 beta 500 T_init 300 (quartz modeled with the BKS force field, metal units)
Two example input scripts are given, including shocked alpha quartz
and shocked liquid methane. The input script first equilibrate an
initial state with the quantum thermal bath at the target temperature
and then apply the qbmsst to simulate shock compression with quantum
nuclear correction. The following two figures plot related quantities
for shocked alpha quartz.
Two example input scripts are given, including shocked
:math:`\alpha-\mathrm{quartz}` and shocked liquid methane.
The input script first equilibrate an initial state with the quantum
thermal bath at the target temperature and then apply the qbmsst to
simulate shock compression with quantum nuclear correction. The
following two figures plot related quantities for shocked alpha quartz.
.. image:: JPG/qbmsst_init.jpg
:align: center

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@ -158,7 +158,7 @@ For style *wall/morse*\ , the energy E is given by a Morse potential:
In all cases, *r* is the distance from the particle to the wall at
position *coord*\ , and Rc is the *cutoff* distance at which the
position *coord*\ , and :math:`r_c` is the *cutoff* distance at which the
particle and wall no longer interact. The energy of the wall
potential is shifted so that the wall-particle interaction energy is
0.0 at the cutoff distance.
@ -185,10 +185,10 @@ box parameters and timestep and elapsed time. Thus it is easy to
specify a time-dependent wall position. See examples below.
For the *wall/lj93* and *wall/lj126* and *wall/lj1043* styles,
*epsilon* and *sigma* are the usual Lennard-Jones parameters, which
:math:`\epsilon` and :math:`\sigma` are the usual Lennard-Jones parameters, which
determine the strength and size of the particle as it interacts with
the wall. Epsilon has energy units. Note that this *epsilon* and
*sigma* may be different than any *epsilon* or *sigma* values defined
the wall. Epsilon has energy units. Note that this :math:`\epsilon` and
:math:`\sigma` may be different than any :math:`\epsilon` or :math:`\sigma` values defined
for a pair style that computes particle-particle interactions.
The *wall/lj93* interaction is derived by integrating over a 3d
@ -197,39 +197,39 @@ interaction is effectively a harder, more repulsive wall interaction.
The *wall/lj1043* interaction is yet a different form of wall
interaction, described in Magda et al in :ref:`(Magda) <Magda>`.
For the *wall/colloid* style, *R* is the radius of the colloid
particle, *D* is the distance from the surface of the colloid particle
to the wall (r-R), and *sigma* is the size of a constituent LJ
particle inside the colloid particle and wall. Note that the cutoff
distance Rc in this case is the distance from the colloid particle
center to the wall. The prefactor *epsilon* can be thought of as an
effective Hamaker constant with energy units for the strength of the
colloid-wall interaction. More specifically, the *epsilon* pre-factor
= 4 \* pi\^2 \* rho\_wall \* rho\_colloid \* epsilon \* sigma\^6, where epsilon
and sigma are the LJ parameters for the constituent LJ
particles. Rho\_wall and rho\_colloid are the number density of the
constituent particles, in the wall and colloid respectively, in units
of 1/volume.
For the *wall/colloid* style, *R* is the radius of the colloid particle,
*D* is the distance from the surface of the colloid particle to the wall
(r-R), and :math:`\sigma` is the size of a constituent LJ particle
inside the colloid particle and wall. Note that the cutoff distance Rc
in this case is the distance from the colloid particle center to the
wall. The prefactor :math:`\epsilon` can be thought of as an effective
Hamaker constant with energy units for the strength of the colloid-wall
interaction. More specifically, the :math:`\epsilon` pre-factor is
:math:`4\pi^2 \rho_{wall} \rho_{colloid} \epsilon \sigma^6`, where
:math:`\epsilon` and :math:`\sigma` are the LJ parameters for the
constituent LJ particles. :math:`\rho_{wall}` and :math:`\rho_{colloid}`
are the number density of the constituent particles, in the wall and
colloid respectively, in units of 1/volume.
The *wall/colloid* interaction is derived by integrating over
constituent LJ particles of size *sigma* within the colloid particle
and a 3d half-lattice of Lennard-Jones 12/6 particles of size *sigma*
constituent LJ particles of size :math:`\sigma` within the colloid particle
and a 3d half-lattice of Lennard-Jones 12/6 particles of size :math:`\sigma`
in the wall. As mentioned in the preceding paragraph, the density of
particles in the wall and colloid can be different, as specified by
the *epsilon* pre-factor.
the :math:`\epsilon` pre-factor.
For the *wall/harmonic* style, *epsilon* is effectively the spring
For the *wall/harmonic* style, :math:`\epsilon` is effectively the spring
constant K, and has units (energy/distance\^2). The input parameter
*sigma* is ignored. The minimum energy position of the harmonic
:math:`\sigma` is ignored. The minimum energy position of the harmonic
spring is at the *cutoff*\ . This is a repulsive-only spring since the
interaction is truncated at the *cutoff*
For the *wall/morse* style, the three parameters are in this order:
*D\_0* the depth of the potential, *alpha* the width parameter, and
*r\_0* the location of the minimum. *D\_0* has energy units, *alpha*
inverse distance units, and *r\_0* distance units.
:math:`D_0` the depth of the potential, :math:`\alpha` the width parameter, and
:math:`r_0` the location of the minimum. :math:`D_0` has energy units, :math:`\alpha`
inverse distance units, and :math:`r_0` distance units.
For any wall, the *epsilon* and/or *sigma* and/or *alpha* parameter can
For any wall, the :math:`\epsilon` and/or :math:`\sigma` and/or :math:`\alpha` parameter can
be specified
as an :doc:`equal-style variable <variable>`, in which case it should be
specified as v\_name, where name is the variable name. As with a
@ -253,7 +253,7 @@ time. Thus it is easy to specify a time-dependent wall interaction.
the finite-size particles of radius R must be a distance larger than R
from the wall position *coord*\ . The *harmonic* style is a softer
potential and does not blow up as r -> 0, but you must use a large
enough *epsilon* that particles always reamin on the correct side of
enough :math:`\epsilon` that particles always reamin on the correct side of
the wall (r > 0).
The *units* keyword determines the meaning of the distance units used

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@ -87,9 +87,9 @@ is thus evaluated as:
where C is an energy-conversion constant, :math:`q_i` and :math:`q_j`
are the charges on the 2 atoms, epsilon is the dielectric constant which
can be set by the :doc:`dielectric <dielectric>` command, alpha is ion
pair dependent damping parameter and erf() is the error-function. The
cutoff Rc truncates the interaction distance.
can be set by the :doc:`dielectric <dielectric>` command, :math:`\alpha`
is the ion pair dependent damping parameter and erf() is the
error-function. The cutoff :math:`r_c` truncates the interaction distance.
The style *buck6d/coul/gauss/dsf* computes the Coulomb interaction
via the damped shifted force model described in :ref:`(Fennell) <Fennell>`

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@ -207,7 +207,7 @@ manipulation of adding and subtracting a self term (for i = j) to the
first and second term on the right-hand-side, respectively, and a
small enough :math:`\alpha` damping parameter, the second term shrinks and
the potential becomes a rapidly-converging real-space summation. With
a long enough cutoff and small enough alpha parameter, the energy and
a long enough cutoff and small enough :math:`\alpha` parameter, the energy and
forces calculated by the Wolf summation method approach those of the
Ewald sum. So it is a means of getting effective long-range
interactions with a short-range potential.

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@ -88,14 +88,14 @@ and three-body coefficients in the formula above:
* B (distance units)
* cutoffA (distance units)
* cutoffC (distance units)
* alpha
* beta
* eta
* gamma (distance units)
* lambda (energy units)
* mu
* tho
* sigma (distance units)
* :math:`\alpha`
* :math:`\beta`
* :math:`\eta`
* :math:`\gamma` (distance units)
* :math:`lambda` (energy units)
* :math:`\mu`
* :math:`\tau`
* :math:`\sigma` (distance units)
* Q0
* u1
* u2

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@ -295,7 +295,7 @@ a self term (for i = j) to the first and second term on the
right-hand-side, respectively, and a small enough :math:`\alpha` damping
parameter, the second term shrinks and the potential becomes a
rapidly-converging real-space summation. With a long enough cutoff and
small enough alpha parameter, the energy and forces calculated by the
small enough :math:`\alpha` parameter, the energy and forces calculated by the
Wolf summation method approach those of the Ewald sum. So it is a means
of getting effective long-range interactions with a short-range
potential.

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@ -128,7 +128,7 @@ where :math:`\alpha` gives the type of atom *i*\ , :math:`\beta` the
type of atom *j*\ , and the coefficients *a* and *b* filter for atom
types as specified by the user. *a* is called the central atom filter as
it determines to which atoms the potential applies; :math:`a_{\alpha} =
1` if the LD potential applies to atom type alpha else zero. On the
1` if the LD potential applies to atom type :math:`\alpha` else zero. On the
other hand, *b* is called the neighbor atom filter because it specifies
which atom types to use in the calculation of the LD; :math:`b_{\beta} =
1` if atom type :math:`\beta` contributes to the LD and zero otherwise.
@ -210,12 +210,15 @@ and potential. In general, blank lines anywhere are ignored.
----------
**Mixing, shift, table, tail correction, restart, info**\ :
This pair style does not support automatic mixing. For atom type pairs alpha,
beta and alpha != beta, even if LD potentials of type (alpha, alpha) and
(beta, beta) are provided, you will need to explicitly provide LD potential
types (alpha, beta) and (beta, alpha) if need be (Here, the notation (alpha,
beta) means that alpha is the central atom to which the LD potential is applied
and beta is the neighbor atom which contributes to the LD potential on alpha).
This pair style does not support automatic mixing. For atom type pairs
:math:`\alpha`, :math:`\beta` and :math:`\alpha` != :math:`\beta`, even
if LD potentials of type (:math:`\alpha`, :math:`\alpha`) and
(:math:`\beta`, :math:`\beta`) are provided, you will need to explicitly
provide LD potential types (:math:`\alpha`, :math:`\beta`) and
(:math:`\beta`, :math:`\alpha`) if need be (Here, the notation
(:math:`\alpha`, :math:`\beta`) means that :math:`\alpha` is the central
atom to which the LD potential is applied and :math:`\beta` is the
neighbor atom which contributes to the LD potential on :math:`\alpha`).
This pair style does not support the :doc:`pair_modify <pair_modify>`
shift, table, and tail options.

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@ -70,9 +70,9 @@ above, or in the data file or restart files read by the
:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
commands:
* D0 (energy units)
* alpha (1/distance units)
* r0 (distance units)
* :math:`D_0` (energy units)
* :math:`\alpha` (1/distance units)
* :math:`r_0` (distance units)
* cutoff (distance units)
The last coefficient is optional. If not specified, the global morse

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@ -91,11 +91,11 @@ For the *peri/pmb* style:
* c (energy/distance/volume\^2 units)
* horizon (distance units)
* s00 (unitless)
* alpha (unitless)
* :math:`\alpha` (unitless)
C is the effectively a spring constant for Peridynamic bonds, the
horizon is a cutoff distance for truncating interactions, and s00 and
alpha are used as a bond breaking criteria. The units of c are such
:math:`\alpha` are used as a bond breaking criteria. The units of c are such
that c/distance = stiffness/volume\^2, where stiffness is
energy/distance\^2 and volume is distance\^3. See the users guide for
more details.
@ -106,10 +106,10 @@ For the *peri/lps* style:
* G (force/area units)
* horizon (distance units)
* s00 (unitless)
* alpha (unitless)
* :math:`\alpha` (unitless)
K is the bulk modulus and G is the shear modulus. The horizon is a
cutoff distance for truncating interactions, and s00 and alpha are
cutoff distance for truncating interactions, and s00 and :math:`\alpha` are
used as a bond breaking criteria. See the users guide for more
details.
@ -119,12 +119,12 @@ For the *peri/ves* style:
* G (force/area units)
* horizon (distance units)
* s00 (unitless)
* alpha (unitless)
* :math:`\alpha` (unitless)
* m\_lambdai (unitless)
* m\_taubi (unitless)
K is the bulk modulus and G is the shear modulus. The horizon is a
cutoff distance for truncating interactions, and s00 and alpha are
cutoff distance for truncating interactions, and s00 and :math:`\alpha` are
used as a bond breaking criteria. m\_lambdai and m\_taubi are the
viscoelastic relaxation parameter and time constant,
respectively. m\_lambdai varies within zero to one. For very small
@ -138,11 +138,11 @@ For the *peri/eps* style:
* G (force/area units)
* horizon (distance units)
* s00 (unitless)
* alpha (unitless)
* :math:`\alpha` (unitless)
* m\_yield\_stress (force/area units)
K is the bulk modulus and G is the shear modulus. The horizon is a
cutoff distance and s00 and alpha are used as a bond breaking
cutoff distance and s00 and :math:`\alpha` are used as a bond breaking
criteria. m\_yield\_stress is the yield stress of the material. For
details please see the description in "(Mtchell2011a)".

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@ -113,9 +113,9 @@ by the following commands:
variable zblz equal 73
pair_style hybrid/overlay &
zbl ${zblcutinner} ${zblcutouter} snap
pair_coeff \* \* zbl 0.0
pair_coeff * * zbl 0.0
pair_coeff 1 1 zbl ${zblz}
pair_coeff \* \* snap Ta06A.snapcoeff Ta06A.snapparam Ta
pair_coeff * * snap Ta06A.snapcoeff Ta06A.snapparam Ta
It is convenient to keep these commands in a separate file that can
be inserted in any LAMMPS input script using the :doc:`include <include>`
@ -164,8 +164,7 @@ into two passes.
Detailed definitions for all the other keywords
are given on the :doc:`compute sna/atom <compute_sna_atom>` doc page.
If *quadraticflag* is set to 1, then the SNAP energy expression includes the quadratic term,
0.5\*B\^t.alpha.B, where alpha is a symmetric *K* by *K* matrix.
If *quadraticflag* is set to 1, then the SNAP energy expression includes the quadratic term, 0.5\*B\^t.alpha.B, where alpha is a symmetric *K* by *K* matrix.
The SNAP element file should contain *K*\ (\ *K*\ +1)/2 additional coefficients
for each element, the upper-triangular elements of alpha.

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@ -113,7 +113,7 @@ For pair\_style *thole*\ , the following coefficients must be defined for
each pair of atoms types via the :doc:`pair_coeff <pair_coeff>` command
as in the example above.
* alpha (distance units\^3)
* :math:`\alpha` (distance units\^3)
* damp
* cutoff (distance units)
@ -126,10 +126,10 @@ For pair style *lj/cut/thole/long*\ , the following coefficients must be
defined for each pair of atoms types via the :doc:`pair_coeff <pair_coeff>`
command.
* epsilon (energy units)
* sigma (length units)
* alpha (distance units\^3)
* damps
* :math:`\epsilon` (energy units)
* :math:`\sigma` (length units)
* :math:`\alpha` (distance units\^3)
* damp
* LJ cutoff (distance units)
The last two coefficients are optional and default to the global values from
@ -168,12 +168,9 @@ are defined using
.. math::
\alpha_{ij} = \sqrt{\alpha_i\alpha_j}
.. math::
a_{ij} = \frac 1 2 (a_i + a_j)
\alpha_{ij} = & \sqrt{\alpha_i\alpha_j} \\
& \\
a_{ij} = & \frac 1 2 (a_i + a_j)
Restrictions
""""""""""""