some more formatting and math conversion improvements

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

   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

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

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

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::

   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

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.

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

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

   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