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2
doc/html/Manual.html
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@ -135,7 +135,7 @@
<H1></H1><div class="section" id="lammps-documentation">
<h1>LAMMPS Documentation</h1>
<div class="section" id="jul-2016-version">
<h2>1 Jul 2016 version</h2>
<h2>9 Jul 2016 version</h2>
</div>
<div class="section" id="version-info">
<h2>Version info:</h2>

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doc/html/_sources/Manual.txt
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@ -5,7 +5,7 @@
LAMMPS Documentation
====================
1 Jul 2016 version
9 Jul 2016 version
------------------
Version info:

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doc/html/_sources/compute_modify.txt
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@ -19,8 +19,6 @@ Syntax
N = # of extra degrees of freedom to subtract
*dynamic* value = *yes* or *no*
yes/no = do or do not recompute the number of atoms contributing to the temperature
*thermo* value = *yes* or *no*
yes/no = do or do not add contributions from fixes to the potential energy
@ -51,18 +49,12 @@ for an example.
The *dynamic* keyword determines whether the number of atoms N in the
compute group is re-computed each time a temperature is computed.
Only compute styles that compute a temperature use this option. By
Only compute styles that calculate a temperature use this option. By
default, N is assumed to be constant. If you are adding atoms to the
system (see the :doc:`fix pour <fix_pour>` or :doc:`fix deposit <fix_deposit>` commands) or expect atoms to be lost
(e.g. due to evaporation), then this option should be used to insure
the temperature is correctly normalized.
The *thermo* keyword determines whether the potential energy
contribution calculated by some :doc:`fixes <fix>` is added to the
potential energy calculated by the compute. Currently, only the
compute of style *pe* uses this option. See the doc pages for
:doc:`individual fixes <fix>` for details.
Restrictions
""""""""""""
none
@ -76,8 +68,7 @@ Default
"""""""
The option defaults are extra = 2 or 3 for 2d or 3d systems and
dynamic = no. Thermo is *yes* if the compute of style *pe* was
defined with no extra keywords; otherwise it is *no*\ .
dynamic = no.
.. _lws: http://lammps.sandia.gov

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doc/html/_sources/compute_pe.txt
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@ -13,7 +13,7 @@ Syntax
* ID, group-ID are documented in :doc:`compute <compute>` command
* pe = style name of this compute command
* zero or more keywords may be appended
* keyword = *pair* or *bond* or *angle* or *dihedral* or *improper* or *kspace*
* keyword = *pair* or *bond* or *angle* or *dihedral* or *improper* or *kspace* or *fix*
Examples
""""""""
@ -35,8 +35,9 @@ via the :doc:`compute reduce <compute_reduce>` command.
The energy is calculated by the various pair, bond, etc potentials
defined for the simulation. If no extra keywords are listed, then the
potential energy is the sum of pair, bond, angle, dihedral, improper,
and kspace (long-range) energy. If any extra keywords are listed,
then only those components are summed to compute the potential energy.
kspace (long-range), and fix energy. I.e. it is as if all the
keywords were listed. If any extra keywords are listed, then only
those components are summed to compute the potential energy.
The Kspace contribution requires 1 extra FFT each timestep the energy
is calculated, if using the PPPM solver via the :doc:`kspace_style pppm <kspace_style>` command. Thus it can increase the cost of the
@ -44,12 +45,14 @@ PPPM calculation if it is needed on a large fraction of the simulation
timesteps.
Various fixes can contribute to the total potential energy of the
system. See the doc pages for :doc:`individual fixes <fix>` for
details. The *thermo* option of the
:doc:`compute_modify <compute_modify>` command determines whether these
contributions are added into the computed potential energy. If no
keywords are specified the default is *yes*\ . If any keywords are
specified, the default is *no*\ .
system if the *fix* contribution is included. See the doc pages for
:doc:`individual fixes <fix>` for details of which ones compute a
potential energy.
.. note::
The :doc:`fix_modify energy yes <fix_modify>` command must also be
specified if a fix is to contribute potential energy to this command.
A compute of this style with the ID of "thermo_pe" is created when
LAMMPS starts up, as if this command were in the input script:

19
doc/html/_sources/compute_pe_atom.txt
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@ -13,7 +13,7 @@ Syntax
* ID, group-ID are documented in :doc:`compute <compute>` command
* pe/atom = style name of this compute command
* zero or more keywords may be appended
* keyword = *pair* or *bond* or *angle* or *dihedral* or *improper* or *kspace*
* keyword = *pair* or *bond* or *angle* or *dihedral* or *improper* or *kspace* or *fix*
Examples
""""""""
@ -34,9 +34,9 @@ you want the potential energy of the entire system.
The per-atom energy is calculated by the various pair, bond, etc
potentials defined for the simulation. If no extra keywords are
listed, then the potential energy is the sum of pair, bond, angle,
dihedral,improper, and kspace energy. If any extra keywords are
listed, then only those components are summed to compute the potential
energy.
dihedral,improper, kspace (long-range), and fix energy. I.e. it is as
if all the keywords were listed. If any extra keywords are listed,
then only those components are summed to compute the potential energy.
Note that the energy of each atom is due to its interaction with all
other atoms in the simulation, not just with other atoms in the group.
@ -57,6 +57,17 @@ For PPPM, the calcluation requires 1 extra FFT each timestep that
per-atom energy is calculated. Thie `document <PDF/kspace.pdf>`_
describes how the long-range per-atom energy calculation is performed.
Various fixes can contribute to the per-atom potential energy of the
system if the *fix* contribution is included. See the doc pages for
:doc:`individual fixes <fix>` for details of which ones compute a
per-atom potential energy.
.. note::
The :doc:`fix_modify energy yes <fix_modify>` command must also be
specified if a fix is to contribute per-atom potential energy to this
command.
As an example of per-atom potential energy compared to total potential
energy, these lines in an input script should yield the same result
in the last 2 columns of thermo output:

22
doc/html/_sources/fix_modify.txt
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@ -57,13 +57,21 @@ default method for computing P.
For fixes that calculate a contribution to the potential energy of the
system, the *energy* keyword will include that contribution in
thermodynamic output of potential energy. See the
:doc:`thermo_style <thermo_style>` command for info on how potential
energy is output. The contribution by itself can be printed by using
the keyword f_ID in the thermo_style custom command, where ID is the
fix-ID of the appropriate fix. Note that you must use this setting
for a fix if you are using it when performing an :doc:`energy minimization <minimize>` and if you want the energy and forces it
produces to be part of the optimization criteria.
thermodynamic output of potential energy. This is because the *energy
yes* setting must be specfied to include the fix's global or per-atom
energy in the calculation performed by the :doc:`compute pe <compute_pe>` or :doc:`compute pe/atom <compute_pe_atom>`
commands. See the :doc:`thermo_style <thermo_style>` command for info
on how potential energy is output. For fixes that tally a global
energy, it can be printed by using the keyword f_ID in the
thermo_style custom command, where ID is the fix-ID of the appropriate
fix.
.. note::
You must also specify the *energy yes* setting for a fix if you
are using it when performing an :doc:`energy minimization <minimize>`
and if you want the energy and forces it produces to be part of the
optimization criteria.
For fixes that set or modify forces, it may be possible to select at
which :doc:`r-RESPA <run_style>` level the fix operates via the *respa*

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doc/html/_sources/fix_rx.txt
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@ -8,23 +8,30 @@ Syntax
.. parsed-literal::
fix ID group-ID rx file localTemp solver ...
fix ID group-ID rx file localTemp matrix solver minSteps ...
* ID, group-ID are documented in :doc:`fix <fix>` command
* rx = style name of this fix command
* file = filename containing the reaction kinetic equations and Arrhenius parameters
* localTemp = *none,lucy* = no local temperature averaging or local temperature defined through Lucy weighting function
* solver = *lammps_rk4* = Explicit 4th order Runge-Kutta method
* minSteps = # of steps for rk4 solver
* matrix = *sparse, dense* format for the stoichiometric matrix
* solver = *lammps_rk4,rkf45* = rk4 is an explicit 4th order Runge-Kutta method; rkf45 is an adaptive 4th-order Runge-Kutta-Fehlberg method
* minSteps = # of steps for rk4 solver or minimum # of steps for rkf45 (rk4 or rkf45)
* maxSteps = maximum number of steps for the rkf45 solver (rkf45 only)
* relTol = relative tolerance for the rkf45 solver (rkf45 only)
* absTol = absolute tolernace for the rkf45 solver (rkf45 only)
* diag = Diagnostics frequency for the rkf45 solver (optional, rkf45 only)
Examples
""""""""
.. parsed-literal::
fix 1 all rx kinetics.rx none lammps_rk4
fix 1 all rx kinetics.rx none lammps_rk4 1
fix 1 all rx kinetics.rx lucy lammps_rk4 10
fix 1 all rx kinetics.rx none dense lammps_rk4
fix 1 all rx kinetics.rx none sparse lammps_rk4 1
fix 1 all rx kinetics.rx lucy sparse lammps_rk4 10
fix 1 all rx kinetics.rx none dense rkf45 1 100 1e-6 1e-8
fix 1 all rx kinetics.rx none dense rkf45 1 100 1e-6 1e-8 -1
Description
"""""""""""
@ -49,13 +56,47 @@ of *m* ordinary differential equations (ODEs) that describe the change
in concentration of a given species as a function of time are then
constructed based on the *n* reaction rate equations.
The ODE systems are solved over the full DPD timestep *dt* using a 4th
The ODE systems are solved over the full DPD timestep *dt* using either a 4th
order Runge-Kutta *rk4* method with a fixed step-size *h*\ , specified
by the *lammps_rk4* keyword. The number of ODE steps per DPD timestep
by the *lammps_rk4* keyword, or a 4th order Runge-Kutta-Fehlberg (rkf45) method
with an adaptive step-size for *h*\ . The number of ODE steps per DPD timestep
for the rk4 method is optionally specified immediately after the rk4
keyword. The ODE step-size is set as *dt/num_steps*\ . Smaller
step-sizes tend to yield more accurate results but there is not
control on the error.
control on the error. For error control, use the rkf45 ODE solver.
The rkf45 method adjusts the step-size so that the local truncation error is held
within the specified absolute and relative tolerances. The initial step-size *h0*
can be specified by the user or estimated internally. It is recommeded that the user
specify *h0* since this will generally reduced the number of ODE integration steps
required. *h0* is defined as *dt / min_steps* if min_steps >= 1. If min_steps == 0,
*h0* is estimated such that an explicit Euler method would likely produce
an acceptable solution. This is generally overly conservative for the 4th-order
method and users are advised to specify *h0* as some fraction of the DPD timestep.
For small DPD timesteps, only one step may be necessary depending upon the tolerances.
Note that more than min_steps ODE steps may be taken depending upon the ODE stiffness
but no more than max_steps will be taken. If max_steps is reached, an error warning
is printed and the simulation is stopped.
After each ODE step, the solution error *e* is tested and weighted using the absTol
and relTol values. The error vector is weighted as *e* / (relTol * |\ *u*\ | + absTol)
where *u* is the solution vector. If the norm of the error is <= 1, the solution is
accepted, *h* is increased by a proportional amount, and the next ODE step is begun.
Otherwise, *h* is shrunk and the ODE step is repeated.
Run-time diagnostics are available for the rkf45 ODE solver. The frequency
(in time-steps) that diagnostics are reported is controlled by the last (optional)
12th argument. A negative frequency means that diagnostics are reported once at the
end of each run. A positive value N means that the diagnostics are reported once
per N time-steps.
The diagnostics report the average # of integrator steps and RHS function evaluations
and run-time per ODE as well as the the average/RMS/min/max per process. If the
reporting frequency is 1, the RMS/min/max per ODE are also reported. The per ODE
statistics can be used to adjust the tolerance and min/max step parameters. The
statistics per MPI process can be useful to examine any load imbalance caused by the
adaptive ODE solver. (Some DPD particles can take longer to solve than others. This
can lead to an imbalance across the MPI processes.)
----------
@ -100,6 +141,17 @@ where the Lucy function is expressed as:
The self-particle interaction is included in the above equation.
The stoichiometric coefficients for the reaction mechanism are stored
in either a sparse or dense matrix format. The dense matrix should only be
used for small reaction mechanisms. The sparse matrix should be used when there
are many reactions (e.g., more than 5). This allows the number of reactions and
species to grow while keeping the computational cost tractable. The matrix
format can be specified as using either the *sparse* or *dense* keywords.
If all stoichiometric coefficients for a reaction are small integers (whole
numbers <= 3), a fast exponential function is used. This can save significant
computational time so users are encouraged to use integer coefficients
where possible.
----------

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@ -141,8 +141,6 @@
N = # of extra degrees of freedom to subtract
<em>dynamic</em> value = <em>yes</em> or <em>no</em>
yes/no = do or do not recompute the number of atoms contributing to the temperature
<em>thermo</em> value = <em>yes</em> or <em>no</em>
yes/no = do or do not add contributions from fixes to the potential energy
</pre>
</div>
<div class="section" id="examples">
@ -169,16 +167,11 @@ the <em>extra</em> parameter if you need to add degrees-of-freedom.</p>
<p>for an example.</p>
<p>The <em>dynamic</em> keyword determines whether the number of atoms N in the
compute group is re-computed each time a temperature is computed.
Only compute styles that compute a temperature use this option. By
Only compute styles that calculate a temperature use this option. By
default, N is assumed to be constant. If you are adding atoms to the
system (see the <a class="reference internal" href="fix_pour.html"><span class="doc">fix pour</span></a> or <a class="reference internal" href="fix_deposit.html"><span class="doc">fix deposit</span></a> commands) or expect atoms to be lost
(e.g. due to evaporation), then this option should be used to insure
the temperature is correctly normalized.</p>
<p>The <em>thermo</em> keyword determines whether the potential energy
contribution calculated by some <a class="reference internal" href="fix.html"><span class="doc">fixes</span></a> is added to the
potential energy calculated by the compute. Currently, only the
compute of style <em>pe</em> uses this option. See the doc pages for
<a class="reference internal" href="fix.html"><span class="doc">individual fixes</span></a> for details.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</h2>
@ -192,8 +185,7 @@ compute of style <em>pe</em> uses this option. See the doc pages for
<div class="section" id="default">
<h2>Default</h2>
<p>The option defaults are extra = 2 or 3 for 2d or 3d systems and
dynamic = no. Thermo is <em>yes</em> if the compute of style <em>pe</em> was
defined with no extra keywords; otherwise it is <em>no</em>.</p>
dynamic = no.</p>
</div>
</div>

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@ -135,7 +135,7 @@
<li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> command</li>
<li>pe = style name of this compute command</li>
<li>zero or more keywords may be appended</li>
<li>keyword = <em>pair</em> or <em>bond</em> or <em>angle</em> or <em>dihedral</em> or <em>improper</em> or <em>kspace</em></li>
<li>keyword = <em>pair</em> or <em>bond</em> or <em>angle</em> or <em>dihedral</em> or <em>improper</em> or <em>kspace</em> or <em>fix</em></li>
</ul>
</div>
<div class="section" id="examples">
@ -155,19 +155,22 @@ via the <a class="reference internal" href="compute_reduce.html"><span class="do
<p>The energy is calculated by the various pair, bond, etc potentials
defined for the simulation. If no extra keywords are listed, then the
potential energy is the sum of pair, bond, angle, dihedral, improper,
and kspace (long-range) energy. If any extra keywords are listed,
then only those components are summed to compute the potential energy.</p>
kspace (long-range), and fix energy. I.e. it is as if all the
keywords were listed. If any extra keywords are listed, then only
those components are summed to compute the potential energy.</p>
<p>The Kspace contribution requires 1 extra FFT each timestep the energy
is calculated, if using the PPPM solver via the <a class="reference internal" href="kspace_style.html"><span class="doc">kspace_style pppm</span></a> command. Thus it can increase the cost of the
PPPM calculation if it is needed on a large fraction of the simulation
timesteps.</p>
<p>Various fixes can contribute to the total potential energy of the
system. See the doc pages for <a class="reference internal" href="fix.html"><span class="doc">individual fixes</span></a> for
details. The <em>thermo</em> option of the
<a class="reference internal" href="compute_modify.html"><span class="doc">compute_modify</span></a> command determines whether these
contributions are added into the computed potential energy. If no
keywords are specified the default is <em>yes</em>. If any keywords are
specified, the default is <em>no</em>.</p>
system if the <em>fix</em> contribution is included. See the doc pages for
<a class="reference internal" href="fix.html"><span class="doc">individual fixes</span></a> for details of which ones compute a
potential energy.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify energy yes</span></a> command must also be
specified if a fix is to contribute potential energy to this command.</p>
</div>
<p>A compute of this style with the ID of &#8220;thermo_pe&#8221; is created when
LAMMPS starts up, as if this command were in the input script:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="n">thermo_pe</span> <span class="nb">all</span> <span class="n">pe</span>

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doc/html/compute_pe_atom.html
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@ -135,7 +135,7 @@
<li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> command</li>
<li>pe/atom = style name of this compute command</li>
<li>zero or more keywords may be appended</li>
<li>keyword = <em>pair</em> or <em>bond</em> or <em>angle</em> or <em>dihedral</em> or <em>improper</em> or <em>kspace</em></li>
<li>keyword = <em>pair</em> or <em>bond</em> or <em>angle</em> or <em>dihedral</em> or <em>improper</em> or <em>kspace</em> or <em>fix</em></li>
</ul>
</div>
<div class="section" id="examples">
@ -154,9 +154,9 @@ you want the potential energy of the entire system.</p>
<p>The per-atom energy is calculated by the various pair, bond, etc
potentials defined for the simulation. If no extra keywords are
listed, then the potential energy is the sum of pair, bond, angle,
dihedral,improper, and kspace energy. If any extra keywords are
listed, then only those components are summed to compute the potential
energy.</p>
dihedral,improper, kspace (long-range), and fix energy. I.e. it is as
if all the keywords were listed. If any extra keywords are listed,
then only those components are summed to compute the potential energy.</p>
<p>Note that the energy of each atom is due to its interaction with all
other atoms in the simulation, not just with other atoms in the group.</p>
<p>For an energy contribution produced by a small set of atoms (e.g. 4
@ -172,6 +172,16 @@ as specified by the <a class="reference internal" href="kspace_style.html"><span
For PPPM, the calcluation requires 1 extra FFT each timestep that
per-atom energy is calculated. Thie <a class="reference external" href="PDF/kspace.pdf">document</a>
describes how the long-range per-atom energy calculation is performed.</p>
<p>Various fixes can contribute to the per-atom potential energy of the
system if the <em>fix</em> contribution is included. See the doc pages for
<a class="reference internal" href="fix.html"><span class="doc">individual fixes</span></a> for details of which ones compute a
per-atom potential energy.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify energy yes</span></a> command must also be
specified if a fix is to contribute per-atom potential energy to this
command.</p>
</div>
<p>As an example of per-atom potential energy compared to total potential
energy, these lines in an input script should yield the same result
in the last 2 columns of thermo output:</p>

22
doc/html/fix_modify.html
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@ -173,13 +173,21 @@ documentation. Thus this option allows the user to override the
default method for computing P.</p>
<p>For fixes that calculate a contribution to the potential energy of the
system, the <em>energy</em> keyword will include that contribution in
thermodynamic output of potential energy. See the
<a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style</span></a> command for info on how potential
energy is output. The contribution by itself can be printed by using
the keyword f_ID in the thermo_style custom command, where ID is the
fix-ID of the appropriate fix. Note that you must use this setting
for a fix if you are using it when performing an <a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a> and if you want the energy and forces it
produces to be part of the optimization criteria.</p>
thermodynamic output of potential energy. This is because the <em>energy
yes</em> setting must be specfied to include the fix&#8217;s global or per-atom
energy in the calculation performed by the <a class="reference internal" href="compute_pe.html"><span class="doc">compute pe</span></a> or <a class="reference internal" href="compute_pe_atom.html"><span class="doc">compute pe/atom</span></a>
commands. See the <a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style</span></a> command for info
on how potential energy is output. For fixes that tally a global
energy, it can be printed by using the keyword f_ID in the
thermo_style custom command, where ID is the fix-ID of the appropriate
fix.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">You must also specify the <em>energy yes</em> setting for a fix if you
are using it when performing an <a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>
and if you want the energy and forces it produces to be part of the
optimization criteria.</p>
</div>
<p>For fixes that set or modify forces, it may be possible to select at
which <a class="reference internal" href="run_style.html"><span class="doc">r-RESPA</span></a> level the fix operates via the <em>respa</em>
keyword. The RESPA level at which the fix is active can be selected.

67
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@ -128,7 +128,7 @@
<span id="index-0"></span><h1>fix rx command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">rx</span> <span class="n">file</span> <span class="n">localTemp</span> <span class="n">solver</span> <span class="o">...</span>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">rx</span> <span class="n">file</span> <span class="n">localTemp</span> <span class="n">matrix</span> <span class="n">solver</span> <span class="n">minSteps</span> <span class="o">...</span>
</pre></div>
</div>
<ul class="simple">
@ -136,15 +136,22 @@
<li>rx = style name of this fix command</li>
<li>file = filename containing the reaction kinetic equations and Arrhenius parameters</li>
<li>localTemp = <em>none,lucy</em> = no local temperature averaging or local temperature defined through Lucy weighting function</li>
<li>solver = <em>lammps_rk4</em> = Explicit 4th order Runge-Kutta method</li>
<li>minSteps = # of steps for rk4 solver</li>
<li>matrix = <em>sparse, dense</em> format for the stoichiometric matrix</li>
<li>solver = <em>lammps_rk4,rkf45</em> = rk4 is an explicit 4th order Runge-Kutta method; rkf45 is an adaptive 4th-order Runge-Kutta-Fehlberg method</li>
<li>minSteps = # of steps for rk4 solver or minimum # of steps for rkf45 (rk4 or rkf45)</li>
<li>maxSteps = maximum number of steps for the rkf45 solver (rkf45 only)</li>
<li>relTol = relative tolerance for the rkf45 solver (rkf45 only)</li>
<li>absTol = absolute tolernace for the rkf45 solver (rkf45 only)</li>
<li>diag = Diagnostics frequency for the rkf45 solver (optional, rkf45 only)</li>
</ul>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">none</span> <span class="n">lammps_rk4</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">none</span> <span class="n">lammps_rk4</span> <span class="mi">1</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">lucy</span> <span class="n">lammps_rk4</span> <span class="mi">10</span>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">none</span> <span class="n">dense</span> <span class="n">lammps_rk4</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">none</span> <span class="n">sparse</span> <span class="n">lammps_rk4</span> <span class="mi">1</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">lucy</span> <span class="n">sparse</span> <span class="n">lammps_rk4</span> <span class="mi">10</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">none</span> <span class="n">dense</span> <span class="n">rkf45</span> <span class="mi">1</span> <span class="mi">100</span> <span class="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">6</span> <span class="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">8</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">none</span> <span class="n">dense</span> <span class="n">rkf45</span> <span class="mi">1</span> <span class="mi">100</span> <span class="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">6</span> <span class="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">8</span> <span class="o">-</span><span class="mi">1</span>
</pre></div>
</div>
</div>
@ -162,13 +169,43 @@ of <em>n</em> reaction equations will contain a total of <em>m</em> species. A
of <em>m</em> ordinary differential equations (ODEs) that describe the change
in concentration of a given species as a function of time are then
constructed based on the <em>n</em> reaction rate equations.</p>
<p>The ODE systems are solved over the full DPD timestep <em>dt</em> using a 4th
<p>The ODE systems are solved over the full DPD timestep <em>dt</em> using either a 4th
order Runge-Kutta <em>rk4</em> method with a fixed step-size <em>h</em>, specified
by the <em>lammps_rk4</em> keyword. The number of ODE steps per DPD timestep
by the <em>lammps_rk4</em> keyword, or a 4th order Runge-Kutta-Fehlberg (rkf45) method
with an adaptive step-size for <em>h</em>. The number of ODE steps per DPD timestep
for the rk4 method is optionally specified immediately after the rk4
keyword. The ODE step-size is set as <em>dt/num_steps</em>. Smaller
step-sizes tend to yield more accurate results but there is not
control on the error.</p>
control on the error. For error control, use the rkf45 ODE solver.</p>
<p>The rkf45 method adjusts the step-size so that the local truncation error is held
within the specified absolute and relative tolerances. The initial step-size <em>h0</em>
can be specified by the user or estimated internally. It is recommeded that the user
specify <em>h0</em> since this will generally reduced the number of ODE integration steps
required. <em>h0</em> is defined as <em>dt / min_steps</em> if min_steps &gt;= 1. If min_steps == 0,
<em>h0</em> is estimated such that an explicit Euler method would likely produce
an acceptable solution. This is generally overly conservative for the 4th-order
method and users are advised to specify <em>h0</em> as some fraction of the DPD timestep.
For small DPD timesteps, only one step may be necessary depending upon the tolerances.
Note that more than min_steps ODE steps may be taken depending upon the ODE stiffness
but no more than max_steps will be taken. If max_steps is reached, an error warning
is printed and the simulation is stopped.</p>
<p>After each ODE step, the solution error <em>e</em> is tested and weighted using the absTol
and relTol values. The error vector is weighted as <em>e</em> / (relTol * <a href="#id1"><span class="problematic" id="id2">|</span></a><em>u</em>| + absTol)
where <em>u</em> is the solution vector. If the norm of the error is &lt;= 1, the solution is
accepted, <em>h</em> is increased by a proportional amount, and the next ODE step is begun.
Otherwise, <em>h</em> is shrunk and the ODE step is repeated.</p>
<p>Run-time diagnostics are available for the rkf45 ODE solver. The frequency
(in time-steps) that diagnostics are reported is controlled by the last (optional)
12th argument. A negative frequency means that diagnostics are reported once at the
end of each run. A positive value N means that the diagnostics are reported once
per N time-steps.</p>
<p>The diagnostics report the average # of integrator steps and RHS function evaluations
and run-time per ODE as well as the the average/RMS/min/max per process. If the
reporting frequency is 1, the RMS/min/max per ODE are also reported. The per ODE
statistics can be used to adjust the tolerance and min/max step parameters. The
statistics per MPI process can be useful to examine any load imbalance caused by the
adaptive ODE solver. (Some DPD particles can take longer to solve than others. This
can lead to an imbalance across the MPI processes.)</p>
<hr class="docutils" />
<p>The filename specifies a file that contains the entire set of reaction
kinetic equations and corresponding Arrhenius parameters. The format of
@ -197,6 +234,16 @@ particle internal temperature is defined as:</p>
<p>where the Lucy function is expressed as:</p>
<img alt="_images/fix_rx_localTemp2.jpg" class="align-center" src="_images/fix_rx_localTemp2.jpg" />
<p>The self-particle interaction is included in the above equation.</p>
<p>The stoichiometric coefficients for the reaction mechanism are stored
in either a sparse or dense matrix format. The dense matrix should only be
used for small reaction mechanisms. The sparse matrix should be used when there
are many reactions (e.g., more than 5). This allows the number of reactions and
species to grow while keeping the computational cost tractable. The matrix
format can be specified as using either the <em>sparse</em> or <em>dense</em> keywords.
If all stoichiometric coefficients for a reaction are small integers (whole
numbers &lt;= 3), a fast exponential function is used. This can save significant
computational time so users are encouraged to use integer coefficients
where possible.</p>
<hr class="docutils" />
<p>The format of a tabulated file is as follows (without the
parenthesized comments):</p>
@ -224,7 +271,7 @@ temperature exponent <em>n</em>, and the activation energy <em>Ea</em>.</p>
are used by the <a class="reference internal" href="fix_eos_table_rx.html"><span class="doc">fix eos/table/rx</span></a> command to
define the thermodynamic properties of each species. Furthermore, the
number of species molecules (i.e., concentration) can be specified
either with the <a class="reference internal" href="set.html"><span class="doc">set</span></a> command using the &#8220;<a href="#id1"><span class="problematic" id="id2">d_</span></a>&#8221; prefix or by
either with the <a class="reference internal" href="set.html"><span class="doc">set</span></a> command using the &#8220;<a href="#id3"><span class="problematic" id="id4">d_</span></a>&#8221; prefix or by
reading directly the concentrations from a data file. For the latter
case, the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command with the fix keyword
should be specified, where the fix-ID will be the &#8220;fix rx`ID with a &lt;SPECIES&#8221;&gt;`_ suffix, e.g.</p>

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