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@ -156,46 +156,50 @@ defined within the file associated with this command.</p>
<img alt="_images/fix_rx_reaction.jpg" class="align-center" src="_images/fix_rx_reaction.jpg" />
<p>the reaction rate equation is defined to be of the form</p>
<img alt="_images/fix_rx_reactionRate.jpg" class="align-center" src="_images/fix_rx_reactionRate.jpg" />
<p>In the current implementation, the exponents are defined to be equal to the
stoichiometric coefficients. A given reaction set consisting of <em>n</em> reaction
equations will contain a total of <em>m</em> species. A set 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 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 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>
<p>In the current implementation, the exponents are defined to be equal
to the stoichiometric coefficients. A given reaction set consisting
of <em>n</em> reaction equations will contain a total of <em>m</em> species. A set
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
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
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>
<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
this file is described below.</p>
<p>There is no restriction on the total number or reaction equations that are
specified. The species names are arbitrary string names that are associated
with the species concentrations.
Each species in a given reaction must be preceded by it&#8217;s stoichiometric
coefficient. The only delimiters that are recognized between the species are
either a <em>+</em> or <em>=</em> character. The <em>=</em> character corresponds to an
irreversible reaction. After specifying the reaction, the reaction rate
constant is determined through the temperature dependent Arrhenius equation:</p>
<p>There is no restriction on the total number or reaction equations that
are specified. The species names are arbitrary string names that are
associated with the species concentrations. Each species in a given
reaction must be preceded by it&#8217;s stoichiometric coefficient. The
only delimiters that are recognized between the species are either a
<em>+</em> or <em>=</em> character. The <em>=</em> character corresponds to an
irreversible reaction. After specifying the reaction, the reaction
rate constant is determined through the temperature dependent
Arrhenius equation:</p>
<img alt="_images/fix_rx.jpg" class="align-center" src="_images/fix_rx.jpg" />
<p>where <em>A</em> is the Arrhenius factor in time units or concentration/time units,
<em>n</em> is the unitless exponent of the temperature dependence, and <em>E_a</em> is the
activation energy in energy units. The temperature dependence can be removed
by specifying the exponent as zero.</p>
<p>The internal temperature of the coarse-grained particles can be used in constructing the
reaction rate constants at every DPD timestep by specifying the keyword <em>none</em>.
Alternatively, the keyword <em>lucy</em> can be specified to compute a local-average particle
internal temperature for use in the reaction rate constant expressions.
The local-average particle internal temperature is defined as:</p>
<p>where <em>A</em> is the Arrhenius factor in time units or concentration/time
units, <em>n</em> is the unitless exponent of the temperature dependence, and
<em>E_a</em> is the activation energy in energy units. The temperature
dependence can be removed by specifying the exponent as zero.</p>
<p>The internal temperature of the coarse-grained particles can be used
in constructing the reaction rate constants at every DPD timestep by
specifying the keyword <em>none</em>. Alternatively, the keyword <em>lucy</em> can
be specified to compute a local-average particle internal temperature
for use in the reaction rate constant expressions. The local-average
particle internal temperature is defined as:</p>
<img alt="_images/fix_rx_localTemp.jpg" class="align-center" src="_images/fix_rx_localTemp.jpg" />
<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>
<hr class="docutils" />
<p>The format of a tabulated file is as follows (without the parenthesized comments):</p>
<p>The format of a tabulated file is as follows (without the
parenthesized comments):</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Rxn equations and parameters (one or more comment or blank lines)</span>
</pre></div>
</div>
@ -208,29 +212,34 @@ The local-average particle internal temperature is defined as:</p>
<p>A section begins with a non-blank line whose 1st character is not a
&#8220;#&#8221;; blank lines or lines starting with &#8220;#&#8221; can be used as comments
between sections.</p>
<p>Following a blank line, the next N lines list the N reaction equations.
Each species within the reaction equation is specified through its
stoichiometric coefficient and a species tag. Reactant species are specified
on the left-hand side of the equation and product species are specified on the
right-hand side of the equation. After specifying the reactant and product
species, the final three arguments of each line represent the Arrhenius
parameter <em>A</em>, the temperature exponent <em>n</em>, and the activation energy <em>Ea</em>.</p>
<p>Note that the species tags that are defined in the reaction equations 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 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>
<p>Following a blank line, the next N lines list the N reaction
equations. Each species within the reaction equation is specified
through its stoichiometric coefficient and a species tag. Reactant
species are specified on the left-hand side of the equation and
product species are specified on the right-hand side of the equation.
After specifying the reactant and product species, the final three
arguments of each line represent the Arrhenius parameter <em>A</em>, the
temperature exponent <em>n</em>, and the activation energy <em>Ea</em>.</p>
<p>Note that the species tags that are defined in the reaction equations
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
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>
<p>fix foo all rx reaction.file ...
read_data data.dpd fix foo_SPECIES NULL Species</p>
</div>
<hr class="docutils" />
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>The fix <em>rx</em> is only available if LAMMPS is built with the USER-DPD package.</p>
<p>The fix <em>rx</em> must be used with the <a class="reference internal" href="atom_style.html"><span class="doc">atom_style dpd</span></a> command.</p>
<p>The fix <em>rx</em> can only be used with a constant energy or constant enthalpy DPD simulation.</p>
<p>This command is part of the USER-DPD package. It is only enabled if
LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<p>This command also requires use of the <a class="reference internal" href="atom_style.html"><span class="doc">atom_style dpd</span></a>
command.</p>
<p>This command can only be used with a constant energy or constant
enthalpy DPD simulation.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
@ -238,7 +247,6 @@ read_data data.dpd fix foo_SPECIES NULL Species</p>
<a class="reference internal" href="fix_shardlow.html"><span class="doc">fix shardlow</span></a>,
<span class="xref doc">pair dpd/fdt/energy</span></p>
<p><strong>Default:</strong> none</p>
<hr class="docutils" />
</div>
</div>