# fix eos/table/rx command¶

Accelerator Variants: eos/table/rx/kk

## Syntax¶

fix ID group-ID eos/table/rx style file1 N keyword ...

• ID, group-ID are documented in fix command

• eos/table/rx = style name of this fix command

• style = linear = method of interpolation

• file1 = filename containing the tabulated equation of state

• N = use N values in linear tables

• keyword = name of table keyword corresponding to table file

• file2 = filename containing the heats of formation of each species (optional)

• deltaHf = heat of formation for a single species in energy units (optional)

• energyCorr = energy correction in energy units (optional)

• tempCorrCoeff = temperature correction coefficient (optional)

## Examples¶

fix 1 all eos/table/rx linear eos.table 10000 KEYWORD thermo.table
fix 1 all eos/table/rx linear eos.table 10000 KEYWORD 1.5
fix 1 all eos/table/rx linear eos.table 10000 KEYWORD 1.5 0.025 0.0


## Description¶

Fix eos/table/rx applies a tabulated mesoparticle equation of state to relate the concentration-dependent particle internal energy ($$u_i$$) to the particle internal temperature ($$\theta_i$$).

The concentration-dependent particle internal energy ($$u_i$$) is computed according to the following relation:

$\begin{split}U_{i} = \displaystyle\sum_{j=1}^{m} c_{i,j}(u_{j} + \Delta H_{f,j}) + \frac{3k_{b}T}{2} + Nk_{b}T \\\end{split}$

where m is the number of species, $$c_{i,j}$$ is the concentration of species j in particle i, $$u_j$$ is the internal energy of species j, $$\Delta H_{f,j} is the heat of formation of species *j*\ , N is the number of molecules represented by the coarse-grained particle, :math:$$ is the Boltzmann constant, and T is the temperature of the system. Additionally, it is possible to modify the concentration-dependent particle internal energy relation by adding an energy correction, temperature-dependent correction, and/or a molecule-dependent correction. An energy correction can be specified as a constant (in energy units). A temperature correction can be specified by multiplying a temperature correction coefficient by the internal temperature. A molecular correction can be specified by by multiplying a molecule correction coefficient by the average number of product gas particles in the coarse-grain particle.

Fix eos/table/rx creates interpolation tables of length N from m internal energy values of each species $$u_j$$ listed in a file as a function of internal temperature. During a simulation, these tables are used to interpolate internal energy or temperature values as needed. The interpolation is done with the linear style. For the linear style, the internal temperature is used to find 2 surrounding table values from which an internal energy is computed by linear interpolation. A secant solver is used to determine the internal temperature from the internal energy.

The first filename specifies a file containing tabulated internal temperature and m internal energy values for each species $$u_j$$. The keyword specifies a section of the file. The format of this file is described below.

The second filename specifies a file containing heat of formation $$\Delta H_{f,j}$$ for each species.

In cases where the coarse-grain particle represents a single molecular species (i.e., no reactions occur and fix rx is not present in the input file), fix eos/table/rx can be applied in a similar manner to fix eos/table within a non-reactive DPD simulation. In this case, the heat of formation filename is replaced with the heat of formation value for the single species. Additionally, the energy correction and temperature correction coefficients may also be specified as fix arguments.

The format of a tabulated file is as follows (without the parenthesized comments):

# EOS TABLE                (one or more comment or blank lines)

KEYWORD                    (keyword is first text on line)
N 500 h2 no2 n2 ... no     (N  parameter species1 species2 ... speciesN)
(blank)
1   1.00 0.000 ... 0.0000  (index, internal temperature, internal energy of species 1, ..., internal energy of species m)
2   1.02 0.001 ... 0.0002
...
500 10.0 0.500 ... 1.0000


A section begins with a non-blank line whose first character is not a “#”; blank lines or lines starting with “#” can be used as comments between sections. The first line begins with a keyword which identifies the section. The line can contain additional text, but the initial text must match the argument specified in the fix command.

The next line lists the number of table entries and the species names that correspond with all the species listed in the reaction equations through the fix rx command. The parameter “N” is required and its value is the number of table entries that follow. Let Nfile = “N” in the tabulated file. What LAMMPS does is a preliminary interpolation by creating splines using the Nfile tabulated values as nodal points.

Following a blank line, the next N lines list the tabulated values. On each line, the first value is the index from 1 to N, the second value is the internal temperature (in temperature units), the third value until the m+3 value are the internal energies of the m species (in energy units).

Note that all internal temperature and internal energy values must increase from one line to the next.

Note that one file can contain many sections, each with a tabulated potential. LAMMPS reads the file section by section until it finds one that matches the specified keyword.

The format of a heat of formation file is as follows (without the parenthesized comments):

# HEAT OF FORMATION TABLE  (one or more comment or blank lines)

(blank)
h2      0.00               (species name, heat of formation)
no2     0.34
n2      0.00
...
no      0.93


Note that the species can be listed in any order. The tag that is used as the species name must correspond with the tags used to define the reactions with the fix rx command.

Alternatively, corrections to the EOS can be included by specifying three additional columns that correspond to the energy correction, the temperature correction coefficient and molecule correction coefficient. In this case, the format of the file is as follows:

# HEAT OF FORMATION TABLE     (one or more comment or blank lines)

(blank)
h2      0.00 1.23 0.025  0.0  (species name, heat of formation, energy correction, temperature correction coefficient, molecule correction coefficient)
no2     0.34 0.00 0.000 -1.76
n2      0.00 0.00 0.000 -1.76
...
no      0.93 0.00 0.000 -1.76


Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Speed packages doc page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package doc page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Speed packages doc page for more instructions on how to use the accelerated styles effectively.

## Restrictions¶

This command is part of the USER-DPD package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.

This command also requires use of the atom_style dpd command.

The equation of state must be a monotonically increasing function.

An error will occur if the internal temperature or internal energies are not within the table cutoffs.

none