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fixed correlation function
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simongravelle committed Dec 31, 2023
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24 changes: 22 additions & 2 deletions docs/source/illustrations/lennard-jones-fluids.rst
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.. container:: justify

The correlation function :math:`G^(0)` was first extract for two temperatures, :math:`T = 50`
The correlation function :math:`G^{(0)}` was first extract for two temperatures, :math:`T = 50`
and :math:`140\,\text{K}`, and compared with the correlation functions reported by Grivet :cite:`grivetNMRRelaxationParameters2005`.
Our results show an excellent agreement with the results from Grivet, thus validating the
NMR formalism used here as well as the LJ system and parameters.
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.. container:: figurelegend

Figure: Correlation function :math:`G^(0)` as extracted from the LJ fluid simulation
Figure: Correlation function :math:`G^{(0)}` as extracted from the LJ fluid simulation
for two different temperatures, and compared with the data from Grivet :cite:`grivetNMRRelaxationParameters2005` (open symbols).

.. container:: justify

The NMR relaxation rates :math:`R_1`
and :math:`R_2` was also extracted for all the temperatures, at
a frequency :math:`f_0 = 150\,\text{GHz}`. Our results
show a good agreement with the data from Grivet :cite:`grivetNMRRelaxationParameters2005`.

.. image:: ../figures/illustrations/lennard-jones-fluid/R1_spectra-dark.png
:class: only-dark
:alt: NMR results obtained from the LAMMPS simulation of water

.. image:: ../figures/illustrations/lennard-jones-fluid/R1_spectra-light.png
:class: only-light
:alt: NMR results obtained from the LAMMPS simulation of water
.. container:: figurelegend

Figure: NMR relaxation rates :math:`R_1`
and :math:`R_2` at
a frequency :math:`f_0 = 150\,\text{GHz}`.

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