.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/kinetics/networks/plot_05_parallel_reactions.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_kinetics_networks_plot_05_parallel_reactions.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_kinetics_networks_plot_05_parallel_reactions.py:


Parallel (competing) first-order reactions
============================================

For two competing channels :math:`A \xrightarrow{k_1} B` and
:math:`A \xrightarrow{k_2} C`, the reactant decays with the *sum*
:math:`k_1 + k_2`, while the product ratio :math:`[B]/[C] = k_1/k_2` is
fixed at every instant -- the kinetic basis of product selectivity.
Integrated with
:meth:`~chemistrykit.kinetics.systems.networks.StoichiometricNetwork.parallel`.

.. GENERATED FROM PYTHON SOURCE LINES 14-32



.. image-sg:: /api/gallery/kinetics/networks/images/sphx_glr_plot_05_parallel_reactions_001.png
   :alt: Parallel channels: final [B]/[C] = 4.000 (k1/k2 = 4)
   :srcset: /api/gallery/kinetics/networks/images/sphx_glr_plot_05_parallel_reactions_001.png
   :class: sphx-glr-single-img





.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.kinetics.systems.networks import StoichiometricNetwork
    from chemistrykit.kinetics.visualizers.kinetics_plots import plot_concentration_vs_time

    k1, k2 = 2.0, 0.5
    net = StoichiometricNetwork.parallel(k1=k1, k2=k2, A0=1.0)
    result = net.integrate((0.0, 4.0), dt=1e-3, method="rk4")

    fig, ax = plt.subplots(figsize=(7, 5))
    plot_concentration_vs_time(result, ax=ax)
    ax.plot(result.t, np.exp(-(k1 + k2) * result.t), "k--", linewidth=0.8, label="exp(-(k1+k2)t)")
    ax.legend()
    ratio = result.concentration("B")[-1] / result.concentration("C")[-1]
    ax.set_title(f"Parallel channels: final [B]/[C] = {ratio:.3f} (k1/k2 = {k1 / k2:g})")
    fig.tight_layout()
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.330 seconds)


.. _sphx_glr_download_api_gallery_kinetics_networks_plot_05_parallel_reactions.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_05_parallel_reactions.ipynb <plot_05_parallel_reactions.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_05_parallel_reactions.py <plot_05_parallel_reactions.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_05_parallel_reactions.zip <plot_05_parallel_reactions.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_