.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/const_cs/plot_const_cs_xi_v.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_const_cs_plot_const_cs_xi_v.py:


ConstCSModel xi, v plane
========================

Plot the $\xi, v$ plane for the constant sound speed model

.. GENERATED FROM PYTHON SOURCE LINES 7-64



.. image-sg:: /auto_examples/const_cs/images/sphx_glr_plot_const_cs_xi_v_001.png
   :alt: plot const cs xi v
   :srcset: /auto_examples/const_cs/images/sphx_glr_plot_const_cs_xi_v_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/pttools/checkouts/latest/pttools/models/const_cs.py:681: RuntimeWarning: invalid value encountered in scalar multiply
      return w_b * phase + w_s * (1 - phase)
    /home/docs/checkouts/readthedocs.org/user_builds/pttools/checkouts/latest/pttools/models/const_cs.py:681: RuntimeWarning: invalid value encountered in scalar multiply
      return w_b * phase + w_s * (1 - phase)






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from examples import utils
    from pttools.bubble.bubble import Bubble
    from pttools.bubble.fluid_bag import sound_shell_bag
    from pttools.bubble.boundary import SolutionType
    from pttools.bubble.integrate import add_df_dtau
    from pttools.bubble.relativity import lorentz
    from pttools.models.const_cs import ConstCSModel
    from tests.paper.plane import xiv_plane
    from tests.paper.plot_plane_paper import plot_plane


    def main():
        css = 1 / np.sqrt(3) - 0.05

        fig: plt.Figure = plt.figure()
        ax: plt.Axes = fig.add_subplot()

        # Plane curves
        model = ConstCSModel(a_s=1.1, a_b=1, css2=css**2, csb2=1/3, V_s=1, V_b=0)
        # model = ConstCSModel(a_s=1.1, a_b=1, css2=1/3, csb2=1/3, V_s=1, V_b=0)
        df_dtau_ptr = add_df_dtau("const_cs", model.cs2)
        data_b, data_s = xiv_plane(df_dtau_ptr=df_dtau_ptr, cs2_s=model.css2, cs2_b=model.csb2)
        plot_plane(ax=ax, data_b=data_b, data_s=data_s, cs2_s=model.css2, cs2_b=model.csb2, selected_solutions=False)

        model2 = ConstCSModel(a_s=1.1, a_b=1, css2=1/3, csb2=1/3, V_s=1, V_b=0)
        det2 = Bubble(model2, v_wall=0.85, alpha_n=0.05, sol_type=SolutionType.DETON)
        ax.plot(det2.xi, det2.v, c="b", label=r"$c_{sb}=\frac{1}{\sqrt{3}}$")
        v, w, xi = sound_shell_bag(v_wall=0.85, alpha_n=0.05)
        ax.plot(xi, v, c="g", label="bag", ls=":")
        def2 = Bubble(model2, v_wall=0.5, alpha_n=0.578, sol_type=SolutionType.SUB_DEF)
        ax.plot(def2.xi, def2.v, c="b")
        v, w, xi = sound_shell_bag(v_wall=0.5, alpha_n=0.578)
        ax.plot(xi, v, c="g", ls=":")

        xi = np.linspace(css, 1, 20)
        ax.plot(xi, lorentz(xi, css), c="r", ls="-.", label=rf"$\mu(\xi,c_{{sb}}={css:.3f})$")

        ax.axvline(css, c="r", ls=":")
        ax.axhline(css, c="r", ls=":")
        model3 = ConstCSModel(a_s=1.1, a_b=1, css2=css**2, csb2=css**2, V_s=1, V_b=0)
        det3 = Bubble(model3, v_wall=0.95, alpha_n=0.15, sol_type=SolutionType.DETON)
        ax.plot(det3.xi, det3.v, c="r", label=rf"$c_{{s}}={css:.3f}$")
        # This can be expected to fail due to the shape of the curve
        def3 = Bubble(model3, v_wall=0.4, alpha_n=0.6)
        ax.plot(def3.xi, def3.v, c="r")

        ax.legend()
        return fig


    if __name__ == "__main__":
        fig = main()
        utils.save_and_show(fig, "const_cs_xi_v.png")


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

   **Total running time of the script:** (0 minutes 9.587 seconds)

**Estimated memory usage:**  329 MB


.. _sphx_glr_download_auto_examples_const_cs_plot_const_cs_xi_v.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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