Skip to content

Commit

Permalink
check bibtex issue
Browse files Browse the repository at this point in the history
  • Loading branch information
KulaginVladimir committed Dec 13, 2023
1 parent 24ab6f1 commit fc3642b
Show file tree
Hide file tree
Showing 2 changed files with 6 additions and 13 deletions.
4 changes: 0 additions & 4 deletions docs/source/conf.py
Original file line number Diff line number Diff line change
Expand Up @@ -38,7 +38,6 @@
"sphinx.ext.napoleon",
"sphinx.ext.viewcode",
"sphinx_design",
"sphinxcontrib.bibtex",
"matplotlib.sphinxext.plot_directive",
]

Expand All @@ -63,9 +62,6 @@
# shorten module names in readme
add_module_names = False

# bibliography file
bibtex_bibfiles = ["bibliography/references.bib"]

# -- Options for HTML output -------------------------------------------------

# The theme to use for HTML and HTML Help pages. See the documentation for
Expand Down
15 changes: 6 additions & 9 deletions docs/source/theory.rst
Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,7 @@ Bulk physics

H transport
^^^^^^^^^^^
The model developed by McNabb & Foster :cite:`McNabb1963` is used to model hydrogen transport in materials in FESTIM. The principle is to separate mobile hydrogen :math:`c_\mathrm{m}` and trapped hydrogen :math:`c_\mathrm{t}`. The diffusion of mobile particles is governed by Fick’s law of diffusion where the hydrogen flux is
The model developed by McNabb & Foster [McNabb1963] is used to model hydrogen transport in materials in FESTIM. The principle is to separate mobile hydrogen :math:`c_\mathrm{m}` and trapped hydrogen :math:`c_\mathrm{t}`. The diffusion of mobile particles is governed by Fick’s law of diffusion where the hydrogen flux is

.. math::
:label: eq_difflux
Expand All @@ -36,7 +36,7 @@ These equations can be solved in cartesian coordinates but also in cylindrical a

Soret effect
^^^^^^^^^^^^
FESTIM can include the Soret effect :cite:`Pendergrass1976,Longhurst1985` (also called thermophoresis, temperature-assisted diffusion, or even thermodiffusion) to hydrogen transport. The flux of hydrogen :math:`J` is then written as:
FESTIM can include the Soret effect [Pendergrass1976,Longhurst1985] (also called thermophoresis, temperature-assisted diffusion, or even thermodiffusion) to hydrogen transport. The flux of hydrogen :math:`J` is then written as:

.. math::
:label: eq_Soret
Expand Down Expand Up @@ -87,7 +87,7 @@ At the interface between a Sievert and a Henry material:
It appears from these equilibrium equations that a difference in solubilities introduces a concentration jump at interfaces.

In FESTIM, the conservation of chemical potential is obtained by a change of variables :cite:`Delaporte-Mathurin2021`. The variable :math:`\theta` is introduced and:
In FESTIM, the conservation of chemical potential is obtained by a change of variables [Delaporte-Mathurin2021]. The variable :math:`\theta` is introduced and:

.. math::
:label: eq_theta
Expand Down Expand Up @@ -162,8 +162,8 @@ FESTIM has built-in Dirichlet’s boundary conditions for Sievert’s condition,
Plasma implantation approximation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Dirichlet’s boundary conditions can also be used to approximate plasma implantation in near surface regions to be more computationally efficient :cite:`Delaporte-Mathurin2022`.
Let us consider a volumetric source term of hydrogen :math:`\Gamma=\varphi_{\mathrm{imp}}f(x)`, where :math:`f(x)` is a narrow Gaussian distribution. The concentration profile of mobile species can be approximated by a triangular shape :cite:`Schmid2016` with maximum at :math:`x=R_p` (see the figure below).
Dirichlet’s boundary conditions can also be used to approximate plasma implantation in near surface regions to be more computationally efficient [Delaporte-Mathurin2022].
Let us consider a volumetric source term of hydrogen :math:`\Gamma=\varphi_{\mathrm{imp}}f(x)`, where :math:`f(x)` is a narrow Gaussian distribution. The concentration profile of mobile species can be approximated by a triangular shape [Schmid2016] with maximum at :math:`x=R_p` (see the figure below).

.. figure:: images/recomb_sketch.png
:align: center
Expand Down Expand Up @@ -266,7 +266,4 @@ where :math:`h` is the heat transfer coefficient and :math:`T_{\mathrm{ext}}` is

---------------
References
---------------

.. bibliography:: bibliography/references.bib
:style: unsrt
---------------

0 comments on commit fc3642b

Please sign in to comment.