-
Notifications
You must be signed in to change notification settings - Fork 6
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
41 changed files
with
1,210,581 additions
and
79 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,73 @@ | ||
Planck and Rosseland Means | ||
========================== | ||
|
||
.. _mean: | ||
|
||
With the ``doMean`` option in the ``param.dat`` file, the Plank and Rosseland means, | ||
:math:`\kappa_P` and :math:`\kappa_R` respectively: | ||
|
||
.. math:: | ||
:label: eq_a | ||
\kappa_P = \frac{\int_0^\infty \kappa B_{\nu}(T) d\nu}{\int_0^\infty B_{\nu}(T) d\nu}, | ||
and | ||
|
||
.. math:: | ||
:label: eq_b | ||
\kappa_R = \left( \frac{\int_0^\infty \kappa^{-1} \frac{\partial B_{\nu}(T)}{\partial T} d\nu} {\int_0^\infty \frac{\partial B_{\nu}(T)}{\partial T} d\nu} \right)^{-1} | ||
can be calculated, where the infinity integral is truncated to the specified wavenumber limits, and :math:`d\nu` is | ||
equal to ``dnu`` set in the ``param.dat`` file. | ||
|
||
Note that the denominators in :math:`\kappa_P` and :math:`\kappa_R` can be computed analytically as | ||
|
||
.. math:: | ||
:label: eq_0 | ||
\int_0^\infty B_{\nu}(T) d\nu = \frac{\sigma T^4} {\pi} | ||
and | ||
|
||
.. math:: | ||
:label: eq_1 | ||
\int_0^\infty \frac{\partial(B_{\nu}(T))}{ \partial (T)} d\nu = \frac{4 \sigma T^3} {\pi}. | ||
Therefor, it is usefull to compare those analytic results to the numerical integration | ||
|
||
.. math:: | ||
:label: eq_2 | ||
\int_0^\infty B_{\nu}(T) d\nu = \sum_i B_{\nu}(T) dnu | ||
and | ||
|
||
.. math:: | ||
:label: eq_3 | ||
\int_0^\infty \frac{\partial(B_{\nu}(T))}{ \partial (T)} d\nu = \sum_i \frac{\partial(B_{\nu}(T))}{ \partial (T)} dnu | ||
The results of the Planck and Resseland means are stored in the file ``Out<name>_mean.dat``, together with | ||
the analytic and numerical expressions :eq:`eq_0` to :eq:`eq_3`. If the numerical expressions deviate strongly | ||
from the analytical expression, then it is a hint that the wavenumber resolution is not set fine enough. | ||
|
||
|
||
An example of the Planck and Rosseland means is shown in :numref:`figmean`. | ||
|
||
|
||
| Relevant parameters for this example: | ||
- doStoreFullK = 1 | ||
- doMean = 1 | ||
|
||
|
||
.. figure:: ../plots/p007/plot001.png | ||
:name: figmean | ||
|
||
Planck and Rosseland means | ||
|
||
|
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,41 @@ | ||
The transmission function | ||
========================= | ||
|
||
.. _transmission: | ||
|
||
With the ``doTransmission`` option in the ``param.dat`` file, the transmissions function | ||
:math:`\tau` | ||
|
||
.. math:: | ||
\tau = \int_0^\infty e^{-\kappa \tilde{m}} d\nu = \int_0^1 e^{-\kappa \tilde{m}} dy | ||
can be calculated for a set of column masses :math:`\tilde{m}`, where :math:`\tilde{m}` | ||
is set according to: | ||
|
||
.. math:: | ||
\tilde{m}_i = e^{((i - nTr/2) \cdot dTr)}. | ||
The parameters ``nTr`` and ``dTr`` can be set in the ``param.dat`` file. | ||
The transmission function is stored in the file ``Out<name>_tr.dat``, | ||
|
||
|
||
An example of the transmission function for fife bins is shown in :numref:`figtransmission`. | ||
|
||
|
||
| Relevant parameters for this example: | ||
- doStoreFullK = 1 | ||
- doTransmission = 2 | ||
- nbins = 5 | ||
- nTr = 1000 | ||
- dTr = 0.05 | ||
|
||
|
||
.. figure:: ../plots/p006/plot001.png | ||
:name: figtransmission | ||
|
||
Transmission function | ||
|
||
|
Oops, something went wrong.