Hasan al Rasyid 3 years ago
parent c8f9322f80
commit f1e35b8389
  1. 60
      manuscript.md

@ -74,11 +74,8 @@ similarities in the (micro)physics, i.e., constitutive relations of
protostellar cores and protogiant planets serve as a further protostellar cores and protogiant planets serve as a further
motivation for this study. motivation for this study.
# Baker's standard one-zone model # Baker's standard one-zone model
<!-- we need figure* for make it full screen, so it must be in latex code as follows <!-- we need figure* for make it full screen, so it must be in latex code as follows
--> -->
@ -102,6 +99,14 @@ constitutive relations.
self-gravitating, self-gravitating,
spherical gas clouds with the following properties: spherical gas clouds with the following properties:
~~~
* hydrostatic equilibrium,
* thermal equilibrium,
* energy transport by grey radiation diffusion.
~~~
non-numbered list can be written as above, and shown as:
* hydrostatic equilibrium, * hydrostatic equilibrium,
* thermal equilibrium, * thermal equilibrium,
* energy transport by grey radiation diffusion. * energy transport by grey radiation diffusion.
@ -109,12 +114,11 @@ spherical gas clouds with the following properties:
For equations, we can use several environment: For equations, we can use several environment:
~~~ ~~~
\begin{equation} $$ $$ is equal with \begin{equation}
\begin{eqnarray} \begin{eqnarray}
\begin{array} \begin{array}
\begin{displaymath} \begin{displaymath}
\begin{align} \begin{align}
~~~ ~~~
This is an example: This is an example:
@ -133,6 +137,16 @@ This is an example:
\nabla \times \vec{E} &= -\frac{\vec{B}}{t} \nabla \times \vec{E} &= -\frac{\vec{B}}{t}
\end{align} \end{align}
And this is another example for inline equation, such as: $$y = 5\cdot x^2$$
You can see that inline equation have automatically numbered.
Independent paragraph equation is not numbered, as below.
$$
\nabla \cdot \vec{W} = \sigma W \nonumber
$$
The block should be as an independent paragraph (blank line above and under the block).
For the one-zone-model Baker obtains necessary conditions For the one-zone-model Baker obtains necessary conditions
for dynamical, secular and vibrational (or pulsational) for dynamical, secular and vibrational (or pulsational)
stability (Eqs. (34a,b,c) in Baker \citeyear{DudaHart2nd}). Using Baker's stability (Eqs. (34a,b,c) in Baker \citeyear{DudaHart2nd}). Using Baker's
@ -412,25 +426,23 @@ create label for \ref{FigVibStab} using #FigVibStab
# Conclusions # Conclusions
\begin{enumerate} 1. The conditions for the stability of static, radiative
\item The conditions for the stability of static, radiative layers in gas spheres, as described by Baker's (\citeyear{DudaHart2nd})
layers in gas spheres, as described by Baker's (\citeyear{DudaHart2nd}) standard one-zone model, can be expressed as stability
standard one-zone model, can be expressed as stability equations of state. These stability equations of state depend
equations of state. These stability equations of state depend only on the local thermodynamic state of the layer.
only on the local thermodynamic state of the layer. 2. If the constitutive relations -- equations of state and
\item If the constitutive relations -- equations of state and Rosseland mean opacities -- are specified, the stability
Rosseland mean opacities -- are specified, the stability equations of state can be evaluated without specifying
equations of state can be evaluated without specifying properties of the layer.
properties of the layer. 3. For solar composition gas the $\kappa$-mechanism is
\item For solar composition gas the $\kappa$-mechanism is working in the regions of the ice and dust features
working in the regions of the ice and dust features in the opacities, the $\mathrm{H}_2$ dissociation and the
in the opacities, the $\mathrm{H}_2$ dissociation and the combined H, first He ionization zone, as
combined H, first He ionization zone, as indicated by vibrational instability. These regions
indicated by vibrational instability. These regions of instability are much larger in extent and degree of
of instability are much larger in extent and degree of instability than the second He ionization zone
instability than the second He ionization zone that drives the Cephe\text{\"\i}d pulsations.
that drives the Cephe\text{\"\i}d pulsations.
\end{enumerate}

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