Hasan al Rasyid 3 years ago
parent c8f9322f80
commit f1e35b8389
  1. 32
      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
motivation for this study.
# Baker's standard one-zone model
<!-- 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,
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,
* thermal equilibrium,
* energy transport by grey radiation diffusion.
@ -109,12 +114,11 @@ spherical gas clouds with the following properties:
For equations, we can use several environment:
~~~
\begin{equation}
$$ $$ is equal with \begin{equation}
\begin{eqnarray}
\begin{array}
\begin{displaymath}
\begin{align}
~~~
This is an example:
@ -133,6 +137,16 @@ This is an example:
\nabla \times \vec{E} &= -\frac{\vec{B}}{t}
\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 dynamical, secular and vibrational (or pulsational)
stability (Eqs. (34a,b,c) in Baker \citeyear{DudaHart2nd}). Using Baker's
@ -412,17 +426,16 @@ create label for \ref{FigVibStab} using #FigVibStab
# Conclusions
\begin{enumerate}
\item The conditions for the stability of static, radiative
1. The conditions for the stability of static, radiative
layers in gas spheres, as described by Baker's (\citeyear{DudaHart2nd})
standard one-zone model, can be expressed as stability
equations of state. These stability equations of state depend
only on the local thermodynamic state of the layer.
\item If the constitutive relations -- equations of state and
2. If the constitutive relations -- equations of state and
Rosseland mean opacities -- are specified, the stability
equations of state can be evaluated without specifying
properties of the layer.
\item For solar composition gas the $\kappa$-mechanism is
3. For solar composition gas the $\kappa$-mechanism is
working in the regions of the ice and dust features
in the opacities, the $\mathrm{H}_2$ dissociation and the
combined H, first He ionization zone, as
@ -430,7 +443,6 @@ create label for \ref{FigVibStab} using #FigVibStab
of instability are much larger in extent and degree of
instability than the second He ionization zone
that drives the Cephe\text{\"\i}d pulsations.
\end{enumerate}

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