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 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
@ -412,17 +426,16 @@ 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.
\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 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.
\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 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
@ -430,7 +443,6 @@ create label for \ref{FigVibStab} using #FigVibStab
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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