clearer... tinggal table, numlist, dan formula

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Hasan al Rasyid 3 years ago
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article:
pubsEngine manuscript article

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# 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
-->
\begin{figure*} \begin{figure*}
\centering \centering
\includegraphics{Figure/icml_numpapers.eps}
\caption{Adiabatic exponent $\Gamma_1$. \caption{Adiabatic exponent $\Gamma_1$.
$\Gamma_1$ is plotted as a function of $\Gamma_1$ is plotted as a function of
$\lg$ internal energy $\mathrm{[erg\,g^{-1}]}$ and $\lg$ $\lg$ internal energy $\mathrm{[erg\,g^{-1}]}$ and $\lg$
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\end{figure*} \end{figure*}
In this section the one-zone model of \citet{DudaHart2nd}, In this section the one-zone model of \citet{DudaHart2nd},
originally used to study the Cephe{\"{\i}}d pulsation mechanism, will originally used to study the Cephe\text{\"{\i}}d pulsation mechanism, will
be briefly reviewed. The resulting stability criteria will be be briefly reviewed. The resulting stability criteria will be
rewritten in terms of local state variables, local timescales and rewritten in terms of local state variables, local timescales and
constitutive relations. constitutive relations.
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\citet{DudaHart2nd} investigates the stability of thin layers in \citet{DudaHart2nd} investigates the stability of thin layers in
self-gravitating, self-gravitating,
spherical gas clouds with the following properties: spherical gas clouds with the following properties:
\begin{itemize}
\item hydrostatic equilibrium, * hydrostatic equilibrium,
\item thermal equilibrium, * thermal equilibrium,
\item energy transport by grey radiation diffusion. * energy transport by grey radiation diffusion.
\end{itemize}
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
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\noindent \noindent
and with the definitions of the \emph{local cooling time\/} and with the definitions of the \emph{local cooling time\/}
(see Fig.~\ref{FigGam}) (see Fig. \ref{FigGam})
\begin{equation} \begin{equation}
\tau_{\mathrm{co}} = \frac{E_{\mathrm{th}}}{L_{r0}} \,, \tau_{\mathrm{co}} = \frac{E_{\mathrm{th}}}{L_{r0}} \,,
\end{equation} \end{equation}
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from a simple equation of state, given for example, as a function from a simple equation of state, given for example, as a function
of density and of density and
temperature. Once the microphysics, i.e.\ the thermodynamics temperature. Once the microphysics, i.e.\ the thermodynamics
and opacities (see Table~\ref{KapSou}), are specified (in practice and opacities (see Table \ref{KapSou}), are specified (in practice
by specifying a chemical composition) the one-zone stability can by specifying a chemical composition) the one-zone stability can
be inferred if the thermodynamic state is specified. be inferred if the thermodynamic state is specified.
The zone -- or in The zone -- or in
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thermodynamical state of the layer. Therefore the above relations thermodynamical state of the layer. Therefore the above relations
define the one-zone-stability equations of state define the one-zone-stability equations of state
$S_{\mathrm{dyn}},\,S_{\mathrm{sec}}$ $S_{\mathrm{dyn}},\,S_{\mathrm{sec}}$
and $S_{\mathrm{vib}}$. See Fig.~\ref{FigVibStab} for a picture of and $S_{\mathrm{vib}}$. See Fig. \ref{FigVibStab} for a picture of
$S_{\mathrm{vib}}$. Regions of secular instability are $S_{\mathrm{vib}}$. Regions of secular instability are
listed in Table~1. listed in Table 1.
<!-- calculate height and width of picture manually in inch, using evince -> Properties
create label for \ref{FigVibStab} using #FigVibStab
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![Vibrational stability equation of state $S_{\mathrm{vib}}(\lg e, \lg \rho)$. $>0$ means vibrational stability.](Figure/icml_numpapers.eps){#FigVibStab width=3.43in height=2.71in}
<!--
\begin{figure} \begin{figure}
\centering \centering
\caption{Vibrational stability equation of state \caption{Vibrational stability equation of state
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} }
\label{FigVibStab} \label{FigVibStab}
\end{figure} \end{figure}
-->
# Conclusions # Conclusions

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