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\section{Mixed Modes}  Acoustic waves (p-modes) excited by turbulent convection in red giant envelopes can couple to internal gravity waves. This is because, as a red giant increase its radius, the frequency $\omega$ of p-modes decreases and becomes comparable to the frequency of waves in the g-mode cavity. In this situation some of the energy in the p-modes can leak into the g-modes cavity, where waves with frequency $\omega < N$ can be excited ($N$ is the Brunt-Vaisala frequency). These pulsation modes, called mixed-modes, are characterized by significant displacements in both the envelope and the core of a red giant. Their particular nature has enabled important asteroseismic discoveries, in particular the ability to distinguish He-burning clump stars from red giant stars burning hydrogen in a shell \cite{Bedding_2011}, as well as the measurement of core-envelope differential rotation in RGB stars \cite{Beck_2011}.   \begin{itemize}  \item Excitation of stochastically excited p-modes  \item Coupling to g-modes   \item Canonical Damping mechanisms (radiative damping) \cite{Dupret_2009}  \item Tunneling and evolution of tunneling integral for l=1,2  \end{itemize}  \subsection{Tunneling Integral}  The radial displacement  \begin{equation}  \label{eqn:dr}  k_r^2=\Bigg( 1 - \frac{N^2}{\omega^2}\Bigg) \Bigg(1 - \frac{S_\ell^2}{\omega^2}\Bigg)\,\frac{\omega^2}{c_s^2}  \end{equation}  Here, $\omega$ is the angular frequency of the wave, $N$ is the Brunt-Vaisala frequency, $S_\ell$ is the Lamb frequency for waves with harmonic degree $\ell$ and $c_s$ is the sound speed.  diff --git a/layout.md b/layout.md  index a65be23..4476229 100644  --- a/layout.md  +++ b/layout.md 
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section_Magneto_Gravity_Waves_In__.tex  figures/sketch1/sketch3_noborders.png  figures/DipoleProp/DipoleEvolProp.png  Mixed Modes.tex  figures/visibility_mosser_suppressed_band/visibility_mosser_suppressed_band.png  Magnetic Trapping.tex  Mode Visibility.tex