this is for holding javascript data
Brian Jackson edited Whether_a_devil_with_a__.tex
almost 9 years ago
Commit id: 681d6092d64a8bbc837e924b5053023e2df4edad
deletions | additions
diff --git a/Whether_a_devil_with_a__.tex b/Whether_a_devil_with_a__.tex
index d059dbe..5fcd78e 100644
--- a/Whether_a_devil_with_a__.tex
+++ b/Whether_a_devil_with_a__.tex
...
$b_{\rm max}$ can also be written in terms of a devil's central pressure $P_{\rm act}$: $b_{\rm max} = \dfrac{\Gamma_{\rm act}}{2} \sqrt{ \dfrac{P_{\rm act}}{P_{\rm min}} - 1}$, giving the following expression for the probability density:
\begin{equation}\label{eqn:dpdP_obs}
\dfrac{dp}{dP_{\rm obs}} = \left( \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}} \right) P_{\rm
act} act}\ P_{\rm obs}^{-2}.
\end{equation}
Combining the recovery bias and distortion expression gives a probability density for a devil with a given $P_{\rm act}$ to be observed with a pressure between $P_{\rm obs}$ and $P_{\rm obs} + dP_{\rm obs}$:
\begin{equation}\label{eqn:probability-density_Pobs-Pact}
f_{\left( \Gamma_{\rm act} = {\rm const.} \right)}\ \dfrac{dp}{dP_{\rm obs}} = \left( \dfrac{P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right) P_{\rm act}\ P_{\rm obs}^{-2}.
\end{equation}Figure \ref{fig:probabilty-density_Pobs-Pact} illustrates this density, assuming $P_{\rm min} = 0.1$ hPa and $P_{\rm max} = 10$ hPa.