deletions | additions       diff --git a/We_will_consider_the_influence__.tex b/We_will_consider_the_influence__.tex  index 0a7987e..2aa3cba 100644  --- a/We_will_consider_the_influence__.tex  +++ b/We_will_consider_the_influence__.tex 
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We will consider the influence of the miss distance effect in a probabilistic way. For simplicity, we will assume $\upsilon$ is constant in magnitude and direction, while in reality, the ambient wind field carrying a devil can be complex, even causing multiple encounters between devil and sensor and consequently more complex pressure signals \citep{Lorenz_2013}. \subsection*{The $P$ Distortion}  From the encounter geometry, we can see that the probability $dp$ for the center of a devil to pass within a certain range of radial distances, between $r$ and $r + dr$, is given by $dp \propto r\ dr$. This expression indicates that the probability increases without limit as $r$ increases. However, detecting the pressure signal from a dust devil drops to zero once the devil is too far away to detect: beyond some $r_{\rm max}$, the pressure signal $P(r = r_{\rm max})$ drops below a detectability threshold, so $r_{\rm max}$ is really just another way to express that minimum pressure threshold. Thus, $dp = \dfrac{2 r\ dr}{r_{\rm max}^2}$.  Given a profile shape for a dust devil, we can relate the radial distance $r$ to the observed pressure signal $P_{\rm obs} = P(r)$. Assuming a Lorentz profile, we find  
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