# Caltech Demo 2 - New title!  www.authorea.com/108157

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A tornado $$e^{i\pi}+1=0$$ is a violently rotating column of air that is in contact with both the surface of the earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud. They are often referred to as twisters or cyclones, although the word cyclone is used in you can wire meteorology, in a wider sense, to name any closed low pressure circulation Pepe 2012. Tornadoes often develop from a class of thunderstorms known as super cells. As the mesocyclone lowers below the cloud base Lane, it begins to take in cool, moist air from the downdraft region of the storm. Supercells contain mesocyclones, an area of organized rotation a few miles up Pepe in the atmosphere, usually 1–6 miles (2–10 km) across. Most intense tornadoes (EF3 to EF5 on the Enhanced Fujita Scale) develop from supercells. In addition to tornadoes, very heavy rain, frequent lightning, strong wind gusts, and hail are common in such storms. Most tornadoes take on the appearance of a narrow funnel, a few hundred yards (meters) across, with a small cloud of debris near the ground. Tornadoes may be obscured completely by rain or dust. These tornadoes are especially dangerous, as even experienced meteorologists might not see them Thorne 1996.
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We now hihiihihihihutilize the same method to calculate expected visibilities of both dipole and quadrupole modes in stars with $$1.25 \, M_\odot \leq M \leq 3 \, M_\odot$$. The ratio of suppressed mode power to normal mode power is $\label{eqn:vsup} \frac{V_{\rm sup}^2}{V_{\rm norm}^2} = \bigg[ 1 + \Delta \nu \,\tau \,T^2 \bigg]^{-1} \, .$ Here, $$\Delta \nu$$ is the large frequency separation, $$\tau$$ is the radial mode lifetime, and $$T$$ is the wave transmission coefficient through the evanescent zone. The value of $$T$$ can be calculated via $\label{eqn:T} T = \exp \bigg[ - \int^{r_2}_{r_1} dr \sqrt{ - \frac{ \big( L_\ell^2 - \omega^2 \big) \big(N^2 - \omega^2 \big) }{v_s^2 \omega^2} } \bigg] \, .$ Here, $$r_1$$ and $$r_2$$ are the lower and upper boundaries of the evanescent zone, $$L_\ell^2 = l(l+1)v_s^2/r^2$$ is the Lamb frequency squared, $$N$$ is the Brunt-Vaisala frequency, $$\omega$$ is the angular wave frequency, and $$v_s$$ is the sound speed. We calculate $$\Delta \nu$$ and the frequency of maximum power $$\nu_{\rm max}$$ using scaling relations.

Infinite Taylor series

### References

1. Alberto Pepe, Spencer Wolff, Karen Van Godtsenhoven. One none and one hundred thousand profiles. First Monday 17 University of Illinois Libraries, 2012. Link

2. Julia Lane, Victoria Stodden, Stefan Bender, Helen Nissenbaum, Julia Lane, Victoria Stodden, Stefan Bender, Helen Nissenbaum. Editors’ Introduction. xi–xx In Frameworks for Engagement. Cambridge University Press (CUP) Link

3. Alberto Pepe. Structure and Evolution of Scientific Collaboration Networks in a Modern Research Collaboratory. SSRN Electronic Journal Social Science Electronic Publishing Link

4. Kip S. Thorne. Gravitational Waves from Compact Bodies. 153–183 In Compact Stars in Binaries. Springer Science $$\mathplus$$ Business Media, 1996. Link