Recent content by colinjohnstoe

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    I Are Red Dwarfs Home to Earth-Sized Water Worlds?

    By the way, the reason I mentioned X-rays from active stars in relation to flares is that there are some reasons to think that the X-rays coming from very active stars are simply the super-position of many flares.
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    I Are Red Dwarfs Home to Earth-Sized Water Worlds?

    This isn't true. They considered 6733 CMEs and found only a small fraction of them to be associated with flares. They discuss at several points in the paper the differences between CMEs associated with flares and those that are not. Have a look at the first sentence of the second paragraph of...
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    I Are Red Dwarfs Home to Earth-Sized Water Worlds?

    Sure, but what I wrote is not that the existence of CMEs from other stars is speculative. The point is that the existence of strong CME dominated winds from other stars is speculative. Our solar wind is very far from being dominated by CMEs but there is speculation that more active stars shoot...
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    I Are Red Dwarfs Home to Earth-Sized Water Worlds?

    The mechanisms are quite poorly understood and the link between flares are CMEs are also quite poorly understood. Both are a result of the magnetic field, and more specifically, both are a likely to be a result of energy release from magnetic reconnection. However, a flare on the Sun is not...
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    I Are Red Dwarfs Home to Earth-Sized Water Worlds?

    Sure, many flares have been observed on many stars, but CMEs (i.e. the actual ejected material) have not been detected. There have been some attempts, and some hints for CMEs, but nothing concrete.
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    I Are Red Dwarfs Home to Earth-Sized Water Worlds?

    Yes, you of course came to the correct conclusions based on the paper. What I meant is the arguments in the paper that CMEs can cause a significant amount of atmospheric mass loss are quite speculative. The reason is that it is unclear that these strong continuous streams of CMEs even exist...
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    I Are Red Dwarfs Home to Earth-Sized Water Worlds?

    This is a very interesting topic, and Glitch has done a great job summarising some of the main question. I work on these topics in my own research so I am always interested in getting into any discussion on it. I have some comments about what has been written so far. Another factor is the...
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    Specific heat ratio of gas mixture

    You are right! Thanks. That should solve the problem.
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    Specific heat ratio of gas mixture

    How do I get the individual specific heat values from ##\gamma##? Knowing ##\gamma## only means I know the ratio of the two.
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    Specific heat ratio of gas mixture

    Thanks for the response. It doesn't really answer the question though. I am asking about the specific heat ratio ##\gamma=C_\mathrm{P}/C_\mathrm{V}##. If we use the weighted sums, we get $$\gamma=\frac{C_\mathrm{P}}{C_\mathrm{V}} = \frac{\sum_i y_i C_{\mathrm{P},i}}{ \sum_i y_i C_{\mathrm{V},i}...
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    Specific heat ratio of gas mixture

    I am doing some multi-fluid hydrodynamic modelling and I have a quick question. I think I know the answer, but I am not convinced. One of the things that I need to know is the specific heat ratio, ##\gamma##, for the gas and my question is, how does one calculate this from the values of each...
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    Associated Legendre functions and orthogonality

    I am looking for a similar thing. I have looked in all the spherical harmonics textbooks I can find, but have had no luck. I will let you know if I have anything.
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    Proof of orthogonality of associated Legendre polynomial

    The relation that was asked for in the first post is not correct. It is not the case that \int_{-1}^1 P_l^m(x)P_{l'}^{m'} (x)dx = \frac{2}{2l+1} \frac {(l+m)!} {(l-m)!} \delta_{ll'} \delta_{mm'} for all values of l, m, l' and m'. This would imply that the integral \int_{-1}^1...
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