Recent content by Robert M

  1. R

    What's the formula? - eigenvectors from eigenvalues

    https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/#more-11249
  2. R

    B Why did Max Planck assume discrete energy values?

    After-the-fact presentations of scientific discovery tend to gloss over a lot of details. Planck's understanding of the state of the art was apparently encyclopedic, and he apparently really covered the territory in getting to his famous result which was, in my estimation, one of the top ten...
  3. R

    Insights How Does an Airplane Wing Work: a Primer on Lift - Comments

    Your audience included me. I didn't write an article. I made a comment. The idea that truth (or whatever you choose to call it) should depend on an audience's tolerance for detail or for being told that the necessary detail may be beyond any likely audience, is--in my opinion--dangerous...
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    Insights How Does an Airplane Wing Work: a Primer on Lift - Comments

    One possible purpose of a discussion like this is to clear the air. Mathematical fluid mechanics is a very mature discipline, but, in order to understand what has been concluded and how it has been concluded, you need some mathematics beyond what many will be unwilling to commit the time to...
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    Insights How Does an Airplane Wing Work: a Primer on Lift - Comments

    A different thread on lift offers a talk from someone who doesn't underestimate the problem. In the end, if you stay with the talk that far, the difficulties of even the best discussions of lift don't become apparent until you examine whether or not integrals over reasonably obvious control...
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    Insights How Does an Airplane Wing Work: a Primer on Lift - Comments

    Vorticity is so much more productive than primitive variables in explaining and analyzing low Mach number flow, and it fits naturally with the actual physics of a standard airfoil. https://en.wikipedia.org/wiki/Kutta%E2%80%93Joukowski_theorem For potential flow--no vorticity, or, equivalently...
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    Insights Damped Motion in Classical and Quantum Mechanics - Comments

    Line-broadening may, after all, be a better way to characterize the topic than anything to do with (say) opposing motion, as it generalizes naturally (as you have shown) to quantum mechanics. For many applications, the "Q" of resonant processes is more important for calculation than intuitive...
  8. R

    Insights Damped Motion in Classical and Quantum Mechanics - Comments

    Thanks. It occurred to me after I had posted my comment that there must be examples in solid state physics where it is generally thought to be appropriate to speak of damped motion, the first likely example of which that occurred to me was phonon damping. If I understand your offered article...
  9. R

    Insights Damped Motion in Classical and Quantum Mechanics - Comments

    Energy dissipation in turbulent flow is certainly a problem of great interest to scientists, engineers, and mathematicians, but it is not the first path I would choose to study "damped motion." One natural analog of damped oscillator problems, which have generally been rendered artificially...
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