Week 16
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Indiana Jones vs. Fancy Footwork |
- 31. “Turbulence” - a one spatial dimension warmup / 3 May 2022 /
- 32. Turbulence? / 5 May 2022 /
- The last of all homeworks Hard deadline for all homeworks: 26 April 2022
- Optional
- Course conclusion
Flows described by PDEs are said to be `infinite dimensional' because if one writes them down as a set of ODEs, one needs infinitely many of them to represent the dynamics of one PDE. The long-time dynamics of many such systems of physical interest is finite-dimensional. Here we cure you of the fear of infinite-dimensional flows.
In the world of everyday, moderately turbulent fluids flowing across planes and down pipes, a velvet revolution is taking place. Experiments are as detailed as simulations, there is a zoo of exact numerical solutions that one dared not dream about a decade ago, and portraits of turbulent fluid's state space geometry are unexpectedly elegant. We take you on a tour of this newly breached, hitherto inaccessible territory. Mastery of fluid mechanics is no prerequisite, and perhaps a hindrance: the tutorial is aimed at anyone who had ever wondered how we know a cloud when we see one, if no cloud is ever seen twice? And how do we turn that into mathematics?
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Tutorial - A stroll through 61,506 dimensions Ladies and gentlemen, this is no model: this is Navier-Stokes! |
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Delirious ambitions |
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What have we learned? |
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Quantum chaos |
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Gutzwiller semiclassical quantization |
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Be brave: do QFT |
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From fluid dynamics to Yang-Mills |
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Knowing where to stop: h-bar |
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Turbulence (optional: earn bonus points)
Due 8 May 2022 |
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Discussion forum for week 16 |
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Symmetries of the solutions |
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Equilibria of equilibria |
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Daniel Kleppner - Quantum Mechanics and Chaos |
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Richard Feynman - The Principle of Least Action |
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Epilogue |