Week 16
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 longtime dynamics of many such systems of physical interest is finitedimensional. Here we cure you of the fear of infinitedimensional 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?
Tutorial  A stroll through 61,506 dimensions Ladies and gentlemen, this is no model: this is NavierStokes! 

Delirious ambitions  
What have we learned?  
Quantum chaos  
Gutzwiller semiclassical quantization  
Be brave: do QFT  
From fluid dynamics to YangMills  
Knowing where to stop: hbar 
Turbulence (optional: earn bonus points)
Due 8 May 2022 

Discussion forum for week 16 
Symmetries of the solutions  
Equilibria of equilibria 
Daniel Kleppner  Quantum Mechanics and Chaos  
Richard Feynman  The Principle of Least Action  
Epilogue 