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Fluid Mechanics = "Single"-Particle Control: From Control to Turbulence and Back
Published on Oct 16, 20124190 Views
We show that different flows studied in fluid mechanics can be understood as following from generalized gauge-invariant stochastic control formulations of a single particle under different conditions.
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Chapter list
Fluid Mechanics = "Single"-Particle Control: From Control to Turbulence and Back00:00
Disclaimers/Warnings00:20
Outline03:47
SC: (Almost) Classical Formulation (example)05:22
Averaged Density & Current (under fixed control)10:41
SC via Density & Current14:15
Generalized Bellman-Hamilton-Jacobi Eq.16:16
Outline: From BHJ to Burgers Eq. and Burgulence19:45
Control Field = (Phase-Space) Velocity19:51
Interpretations of Potentials23:01
Burgers Eq. and KPZ Eq.31:36
Schock(s) in Control32:27
Example: Burgulence in 1d (decay or stationary)41:04
Example: 1d Brownian Decay41:55
Example: Burgulence in 2d and 3d44:46
Outline: (In)compressibility/Navier-Stocks & Control45:58
Are there other, than "burgers/KPZ", fluid mechanics relevant for control?46:09
Pressure as a Potential. Equation of State.46:18
Uncertainty? Robust Control? Control by Turbulence?51:47
Conclusions/Summary54:07
Path Forward55:37