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   Category Theory and AWES Architectures?
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We archive what Dave Santos posted in Azimuth
December 1 edited December 1 in Chat                                   2020
Hi Folks,

Am interested in Category Theory application to classification of Airborne Wind Energy Systems (AWES), which is a Work Package in process by the National Renewable Energy Lab (NREL) for the International Energy Agency (IEA). There are many ways to define computable knowledge-based engineering ontologies, and many researchers have specific skills, but Categorical Diagrams are especially intuitive, powerful, and rigorous for knowledge representation teamwork.

With regard to Green Mathematics and Azimuth's Values Commitments, AWE, also known as "Kite Energy", has tremendous potential to perhaps resolve the Holocene Extinction (or make it worse) because no other renewable energy source is so vast, dense, and ubiquitous as Upper Wind. The futurisms are mind-blowing, from game-changing green-energy super-abundance, to decisive climate geo-engineering, to levitating civilization en-masse for a techno-utopian Golden Age (Aerotecture).

Its a mathematical engineering-physics wonderland to contemplate "polymerizing the sky" by directly embodied metamaterial topologies at extreme-scale, with analog-QM phonon dynamics, sonic relativity, and so on. These dynamics apply to any geophysical flow; wind, water, solar wind, etc.. Precise AWES Categorization may inform a Multi-Physics Multi-Solver Sim, to run on an exaflop supercomputer NREL will have access to in 2022.

A starting puzzle, a Rabbit Hole Entrance into exotic AWE science-

A large ship tows another by a polymer rope (hawser) a few cm in diameter. The towed ship's drag and velocity amount to 10MW of thermodynamic work, yet the polymer rope conveying 10MW remains cool to the touch(!) Explain this mechanical superconducting (conservation of energy) according to Phonon QFT or thermodynamics. Extra points for a Feynman or Categorical Diagram.

"We might extend the application of [wind] power to the heights of the clouds, by means of kites."

John Etzler, 1833
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December 2, 2020
Working thru Fong and Spivak's 7 Sketches text, in the present context, an AWES has a layered structure comprising a Preorder. A Monotone Map may start with Wind, then Kite, then Bridle, then Tether, then Anchor. Expanded Hasse Diagramming could show the Tether-fibers, typical multiple Bridle Lines, and even define Multi-Kite Parallel Networks.

Its rather cool that these physical kite objects embody mathematical objects like lines, surfaces, braids, knots, and so on. The Wind and Anchoring Media are Fields in 4Space. Energy flowing across the Kite Preorder is primitive Information under Shannon Energy-Information Equivalence, but its not some invisible nano world buzzing at THz frequency, but our familiar world, at our own scale and time.

Clues to the starting Puzzle- The Power in the tow-rope is a Frozen Wave, just as a surfer rides a wave that is static to herself (Galilean Relativity). Thermodynamic Temperature occurs at various scales; at the scale of the tow-rope, the effective temperature is near absolute zero.