What is Diffusivity? (Why does it keep showing up? Why do they have the same units?)

#SoMEpi #SoME4 Diffusivity is a parameter that shows up in molecular diffusion, heat conduction, and fluid dynamics. In each of those cases, it has the same units: m^2/s. To understand why, let's go on an... inebriated stroll... through the mathematical model. REFERENCES *** Text *** D.R. Poirier, G.H. Geiger, Transport Phenomena in Materials Processing. The Minerals, Metals & Materials Society, 1994. Leonard Mlodinow, The Drunkard's Walk - How Randomness Rules Our Lives. Vintage Books, A Division of Random House, Inc. 2008. https://alcohol.org/alcoholism/street-slang-terms-drunk-drink/ *** Videos *** @3Blue1Brown But what is the Central Limit Theorem? https://www.youtube.com/watch?v=zeJD6dqJ5lo Why pi is in the normal distribution (beyond integral tricks) https://www.youtube.com/watch?v=cy8r7WSuT1I But what is a partial differential equation? | DE2 https://www.youtube.com/watch?v=ly4S0oi3Yz8 Solving the heat equation | DE3 https://www.youtube.com/watch?v=ToIXSwZ1pJU @PBSSpaceTime - How Quantum Entanglement Creates Entropy https://www.youtube.com/watch?v=vgYQglmYU-8 @AdianLiusie590 - Intuitively Understanding the Shannon Entropy https://www.youtube.com/watch?v=0GCGaw0QOhA @UpandAtom - Intro to Information Theory | Digital Communication | Informational Technology https://www.youtube.com/watch?v=_PG-jJKB_do @AlphaPhoenixChannel - You can mix 10 marbles until they sort themselves. Why not 100? https://www.youtube.com/watch?v=VCXqELB3UPg @TheEfficientEngineer - Understanding Conduction and the Heat Equation https://www.youtube.com/watch?v=6jQsLAqrZGQ *** Images *** Sbyrnes321, Public Domain, https://commons.wikimedia.org/w/index.php?curid=8995324 CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1426994 Garry Olsh, CC0, https://commons.wikimedia.org/w/index.php?curid=148383228 Yasrena, CC BY-SA 4.0 https://commons.wikimedia.org/wiki/File:Brownian_Motion.gif M. W. Toews, CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=1903871 Unknown author - Uni Frankfurt, Public Domain, https://commons.wikimedia.org/w/index.php?curid=865671 Unknown author - Tekniska Museet, CC BY 2.0, https://commons.wikimedia.org/w/index.php?curid=144716444 Aaron Rees - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=94023198