Summer of Math Exposition

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

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. [A familiarity with derivatives (basic calculus) is recommended.]

Analytics

6.7 Overall score*
30 Votes
11 Comments
Rank 20

Comments

I understand you might want to address the commenters / audience preemptively, i.e. thinking of possible questions they might have and answering them immediately in the relevant portions of the video. However, it often interrupts the flow, and the audience that doesn't have that many questions might actually get lost instead. I guess it's better to do that in adequate amounts, rather than at almost every point of the explanation, because I imagine if you take out those parts, the central argument isn't that long.

5

for the goal of this video (explaining a concept in-deph to students that might be interested in knowing what the constant they often see represent) this is style is just right, it gives a good explanation while being welcoming and understandable to people with no prior expirance.

5.1

I thought this video was very informative! The only critique I would say is that personally, I would have preferred more background into some of the things that you left as an appendix in the video

4.1

This is a very minor suggestion: I've seen such linear transport laws before (in a pchem class), and even for me I think it would've been helpful for you to say what each symbol/variable represents very briefly in addition to listing them at some point—my eyes/ears focus more on what's being said, and I feel like that would've helped prevent confusion throughout the video.

5.7

Nice explainer, but lacks polish

4.4

Good video, but it never actually gave an intuitive explanation for why diffusivity should have units of m^2 / s.

6.5

This was a really really great video! As context, I have a PhD in applied physics, so I know this content very well — and thought it was exceptionally well explained. It is true that the current methods of teaching doesn’t emphasize enough on the random-walk / wiener process to explain the diffusion equation!

9

I liked your presentation style

6.6

Nice that you told us what was expected as background at the beginning.

7.1

A bit too many formulas and concepts to follow. I really like that in the beginning of the video you said that you don't necessarily have to follow them, and I really don't think the average viewer will be able to, though I do think it's better if you could find some way to entirely omit the things that people won't understand.

2.8

Interesting, but it would have been nice to go into the units. I was left wondering why it was *area* per second.

6.8