Arnaldo Rodriguez-Gonzalez

Honored to have been featured as today’s mathematician in Lathisms’ annual calendar for Hispanic Heritage Month!

(Also delighted to see some familiar faces in this year’s cohort!)

I hesitate to share things publicly these days, for perhaps obvious reasons. But I suppose that the fear of evil should not drive inaction; the hope for good should drive action instead. And so I have to proverbially put my money where my mouth is.

I hope they're useful to someone out there.

YouTube video by Arnaldo Rodriguez-Gonzalez Lecture 33: Thermoregulation and extreme heat events

If anything, thinking of making this lecture on thermoregulation and extreme heat events motivated me to make and post these recordings in the first place; although highly simplified, it is important knowledge for anyone invested in the global health of humanity this century.

Commentary on Heat Transfer - YouTube These are a series of lectures designed for the summer undergraduate heat transfer course in the University at Buffalo's Mechanical and Aerospace Engineering...

I've uploaded my lectures for my summer heat transfer course on YouTube, free to watch.

They are largely unedited and a tad sloppy; but I made a commitment years ago to the free distribution of knowledge, and I have to see it through.

Commentary on Heat Transfer - YouTube These are a series of lectures designed for the summer undergraduate heat transfer course in the University at Buffalo's Mechanical and Aerospace Engineering...

That's why radiation is not technically a transference of heat!

If you'd like to learn more about heat transfer, I've made my (currently incomplete) summer course lectures on heat transfer available for free on YouTube: check them out if you like!

www.youtube.com/playlist?lis...

And, key to note, no actual heat flow occurs in radiative temperature equilibration. /Electromagnetic/ energy flows between the objects, /some/ of which is converted back into thermal energy; and since the flow is affected by the objects's temperatures, this (potentially) leads to equilibrium.

This means that modeling radiation involves modeling three separate physical processes; the emission of electromagnetic energy, its propagation through space, and its (partial) conversion back into thermal energy upon interacting with matter.

THIS is what makes modeling radiation so hard!

What happens, in short, is that objects will emit /electromagnetic/ energy into their surroundings (in the form of light) as a function of their temperature. That electromagnetic energy travels through space, and upon interacting with matter, may be partially converted back into thermal energy.

If the temperature of something is based on the random kinetic energy of its molecules, what is the temperature of empty space? If empty space has no temperature, how can it have thermal energy, and therefore how can heat flow occur in it?

The answer; it doesn't! No heat flow occurs in radiation.

The field of study called "heat transfer" is then called this because most of its modeling efforts are focused on relating heat fluxes and heat transfer rates to temperature imbalances, as well as other properties of the physical system being studied.

But this idea breaks down for radiation.

Heat flow then occurs as a result of imbalances in temperature, like how fluids flow under pressure imbalances! A temperature imbalance in matter causes a flow of thermal energy from hot to cold that "corrects" the imbalance over time, in the absence of "thermal forcing" or anything like that.

For the first two modes, we hypothesize that there is a quantity—thermal energy, or heat—that is a function of the temperature of the object/point being studied, which can flow through matter and be transferred between objects.

However, we observe that temperature equilibration can occur even between two objects separated by empty space, with no matter between them! This is the mode we call "radiation".

So this /empirically/ describes the three modes of "heat transfer". How do we model and describe them?

Between solids in contact (and within them), we call the mode that induces temperature equilibration "conduction".

Between solids and fluids in contact, or between just fluids, we call that mode "convection". (There's a bit more refinement to these descriptions, but this describes most of it.)

What we call "modes" of heat transfer (in the field-of-study sense) are just different physical contexts in which we observe a key empirical behavior; that objects with different temperatures, in the absence of "thermal perturbations", will eventually "equilibrate" to the same temperature over time.

To explain why, we first need to answer what the /field of study/ we call "heat transfer" is.

In short, it's the field of study that seeks to describe how temperature changes, in time and in space, across and within objects. Notice no actual definition of what "heat" is!

One of my favorites parts of teaching heat transfer:

Explaining that radiation is not /technically/ a form of heat transfer! (A thread.) #physics

I saw this model work well for artists and writers I know; it comes with its own challenges (who owns IP/usage permissions, collective identity, interpersonal disputes, etc.) but I agree that this might be a good way forward for folks starting out.

Community always helps!

Anyways, this is a relatively self-centered overshare, which I’ll likely delete later (too risky to share things on social media now), but I’m not alone in feeling this way. I guess this is just my way of grieving what was, and what could’ve been. It also explains why I post so rarely now.

Although it seems like this’d be good on the “consumer” side—higher quality for far cheaper on written content, for example—my guess is that this’ll heavily discourage potential authors from even considering writing in the first place. We will go the same way that stonemasons did.

The only way to perhaps beat AI—for now—is to have enough resources to considerably improve quality (using a good, fancy publisher, for example), and to have name recognition that both set the content apart from “slop”. Not great for folks starting out, or who want to make open/free material.

2) I don’t think there’ll be an “economy” for free long-form human-made content in the AI age. No point debating good or bad; the fact is that even if I’d like to think I can write free books or make science lectures in my spare time better than AI, AIs will just churn out that content far faster.

That’s a shame for us early-career folks; I co-authored a paper on perturbation theory that came about as a collaboration via social media! That sort of incentive for public sharing was meaningful. But now it feels like sharing anything is just a risk to get your career killed by engagement-farmers.

There are two key reasons in my mind for this:

1) Using social media as an identifiable person feels like far more of a risk than sensible relative to rewards. You either have to be anonymous (what every big account does now) and/or already secure and fully established in your life and career.

It’s been interesting to reflect on how steeply my feelings on sharing things—educational and otherwise—on social media have changed over the last year.

For example; I’m making a series of lecture videos for my summer heat transfer course. The original plan was to share them freely. Now—not sure.

Another semester of teaching at UB concluded. Eternally grateful to have the ability to teach—it is not an easy time right now to be a professor, but it is a far harder time to be a student.

They’ve done amazing work in the face of great adversity and fear. What a privilege it is to help them.

More fun with computational fluid mechanics:

Here's a 2-D simulation of a layer of air (red) below a layer of water (blue) in a closed container. As air is lighter, buoyant forces cause the interface to be unstable, leading to the complex flow shown here as the air eventually rises to the top.

For the rotating cylinder and using water as the main phase, about one million, so pretty high! But the multiphase flow muddles things up, as the characteristic Reynolds number of the bubbles is relevant too, and I haven’t post-processed enough to get their equilibrium speed/radius out.

More fun with CFD for my course; here's a simulation of air bubbles being generated in a container of water with a rapidly rotating cylinder inside of it.

As time goes by, the cylinder rotation begins to affect the flow in the whole tank, and droplets start to drift to the right!

a plane is flying through a cloud of green smoke . ALT: a plane is flying through a cloud of green smoke .

These wingtip vortices are a ubiquitous phenomenon in aircraft! And as expected, accounting for these vortices is an important part of designing aerodynamic systems.

Anyways, that's all I can think of posting. Hope you enjoyed it!