Arnaldo Rodriguez-Gonzalez
@aghostinthefigures.bsky.social
Dynamicist, writer, asker of questions. Assistant professor of teaching in the University at Buffalo. Ph.D. in theoretical & applied mechanics from Cornell, B.S. in mechanical engineering from UPR Mayagüez. 🇵🇷 He/him.
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!)
(Also delighted to see some familiar faces in this year’s cohort!)
Lathisms
www.lathisms.org
October 10, 2025 at 3:57 PM
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!)
(Also delighted to see some familiar faces in this year’s cohort!)
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.
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...
www.youtube.com
August 7, 2025 at 12:35 PM
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.
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.
One of my favorites parts of teaching heat transfer:
Explaining that radiation is not /technically/ a form of heat transfer! (A thread.) #physics
Explaining that radiation is not /technically/ a form of heat transfer! (A thread.) #physics
July 21, 2025 at 10:11 PM
One of my favorites parts of teaching heat transfer:
Explaining that radiation is not /technically/ a form of heat transfer! (A thread.) #physics
Explaining that radiation is not /technically/ a form of heat transfer! (A thread.) #physics
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.
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.
June 19, 2025 at 5:14 PM
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.
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.
They’ve done amazing work in the face of great adversity and fear. What a privilege it is to help them.
May 23, 2025 at 11:09 PM
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.
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.
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.
May 7, 2025 at 2:10 PM
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.
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.
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!
As time goes by, the cylinder rotation begins to affect the flow in the whole tank, and droplets start to drift to the right!
April 22, 2025 at 2:40 PM
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!
As time goes by, the cylinder rotation begins to affect the flow in the whole tank, and droplets start to drift to the right!
More fun with computational fluid dynamics; what does flow past an airfoil look like? #FluidDynamics
A thread:
A thread:
April 17, 2025 at 9:07 PM
More fun with computational fluid dynamics; what does flow past an airfoil look like? #FluidDynamics
A thread:
A thread:
A perk of teaching students how to use finite element/volume methods; making cool animations!
This is "vortex shedding" in 2-D flow past a cylinder; a pair of symmetric counter-rotating vortices develop in the back, which then destabilize to form a long, oscillatory, transient wake. #fluidmechanics
This is "vortex shedding" in 2-D flow past a cylinder; a pair of symmetric counter-rotating vortices develop in the back, which then destabilize to form a long, oscillatory, transient wake. #fluidmechanics
April 12, 2025 at 5:46 PM
A perk of teaching students how to use finite element/volume methods; making cool animations!
This is "vortex shedding" in 2-D flow past a cylinder; a pair of symmetric counter-rotating vortices develop in the back, which then destabilize to form a long, oscillatory, transient wake. #fluidmechanics
This is "vortex shedding" in 2-D flow past a cylinder; a pair of symmetric counter-rotating vortices develop in the back, which then destabilize to form a long, oscillatory, transient wake. #fluidmechanics
For a lot of people, the key hallmark of chaotic behavior is sensitivity to initial conditions—I disagree!
To me, the key hallmark of chaos is complexity. Everything follows from that; roughly speaking, cramming “many” dynamical behaviors into a “small” set of states is what causes sensitivity!
To me, the key hallmark of chaos is complexity. Everything follows from that; roughly speaking, cramming “many” dynamical behaviors into a “small” set of states is what causes sensitivity!
March 22, 2025 at 12:54 PM
For a lot of people, the key hallmark of chaotic behavior is sensitivity to initial conditions—I disagree!
To me, the key hallmark of chaos is complexity. Everything follows from that; roughly speaking, cramming “many” dynamical behaviors into a “small” set of states is what causes sensitivity!
To me, the key hallmark of chaos is complexity. Everything follows from that; roughly speaking, cramming “many” dynamical behaviors into a “small” set of states is what causes sensitivity!
It's interesting to think that (IMO) the axioms of topology generate structure that is right in the Goldilocks zone for mathematical exploration.
There are far fewer "interesting" results about the structure of measurable spaces, because their structure is "too" fine to vary much between spaces!
There are far fewer "interesting" results about the structure of measurable spaces, because their structure is "too" fine to vary much between spaces!
February 24, 2025 at 3:21 PM
It's interesting to think that (IMO) the axioms of topology generate structure that is right in the Goldilocks zone for mathematical exploration.
There are far fewer "interesting" results about the structure of measurable spaces, because their structure is "too" fine to vary much between spaces!
There are far fewer "interesting" results about the structure of measurable spaces, because their structure is "too" fine to vary much between spaces!
Getting back in the habit of making math/physics animations in my spare time. Here's an old favorite of mine; the formation of a homoclinic tangle!
I'm hoping to upload the code for a few of these on GitHub, once I feel it's polished enough for public viewing. Hopefully won't take too long!
I'm hoping to upload the code for a few of these on GitHub, once I feel it's polished enough for public viewing. Hopefully won't take too long!
February 23, 2025 at 4:34 PM
Getting back in the habit of making math/physics animations in my spare time. Here's an old favorite of mine; the formation of a homoclinic tangle!
I'm hoping to upload the code for a few of these on GitHub, once I feel it's polished enough for public viewing. Hopefully won't take too long!
I'm hoping to upload the code for a few of these on GitHub, once I feel it's polished enough for public viewing. Hopefully won't take too long!
Tried a fun exercise with my finite elements students a few weeks ago:
Do the empirical equations we use for finding the stress concentration factor in the bar below match the results we'd get from doing finite element analysis?
Do the empirical equations we use for finding the stress concentration factor in the bar below match the results we'd get from doing finite element analysis?
February 17, 2025 at 9:40 PM
Tried a fun exercise with my finite elements students a few weeks ago:
Do the empirical equations we use for finding the stress concentration factor in the bar below match the results we'd get from doing finite element analysis?
Do the empirical equations we use for finding the stress concentration factor in the bar below match the results we'd get from doing finite element analysis?
Happy, but more importantly proud, to have received this fellowship.
I am also taking the time to reflect on the fact that many of the programs that got me to where I am today—a job where I have the power to teach and help a new generation of engineers help others—are being dismantled as we speak.
I am also taking the time to reflect on the fact that many of the programs that got me to where I am today—a job where I have the power to teach and help a new generation of engineers help others—are being dismantled as we speak.
2025 Class of MGB-SIAM Early Career Fellows | SIAM
SIAM celebrates the distinguished 2025 Class of MGB-SIAM Early Career Fellows.
www.siam.org
February 14, 2025 at 8:20 PM
Happy, but more importantly proud, to have received this fellowship.
I am also taking the time to reflect on the fact that many of the programs that got me to where I am today—a job where I have the power to teach and help a new generation of engineers help others—are being dismantled as we speak.
I am also taking the time to reflect on the fact that many of the programs that got me to where I am today—a job where I have the power to teach and help a new generation of engineers help others—are being dismantled as we speak.
Been writing a handbook on finite element methods for a bit now; unsure why. Hope to make it, and a few algorithms within it, free and publicly accessible once I'm done.
Tough to feel as if this sort of thing matters in the new Age. Logic fights volition and electrochemistry. Let's see what wins.
Tough to feel as if this sort of thing matters in the new Age. Logic fights volition and electrochemistry. Let's see what wins.
January 29, 2025 at 9:32 PM
Been writing a handbook on finite element methods for a bit now; unsure why. Hope to make it, and a few algorithms within it, free and publicly accessible once I'm done.
Tough to feel as if this sort of thing matters in the new Age. Logic fights volition and electrochemistry. Let's see what wins.
Tough to feel as if this sort of thing matters in the new Age. Logic fights volition and electrochemistry. Let's see what wins.
I obtained a copy of Physics of Continuous Matter in December—was incredibly impressed by what I consider to be a singular work in continuum physics—and thought I would send a “thank you” e-mail to the author, Benny Lautrup, after the semester had started. I just learned he passed away on the 3rd.
January 22, 2025 at 3:43 PM
I obtained a copy of Physics of Continuous Matter in December—was incredibly impressed by what I consider to be a singular work in continuum physics—and thought I would send a “thank you” e-mail to the author, Benny Lautrup, after the semester had started. I just learned he passed away on the 3rd.
Replayed Portal 2 for the holidays; pleasantly surprised to find some decorative fluid mechanics on the whiteboards!
(Not sure if that Reynolds transport theorem statement is correct, though.)
(Not sure if that Reynolds transport theorem statement is correct, though.)
December 26, 2024 at 5:16 PM
Replayed Portal 2 for the holidays; pleasantly surprised to find some decorative fluid mechanics on the whiteboards!
(Not sure if that Reynolds transport theorem statement is correct, though.)
(Not sure if that Reynolds transport theorem statement is correct, though.)
Reposted by Arnaldo Rodriguez-Gonzalez
In today's lecture in my nonlinear dynamics and chaos course, I tried to give intuition for where chaos comes from. It's caused by repeated stretching and folding of phase space.
December 9, 2024 at 9:26 PM
In today's lecture in my nonlinear dynamics and chaos course, I tried to give intuition for where chaos comes from. It's caused by repeated stretching and folding of phase space.
What does flow past a sphere look like when viscous friction dominates versus when it's neglected? Take a look for yourself! #physics
The flow below is creeping flow, where frictional effects dominate. Particles that get close to the sphere slow down drastically due to the no-slip condition.
The flow below is creeping flow, where frictional effects dominate. Particles that get close to the sphere slow down drastically due to the no-slip condition.
December 7, 2024 at 9:21 PM
What does flow past a sphere look like when viscous friction dominates versus when it's neglected? Take a look for yourself! #physics
The flow below is creeping flow, where frictional effects dominate. Particles that get close to the sphere slow down drastically due to the no-slip condition.
The flow below is creeping flow, where frictional effects dominate. Particles that get close to the sphere slow down drastically due to the no-slip condition.
Long nights and low lights at UB as the semester winds down and the first few snowfalls come in.
I’m so lucky I get to do what I do.
I’m so lucky I get to do what I do.
December 7, 2024 at 1:50 AM
Long nights and low lights at UB as the semester winds down and the first few snowfalls come in.
I’m so lucky I get to do what I do.
I’m so lucky I get to do what I do.
There's no simpler way to show that boundary value problems are much trickier than initial value problems than by analyzing the simple harmonic oscillator.
The following boundary value problem has no solution! #math
The following boundary value problem has no solution! #math
November 27, 2024 at 9:05 PM
There's no simpler way to show that boundary value problems are much trickier than initial value problems than by analyzing the simple harmonic oscillator.
The following boundary value problem has no solution! #math
The following boundary value problem has no solution! #math
Lectured a bit today on one of my favorite prototype aircraft; the Plymouth A-A-2004.
Notice the fact that, technically speaking, it has no wings! #physics
Notice the fact that, technically speaking, it has no wings! #physics
November 19, 2024 at 10:27 PM
Lectured a bit today on one of my favorite prototype aircraft; the Plymouth A-A-2004.
Notice the fact that, technically speaking, it has no wings! #physics
Notice the fact that, technically speaking, it has no wings! #physics
Random thought while teaching fluid mechanics: it’s crazy to consider that we could’ve just as easily developed a theory of hydraulics based on /forces/ and not power, and had it work just as well, but didn’t.
Wouldn’t have made a huge difference practically, but it’s a huge conceptual difference!
Wouldn’t have made a huge difference practically, but it’s a huge conceptual difference!
November 12, 2024 at 2:46 PM
Random thought while teaching fluid mechanics: it’s crazy to consider that we could’ve just as easily developed a theory of hydraulics based on /forces/ and not power, and had it work just as well, but didn’t.
Wouldn’t have made a huge difference practically, but it’s a huge conceptual difference!
Wouldn’t have made a huge difference practically, but it’s a huge conceptual difference!
Hard to think it’s already been a year.
The end of an era for me—written right while I was switching jobs/career goals, at my most desperate, a last throe in the dark for a grand goal I had since I started graduate school.
Finishing it was a long shot; I’m so glad I got to.
The end of an era for me—written right while I was switching jobs/career goals, at my most desperate, a last throe in the dark for a grand goal I had since I started graduate school.
Finishing it was a long shot; I’m so glad I got to.
After all this time, my free textbook on qualitative dynamics and chaos is finally done!
Access it on my webpage (wp.me/P7zu73-2a8) or on Google Books/Play (bit.ly/498vI61). (1/7)
Access it on my webpage (wp.me/P7zu73-2a8) or on Google Books/Play (bit.ly/498vI61). (1/7)
October 31, 2024 at 10:00 PM
Hard to think it’s already been a year.
The end of an era for me—written right while I was switching jobs/career goals, at my most desperate, a last throe in the dark for a grand goal I had since I started graduate school.
Finishing it was a long shot; I’m so glad I got to.
The end of an era for me—written right while I was switching jobs/career goals, at my most desperate, a last throe in the dark for a grand goal I had since I started graduate school.
Finishing it was a long shot; I’m so glad I got to.