This Magnetic Simulation Took Nearly A Month! 🧲

Dear Fellow Scholars, this is Two Minute Papers with Dr. Károly Zsolnai-Fehér. Have a look at these beautiful ferrofluid simulations from a previous paper. These are fluids that have magnetic properties and thus respond to an external magnetic field, and you are seeing correctly, they are able to even climb things. And the best part is that simulator was so accurate that we could run it side-by-side with real-life footage, and see that they run very similarly. Excellent. Now, running these simulations took a considerable amount of time. To address this, a followup paper appeared that showcased a surface-only formulation. What does that mean? Well, a key observation here was that for a class of ferrofluids, we don’t have to compute how the magnetic forces act on the entirety of the 3D fluid domain, we only have to compute them on the surface of the model. So what does this get us? Well, these amazing fluid labyrinths, and all of these ferrofluid simulations, but… faster! So, remember, the first work did something new, but took a very long time, and the second work improved it to make it faster and more practical. Please remember this for later in this video. And now let’s fast forward to today’s paper, this new work can also simulate ferrofluids, and not only that, but also supports a broader range of magnetic phenomena, including rigid and deformable magnetic bodies and two-way coupling too! Oh my! That is sensational, but first, what do these terms mean exactly? Let’s perform four experiments, and after you watch them, I promise that you will understand all about them. Let’s look at the rigid bodies first in experiment number one. Iron box versus magnet. We are starting out slow, and now, we are waiting for the attraction to kick in, and there we go. Wonderful. Experiment number two, deformable magnetic bodies. In other words, magnetic lotus versus a moving magnet. This one is absolutely beautiful, look at how the petals here are modeled as thin elastic sheets that dance around in the presence of a moving magnet. And if you think this is dancing, stay tuned, there will be an example with even better dance moves in a moment. And experiment number three, two-way coupling. We noted this coupling thing earlier, so, what does that mean? What coupling means is that here, the water can have an effect on the magnet, and the two-way part means that in return, the magnet can also have an effect on the water as well. This is excellent, because we don’t have to think about the limitations of the simulation, we can just drop nearly anything into our simulation domain, be it a fluid, solid, magnetic or not, and we can expect that their interactions are going to be modeled properly. Outstanding. And, I promised some more dancing, so here goes, experiment number four, the dancing ferrofluid. I love how informative the compass is here, it is a simple object that tells us how an external magnetic field evolves over time. I love this elegant solution. Normally, we have to visualize the magnetic induction lines so we can better see why the tentacles of a magnetic octopus move, or why two ferrofluid droplets repel or attract each other. In this case, the authors opted for a much more concise and elegant solution, and I also liked that the compass is not just a 2D overlay, but a properly shaded 3D object with specular reflections as well. Excellent attention to detail. This is really my kind of paper. Now, these simulations were not run on any kind of supercomputer or a network of computers, this runs on the processor of your consumer machine at home. However, simulating even the simpler scenes takes hours. For more complex scenes, even days. And that’s not all, the ferrofluid with the Yin-Yang symbol took nearly a month to compute. So, is that a problem? No, of course not. Not in the slightest. Thanks to this paper, general magnetic simulations that were previous impossible are now possible, and don’t forget, research is a process. As you saw in the example at the start of this video with the surface-only ferrofluid formulation, it may become much faster just one more paper down the line. I wanted to show you the first two papers in this video to demonstrate how quickly that

can happen. And two more papers down the line, oh my, then, the sky is the limit. What a time to be alive! Thanks for watching and for your generous support, and I'll see you next time!