 Dear Fellow Scholars, this is Two Minute Papers with Károly Zsolnai-Fehér. Everyone who watches this series knows that among many other scientific topics I am severely addicted to fluid simulations. And today it's time to relapse. And this time we are going to run wind tunnel tests on hummingbirds. Typically when a new engine, airplane, or even a new phone is being designed, we are interested in knowing how the heat flow and dissipation will look like, preferably before we are designing an object. To do so, we often run some virtual wind tunnel tests and optimize our design until we are happy with the results. Then we can proceed to build these new contractions. Simulating the pressure distribution and the aerodynamic forces is a large topic. However, visualizing these results is at least as well studied and difficult as writing a simulator. What is it exactly that we are interested in? Even if we have an intuitive particle-based simulation, millions and millions of particles, it is clearly impossible to show the path for every one of them. Grid-based simulations are often even more challenging to visualize well. So how do we choose what to visualize and what not to show on the screen? And in this paper, we can witness a new way of visualizing velocity and vorticity fields. And this visualization happens through clapsh maps. This is a mathematical transformation where we create a sphere and a set of points on this sphere correspond to vortex lines and their evolution over time. However, if instead of only points, we pick an entire region on this sphere, as you can see the north and south pole regions here, we obtain vortex tubes. These vortex tubes provide an accurate representation of the vorticity information within the simulation, and this is one of the rare cases where the validity of such a solution can also be shown. Such a crazy idea, loving it. And with this, we can get a better understanding of the airflow around the wings of the hummingbird, but we can also learn more from pre-existing NASA aircraft data sets. Have a look at these incredible results. Publishing a paper at the CIGARF conference is an incredible feat that typically takes a few brilliant guys and several years of unbelievably hard work. Well, apparently this is not such a challenge for Albert Churn, who was also the first author of this and the Schrodinger smoke paper just a year ago that we reported on. He's doing incredible work at taking a piece of mathematical theory and showing remarkable applications of it in new areas where we would think it doesn't belong at all. The link is available in the video description, both for this and the previous works, make sure to have a look. There's lots of beautifully written mathematics to be read there that seems to be from another world. It's a truly unique experience. The paper reports that the source code is also available, but I was unable to find it yet. If you have found a public implementation, please let me know and I'll update the video description with your link. Thanks for watching and for your generous support and I'll see you next time.