A new method simulates soap bubble collisions in milliseconds instead of seconds by using mean curvature flow instead of traditional fluid equations. The approach handles bubble splitting and merging, runs 3 to 20 times faster than previous methods, and matches real-world experiments.
Questions this video answers
February 25, 2018.
Approximately 10–800 nm.
Typically 3 to 20 times faster.
Computation times moved from seconds to the order of milliseconds.
Episode number 18.
Chapters
Dear fellow scholars, this is two minute papers with this paper is about simulating on a computer what happens when bubbles collide. Prepare for lots of beautiful footage. This is typically done by simulating the Navier Stokes equations that describe the evolution of the velocity within a piece of fluid over time. However, because the world around us is a continuum, we cannot compute these quantities in an infinite number of points. So we have to subdivide the 3D space into a grid and compute them only in these grid points. The finer the grid, the more details appear in our simulations. If we try to simulate what happens when these bubbles collide, we would need to create a grid that can capture these details. This is an issue because the thickness of a bubble film is in the order of 10-800nm and this would require a hopelessly fine, high resolution grid. By the way, measuring the thickness of bubbles is a science of its own. There is a fantastic Reddit discussion on it. I put a link to it in the video description. Make sure to check it out. So these overly fine grids take too long to compute. So what do we do? Well, first we need to focus on how to directly compute how the shape of soap bubbles evolves over time. Fortunately, from Belgian physicist Joseph Plateau, we know that they seek to reduce their surface area but retain their volume over time, one of the many beautiful phenomena in nature. So this shall be the first step. We simulate forces that create the appropriate shape changes and proceed into an intermediate state. However, by pushing the film inwards, its volume has decreased. Therefore, this intermediate state is not how it should look in nature. This is to be remedied now, where we apply a volume correction step. In the validation section, it is shown that the results follow Plateau's laws quite closely. Also, you know well that my favorite kind of validation is when we let reality be our judge. And in this work, the results have been compared to a real life experimental setup and proved to be very close to it. Take a little time to absorb this. We can write a computer program that reproduces what would happen in reality and result in lots of beautiful video footage. Loving it. And the best part is that the first surface evolution step is done through an effective implementation of the hyperbolic mean curvature flow, which means that the entirety of the process is typically 3 to 20 times faster than the state of the art, while being more robust in handling splitting and merging scenarios. The computation times are now in the order of milliseconds instead of seconds. The earlier work in this comparison was also showcased in two minute papers. If I see it correctly, it was in episode number 18. Holy mother of papers. How far we have come since I've put a link to it in the video description. The paper is beautifully written and there are plenty of goodies therein. For instance, an issue with non manifold junctions is addressed, so make sure to have a look. The source code of this project is also available. Thanks for watching and for your generous support and I'll see you next time.
