FYFD

Tag: optimization

  • Optimal Bubble Clusters

    Optimal Bubble Clusters

    With a bubble wand, it’s quite easy to create clusters of two or more soap bubbles. These clusters seem to instantly find the lowest energy state, forming a shape that minimizes the cluster’s surface area (including interior walls) for the volume of air they enclose. But mathematicians have struggled for thousands of years to prove that this is actually the case.

    In 1995, mathematician John Sullivan had a breakthrough conjecture, at least for some types of bubble clusters. A proof for double bubble clusters quickly followed. But then progress stalled out, with the triple bubble version seemingly out of reach. But now a duo of mathematicians have published proofs for Sullivan’s bubble clusters in triple and quadruple clusters. Learn their story over at Quanta. (Image credit: N. Franz; via Quanta Magazine)

  • Swimming Intermittently

    Swimming Intermittently

    Many fish do not swim continuously; instead, they use an intermittent motion, swimming in a sudden burst and then coasting. This intermittent swimming is tough to simulate, due to its unsteady nature, but a new study does so using some clever computational techniques.

    Animation showing a fish swimming in a burst-and-coast pattern.
    Animation showing a fish swimming in a burst-and-coast pattern.

    Researchers suspected that the energy intensity of a fish’s burst could be balanced by the low-drag, low-effort phase of coasting. And, indeed, that’s consistent with the team’s results. But they found that the swimming method does require careful optimization; with the wrong cadence, the burst-and-coast technique can be incredibly energy intensive. In nature, of course, fish have had millions of years to optimize their technique, but the results serve as a warning to those building fish-based robots. Those biorobots will need careful optimization to benefit from this swimming style. (Image credit: tetra – Adobe Stock Images, simulation – G. Li et al.; research credit: G. Li et al.; via APS Physics; submitted by Kam-Yung Soh)

  • Mixing Effectively

    Mixing Effectively

    Mixing two fluids is a tougher task than you might think. One of my favorite asides from a fluids lecture concerned how to mix fruit into yogurt in an industrial setting. Mix too quickly, and you’ll obliterate the yogurt’s consistency, but mix too little and you may as well sell it as fruit-on-the-bottom. Apparently that particular problem got solved by sending the fruit and yogurt flowing through a series of specially-shaped ducts to slowly and carefully mix them together.

    In this study, researchers tackle a similar problem — mixing two fluids in a circular cross-section — through optimization. As you can see above, circular stirrers on their own don’t do a great job of mixing. So the researchers searched for the right combination of stirrer shape, mixing speed, and mixing trajectory to give the best mixing for a set mixing time and energy input. Their final stirrer shapes are anything but circular and often move in jerks and fits to help shed vortices that do the actual job of mixing. (Image and research credit: M. Eggl and P. Schmid; via APS Physics)