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# ACMD Seminar: Membrane Mechanics Meet Minimal Manifolds

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Leroy  Jia*Flatiron Research Fellow, Flatiron Institute's Center for Computational Biology*

**Wednesday**, February 15, 2023, 3:00-4:00 PM ET (1:00-2:00 PM MT)

**A video of this talk will be made available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page. It will be taken down from NISTube after 12 months at which point it can be requested by emailing the ACMD Seminar Chair.**

**Abstract**: A time-honored problem in mathematical physics is to show that an area-minimizing fluid interface such as a soap film forms a special surface whose mean curvature vanishes. In the axisymmetric setting, this surface is called a catenoid. We recap Euler's original solution to the catenoid problem and then proceed to discuss a generalization of this problem where the fluid interface is replaced by a membrane with a bending stiffness. The shapes that such a membrane can make, which are critical surfaces of an energy called the Willmore functional, are intimately related to the catenoid and also to the shapes of a compressed rod (i.e., the elastica) in a precise mathematical way that informs us about their mechanics.

**Bio:** Dr. Leroy Jia is a Flatiron Research Fellow in the Biophysical Modeling Group at the Flatiron Institute's Center for Computational Biology. He works on the applied analysis and geometry of soft, fluid, and active matter systems. Prior to his current appointment, he studied physics and mathematics at the Georgia Institute of Technology and obtained a Ph.D. in applied mathematics from Brown University under the supervision of Profs. Thomas Powers (Engineering & Physics) and Robert Pelcovits (Physics).

**Host:** Paul Patrone

**Note**: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

**Note**: Visitors from outside NIST must contact Lochi Orr (301) 975-3800; at least 24 hours in advance.

Mathematics and statistics

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                -  Paul Patrone  paul.patrone@nist.gov      (301) 975-5551   
                -  Zachary Grey  zachary.grey@nist.gov      (303) 497-5920   
                -  Lochi Orr  lochi.orr@nist.gov      (410) 598-6986   

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