Applied Math Seminar- Geodesics in natural and man-made pneumatic structures
Fri, 15 December, 2023
3:00pm - 4:00pm
Speaker: Frank Baginski, GWU
Date and Time: 12/15/2023, 3pm-4pm
Place: Phillips 736
Title: Geodesics in natural and man-made pneumatic structures
Abstract: Geodesics arise in a myriad of applications. One reason might be the intrinsic nature of a geodesic curve. In this talk, we will provide a brief introduction to geodesics and some real world applications where
geodesics arise - high altitude balloons, aerodynamic decelerators, red blood cells, and the production of salami. We will focus on a particular pressurized structure, the {\em mylar balloon} and utilize its closed geodesics as a guide for a network of fibers to reinforce this membrane. To begin, we ask the question {\em what are the closed geodesics in a mylar balloon?} In 2006, Alexander proved a result that implied for the mylar balloon shape, if $n$ is the number of times a closed geodesic winds around the axis of rotation and $m$ is the number of times the geodesic crosses the equator, then $n/m \in (1/\sqrt{2}, 1]$. We will provide a simpler proof of this result,
extend the approach to Weingarten surfaces with $\kappa_1/\kappa_2 >0$, and present some examples to illustrate the result. Future research directions will be discussed. This is joint work with Valerio Ramos-Batista, Federal University of ABC, Brazil.
Title: Geodesics in natural and man-made pneumatic structures
Abstract: Geodesics arise in a myriad of applications. One reason might be the intrinsic nature of a geodesic curve. In this talk, we will provide a brief introduction to geodesics and some real world applications where
geodesics arise - high altitude balloons, aerodynamic decelerators, red blood cells, and the production of salami. We will focus on a particular pressurized structure, the {\em mylar balloon} and utilize its closed geodesics as a guide for a network of fibers to reinforce this membrane. To begin, we ask the question {\em what are the closed geodesics in a mylar balloon?} In 2006, Alexander proved a result that implied for the mylar balloon shape, if $n$ is the number of times a closed geodesic winds around the axis of rotation and $m$ is the number of times the geodesic crosses the equator, then $n/m \in (1/\sqrt{2}, 1]$. We will provide a simpler proof of this result,
extend the approach to Weingarten surfaces with $\kappa_1/\kappa_2 >0$, and present some examples to illustrate the result. Future research directions will be discussed. This is joint work with Valerio Ramos-Batista, Federal University of ABC, Brazil.