Georgia Institute of Technology College of Sciences

The Reynolds number (Re) is often used to describe scaling effects in fluid dynamics and may be thought of as roughly describing the ratio of inertial to viscous forces in the fluid. It can be shown that ’reciprocal’ methods of macroscopic propulsion (e.g. flapping, undulating, and jetting) do not work in the limit as Re approaches zero. However, such macroscopic forms of locomotion do not appear in nature below Re on the order of 1 − 10. Similarly, macroscopic forms of feeding do not occur below a similar range of Reynolds numbers. The focus of this presentation is to describe the scaling effects in feeding and swimming of the upside down jellyfish (Cassiopeia sp.) using computational fluid dynamics and experiments with live animals. The immersed boundary method is used to solve the Navier-Stokes equations with an immersed, flexible boundary. Particle image velocimetry is used to quantify the flow field around the live jellyfish and compare it to the simulations.

I will discuss a conjecture that relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement. I will present examples, as well as computational challenges.

How do animals move without legs? In this experimental and theoretical study, we investigate the slithering of snakes on flat surfaces. Previous studies of slithering have rested on the assumption that snakes slither by pushing laterally against rocks and branches. In this combined experimental and theoretical study, we develop a model for slithering locomotion by observing snake motion kinematics and experimentally measuring the friction coefficients of snake skin. Our predictions of body speed show good agreement with observations, demonstrating that snake propulsion on flat ground, and possibly in general, relies critically on the frictional anisotropy of their scales. We also highlight the importance of the snake's dynamically redistributing its weight during locomotion in order to improve speed and efficiency. We conclude with an overview of our experimental observations of other methods of propulsion by snakes, including sidewinding and a unidirectional accordion-like mode.

We will state Serre's fundamental finiteness and vanishing results for the cohomology of coherent sheaves on a projective algebraic variety. As an application, we'll prove that the constant term of the Hilbert Polynomial does not depend on the projective embedding, a fact which is hard to understand using classical (non-cohomological) methods.