Title: Hydrodynamics of Ciliary Swimming

Abstract:

Planktonic microorganisms are ubiquitous in water, and their population dynamics are essential for forecasting the behavior of global aquatic ecosystems. Their population dynamics are strongly affected by these organisms’ motility, which is generated by their hair-like organelles, called cilia or flagella. However, because of the complexity of ciliary dynamics, the precise role of ciliary flow in microbial life remains unclear.

In terms of fluid dynamics, ciliary swimming has been analyzed by using a squirmer model. A classical squirmer model propels itself by generating surface tangential and radial velocities. Recently, we developed a novel squirmer model in which, instead of a velocity being imposed on the cell surface, a shear stress is applied to the fluid on a stress shell placed slightly above the cell body. The shear stress expresses the thrust force generated by cilia, and the fluid must satisfy the no-slip condition on the cell body surface. The stress squirmer model has been successful in reproducing experimentally observed cell-cell interactions and cell-wall interactions.

In order to understand swimming energetics, we further developed a ciliate model incorporating the distinct ciliary apparatus. The hairy squirmer model revealed that over 90% of energy is dissipated inside the ciliary envelope. By using the hairy squirmer model, we found that there exists an optimal number density of cilia, which provides the maximum propulsion efficiency for all ciliates. The propulsion efficiency in this case decreases inversely proportionally to body length. Our estimated optimal density of cilia corresponds to those of actual microorganisms, including species of ciliates and microalgae, which suggests that now-existing motile ciliates and microalgae may have survived by acquiring the optimal propulsion efficiency.

Math club will meet this Thursday (March 9) at 5PM in Keller 303. There will be free pizza and soda. If you wish to attend, please RSVP at the discord group (contact Prof. Lodha for the link)..

The speaker is Dr. Samantha Schumacher who is a Mathematician at Target.

Title: Machine Learning & Artificial Intelligence for Product Availability at Target

Abstract: In this casual talk, we’ll talk about my semi-bizarre mathematical background and the non-linear path that got me into Supply Chain at Target. I will share how a direct application of ML and AI on my team is leading to extraordinary outcomes for Target’s Product Availability. I also want to offer some resume & application advice for those interested in a mathematical career in industry, particularly in retail. Because the direct path looks great on paper, but sometimes the meandering path can provide critical skills for future success.

Title: Free resolutions of projective curves

Abstract: I will give an introduction to a circle of ideas lying at the intersection of commutative algebra and algebraic geometry concerning the influence of geometry on algebraic gadgets called free resolutions. Specifically, I’ll discuss a landmark 1984 theorem in this direction due to Mark Green, along with a recent generalization of this result due to myself and Daniel Erman.

Title: Simulating Rotating Detonation Rocket Engines

Abstract: Most rocket engines are designed to avoid the formation of detonation waves, due to the tendency of such waves to cause damage inside the engine. However, incorporating detonations into rocket design has the potential to improve engine performance — rotating detonation rocket engines aim to harness this potential, but the associated rapid fluctuations in temperature and pressure make the devices difficult to analyze experimentally. These challenges increase the importance of models that are capable of reproducing and explaining the large-scale behavior that can be observed in experiments. We use a series of simulations to explore how changing nozzle geometries affects detonation dynamics inside the combustion chamber, and show that the simulations capture experimentally-observed wave behavior. The simulations further demonstrate that, although the addition of a nozzle increases engine thrust, the changes in engine behavior can be detrimental to overall engine performance.