Faculty Research Talks - Fall 2020

Professor Yuan-Nan Young

Where is the Math in Fluid Mechanics and Biology?

Life on earth happens in fluid, and after millions of years of evolution we humans are organisms that (1) consist of mostly water,  (2) rely on water for food and basic survival, and (3) I would argue that human beings need to know fluid mechanics to advance as a species. Trained as a theoretical physicist in fluid mechanics and dynamics, I want to take this opportunity to show you some interesting math in fluid mechanics and biology from the viewpoints of applied math and physics.

Professor Cyrill Muratov

Magnetic Skyrmions in the Conformal Limit

We characterize skyrmions in ultrathin ferromagnetic films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction. The minimization is carried out in a suitable class of two-dimensional magnetization configurations that prevents the energy from going to negative infinity, while not imposing any restrictions on the spatial scale of the configuration. We first demonstrate existence of minimizers for an explicit range of the model parameters when the energy is dominated by the exchange energy. We then investigate the conformal limit, in which only the exchange energy survives and identify the asymptotic profiles of the skyrmions as degree 1 harmonic maps from the plane to the sphere, together with their radii, angles and energies. A byproduct of our analysis is a quantitative rigidity result for degree ±1 harmonic maps from the two-dimensional sphere to itself.

Professor Enkeleida Lushi

Active and Driven Particles at the Micro-Scale

Recent advances in chemistry and engineering have made possible the synthesis of micro-scale particles that can move and rotate. These active particles can be rendered motile by a surface catalysis with a chemical dispersed in the immersing medium, or can be driven by external stimuli such as light, acoustics or electromagnetic fields. I will discuss a few examples of such "micro-robots" and the recent efforts made to control and direct their individual and collective behavior. In particular we will focus on how Mathematics and Scientific Computing can help in understanding the dynamics seen in experiments. The two types of active particles we'll discuss in detail are bi-metallic swimmers and driven spinning particles. In both cases, we'll explain the full models, any simplified models and what they can elucidate, as well as full simulations. Lastly, I will discuss our recent work where experiments, analysis and simulations converged to understand new phenomena, and will highlight some new problems. 

Cancelled

Professor Amitabha Bose

Towards a Neural and Mathematical Understanding of How We Generate and Keep a Musical Beat

While many people say they have no rhythm, most humans when listening to music can easily discern and move to a beat. On the other hand, many of us are not so adept at actually generating and maintaining a constant beat over a period of time. Demonstrating a beat is a very complicated task. Among other things, it involves the ability of our brains to estimate time intervals and to make physical movements, for example hitting a drum, in coordination with the time estimates that we make. How our brain and body solves this problem is an open and active area of research. In this talk, I will discuss a new mathematical model for a beat generator, which is defined here as a group of neurons that can learn to keep a constant beat across a range of frequencies relevant to music. The goal of the talk is not just to introduce a new way of thinking of beat generation, but also to raise a series of questions about the nature of time and the role of perception in our ability to make decisions.