Talks will be held at 2:30PM on every other Monday (M) at 2:30PM via WebEx unless otherwise noted. Please see more information below:

Date

Speaker, Title, and Abstract

September 21

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.

October 5

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.