IFS Seminar

Abstract: 

We study the equilibrium temperature distribution in a model for strongly magnetized plasmas in dimension two and higher. Provided the magnetic field is sufficiently structured (integrable in the sense that it is fibered by co-dimension one invariant tori, on most of which the field lines ergodically wander) and the effective thermal diffusivity transverse to the tori is small, it is proved that the temperature distribution is well approximated by a function that only varies across the invariant surfaces. The same result holds for "nearly integrable" magnetic fields up to a "critical" size. In this case, a volume of non-integrability is defined in terms of the temperature defect distribution and related to the non-integrable structure of the magnetic field, confirming a physical conjecture of Paul-Hudson-Helander.

 

Brief Bio:

Hezekiah Grayer II is a sixth year graduate student in the Program in Applied and Computational Mathematics (PACM) at Princeton University, advised by Peter Constantin. His research interests intersect nonlinear dynamics, partial differential equations, mathematical analysis and plasma physics.