Dr. Catherine Drysdale “From Fluid Mechanics to the HPA Axis: Exploring Non-self-adjoint systems”

This talk is about non-self-adjoint systems using analytical and numerical
techniques. We study the non-self-adjoint Ginzburg Landau equation and
why common weakly nonlinear analysis techniques fail. By using
pseudospectra and the quasi-basis structure that arose, it is possible to
give insight into the failure of weakly nonlinear expansions.
We will then look at the process of pseudospectra certification.
Pseudospectral certification in this context is the verification process that
tells us that the pseudospectra of an infinite-dimensional, unbounded
operator is the same as the pseudospectra of the projection of the operator
on a finite number of modes, i.e. the projection that we do to put the
operator into the computer. The latter works is to computer the pseudospectra for two equations that model the HPA (hyperthalamus- pituitary-adrenal) axis and answer questions regarding what types of perturbations cause misalignment in the hormonal rhythms of the HPA axis.