Applied Math Seminar

Stability of (steady) pipe flow is a classical problem in fluid mechanics that dates back to Reynolds' experiments done in 1883. Although one can easy find a solution to the governing equations (the Navier--Stokes equations)---the parabolic velocity profile---this solution can be, in a real experiment, observed only for certain values of the Reynolds number. If the Reynolds number is higher that a certain critical value, the unidirectional laminar flow ceases to exist and the flow becomes "turbulent". The question is to find the value of the critical Reynolds number that marks transition from laminar to turbulent flow and (maybe equivalently) loss of stability of the laminar flow. In the first part of the talk I will discuss several classical approaches to the problem and their limitations, and then I will present some new results concerning (mainly) the oscillating pipe flow. At the end I will briefly comment some promising recent approaches to the problem that are based on "numerical experiments", and that call for more rigorous mathematical treatment.

Perceptual decision making, an omnipresent component of everyday life, plays a pivotal role in cognitive tasks. In this presentation, I will talk about mechanisms underlying simple two-option perceptual decision making processes by studying a biological-realistic reduced two-variable model and phenomenological drift-diffusion models.