Guest lectures and seminars - Page 36

I will discuss the question in the title. This is joint work with Alex Degtyarev and Ilia Itenberg. This will be a talk involving very classical topics in algebraic geometry. I will try to make the talk accessible to students at master- and PhD level.

QOMBINE seminar by Daniel Stilck Franca (ENS Lyon)

C*-algebra seminar talk by Pinhas Grossman (University of New South Wales)

The simulation of multi-phase fluids has attained growing interest in the last decades. While for single-phase flow with the Navier-Stokes system the basic model is well understood, for multi-phase systems additional challenges by the necessity to track the transition zones or interfaces between different fluid components arise. 
We propose to use a phase field as a smooth indicator function to describe this situation. Using phase-field models, one introduces a small layer of mixed fluids as a so-called diffuse interface. One benefit of phase-field models is, that they can naturally deal with topology changes and can easily be extended to cope with contact line dynamics.
This model allows for discussing the optimal control problem for two-phase flow. We introduce a thermodynamically consistent phase-field model for two-phase flow including a model for contact line dynamics and introduce an energy stable numerical scheme. 
This scheme allows us to investigate the time-discrete (open loop) optimal control problem, where we investigate different control actions to steer a given distribution of phases towards the desired distribution. We derive the existence of solutions to the optimal control problem and provide first-order optimality conditions.

Hybrid format via Zoom possible on demand (contact timokoch at uio.no)