Numerics and optimal control of phase-field models for multiphase flow

Lunari A. Numerics and optimal control of phase-field models for multiphase flow. Bielefeld: Universität Bielefeld; 2018.The thesis is organized in two main parts. In the first part, the distributed optimal control problem of the non-smooth Cahn-Hilliard-Stokes system is considered, assuming that the homogeneous free energy density in the Cahn-Hilliard equations corresponds to the double-obstacle potential. The analysis is performed at continuous level and by a finite dimensional approach. Numerical experiments are displayed. In the second part, the distributed optimal control problem of the smooth Cahn-Hilliard-Navier-Stokes system is studied. In this case the homogeneous free energy density is equal to the double-well potential. This problem is analyzed considering infinite dimensional settings and a discrete approach. Significant numerical experiments are proposed

Test particle motion in a gravitational plane wave collision background

Test particle geodesic motion is analysed in detail for the background spacetimes of the degenerate Ferrari-Ibanez colliding gravitational wave solutions. Killing vectors have been used to reduce the equations of motion to a first order system of differential equations which have been integrated numerically. The associated constants of the motion have also been used to match the geodesics as they cross over the boundary between the single plane wave and interaction zones.Comment: 11 pages, 6 Postscript figure

Neutrino current in a gravitational plane wave collision background

The behaviour of a massless Dirac field on a general spacetime background representing two colliding gravitational plane waves is discussed in the Newman-Penrose formalism. The geometrical properties of the neutrino current are analysed and explicit results are given for the special Ferrari-Ibanez solution.Comment: 17 pages, 6 Postscript figures, accepted by International Journal of Modern Physics