Deeply virtual Compton scattering in a relativistic quark model

This thesis is mainly concerned with a model calculation for generalized parton distributions (GPDs). We calculate vectorial- and axial GPDs for the N N and N Delta transition in the framework of a light front quark model. This requires the elaboration of a connection between transition amplitudes and GPDs. We provide the first quark model calculations for N Delta GPDs. The examination of transition amplitudes leads to various model independent consistency relations. These relations are not exactly obeyed by our model calculation since the use of the impulse approximation in the light front quark model leads to a violation of Poincare covariance. We explore the impact of this covariance breaking on the GPDs and form factors which we determine in our model calculation and find large effects. The reference frame dependence of our results which originates from the breaking of Poincare covariance can be eliminated by introducing spurious covariants. We extend this formalism in order to obtain frame independent results from our transition amplitudes.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.