In the research field of heavy-ion collisions there are a bunch of interesting questions to be answered. Here we address two of them.

The first is about the transition from a hydrodynamical modelling to a particle-based approach. This transition is a crucial element of the description of ultra-relativistic heavy- ion collisions. By employing kinetic theory within polar Milne coordinates and anisotropic hydrodynamical tools, we show that an anisotropic local phase-space distribution of the emitted particles can smooth such a transition. In addition we derive the so called anisotropy parameter from a kinetic description. We discuss how final state observables – within this new freeze out procedure – depend less on system’s quantities at the freeze out surface.

Further we present a way how our procedure of the kinetic freeze out can be further improved, via incorporating the effect of interparticle interactions. Therefore we present the arising equations of motion which were obtained by the computation of the various moments.

The second question we are addressing is dealing with the investigation of two-particle distributions. We present studies which are essential for investigating the azimuthally dependent two-particle distributions. Therefore we continued the concept of one-particle azimuthally distributions to the case of two-particle observables. Afterward we present a model to incorporate the fluctuations of one-particle distributions, in order to not mix up the effect of one-particle fluctuations and two-particle correlations.