The goals of the research were the following: (1) To investigate the accretion of matter onto rottating magnetized stars from ionized discs due to the magneto-rotational instability (MRI) driven turbulence;  (2) To  investigate the MRI driven accretion onto a star with a weak magnetic field; (3) To investigate theoretically and with MHD simulations possible instabilities of the disc/magnetosphere boundary; and (4) To compare the light curves and speccttra obtained from our simulations with those observed in different Classical T-Tauri Stars (CTTS).

   Our main results from this research include the following works:

(1) `` MRI-driven accretion on to magnetized stars: axisymmetric MHD simulations,'' 2011, MNRAS, 416, pp. 416-438.  We present the first results of a global axisymmetric simulation of accretion on to rotating magnetized stars from a turbulent accretion disc, where the turbulence is driven by the magnetorotational instability (MRI). We observed that the angular momentum is transported outwards by the magnetic stress and accretion rate corresponds to a Shakura-Sunyaev viscosity parameter α≈ 0.01-0.04. The disc is stopped by the magnetic pressure of the magnetosphere, and matter flows on to the star in funnel streams, which usually choose a path along top or bottom side of the magnetosphere. c, and that it slowly expands outwards, driven by the magnetic force.

(2) ``MRI-driven accretion on to magnetized stars: global 3D MHD simulations of magnetospheric and boundary layer regimes,''  2012, MNRAS, 421, pp. 63-77.  We discuss results of global three-dimensional magnetohydrodynamic simulations of accretion on to a rotating magnetized star with a tilted dipole magnetic field, where the accretion is driven by the magnetorotational instability (MRI). The simulations show that MRI-driven turbulence develops in the disc, and angular momentum is transported outwards primarily due to the magnetic stress. The turbulent flow is strongly inhomogeneous and the densest matter is in azimuthally stretched turbulent cells. We investigate two regimes of accretion: a magnetospheric regime and a boundary layer (BL) regime.

(3) ``Magnetic launching and collimation of jets from the disc-magnetosphere boundary: 2.5D MHD simulations,''  2012, MNRAS, 420, pp. 2020-2033. We use axisymmetric magnetohydrodynamic simulations to investigate the launching and collimation of jets emerging from the disc-magnetosphere boundary of accreting magnetized stars. Our analysis shows that the matter flows into the jet from the inner edge of the accretion disc. It is magnetically accelerated along field lines extending up from the disc and simultaneously collimated by the magnetic pinch force.

(4) ``Spectral variability of classical T Tauri stars accreting in an unstable regime,''  2013, MNRAS, 431, pp. 2673-2689.   Classical T Tauri stars (CTTSs) are variable in different time-scales. One type of variability is possibly connected with the accretion of matter through the Rayleigh-Taylor instability that occurs at the interface between an accretion disc and a stellar magnetosphere. In this regime, matter accretes in several temporarily formed accretion streams or `tongues' which appear in random locations, and produce stochastic photometric and line variability. We use the results of global three-dimensional magnetohydrodynamic simulations of matter flows in both stable and unstable accretion regimes to calculate time-dependent hydrogen line profiles and study their variability behaviours. In the stable regime, some hydrogen lines (e.g. Hβ, Hγ, Hδ, Paβ and Brγ) show a redshifted absorption component only during a fraction of a stellar rotation period, and its occurrence is periodic. However, in the unstable regime, the redshifted absorption component is presen...

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