The problem of heating the solar corona requires the conversion of magnetic energy into thermal energy. Presently, there are two promising mechanisms for heating the solar corona: wave heating and nanoflare heating. In this thesis, we consider nanoflare heating only. Previous modelling has shown that the kink instability can trigger energy release and heating in large scale loops, as the field rapidly relaxes to a lower energy state under the Taylor relaxation theory. Two distinct experiments were developed to understand the coronal heating problem: the avalanche effect within a multiple loop system, and the importance of thermal conduction and optically thin radiation during the evolution of the kinked-unstable coronal magnetic field. The first experiment showed that a kink-unstable thread can also destabilise nearby threads under some conditions. The second experiment showed that the inclusion of thermal conduction and optically thin radiation causes significant change to the internal energy of the coronal loop. After the initial instability occurs, there is continual heating throughout the relaxation process. Our simulation results show that the data is consistent with observation values, and the relaxation process can take over 200 seconds to reach the final relaxed state. The inclusion of both effects perhaps provides a more realistic and rapid heating experiment compared to previous investigations.

No description available.

<p>Active Galactic Nuclei (AGNs) are accreting supermassive black holes at the center of galaxies, known for rich spectral features and multi-time scale variability in their electromagnetic emission. The origin of the variability in AGN light curves can be either intrinsic, meaning related processes that take place inside the AGN system, or extrinsic, i.e., from the propagation of light towards Earth. In this dissertation, I present my work focusing on AGN variability. The first two works focus on the variability of blazars, a subclass of AGN with their relativistic jets beaming towards the observer. The first work combines 3D relativistic magnetohydrodynamics (RMHD) simulations with radiation transfer and shows the kink instability within the blazar jet can cause quasi-periodic radiation signatures within a typical period of time scales from weeks to months. The second work combines 2D Particle-in-Cell (PIC) simulations with radiation transfer and shows that isolated and merging plasmoids due to magnetic reconnection in a blazar environment could produce rich radiation and polarization signatures. The last work explores an extrinsic origin for AGN variability: a scenario in which interstellar medium (ISM) within our galaxy can refract light coming from AGNs. It suggests that plasma structures in ISM with an axisymmetric geometry can account for extreme scattering events (ESEs) in AGN observations. Future research directions include studies of the kink instability in jets that propagate in different environments and simulations of magnetic reconnection in 3D which may reveal additional particle acceleration mechanisms, which may play important role in the resulting radiation and polarization signatures. </p>