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We present an overview of some recent developments concerning the error analysis and adaptive mesh refinement of non-conforming discontinuous Galerkin (DG) finite element methods for the numerical solution of second-order PDEs with non-negative characteristic form. Here, we shall be particularly concerned with the derivation of a priori and a posteriori… (More)

Self-Organised Criticality (SOC), embedded in cellular automata models, has been so far viewed as an attractive phenomenological approach for studying the statistical behaviour of flaring activity in solar active regions. Well-known statistical properties of flares, like the robust scaling laws seen in the distribution functions of characteristic parameters… (More)

Cellular automata (CA) models account for the power-law distributions found for solar flare hard X-ray observations, but their physics has been unclear. We examine four of these models and show that their criteria and magnetic field distribution rules can be derived by discretizing the MHD diffusion equation as obtained from a simplified Ohm's law.… (More)

We investigate the statistical properties of possible magnetic discontinuities in two solar active regions over the course of several hours. We use linear force-free extrapolations to calculate the three-dimensional magnetic structure in the active regions. Magnetic discontinuities are identified using various selection criteria. Independently of the… (More)

We self-consistently derive the magnetic energy and relative magnetic helic-ity budgets of a three-dimensional linear force-free magnetic structure rooted in a lower boundary plane. For the potential magnetic energy we derive a general expression that gives results practically equivalent to those of the magnetic Virial theorem. All magnetic energy and… (More)

Intermittent magnetohydrodynamical turbulence is most likely at work in the magnetized solar atmosphere. As a result, an array of scaling and multi-scaling image processing techniques can be used to measure the expected self-organization of solar magnetic fields. While these techniques advance our understanding of the physical system at work, it is unclear… (More)

- Markus J. Aschwanden, Norma B. Crosby, +9 authors Vadim Uritsky
- 2015

Shortly after the seminal paper " Self-Organized Criticality: An explanation of 1/f noise " by Bak et al. (1987), the idea has been applied to solar physics, in " Avalanches and the Distribution of Solar Flares " by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place,… (More)

It has been proposed that flares in the solar corona may well be a result of an internal self-organized critical (SOC) process in active regions. We have developed a cellular automaton SOC model that simulates flaring activity extending over an active subflaring background. In the resulting frequency distributions we obtain two distinct power laws. That of… (More)

The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent… (More)

The formation and evolution of active regions are inherently complex phenomena. Magnetic fields generated at the base of the convection zone follow a chaotic evolution before reaching the solar surface. In this article, we use a two-dimensional probabilistic cellular automaton to model the statistical properties of the magnetic patterns formed on the solar… (More)