Quasinormal mode spectra for gravitational perturbations of black holes in four dimensional de Sitter and anti-de Sitter space are investigated. The de Sitter case lends itself to approximation by a Pöshl-Teller potential. The anti-de Sitter case is relevant to the ADS-CFT correspondence in superstring theory. The ADS-CFT correspondence suggests a prefered set of boundary conditions.
We investigate the geometrical properties of avalanches in self-organized critical models of solar flares. Traditionally, such models differ from the classical sandpile model in their formulation of stability criteria in terms of the curvature of the nodal field, and belong to a distinct universality class. With a view toward comparing these properties to those inferred from spatially and temporally resolved flare observations, we consider the properties of avalanche peak snapshots, time-integrated avalanches in two and three dimensions, and the two-dimensional projections of the latter. The nature of the relationship between the avalanching volume and its projected area is an issue of particular interest in the solar flare context. Using our simulation results we investigate this relationship, and demonstrate that proper accounting of the fractal nature of avalanches can bring into agreement hitherto discrepant results of observational analyses based on simple, nonfractal geometries for the flaring volume.
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