A statistical analysis of Electromagnetic Ion Cyclotron (EMIC) waves and their correlation to the 11-year solar cycle

This thesis presents a statistical analysis of EMIC waves measured at Halley Research Station from 2008 through 2012. An introduction covering the origin of and theory behind EMIC waves is provided, along with a background covering previous statistical research regarding EMIC waves. Guidelines regarding EMIC wave definition and analysis are described along with examples of how they were used. The data shows an increase in the total number of EMIC waves as well as the number and percentage of EMIC waves with maximum frequency above 1 Hz during the 5-year period. The results suggest that the total number of EMIC waves and the proportion of EMIC waves with maximum frequency above 1 Hz increase with increasing solar activity. A future perspective in EMIC wave research is also provided

Infinity-Harmonic Potentials and Their Streamlines

We consider certain solutions of the Infinity-Laplace Equation in planar convex rings. Their ascending streamlines are unique while the descending ones may bifurcate. We prove that bifurcation occurs in the generic situation and as a consequence, the solutions cannot have Lipschitz continuous gradients.Comment: 21 pages; 1 pictur

Pointwise regularity of the free boundary for the parabolic obstacle problem

We study the parabolic obstacle problem \lap u-u_t=f\chi_{\{u>0\}}, \quad u\geq 0,\quad f\in L^p \quad \mbox{with}\quad f(0)=1 and obtain two monotonicity formulae, one that applies for general free boundary points and one for singular free boundary points. These are used to prove a second order Taylor expansion at singular points (under a pointwise Dini condition), with an estimate of the error (under a pointwise double Dini condition). Moreover, under the assumption that $f$ is Dini continuous, we prove that the set of regular points is locally a (parabolic) $C^1$-surface and that the set of singular points is locally contained in a union of (parabolic) $C^1$ manifolds