Intersecting brane models and F-theory in six dimensions

We analyze six-dimensional supergravity theories coming from intersecting brane models on the toroidal orbifold T^4/Z_2. We use recently developed tools for mapping general 6D supergravity theories to F-theory to identify F-theory constructions dual to the intersecting brane models. The F-theory picture illuminates several aspects of these models. In particular, we have some new insight into the matter spectrum on intersecting branes, and analyze gauge group enhancement as branes approach orbifold points. These novel features of intersecting brane models are also relevant in four dimensions, and are confirmed in 6D using more standard Chan-Paton methods.Comment: 28 pages, 5 figures, added references, typos corrected, minor corrections. Version to appear in Nucl. Phys.

Navigation Constellation Design Using a Multi-Objective Genetic Algorithm

In satellite constellation design, performance and cost of the system drive the design process. The Global Positioning System (GPS) constellation is currently used to provide positioning and timing worldwide. As satellite technology has improved over the years, the cost to develop and maintain the satellites has increased. Using a constellation design tool, it is possible to analyze the tradeoffs of new navigation constellation designs (Pareto fronts) that illustrate the tradeoffs between position dilution of precision (PDOP) and system cost. This thesis utilized Satellite Tool Kit (STK) to calculate PDOP values of navigation constellations, and the Unmanned Spacecraft Cost Model (USCM) along with the Small Spacecraft Cost Model (SSCM) to determine system cost. The design parameters used include Walker constellation parameters, orbital elements, and transmit power. The results show that the constellation design tool produces realistic solutions. Using the generated solutions, an analysis of the navigation constellation designs was presented

Type IIA Orientifolds on General Supersymmetric Z_N Orbifolds

We construct Type IIA orientifolds for general supersymmetric Z_N orbifolds. In particular, we provide the methods to deal with the non-factorisable six-dimensional tori for the cases Z7, Z8, Z8', Z12 and Z12'. As an application of these methods we explicitly construct many new orientifold models.Comment: 48 pages, LaTeX, 14 figures, refs. added, closed string spectra slightly change

Global stability of steady states in the classical Stefan problem

The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of such steady states, assuming a sufficient degree of smoothness on the initial domain, but without any a priori restriction on the convexity properties of the initial shape. This is an extension of our previous result [28] in which we studied nearly spherical shapes.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1212.142