Outer planet mission guidance and navigation for spinning spacecraft

The orbit determination accuracies, maneuver results, and navigation system specification for spinning Pioneer planetary probe missions are analyzed to aid in determining the feasibility of deploying probes into the atmospheres of the outer planets. Radio-only navigation suffices for a direct Saturn mission and the Jupiter flyby of a Jupiter/Uranus mission. Saturn ephemeris errors (1000 km) plus rigid entry constraints at Uranus result in very high velocity requirements (140 m/sec) on the final legs of the Saturn/Uranus and Jupiter/Uranus missions if only Earth-based tracking is employed. The capabilities of a conceptual V-slit sensor are assessed to supplement radio tracking by star/satellite observations. By processing the optical measurements with a batch filter, entry conditions at Uranus can be controlled to acceptable mission-defined levels (+ or - 3 deg) and the Saturn-Uranus leg velocity requirements can be reduced by a factor of 6 (from 139 to 23 m/sec) if nominal specified accuracies of the sensor can be realized

Crossing Patterns in Nonplanar Road Networks

We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross each other. In this paper, we study the sparsity properties of crossing graphs of real-world road networks. We show that, in large road networks (the Urban Road Network Dataset), the crossing graphs have connected components that are primarily trees, and that the remaining non-tree components are typically sparse (technically, that they have bounded degeneracy). We prove theoretically that when an embedded graph has a sparse crossing graph, it has other desirable properties that lead to fast algorithms for shortest paths and other algorithms important in geographic information systems. Notably, these graphs have polynomial expansion, meaning that they and all their subgraphs have small separators.Comment: 9 pages, 4 figures. To appear at the 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems(ACM SIGSPATIAL 2017

Hidden supersymmetry of domain walls and cosmologies

We show that all domain-wall solutions of gravity coupled to scalar fields for which the worldvolume geometry is Minkowski or anti-de Sitter admit Killing spinors, and satisfy corresponding first-order equations involving a superpotential determined by the solution. By analytic continuation, all flat or closed FLRW cosmologies are shown to satisfy similar first-order equations arising from the existence of ``pseudo-Killing'' spinors.Comment: 4 pages, v2:minor improvements, refs added, version to appear in PR