Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

High-Fidelity Gravity Modeling Applied to Spacecraft Trajectories and Lunar Interior Analysis

As the complexity and boldness of emerging mission proposals increase, and with the rapid evolution of the available computational capabilities, high-accuracy and high-resolution gravity models and the tools to exploit such models are increasingly attractive within the context of spaceflight mechanics, mission design and analysis, and planetary science in general. First, in trajectory design applications, a gravity representation for the bodies of interest is, in general, assumed and exploited to determine the motion of a spacecraft in any given system. The focus is the exploration of trajectories in the vicinity of a system comprised of two small irregular bodies. Within this context, the primary bodies are initially modeled as massive ellipsoids and tools to construct third-body trajectories are developed. However, these dynamical models are idealized representations of the actual dynamical regime and do not account for any perturbing effects. Thus, a robust strategy to maintain a spacecraft near reference third-body trajectories is constructed. Further, it is important to assess the perturbing effect that dominates the dynamics of the spacecraft in such a region as a function of the baseline orbit. Alternatively, the motion of the spacecraft around a given body may be known to extreme precision enabling the derivation of a very high-accuracy gravity field for that body. Such knowledge can subsequently be exploited to gain insight into specific properties of the body. The success of the NASA\u27s GRAIL mission ensures that the highest resolution and most accurate gravity data for the Moon is now available. In the GRAIL investigation, the focus is on the specific task of detecting the presence and extent of subsurface features, such as empty lava tubes beneath the mare surface. In addition to their importance for understanding the emplacement of the mare flood basalts, open lava tubes are of interest as possible habitation sites safe from cosmic radiation and micrometeorite impacts. Tools are developed to best exploit the rich gravity data toward the numerical detection of such small features