A Solenoidal Finite Element Approach for Prediction of Radar Cross Sections

This report considers the solution of problems that involve the scattering of plane electromagnetic waves by perfectly conducting obstacles. Such problems are governed by the Maxwell equations. An interesting facet of the solution of Faraday's law and Ampere's law, which on their own form a complete equation set for the determination of the field intensity components, is that there are the additional conservation statements of Coulomb's law and Gauss's law, which appear to be in excess of requirements. Often, these additional constraints are neglected due to an inability to incorporate them into the solution scheme. With the successful development of a solenoidal finite element for the solution of viscous incompressible flows, such a device now offers a practical means for the solution of the full Maxwell equations. To demonstrate the validity of this assertion, a suitable solution scheme is presented, accompanied by sample results for various test problems

Simulation capability for dynamics of two-body flexible satellites

An analysis and computer program were prepared to realistically simulate the dynamic behavior of a class of satellites consisting of two end bodies separated by a connecting structure. The shape and mass distribution of the flexible end bodies are arbitrary; the connecting structure is flexible but massless and is capable of deployment and retraction. Fluid flowing in a piping system and rigid moving masses, representing a cargo elevator or crew members, have been modeled. Connecting structure characteristics, control systems, and externally applied loads are modeled in easily replaced subroutines. Subroutines currently available include a telescopic beam-type connecting structure as well as attitude, deployment, spin and wobble control. In addition, a unique mass balance control system was developed to sense and balance mass shifts due to the motion of a cargo elevator. The mass of the cargo may vary through a large range. Numerical results are discussed for various types of runs

Water separator

An apparatus for separating liquids from gases or gaseous fluids is described. Features of the apparatus include: (1) the collection and removal of the moisture in the fluid is not dependent upon, or affected by gravity; (2) all the collected water is cyclically drained from the apparatus irrespective of the attitude of the separator; and (3) a fluid actuator is utilized to remove the collected water from the separator

Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures

The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factorization. It has been used in traditional high performance computing and grid computing environments. For MapReduce environments, existing methods to compute the QR decomposition use a numerically unstable approach that relies on indirectly computing the Q factor. In the best case, these methods require only two passes over the data. In this paper, we describe how to compute a stable tall-and-skinny QR factorization on a MapReduce architecture in only slightly more than 2 passes over the data. We can compute the SVD with only a small change and no difference in performance. We present a performance comparison between our new direct TSQR method, a standard unstable implementation for MapReduce (Cholesky QR), and the classic stable algorithm implemented for MapReduce (Householder QR). We find that our new stable method has a large performance advantage over the Householder QR method. This holds both in a theoretical performance model as well as in an actual implementation

Perturbing forces in the lunar gravitational potential, part 3 Final report

Spherical harmonics for evaluating perturbing forces on lunar satellite due to nonsymmetric mass distribution of moo

Tensor Spectral Clustering for Partitioning Higher-order Network Structures

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.Comment: SDM 201

Contamination cannot explain the lack of large-scale power in the cosmic microwave background radiation

Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP. One of these is a lack of large-scale power. Because the data otherwise match standard models extremely well, it is natural to consider perturbations of the standard model as possible explanations. We show that, as long as the source of the perturbation is statistically independent of the source of the primary CMB anisotropy, no such model can explain this large-scale power deficit. On the contrary, any such perturbation always reduces the probability of obtaining any given low value of large-scale power. We rigorously prove this result when the lack of large-scale power is quantified with a quadratic statistic, such as the quadrupole moment. When a statistic based on the integrated square of the correlation function is used instead, we present strong numerical evidence in support of the result. The result applies to models in which the geometry of spacetime is perturbed (e.g., an ellipsoidal Universe) as well as explanations involving local contaminants, undiagnosed foregrounds, or systematic errors. Because the large-scale power deficit is arguably the most significant of the observed anomalies, explanations that worsen this discrepancy should be regarded with great skepticism, even if they help in explaining other anomalies such as multipole alignments.Comment: 9 pages. Submitted to Phys. Rev.

RTCC requirements for mission G - Landing site determination using onboard observations, part 2 Final report

Computer programs for evaluation of telemetered rendezvous radar tracking data of orbiting command module and lunar module landing site determinatio