The three-dimensional shape and relative depth of a smoothly curving layered transparent surface may be communicated particularly effectively when the surface is artistically enhanced with sparsely distributed opaque detail. This paper describes how the set of principal directions and principal curvatures specified by local geometric operators can be understood to define a natural "flow " over the surface of an object, and can be used to guide the placement of the lines of a stroke texture that seeks to represent 3D shape information in a perceptually intuitive way. The driving application for this work is the visualization of layered isovalue surfaces in volume data, where the particular identity of an individual surface is not generally known a priori and observers will typically wish to view a variety of different level surfaces from the same distribution, superimposed over underlying opaque structures. By advecting an evenly distributed set of tiny opaque particles, and the empty space between them, via 3D line integral convolution through the vector field defined by the principal directions and principal curvatures of the level surfaces passing through each gridpoint of a 3D volume, it is possible to generate a

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This report is to acquaint the reader with spacecraft electronic systems failures and anomalies caused by electromagnetic interference (EMI), show the importance of electromagnetic compatibility (EMC) activities in conjunction with space flight programs, and provide an investigation into the history of some well-known EMI system failures and anomalies in military and commercial electronic systems. Military and commercial systems are included due to the limited number of in-flight spacecraft failures and anomalies attributed to EMI that have occurred on National Aeronautics and Space Administration (NASA) programs. The inclusion of nonspace systems also helps to illustrate that evolving electronic systems are increasingly sensitive to EMI and NASA personnel must continue to be diligent in the pursuit of EMC on space flight systems

this report would not have been possible for the team to accomplish in the allotted time without the help of several people. The Biomimetics Team would like to acknowledge significant contributions made by several individuals across the Competencies here at Langley Research Center

This White Paper examines the current state of Hypersonic Airbreathing Propulsion at the NASA Langley Research Center and the factors influencing this area of work and its personnel. Using this knowledge, the paper explores beyond the present day and suggests future directions and strategies for the field. Broad views are first taken regarding potential missions and applications of hypersonic propulsion. Then, candidate propulsion systems that may be applicable to these missions are suggested and discussed. Design tools and experimental techniques are then described, and approaches for applying them in the design process are considered. In each case, current strategies are reviewed and future approaches that may improve the techniques are considered. Finally, the paper addresses needs in each of these areas to take advantage of the opportunities that lay ahead for both the NASA Langley Research Center and the Aerodynamic, Aerothermodynamic, and Aeroacoustics Competency.

Graph embedding techniques for bounding eigenvalues of associated matrices have a wide range of applications. The bounds produced by these techniques are not in general tight, however, and may be off by a log 2 n factor for some graphs. Guattery and Miller showed that, by adding edge directions to the graph representation, they could construct an embedding called the current flow embedding, which embeds each edge of the guest graph as an electric current flow in the host graph. They also showed how this embedding can be used to construct matrices whose nonzero eigenvalues had a one-to-one correspondence to the reciprocals of the eigenvalues of the generalized Laplacians. For the Laplacians of graphs with zero Dirichlet boundary conditions, they showed that the current flow embedding could be used generate thc inverse of the matrix. In this paper, we generalize the definition of graph embeddings to cover all symmetric matrices, and we show a way of computing a generalized current flow embedding. We prove that, for any symmetric matrix A, the generalized current flow embedding of the orthogonal projector for the column space of A into A can be used to construct the generalized inverse, or pseudoinverse, of A. We also show how these results can bc extended to cover Hermitian matrices.