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A new technique for projecting high-dimensional data to low-dimensional spaces, called locally linear embedding (LLE) has recently been introduced.
We demonstrate that nonlinear stochastic systems near criticality (including forced and self-organized criticality) will generally exhibit low-dimensional behavior. We give a connection between the fractal dimensions of finite-dimensional chaotic systems and the anomalous dimensions in stochastic systems near criticality. The effect of additional random noise on stochastic systems will be delineated in terms of the crossover phenomenon between competing criticalities. The possibility of observing such effects in space (such as the onset of substorms) and in the laboratory (such as stochastic particle heating in 'noisy' magnetic fields) will be discussed.
The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.
Topics covered include: Crew Activity Analyzer; Distributing Data to Hand-Held Devices in a Wireless Network; Reducing Surface Clutter in Cloud Profiling Radar Data; MODIS Atmospheric Data Handler; Multibeam Altimeter Navigation Update Using Faceted Shape Model; Spaceborne Hybrid-FPGA System for Processing FTIR Data; FPGA Coprocessor for Accelerated Classification of Images; SiC JFET Transistor Circuit Model for Extreme Temperature Range; TDR Using Autocorrelation and Varying-Duration Pulses; Update on Development of SiC Multi-Chip Power Modules; Radio Ranging System for Guidance of Approaching Spacecraft; Electromagnetically Clean Solar Arrays; Improved Short-Circuit Protection for Power Cells in Series; Electromagnetically Clean Solar Arrays; Logic Gates Made of N-Channel JFETs and Epitaxial Resistors; Improved Short-Circuit Protection for Power Cells in Series; Communication Limits Due to Photon-Detector Jitter; System for Removing Pollutants from Incinerator Exhaust; Sealing and External Sterilization of a Sample Container; Converting EOS Data from HDF-EOS to netCDF; HDF-EOS 2 and HDF-EOS 5 Compatibility Library; HDF-EOS Web Server; HDF-EOS 5 Validator; XML DTD and Schemas for HDF-EOS; Converting from XML to HDF-EOS; Simulating Attitudes and Trajectories of Multiple Spacecraft; Specialized Color Function for Display of Signed Data; Delivering Alert Messages to Members of a Work Force; Delivering Images for Mars Rover Science Planning; Oxide Fiber Cathode Materials for Rechargeable Lithium Cells; Electrocatalytic Reduction of Carbon Dioxide to Methane; Heterogeneous Superconducting Low-Noise Sensing Coils; Progress toward Making Epoxy/Carbon-Nanotube Composites; Predicting Properties of Unidirectional-Nanofiber Composites; Deployable Crew Quarters; Nonventing, Regenerable, Lightweight Heat Absorber; Miniature High-Force, Long-Stroke SMA Linear Actuators; "Bootstrap" Configuration for Multistage Pulse-Tube Coolers; Reducing Liquid Loss during Ullage Venting in Microgravity; Ka-Band Transponder for Deep-Space Radio Science; Replication of Space-Shuttle Computers in FPGAs and ASICs; Demisable Reaction-Wheel Assembly; Spatial and Temporal Low-Dimensional Models for Fluid Flow; Advanced Land Imager Assessment System; Range Imaging without Moving Parts.
The field of space physics has a long history of utilizing dimensionality reduction methods to distill data, including but not limited to spherical harmonics, the Fourier Transform, and the wavelet transform. Here, we present a technique for performing dimensionality reduction on ion counts distributions from the Multiscale Mission/Fast Plasma Investigation (MMS/FPI) instrument using a data-adaptive method powered by neural networks. This has applications to both feeding low-dimensional parameterizations of the counts distributions into other machine learning algorithms, and the problem of data compression to reduce transmission volume for space missions. The algorithm presented here is lossy, and in this work, we present the technique of validating the reconstruction performance with calculated plasma moments under the argument that preserving the moments also preserves fluid-level physics, and in turn a degree of scientific validity. The method presented here is an improvement over other lossy compressions in loss-tolerant scenarios like the Multiscale Mission/Fast Plasma Investigation Fast Survey or in non-research space weather applications.
When designing products, it is crucial to assure failure and risk-free operation in the intended operating environment. Failures are typically studied and eliminated as much as possible during the early stages of design. The few failures that go undetected result in unacceptable damage and losses in high-risk applications where public safety is of concern. Published NASA and NTSB accident reports point to a variety of components identified as sources of failures in the reported cases. In previous work, data from these reports were processed and placed in matrix form for all the system components and failure modes encountered, and then manipulated using matrix methods to determine similarities between the different components and failure modes. In this paper, these matrices are represented in the form of a linear combination of failures modes, mathematically formed using Principal Components Analysis (PCA) decomposition. The PCA decomposition results in a low-dimensionality representation of all failure modes and components of interest, represented in a transformed coordinate system. Such a representation opens the way for efficient pattern analysis and prediction of failure modes with highest potential risks on the final product, rather than making decisions based on the large space of component and failure mode data. The mathematics of the proposed method are explained first using a simple example problem. The method is then applied to component failure data gathered from helicopter, accident reports to demonstrate its potential.
Workers at NASA Ames Research center are endeavoring to develop durable, oxidation-resistant, foam thermal protection systems (TPSs) that would be suitable for covering large exterior spacecraft surfaces, would have low to moderate densities, and would have temperature capabilities comparable to those of carbon-based TPSs [reusable at 3,000 F (.1,650 C)] with application of suitable coatings. These foams may also be useful for repairing TPSs while in orbit. Moreover, on Earth as well as in outer space, these foams might be useful as catalyst supports and filters. Preceramic polymers are obvious candidates for use in making the foams in question. The use of these polymers offers advantages over processing routes followed in making conventional ceramics. Among the advantages are the ability to plastically form parts, the ability to form pyrolized ceramic materials at lower temperatures, and the ability to form high-purity microstructures having properties that can be tailored to satisfy requirements. Heretofore, preceramic polymers have been used mostly in the production of such low-dimensional products as fibers because the loss of volatiles during pyrolysis of the polymers leads to porosity and large shrinkage (in excess of 30 percent). In addition, efforts to form bulk structures from preceramic polymers have resulted in severe cracking during pyrolysis. However, because the foams in question would consist of networks of thin struts (in contradistinction to nonporous dense solids), these foams are ideal candidates for processing along a preceramic-polymer route.
Current shortcomings in both the overall injector design process and its underlying combustion stability assessment methodology are rooted in the use of empirically based or low fidelity representations of complex physical phenomena and geometry details that have first order effects on performance, thermal environments and combustion stability. The result is a design and analysis capability that is often inadequate to reliably arrive at a suitable injector design in an efficient manner. Specifically, combustion instability has been particularly difficult to predict and mitigate. Large hydrocarbon-fueled booster engines have been especially problematic in this regard. Where combustion instability has been a problem, costly and time-consuming redesign efforts have often been an unfortunate consequence. This paper presents an overview of a recently completed effort at NASA Marshall Space Flight Center to advance the state-of-the-practice for liquid rocket engine injector design. Multiple perturbations of a gas-centered swirl coaxial (GCSC) element that burned gaseous oxygen and RP-1 were designed, assessed for combustion stability, and tested. Three designs, one stable, one marginally unstable and one unstable, were used to demonstrate both an enhanced overall injector design process and an improved combustion stability assessment process. High-fidelity results from state-of-the-art computational fluid dynamics CFD simulations were used to substantially augment and improve the injector design methodology. The CFD results were used to inform and guide the overall injector design process. They were also used to upgrade selected empirical or low-dimensional quantities in the ROCket Combustor Interactive Design (ROCCID) stability assessment tool. Hot fire single element injector testing was used to verify both the overall injector designs and the stability assessments. Testing was conducted at the Air Force Research Laboratory and at Purdue University. Companion papers provide details of the overall injector design process, full- and sub-scale testing, ROCCID-based stability assessments and the CFD simulations.
Research work is proceeding in theoretical, numerical, and experimental geophysical fluid dynamics leading up to a reflight of the GFFC (Geophysical Fluid Flow Cell Experiment) on USML-2. The work is intended not only to generate ideas for future space experiments, but to provide fundamental results concerned with nonlinear and chaotic properties of thermal convection and baroclinic waves in terrestrial and planetary atmospheres. The major efforts are focussed on thermal convection in a rapidly rotating annulus relevant to Jovian atmospheric dynamics, and on the chaotic behavior of baroclinic waves relevant to the Earth's atmosphere. The approach, in preparation for USML-2, is primarily theoretical and numerical. Mechanistic process models are solved numerically in order to identify physical mechanisms that may be observed in the GFFC, and which are important in real geophysical applications. The results from numerical simulations of geophysical fluid flow (subject to rotation and stratification) are compared with previous GFFC experiments on Spacelab-3 and with existing and proposed terrestrial laboratory experiments of various types. Pattern recognition algorithms have been employed to generate low-dimensional descriptions of the highly nonlinear and turbulent numerical simulations. Such empirically truncated descriptions provide for simplified but robust physical interpretations of the dynamics, as well as yielding highly efficient computations of these chaotic flows.
Using three separate but related approaches, the question of whether the dynamic response of the magnetosphere to the solar wind input may be described by a low-order system of equations is examined. First, it is determined that the dimension of the subset (the attractor) in the high-dimensional magnetospheric phase space associated with the westward auroral electrojet (AL) index for some of the data sets compiled by Bargatze et al. (1985) is 4.0 + or - 0.2, seemingly independent of activity level. Second, direct modeling of the magnetosphere, considering the bulk properties of the tail plasma, leads to a system of equations that is similar to those previously reported as a dripping faucet model; here, the focus is specifically on the prediction of a natural frequency in this model. Finally, a peak is identified with the predicted frequency in power spectra of AL computed for intervals with both low and high activity. Peaks at other frequencies also appear in the spectra, and such resonances would be expected for a chaotic nonlinear oscillator. Combining these approaches it is concluded that at least some aspects of magnetospheric dynamics may be meaningfully modeled by low-dimensional sets of equations.
In this paper we evaluate the performance of two reduced resolution filter approaches to data assimilation. The main distinction between these approaches is in the manner they propagate error covariances. Both account for error covariances in a space with dimension m smaller than the model's state vector dimension n. In the first approach the m dimensional error covariance matrix is interpolated to the n-dimensional space and propagated with the n-dimensional dynamics. In the second approach the low-dimensional error covariance matrix is propagated by a dynamical operator generated in the m-dimensional space. Our experiments indicate that the first approach provides a more reliable simplified scheme for error covariance propagation than the second approach.
Ankyrin (ANK) repeat proteins are coded by tandem occurrences of patterns with around 33 amino acids. They often mediate protein–protein interactions in a diversity of biological systems. These proteins have an elongated non-globular shape and often display complex folding mechanisms. This work investigates the energy landscape of representative proteins of this class made up of 3, 4 and 6 ANK repeats using the energy-landscape visualisation method (ELViM). By combining biased and unbiased coarse-grained molecular dynamics AWSEM simulations that sample conformations along the folding trajectories with the ELViM structure-based phase space, one finds a three-dimensional representation of the globally funnelled energy surface. In this representation, it is possible to delineate distinct folding pathways. We show that ELViMs can project, in a natural way, the intricacies of the highly dimensional energy landscapes encoded by the highly symmetric ankyrin repeat proteins into useful low-dimensional representations. These projections can discriminate between multiplicities of specific parallel folding mechanisms that otherwise can be hidden in oversimplified depictions.