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All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Reflection Grating Array Associated with the Reflection Grating Spectrometer Developed by the Space Research Organization of the Netherlands for the X-ray Multi-Mirror Mission (XMM)

The University of California, Berkeley (UCB) served as the Principal Investigator institution for the United States participation in the development of the Reflection Grating Spectrometer (RGS) which included the design, development, fabrication, and testing of the Reflection Grating Assembly (RGA). UCB was assisted in this role by the Lawrence Livermore National Laboratory and Columbia University who provided the primary facilities, materials, services and personnel necessary to complete the development. UC Berkeley's Dr. Steven Kahn provided the technical and scientific oversight for the design. development and testing of the RGA units by monitoring the performance of the units at various stages in their development. Dr. Kahn was also the primary contact with the Space Research Organization of the Netherlands (SRON) and represented the RGA development at all SRON and European Space Agency (ESA) reviews of the RGA status. In accordance with the contract, the team designed and developed novel optical technology to meet the unique requirements of the RGS. The ESA XMM-Newton Mission carries two identical Reflection Grating Spectrometers (RGS) behind two of its three nested sets of Wolter I type mirrors. The instrument allows high-resolution measurements in the soft X-ray range (6 to 38 angstroms or 2.1 to 0.3 keV) with a maximum effective area of about 140 sq cm at 15 angstroms. Its design is optimized for the detection of the K-shell transitions of carbon, nitrogen, oxygen, neon, magnesium, and silicon. as well as the L shell transitions of iron. The RGA itself consists of two units. A structure for each unit was designed to hold up to 220 gratings. In its final configuration, one unit holds 182 gratings and the second hold 181 gratings.

Kahn, Steven M.↗
NASA NTRS1999

Sensitivity of High-Resolution Simulations of Hurricane Bob (1991) to Planetary Boundary Layer Parameterizations

The MM5 mesoscale model is used to simulate Hurricane Bob (1991) using grids nested to high resolution (4 km). Tests are conducted to determine the sensitivity of the simulation to the available planetary boundary layer parameterizations, including the bulk-aerodynamic, Blackadar, Medium-RanGe Forecast (MRF) model, and Burk-Thompson boundary-layer schemes. Significant sensitivity is seen, with minimum central pressures varying by up to 17 mb. The Burk-Thompson and bulk-aerodynamic boundary-layer schemes produced the strongest storms while the MRF scheme produced the weakest storm. Precipitation structure of the simulated hurricanes also varied substantially with the boundary layer parameterizations. Diagnostics of boundary-layer variables indicated that the intensity of the simulated hurricanes generally increased as the ratio of the surface exchange coefficients for heat and momentum, C(sub h)/C(sub M), although the manner in which the vertical mixing takes place was also important. Findings specific to the boundary-layer schemes include: 1) the MRF scheme produces mixing that is too deep and causes drying of the lower boundary layer in the inner-core region of the hurricane; 2) the bulk-aerodynamic scheme produces mixing that is probably too shallow, but results in a strong hurricane because of a large value of C(sub h)/C(sub M) (approximately 1.3); 3) the MRF and Blackadar schemes are weak partly because of smaller surface moisture fluxes that result in a reduced value of C(sub h)/C(sub M) (approximately 0.7); 4) the Burk-Thompson scheme produces a strong storm with C(sub h)/C(sub M) approximately 1; and 5) the formulation of the wind-speed dependence of the surface roughness parameter, z(sub 0), is important for getting appropriate values of the surface exchange coefficients in hurricanes based upon current estimates of these parameters.

Braun, Scott A.↗
NASA NTRS2024

FRAAME Version 1.0 User Manual

The code for Forced Response Aeromechanics Analysis in a MATLAB-based (The MathWorks, Inc.) Environment (FRAAME Version 1.0) was developed for internal use in aeromechanics efforts undertaken at the NASA Glenn Research Center for computing turbomachine component forced response and Goodman diagrams via modal summation method. The main working script (FRAAMEv1.m) allows users to input case-specific manual inputs while the triple-nested loop invokes functions to compute forced response per blade, per nodal diameter, and per mode. Secondly, forced response values are applied to modal stresses to compute complex Von Mises stress values and generate Goodman diagrams per blade, per nodal diameter, and per mode using a linear modal summation method. Currently, this code functions in the Windows (Microsoft Corporation) operating system using MATLAB Version R2023a, but it can be adapted for use in the Linux (Linus Torvalds) operating system by changing the appropriate file path structure in the main script, as well as functions that call external results files.

Aeromechanics↗
NASA NTRS2010

A Machine-Checked Proof of A State-Space Construction Algorithm

This paper presents the correctness proof of Saturation, an algorithm for generating state spaces of concurrent systems, implemented in the SMART tool. Unlike the Breadth First Search exploration algorithm, which is easy to understand and formalise, Saturation is a complex algorithm, employing a mutually-recursive pair of procedures that compute a series of non-trivial, nested local fixed points, corresponding to a chaotic fixed point strategy. A pencil-and-paper proof of Saturation exists, but a machine checked proof had never been attempted. The key element of the proof is the characterisation theorem of saturated nodes in decision diagrams, stating that a saturated node represents a set of states encoding a local fixed-point with respect to firing all events affecting only the node s level and levels below. For our purpose, we have employed the Prototype Verification System (PVS) for formalising the Saturation algorithm, its data structures, and for conducting the proofs.

Catano, Nestor↗
NASA NTRS1999

Large Eddy Simulation of Cirrus Clouds

The Regional Atmospheric Modeling System (RAMS) with mesoscale interactive nested-grids and a Large-Eddy Simulation (LES) version of RAMS, coupled to two-moment microphysics and a new two-stream radiative code were used to investigate the dynamic, microphysical, and radiative aspects of the November 26, 1991 cirrus event. Wu (1998) describes the results of that research in full detail and is enclosed as Appendix 1. The mesoscale nested grid simulation successfully reproduced the large scale circulation as compared to the Mesoscale Analysis and Prediction System's (MAPS) analyses and other observations. Three cloud bands which match nicely to the three cloud lines identified in an observational study (Mace et al., 1995) are predicted on Grid #2 of the nested grids, even though the mesoscale simulation predicts a larger west-east cloud width than what was observed. Large-eddy simulations (LES) were performed to study the dynamical, microphysical, and radiative processes in the 26 November 1991 FIRE 11 cirrus event. The LES model is based on the RAMS version 3b developed at Colorado State University. It includes a new radiation scheme developed by Harrington (1997) and a new subgrid scale model developed by Kosovic (1996). The LES model simulated a single cloud layer for Case 1 and a two-layer cloud structure for Case 2. The simulations demonstrated that latent heat release can play a significant role in the formation and development of cirrus clouds. For the thin cirrus in Case 1, the latent heat release was insufficient for the cirrus clouds to become positively buoyant. However, in some special cases such as Case 2, positively buoyant cells can be embedded within the cirrus layers. These cells were so active that the rising updraft induced its own pressure perturbations that affected the cloud evolution. Vertical profiles of the total radiative and latent heating rates indicated that for well developed, deep, and active cirrus clouds, radiative cooling and latent heating could be comparable in magnitude in the cloudy layer. This implies that latent heating cannot be neglected in the construction of a cirrus cloud model. The probability density function (PDF) of w was analyzed to assist in the parameterization of cloud-scale velocities in large-scale models. For the more radiatively-driven, thin cirrus case, the PDFs are approximately Gaussian. However, in the interior of the deep, convectively unstable case, the PDFs of w are multi-modal and very broad, indicating that parameterizing cloud-scale motions for such clouds can be very challenging. The results of this research are described in detail in a paper submitted to the Journal of Atmospheric Science (Wu and Cotton, 1999), which is enclosed as Appendix 2. Using soundings extracted from a mesoscale simulation of the November 26, 1991 cirrus event, the radiative effects on vapor deposition/sublimation of ice crystals was studied using a two-dimensional cloud-resolving model (CRM) version of RAMS, coupled to an explicit bin-resolving microphysics. The CRM simulations of the November 26, 1991 cirrus event demonstrate that the radiative impact on the diffusional growth (or sublimation) of ice crystals is significant. In this case, the ice particles experienced radiative warming. Model results show that radiative feedbacks in the diffusional growth of ice particles can be very complex. Radiative warming of an ice particle will restrict the particle's diffusional growth. In the case of radiative warming, ice particles larger than a certain size will experience so much radiative warming that surface ice saturation vapor pressures become large enough to cause sublimation of the larger crystals, while smaller crystals are growing by vapor deposition. However, ice mass production can be enhanced in the case of radiative cooling of an ice particle. For the November 26, 1991 cirrus event, radiative feedback results in significant reduction in the total ice mass, especially in the production of large ice crystals, and consequently, both radiative and dynamic properties of the cirrus cloud are significantly affected. A complete description of this research has been submitted as a paper to the Journal of Atmospheric Science (Wu et al., 1999), and included as Appendix 3.

Wu, Ting↗
NASA NTRS2004

Deep Moonquakes: Remaining Problems

We have recently reexamined more than 9000 United States previously unidentified seismic events catalogued during the Apollo landing missions and positively identified for the first time about 30 deep moonquake nests on the far side of the Moon. Although only a few of them are currently locatable, the relative arrival times among stations for the rest and presence or absence of seismic signals at particular stations suggest that either (a) the region within about $40\deg$ of the antipode is aseismic or (b) the deep interior of the Moon severely attenuates or deflects seismic waves. Aside from the obvious question of how to distinguish between such hypothetical models, this effort raised several more general questions concerning the use of deep moonquake signals to infer the structure and dynamics of the deep interior of the Moon. Among more important ones are: (1) How reliable are the seismic arrival picks from which to compute the seismic velocity variations in the Moon? (2) How do the possible lateral variations in seismic velocity affect the computed radial variation in seismic velocity at depth? (3) Can we tell more about the distribution and mechanism of deep moonquakes from the newly expanded database of identified deep moonquakes? Questions (1) and (2) are especially important because the inferred deep internal structure of the Moon depends critically on their answers. Answering these questions may demand additional data collected on future lunar missions, but some may be resolved with further examination of the existing data.

Nakamura, Y.↗
NASA NTRS1995

Flow downstream of the heliospheric terminal shock: Magnetic field line topology and solar cycle imprint

The topology of the magnetic field in the heliosheath is illustrated using plots of the field lines. It is shown that the Archimedean spiral inside the terminal shock is rotated back in the heliosheath into nested spirals that are advected in the direction of the interstellar wind. The 22-year solar magnetic cycle is imprinted onto these field lines in the form of unipolar magnetic envelopes surrounded by volumes of strongly mixed polarity. Each envelope is defined by the changing tilt of the heliospheric current sheet, which is in turn defined by the boundary of unipolar high-latitude regions on the Sun that shrink to the pole at solar maximum and expand to the equator at solar minimum. The detailed shape of the envelopes is regulated by the solar wind velocity structure in the heliosheath.

Nerney, Steven↗
NASA NTRSDate not supplied

Impedance Matching a Quarter Wave Resonant Receiver to Improve Efficiency in Unipolar Capacitive Wireless Power Transfer

Impedance matching techniques to achieve high performance in conventional wireless power transfer (WPT) systems are well established. These WPT systems are modelled as a lumped circuit, where the voltages/currents are approximately uniform and mostly unaffected by parasitic elements. However, a group of WPT techniques exist that utilize parasitic elements to form a highly resonant power transfer condition at high quality factors, exploiting a distributed circuit operation that can be modeled as a mutually coupled transmission line. A calculated matching network typically becomes unmatched when connected to the transmission line, as it changes the electrical structure of the coupled transmission line. This is particularly true for WPT systems that use quarter wave (QWR) or half wave resonators (HWR) for the receiver. Here we present one technique of matching to a mutually coupled transmission line where a parallel path is formed that improves the power transfer efficiency without severely altering the transmission line characteristics.

Wireless↗
NASA NTRS2011

Physical Validation of GPM Retrieval Algorithms Over Land: An Overview of the Mid-Latitude Continental Convective Clouds Experiment (MC3E)

The joint NASA Global Precipitation Measurement (GPM) -- DOE Atmospheric Radiation Measurement (ARM) Midlatitude Continental Convective Clouds Experiment (MC3E) was conducted from April 22-June 6, 2011, centered on the DOE-ARM Southern Great Plains Central Facility site in northern Oklahoma. GPM field campaign objectives focused on the collection of airborne and ground-based measurements of warm-season continental precipitation processes to support refinement of GPM retrieval algorithm physics over land, and to improve the fidelity of coupled cloud resolving and land-surface satellite simulator models. DOE ARM objectives were synergistically focused on relating observations of cloud microphysics and the surrounding environment to feedbacks on convective system dynamics, an effort driven by the need to better represent those interactions in numerical modeling frameworks. More specific topics addressed by MC3E include ice processes and ice characteristics as coupled to precipitation at the surface and radiometer signals measured in space, the correlation properties of rainfall and drop size distributions and impacts on dual-frequency radar retrieval algorithms, the transition of cloud water to rain water (e.g., autoconversion processes) and the vertical distribution of cloud water in precipitating clouds, and vertical draft structure statistics in cumulus convection. The MC3E observational strategy relied on NASA ER-2 high-altitude airborne multi-frequency radar (HIWRAP Ka-Ku band) and radiometer (AMPR, CoSMIR; 10-183 GHz) sampling (a GPM "proxy") over an atmospheric column being simultaneously profiled in situ by the University of North Dakota Citation microphysics aircraft, an array of ground-based multi-frequency scanning polarimetric radars (DOE Ka-W, X and C-band; NASA D3R Ka-Ku and NPOL S-bands) and wind-profilers (S/UHF bands), supported by a dense network of over 20 disdrometers and rain gauges, all nested in the coverage of a six-station mesoscale rawinsonde network. As an exploratory effort to examine land-surface emissivity impacts on retrieval algorithms, and to demonstrate airborne soil moisture retrieval capabilities, the University of Tennessee Space Institute Piper aircraft carrying the MAPIR L-band radiometer was also flown during the latter half of the experiment in coordination with the ER-2. The observational strategy provided a means to sample the atmospheric column in a redundant framework that enables inter-calibration and constraint of measured and retrieved precipitation characteristics such as particle size distributions, or water contents- all within the umbrella of "proxy" satellite measurements (i.e., the ER-2). Complimenting the precipitation sampling framework, frequent and coincident launches of atmospheric soundings (e.g., 4-8/day) then provided a much larger mesoscale view of the thermodynamic and winds environment, a data set useful for initializing cloud models. The datasets collected represent a variety cloud and precipitation types including isolated cumulus clouds, severe thunderstorms, mesoscale convective systems, and widespread regions of light to moderate stratiform precipitation. We will present the MC3E experiment design, an overview of operations, and a summary of preliminary results.

Petersen, Walter A.↗
NASA NTRS2002

The Structure of A Pacific Narrow Cold Frontal Rainband

A NOAA P-3 instrumented aircraft observed an intense, fast-moving narrow cold frontal Farmhand as it approached the Pacific Northwest coast on 19 February 2001 during the Pacific Coastal Jets Experiment. Pseudo-dual-Doppler analyses performed on the airborne Doppler radar data while the frontal system was well offshore indicated that a narrow ribbon of very high radar reflectively convective cores characterized the Farmhand at low levels with echo tops to approximately 4-5 km. The NCFR exhibited gaps in its narrow ribbon of high reflectively, probably as a result of hydrodynamic instability all no its advancing cold pool leading edge. In contrast to some earlier studies of cold frontal rainbands, density current theory described well the motion of the overall front. The character of the updraft structure associated with the heavy rainfall at its leading edge varied across the gap region. The vertical shear of the cross-frontal low-level ambient flow exerted a strong influence on the updraft character, consistent with theoretical arguments developed for squall lines describing the balance of vorticity at the leading edge. In short regions south of the gaps the vertical wind shear was strongest with the updrafts and rain shafts more intense, narrower, and more erect or even downshear tilted. North of the gaps the wind shear weakened with less intense Dihedrals which tilted upshear with a broader band of rainfall. Simulations using a nonhydrostatic mesoscale nested grid model are used to investigate the gap regions, particularly the balance of cold pool induced to pre-frontal ambient shears at the leading edge. Observations confirm the model results that the updraft character depends on the balance of vorticity at the leading edge. Downshear-tilted updrafts imply that convection south of the gap regions would weaken with time relative to the frontal segments north of the gaps since inflow air would be affected by passage through the heavy rain region before ascent, suggesting a mechanism for gap filling.

Jorgensen, David P.↗
NASA NTRS1999

The Diurnal Cycle in TOGA-COARE: Regional Scale Model Simulations

The diurnal variation of precipitation processes over the tropics is a well-known phenomenon and has been studied using surface rainfall data, radar reflectivity data, and satellite-derived cloudiness and precipitation. Recently, Sui (1997) analyzed observations from TOGA COARE in the tropical western Pacific ocean to study the relevant mechanisms producing diurnal variation of precipitation. They found that the diurnal SST cycle is important for afternoon showers in the undisturbed periods and diurnal radiative processes for nocturnal rainfall. Takayabu (1996) found a quasi-2-day cycle in precipitation during TOGA COARE and they suggested that inertia-gravity waves may be associated with this 2-day cycle. Chen and Houze (1997), however, suggested that the quasi-2-day oscillation is mainly a function of the time required by the lower-tropospheric moisture field to recover from the drying caused by deep convection. In this study, the Penn State/NCAR Mesoscale Model (MM5) with improved physics (i.e., cloud microphysics, radiation, land-soil-vegetation-surface processes, and TOGA COARE flux scheme) and a multiple level nesting technique will be used to simulate two TOGA COARE convective espisodes, one convectively suppressed phase (mid to late January 1993) and one convectively active phase (mid to late December 1992). We will examine precipitation processes over the open ocean and over land by comparing MM5 simulated rainfall and out-going longwave radiation. By examining the OLR and precipitation, we can determine if there is a temporal lag between the maximum precipitation and the coldest upwelling longwave radiation (the time-lag between stratiform-cirrus and convective towers). The boundary layer response by (or recovery from) precipitation processes will also be shown by examining the PBL thermodynamic structure and the sensible and latent heat fluxes. A preliminary MM5 simulation showed a clear diurnal variation in rainfall over both land and open ocean for the convectively active phase. The results also indicated that a quasi-2-day cycle in precipitation was simulated only over part of the ocean.

Tao, W.-K.↗
NASA NTRS1994

Regional-scale flows in mountainous terrain. Part 1: A numerical and observational comparison

This study uses observed data and a numerical simulation to examine the generation of thermally driven flows across the Colorado mountain barrier on meso-beta to meso-alpha scales. The observations were collected from remote surface observing systems at exposed mountaintop locations throughout the state of Colorado, over the summers of 1984-88, as part of the Rocky Mountain Peaks Experiment (ROMPEX). The data show the development of a recurrent circulation system across the Colorado mountain barrier, operating on a diurnal timescale. From the observations, the basic structure of the flow system appears as a daytime inflow toward the highest terrain, and a nocturnal outflow away from it. However, when examined in detail, the flow system exhibits more unusual behavior, especially west of the barrier crest. Here, winds in the early evening are occasionally observed to onset abruptly from an easterly direction, generally counter to the upper-level winds. Observations from ROMPEX for 26 August 1985 are used to provide comparison data for a numerical simulation with the Regional Atmospheric Modeling System (RAMS). This three-dimensional case study experiment is initialized with data from the National Meteorological Center and incorporates two-way interactive grid nesting. From the observed data and case study simulation, four distinct phases of the regional-scale circulation system have been identified. In the development phase, a deep mountain-plains solenoid is generated through terrain heating along the Front Range. This circulation system transforms in the late afternoon transition phase into a westward-propagating density current (WPDC). The third phase, called the 'density-current propagation phase,' occurs as the WPDC moves westward across the mountains, leaving in its wake strong southeasterly flow at the mountaintop level. This current appears to be the cause of the peculiar easterly component winds found in the ROMPEX mountaintop observations along the western slope. In the final late-night adjustment phase, the WPDC dissipates near the western edge of the Colorado mountains and steady southerly flow evolves over the high mountain terrain. This southerly flow is the steady response to the differential heating that develops between the low-lying plains and the intermountain region.

Bossert, James E.↗
NASA NTRS2010

Endangered and Threatened Species at Kennedy Space Center Merritt Island National Wildlife Refuge

Throughout my internship, I assisted with the long-term monitoring of the Florida Scrub- Jay (Aphelocoma coerulescens), a threatened species endemic to Florida. The Florida Scrub Jay diet consists of insects and small vertebrates throughout most of the year; however, during the winter their primary diet is acorns because the insect population is low. Furthermore, the Florida Scrub-Jay is a habitat specialist that lives in a disappearing plant community called the scrub, which consists of sand live oak, myrtle oak and chapman oak. The Florida Scrub-Jay is considered threatened because its numbers are decreasing primarily due to the loss of habitat that it needs to survive. Scrub habitat is highly desirable for human development because it is high, dry, and sandy. Periodic controlled burns maintain the scrub in a low, open condition favored by Scrub-Jays. Florida Scrub-Jays build their nests approximately 3-5 feet (approximately 1.5 m) above the ground in shrubby oaks (Breininger 153), mate for life and are cooperative breeders; which means that the young jays remain in their natal territory for at least a year to help their parents defend their territory, feed the young, and mob predators. (Breininger 152). I assisted in conducting monthly censuses at long-term monitoring sites and a juvenile in July survey to determine reproductive success for the year. In addition, to Scrub-Jay monitoring, I also had the opportunity to assist with some long term monitoring of ecosystem recovery. Scrub is a fire maintained system. Fire maintains the structure of scrub necessary for many of the threatened species that reside in the scrub habitat.

Galdolfi, Catherine↗
NASA NTRS1977

Nested-crater model of lunar ringed basins

We propose a model for the origin of impact-basin rings whereby the main topographic rim of a basin approximates the limit of excavation and inner rings approximate the rims of craters formed inside the transient crater by some perturbation in the cratering process. The cause of this complexity in transient cavities may be the presence of discontinuities in the target material. The second inward ring may have formed at the seismic discontinuity about 20 km deep in the lunar crust, and the third, innermost ring of a few large basins at the crust-mantle interface about 60 km deep. Slumping increased the original diameters of many rings and split some initially coherent rings into subsidiary or partial rings. Deformation outside the transient crater produced external arcs. This model differs from prevalent hypotheses of ring formation whereby an inner ring approximates the transient crater rim and major faulting of the flank produced the outer ring structures.

Wilhelms, D. E.↗
NASA NTRS1986

Development and use of a linear momentum exchange device

In 1981 the Marshall Space Flight Center (MSFC) began establishing an inhouse facility for testing control concepts to be applied to Large Space Structures (LSS). The original concept called for a long flexible beam suspended from the ceiling by a low friction support system. The lower end of the beam was to be mounted to the Advanced Gimbal System (AGS). Analysis and system engineering soon showed that a more tenable design would be where the whole system was inverted, i.e., the AGS hung from the ceiling with the beam hanging down from it. While this configuration, augmented by a base excitation table (RET) was being built, an ASTROMAST obtained from the Jet Propulsion Laboratory was extended, analyzed and tested. From that basic configuration was evolved the cruciform, VCOSS and ACES configurations as shown. The addition of the cruciform added low frequency nested modes and the additional instrument package at the tip contains gyros to monitor tip motion.

Doane, George B., III↗
NASA NTRS2000

Little Homunculus with in the Homunculus of Eta Carinae

The famous HST/WFPC2 images of Eta Carinae provide a two-dimensional projection of the bipolar nebula that is really a three-dimensional structure. Much is hidden in subtle, projected details that a velocity-tuned instrument can pull apart. We have used the HST/STIS with a 52" x 0.1" aperture and with about 5000 spectral resolving power to examine the kinetic information contained within emission/absorption features. By velocity tuning, we can translate this information into spatial structures. The spectroscopic datasets have been transformed to a set of images, spaced at half instrumental line width steps, 15 - 20 km/s , and with a spatial resolution of 0.1 x 0.1 arcsec near Balmer beta and 0.25 x 0.1 arcsec near Balmer alpha. We examined these narrow-band images and individual spectra to characterize the nature of an internal nebula (formerly known as the Integral nebula). The shape of this nebulosity is an bipolar nebula, deeply embedded within the Homunculus, the well-known bipolar nebula surrounding Eta Carinae. The internal nebula is shaped nearly identically to the Homunculus. It is best described as a "little Homunculus within the Homunculus". Indeed, it is reminiscent of the Russian dolls, known as Matryoshka dolls, that successively nest within each larger doll. For that reason, we call this internal nebula the Matryoshka nebula. This was performed as one of the STIS GTO key projects and was funded by the HST project. Observations were done through the STScI.

Ishibashi, Kazunori↗
NASA NTRS2007

Decision-Tree Formulation With Order-1 Lateral Execution

A compact symbolic formulation enables mapping of an arbitrarily complex decision tree of a certain type into a highly computationally efficient multidimensional software object. The type of decision trees to which this formulation applies is that known in the art as the Boolean class of balanced decision trees. Parallel lateral slices of an object created by means of this formulation can be executed in constant time considerably less time than would otherwise be required. Decision trees of various forms are incorporated into almost all large software systems. A decision tree is a way of hierarchically solving a problem, proceeding through a set of true/false responses to a conclusion. By definition, a decision tree has a tree-like structure, wherein each internal node denotes a test on an attribute, each branch from an internal node represents an outcome of a test, and leaf nodes represent classes or class distributions that, in turn represent possible conclusions. The drawback of decision trees is that execution of them can be computationally expensive (and, hence, time-consuming) because each non-leaf node must be examined to determine whether to progress deeper into a tree structure or to examine an alternative. The present formulation was conceived as an efficient means of representing a decision tree and executing it in as little time as possible. The formulation involves the use of a set of symbolic algorithms to transform a decision tree into a multi-dimensional object, the rank of which equals the number of lateral non-leaf nodes. The tree can then be executed in constant time by means of an order-one table lookup. The sequence of operations performed by the algorithms is summarized as follows: 1. Determination of whether the tree under consideration can be encoded by means of this formulation. 2. Extraction of decision variables. 3. Symbolic optimization of the decision tree to minimize its form. 4. Expansion and transformation of all nested conjunctive-disjunctive paths to a flattened conjunctive form composed only of equality checks when possible. If each reduced conjunctive form contains only equality checks and all of these forms use the same variables, then the decision tree can be reduced to an order-one operation through a table lookup. The speedup to order one is accomplished by distributing each decision variable over a surface of a multidimensional object by mapping the equality constant to an index

James, Mark↗
NASA NTRS2021

Bioinspired Honeycomb Core Design: An Experimental Study of the Role of Corner Radius, Coping, and Interface

The honeybee’s nest has inspired the design of engineering honeycomb core that primarily abstract the hexagonal cell shape and exploit its mass minimizing properties to construct lightweight panels. This work explored three additional design features that are part of the natural honeybee comb but have not been traditionally considered as design features of interest in honeycomb design: the radius at the corner of each cell, the coping at the top of the cell walls, and the interface between cell arrays. These features were first characterized in natural honeycomb using optical and X-ray techniques, and then incorporated into honeycomb core design, and fabricated using an additive manufacturing process. The honeycomb cores were then tested in out-of-plane compression and bending, and since all three design features added mass to the overall structure, all metrics were examined per unit mass to assess performance gains. The study concluded that the addition of an interface increases specific flexural modulus but has little benefit in out-of-plane compression; coping radius positively impacts specific flexural strength; but that the corner radius has no significant effect in bending, and actually is slightly detrimental for out-of-plane compression testing.

honeycomb↗