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NASA NTRS2015

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Gnoffo, Peter A.↗

NASA NTRS2015

Self-Calibration and Laser Energy Monitor Validations for a Double-Pulsed 2-Micron CO2 Integrated Path Differential Absorption Lidar Application

Double-pulsed 2-micron integrated path differential absorption (IPDA) lidar is well suited for atmospheric CO2 remote sensing. The IPDA lidar technique relies on wavelength differentiation between strong and weak absorbing features of the gas normalized to the transmitted energy. In the double-pulse case, each shot of the transmitter produces two successive laser pulses separated by a short interval. Calibration of the transmitted pulse energies is required for accurate CO2 measurement. Design and calibration of a 2-micron double-pulse laser energy monitor is presented. The design is based on an InGaAs pin quantum detector. A high-speed photo-electromagnetic quantum detector was used for laser-pulse profile verification. Both quantum detectors were calibrated using a reference pyroelectric thermal detector. Calibration included comparing the three detection technologies in the single-pulsed mode, then comparing the quantum detectors in the double-pulsed mode. In addition, a self-calibration feature of the 2-micron IPDA lidar is presented. This feature allows one to monitor the transmitted laser energy, through residual scattering, with a single detection channel. This reduces the CO2 measurement uncertainty. IPDA lidar ground validation for CO2 measurement is presented for both calibrated energy monitor and self-calibration options. The calibrated energy monitor resulted in a lower CO2 measurement bias, while self-calibration resulted in a better CO2 temporal profiling when compared to the in situ sensor.

Refaat, Tamer F.↗

NASA NTRS2016

Spiral Structure and Differential Dust Size Distribution in the LkH(alpha) 330 Disk

Dust trapping accelerates the coagulation of dust particles, and, thus, it represents an initial step toward the formation of planetesimals. We report H-band (1.6 microns) linear polarimetric observations and 0.87 mm interferometric continuum observations toward a transitional disk around LkH(alpha) 330. As a result, a pair of spiral arms were detected in the H-band emission, and an asymmetric (potentially arm-like) structure was detected in the 0.87 mm continuum emission. We discuss the origin of the spiral arm and the asymmetric structure and suggest that a massive unseen planet is the most plausible explanation. The possibility of dust trapping and grain growth causing the asymmetric structure was also investigated through the opacity index (beta) by plotting the observed spectral energy distribution slope between 0.87 mm from our Submillimeter Array observation and1.3 mm from literature. The results imply that grains are indistinguishable from interstellar medium-like dust in the east side (beta = 2.0 +/- 0.5) but are much smaller in the west side beta = 0.7+0.5 -0.4, indicating differential dust size distribution between the two sides of the disk. Combining the results of near-infrared and submillimeter observations, we conjecture that the spiral arms exist at the upper surface and an asymmetric structure resides in the disk interior. Future observations at centimeter wavelengths and differential polarization imaging in other bands (Y-K) with extreme AO imagers are required to understand how large dust grains form and to further explore the dust distribution in the disk.

polarimetric observations↗

NASA NTRS2017

Triple-Pulse Integrated Path Differential Absorption Lidar for Carbon Dioxide Measurement - Novel Lidar Technologies and Techniques with Path to Space

The societal benefits of understanding climate change through identification of global carbon dioxide sources and sinks led to the desired NASA's active sensing of carbon dioxide emissions over nights, days, and seasons (ASCENDS) space-based missions of global carbon dioxide measurements. For more than 15 years, NASA Langley Research Center (LaRC) have developed several carbon dioxide active remote sensors using the differential absorption lidar (DIAL) technique operating at the two-micron wavelength. Currently, an airborne two-micron triple-pulse integrated path differential absorption (IPDA) lidar is under development. This IPDA lidar measures carbon dioxide as well as water vapor, the dominant interfering molecule on carbon dioxide remote sensing. Advancement of this triple-pulse IPDA lidar development is presented.

Singh, Upendra N.↗

NASA NTRS2018

Experimental Investigation of Chromium Behavior During Mercury's Differentiation

Mercury is the most reduced terrestrial planet with the largest core/mantle size ratio and highest sulfur concentration on the surface. The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft data allowed mapping of Mercury's surface elemental composition. Recent chromium mapping suggests Mercury's surface has on average 800 parts per million Cr with the highest values in the High Magnesium Region. These new data can give clues about Mercury's internal structure and the redox conditions under which it differentiated. In the present study, we present experimental data on the distribution of Cr among metal, silicate and sulfide liquids. We then combine them with data from previous studies and a model of planetary differentiation to discuss Mercury's bulk composition and its oxidation state.

Boujibar, A.↗

NASA NTRS2018

Solution of Ordinary Differential Equations in Gradient-Based Multidisciplinary Design Optimization

A gradient-based approach to multidisciplinary design optimization enables efficient scalability to large numbers of design variables. However, the need for derivatives causes difficulties when integrating ordinary differential equations (ODEs) in models. To simplify this, we propose the use of the general linear methods framework, which unifies all Runge-Kutta and linear multistep methods. This approach enables rapid implementation of integration methods without the need to differentiate each one, even in a gradient-based optimization context. We also develop a new parallel time integration algorithm that enables vectorization across time steps. We present a set of benchmarking results using a stiff ODE, a non-stiff nonlinear ODE, and an orbital dynamics ODE, and compare integration methods. In a modular gradient-based multidisciplinary design optimization context, we find that the new parallel time integration algorithm with high-order implicit methods, especially Gauss-Legendre collocation, is the best choice for a broad range of problems.

Hwang, John T.↗

NASA NTRS2018

Light Ion Double-Differential Cross Sections for Space Radiation

Neutrons and light ions have been shown to make large contributions to space radiation dose equivalent for realistic shielding scenarios. However, there are considerable uncertainties in the calculation of light ion production. Efficient and accurate calculation of light ion double-differential cross sections are required for input into space radiation transport codes. A thermal proton cross section model is developed which includes proton production from the 3 sources of projectile, central fireball, and target. It is shown that this 3-source model is able to explain the low-momentum, small-angle shoulder seen in proton spectra. Using the coalescence model, the thermal proton model is used to calculate light ion double-differential cross sections for use in space radiation transport codes. The 3-source model is also seen to be essential to explain the light ion shoulders, which are even more pronounced than the proton shoulders. Extensive comparisons between models and experimental measurements are shown and necessary future work is discussed.

Norbury, John W.↗

NASA NTRS2018

Increasing the Statistical Rigor of Cross-Species Differential Expression Analysis

Microgravity inflicts substantial, but undercharacterized, pressure on organisms that induces metabolic responses such as increased microbial virulence and antibiotic resistance, altered organ weights in developing rats, and loss of bone tissue in astronauts. Numerous studies have analyzed the effects of microgravity on specific organisms, tissues, or test conditions, but these projects are necessarily limited by the small sample size of space research. Increasing the sample size of spaceflight studies is non-trivial; however, pooling data from numerous studies can greatly increase the statistical rigor of comparative analyses. The GeneLab houses datasets from 73 spaceflight studies that performed transcription profiling assays. These data encompass a diverse array of organisms ranging from Escherichia coli to Mus musculus to Homo sapiens and comprise studies analyzing ionizing radiation, mammalian pregnancy, etc. Collectively, the GeneLab database contains a large quantity of transcription assays and RNA sequence data analyzing Differential Gene Expression (DGE) between microand normogravity. Xspecies, a cross-species analysis method for DGE developed by Kristiansson, et al. in 2012, identifies homologous genes between species that are universally up- or downregulated in response to test conditions. Previous work by an intern at GeneLab applied Xspecies to 19 datasets containing seven different species and identified 14 homologous groups differentially expressed under spaceflight conditions including several heat shock proteins and cytoskeletal components. Unfortunately, these results may be biased by the disproportionate number of studies on Arabidopsis thaliana (5) and Mus musculus (6) and the results are not normalized by evolutionary distances. Here, we present modifications to the Xspecies algorithm that permits incorporation of multi-omic data and normalizes data for effect size, directionality, and evolutionary distances. We then apply this algorithm to all currently available GeneLab studies

Xspecies↗

NASA NTRS2018

Differential Adaptive Stress Testing of Airborne Collision Avoidance Systems

The next-generation Airborne Collision Avoidance System (ACAS X) is currently being developed and tested to replace the Traffic Alert and Collision Avoidance System (TCAS) as the next international standard for collision avoidance. To validate the safety of the system, stress testing in simulation is one of several approaches for analyzing near mid-air collisions (NMACs). Understanding how NMACs can occur is important for characterizing risk and informingdevelopment of the system. Recently, adaptive stress testing (AST) has been proposed as a way to find the most likely path to a failure event. The simulation-based approach accelerates search by formulating stress testing as a sequential decision process then optimizing it using reinforcement learning. The approach has been successfully applied to stress test a prototype of ACAS Xin various simulated aircraft encounters. In some applications, we are not as interestedin the system's absolute performance as its performance relative to another system. Such situations arise, for example, during regression testing or when deciding whether a new system should replace an existing system. In our collision avoidance application, we are interested in finding cases where ACAS X fails but TCAS succeeds in resolving a conflict. Existing approaches do not provide an efficient means to perform this type of analysis. This paper extends the AST approach to differential analysis by searching two simulators simultaneously and maximizing the difference between their outcomes. We call this approach differential adaptive stress testing (DAST). We apply DAST to compare a prototype of ACAS X against TCAS and show examples of encounters found by the algorithm.

Lee, Ritchie↗

NASA NTRS2018

Evaluation of 2-μm Pulsed Integrated Path Differential Absorption Lidar for Carbon Dioxide Measurement—Technology Developments, Measurements, and Path to Space

The societal benefits of understanding climate change through the identification of global carbon dioxide sources and sinks led to the recommendation for NASA's Active Sensing of Carbon Dioxide Emissions over Nights, Days, and Seasons space-based mission for global carbon dioxide measurements. For more than 15 years, the NASA Langley Research Center has developed several carbon dioxide active remote sensors using the differential absorption lidar technique operating at 2-μm wavelength. Recently, an airborne double-pulsed integrated path differential absorption lidar was developed, tested, and validated for atmospheric carbon dioxide measurement. Results indicated 1.02% column carbon dioxide measurement uncertainty and 0.28% bias over the ocean. Currently, this technology is progressing toward triple-pulse operation targeting both atmospheric carbon dioxide and water vapor-the dominant interfering molecule on carbon dioxide remote sensing. Measurements from the double-pulse lidar and the advancement of the triple-pulse lidar development are presented. In addition, measurement simulations with a space-based IPDA lidar, incorporating new technologies, are also presented to assess feasibility of carbon dioxide measurements from space.

Singh, Upendra N.↗

NASA NTRS2019

Light Ion Double-Differential Cross Section Parameterization and Results from the SHIELD Transport Code

Light ions and neutrons have been shown to make large contributions to space radiation dose equivalent for realistic shielding scenarios. Efficient and accurate calculations of light ion double-differential cross sections are required for input into space radiation transport codes. A thermal proton cross section model is developed which includes proton production from the three sources of projectile, central fireball, and target. It is shown that this three-source model is able to explain the low momentum shoulder seen in proton spectra. Using the coalescence model, the thermal proton model is used to calculate light ion double-differential cross sections employed in space radiation transport codes. The three-source model is also seen to be essential to explain the light ion shoulders, which are even more pronounced than the proton shoulders. Comparisons are also made to the cross section models used in the SHIELD transport code.

Space radiation↗

NASA NTRSDate not supplied

Altered Immune Differentials Between Male and Female Mice Independent of Ionizing Irradiation

As upcoming exploratory missions to the Lunar surface and Mars during the Artemis Program will send both female and male crewmembers, studies identifying sex-specific effects are necessary. It is well-documented that the immune system engages different responses between females and males following exposures to infectious challenge, tumors surveillance, and autoimmune development. Yet, the immune effects of spaceflight-like exposures between the sexes are limited. Therefore, this study sought to address the effects of spaceflight-like conditions on immune differentials in female and male mice. We hypothesized that the spaceflight factor, ionizing radiation, will have sex-specific effects on immune differentials. To test this, singly-housed, 12-month old female and male wildtype (Wt) mice were exposed to acute ionizing gamma irradiation (50 cGy), followed by retro-orbital blood collections at 7-days post-irradiation. Leukocytes were analyzed by flow cytometry characterizing, granulocytes, monocytes, lymphocytes (cytotoxic/helper T cells and B cells), neutrophils, eosinophils, and NK/NKT cells. Briefly, minimal sex-specific effects were observed across the cell types listed at this time point, including changes in granulocyte and lymphocyte populations. The results revealed females displayed elevated granulocytes and reduced lymphocytes compared to their male counterparts, independent of irradiation exposure. These results suggest female mice may be more capable to produce innate inflammatory mediators but may be adaptively immune compromised. In brief, this study provides insight into the sex-specific immune risks following ionizing radiation that may be experienced during spaceflight, which is relevant for future countermeasure development.

spaceflight stressors↗

NASA NTRSDate not supplied

Altered Immune Differentials Between Male and Female Mice Independent of Ionizing Irradiation

spaceflight stressors↗

NASA NTRS2019

An upgraded G-band differential absorption radar system for future airborne studies

A proof-of-concept, 170 GHz frequency-modulated, continuous-wave (FMCW) radar has been developed for measuring water vapor profiles within the cloudy boundary layer from an airborne platform. The measurement concept exploits the differential absorption accrued by two or more transmitted frequencies in the vicinity of the 183 GHz water absorption line to retrieve range-resolved humidity profiles, so-called differential absorption radar (DAR). The upgraded system design includes important considerations for monostatic radar operation with an open fuselage viewport (i.e. no radome). The radar features an all-solid-state tansmitter with > 0:4 W continuous transmit power, a 60 cm primary aperture and corresponding 58 dB antenna gain, and more than 80 dB transmit/receive isolation, enabling near thermal-noise-limited sensitivity with a 8 dB noise figure receiver. Ice-cloud radar returns are detected beyond 8 km in height from the ground, demonstrating the high sensitivity of the system. In addition to in-cloud humidity profiling capabilities, deployment of a water vapor DAR from an airborne platform enables measurements of total column water vapor (TCWV) for all weather and surface scenarios. Precision estimates and potential biases for future TCWV measurements are discussed.

Monje, Raquel↗

NASA NTRS2020

Mars 2020 Center Differential Pivot Restraint: Flexurized Spring System Providing Compliance for Rover Mobility Deployment Prior to Landing

The Center Differential Pivot Restraint (CDPR) for the Mars 2020 mission is designed to constrain motion of the rover differential and to dampen out the load response of during rover’s mobility deployment event in Entry, Descent, and Landing (EDL) phase of the mission. For Mars 2020, it was required to redesign the mechanism to save minimum 33% of the mass from the previous Mars Science Laboratory (MSL) design. The new mechanism architecture used a monolithic spring-like flexure to act as the system compliance, resulting in 50% mass savings from the MSL design. Along the design and prototype testing process, several mechanism design principles were re-affirmed as well as lessons learned about potential race conditions.

Cameron, Matthew↗

NASA NTRSDate not supplied

Adaptive Optimization for System Performance and Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

The emerging urban air mobility (UAM) sector in aerospace is driving development of unconventional multi-modal vehicle configurations and autonomous flight. The combination of multi-modal vehicle dynamics, complex environment, requirements to deal with flight contingencies in an efficient and safe manner, as well as necessity for precise trajectory following and performance, are the driving influence behind adaptive optimization for system performance. We are interested in trajectory optimization algorithm that would system parameter estimation and identifying the optimal switching time between modes of hybrid dynamical systems. This presentation discusses a parameterized optimal control trajectory optimization algorithm that is an extended and generalized version of Differential Dynamic Programming (DDP), titled Parameterized Differential Dynamic Programming (PDDP). DDP is an efficient trajectory optimization algorithm relying on second order approximations of a system’s dynamics and cost function and has recently been applied to optimize systems with time invariant parameters. Experiments are presented applying PDDP to solve model predictive control (MPC) and moving horizon estimation (MHE) tasks simultaneously. In particular, PDDP is used to determine the optimal transition point between flight regimes of a complex urban air mobility (UAM) class vehicle exhibiting multiple phases of flight and to identify and compensate for actuation faults.

optimization↗

NASA NTRS2022

Constrained Reference Star Differential Imaging: Enabling High-fidelity Imagery of Highly Structured Circumstellar Disks

High-contrast imaging presents us with the opportunity to study circumstellar disks and the planets still embedded within them, providing key insights into the formation and evolution of planetary systems. However, the postprocessing techniques that are often needed to suppress stellar halo light typically result in significant and variable loss of circumstellar light, even when using relatively conservative approaches like reference star differential imaging (RDI). We introduce “constrained reference star differential imaging” (constrained RDI), a new class of RDI point-spread-function (PSF) subtraction techniques for systems with circumstellar disks. Constrained RDI utilizes either high-resolution polarized-intensity (PI) images or disk models to severely limit or even eliminate the signal loss due to oversubtraction that is common to RDI. We demonstrate the ability of constrained RDI utilizing polarimetric data to yield an oversubtraction-free detection of the AB Aurigae protoplanetary disk in total intensity. PI-constrained RDI allows us to decisively recover the spectral signature of the confirmed, recently discovered protoplanet, AB Aurigae b. We further demonstrate that constrained RDI can be a powerful analysis tool for soon-to-be-acquired James Webb Space Telescope coronagraphic imaging of disks. In both cases, constrained RDI provides analysis-ready products that enable more detailed studies of disks and more robust verification of embedded exoplanets.

Kellen Lawson↗

NASA NTRS2023

T-Cell Shenanigans: The Impact of MHC Pathway & Lipid Metabolism Genes on T-Cell Differentiation in the Thymus

Astronaut health and proper immune function are key to the success and sustainability of long term missions in space. While previous studies have observed adaptive immune dysfunction such as diminished WBC counts and cytokine production during spaceflight, the underlying mechanisms behind why immune function worsens are poorly understood. Using transcriptomic data analyzed from mouse thymus tissues available from the GLDS-421 experiment on the Rodent Research-9 mission, we used the GeneLab standardized RNA-Seq pipeline and identified four genes that were largely dysregulated (p<0.05): lipid metabolic genes Hpgd and Pgr and cell cycle regulator genes Cenpe and Kif11. We analyzed how these genes regulate the MHC-TCR interaction, and used this understanding to propose a novel mechanism for alterations to T-cell differentiation. In our experimental methodology, we propose to use 36 transgenic CD4-CD8 mice and 12 wild-type mice from the Jackson Lab to create a microgravity-simulating hindlimb unloading model and test our hypothesis. By silencing the aforementioned genes using custom siRNA based primers, we will use flow cytometry and RNA-Seq to quantify Treg counts in comparison to naive CD4+ cells, Alamar Blue assay for observing the metabolic activity in T-cells, and Enzyme-Linked Immunosorbent Assay (ELISA) to observe the general immune response in terms of T-cell differentiation. We hope this methodology will improve our knowledge of MHC-TCR interaction, contribute to a better understanding of the mechanisms of autoimmune diseases such as lupus, and improve the success rate of newer cancer treatments such as CAR-T cell therapy.

GL4HS↗