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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2010

A National Partnership-Based Summer Learning Initiative to Engage Underrepresented Students with Science, Technology, Engineering and Mathematics

In response to the White House Educate to Innovate campaign, NASA developed a new science, technology, engineering, and mathematics (STEM) education program for non-traditional audiences that also focused on public-private partnerships and nationwide participation. NASA recognized that summer break is an often overlooked but opportune time to engage youth in STEM experiences, and elevated its ongoing commitment to the cultivation of diversity. The Summer of Innovation (SoI) is the resulting initiative that uses NASA's unique missions and resources to boost summer learning, particularly for students who are underrepresented, underserved and underperforming in STEM. The SoI pilot, launched in June 2010, is a multi-faceted effort designed to improve STEM teaching and learning through partnership, multi-week summer learning programs, special events, a national concluding event, and teacher development. The SoI pilot features strategic infusion of NASA content and educational resource materials, sustainability through STEM Learning Communities, and assessments of effectiveness of SoI interventions with other pilot efforts. This paper examines the inception and development of the Summer of Innovation pilot project, including achievements and effectiveness, as well as lessons learned for future efforts.

Melvin, Leland↗
NASA NTRS2003

Software for Training in Pre-College Mathematics

The Intelligent Math Tutor (IMT) is a computer program for training students in pre-college and college-level mathematics courses, including fundamentals, intermediate algebra, college algebra, and trigonometry. The IMT can be executed on a server computer for access by students via the Internet; alternatively, it can be executed on students computers equipped with compact- disk/read-only-memory (CD-ROM) drives. The IMT provides interactive exercises, assessment, tracking, and an on-line graphing calculator with algebraic-manipulation capabilities. The IMT provides an innovative combination of content, delivery mechanism, and artificial intelligence. Careful organization and presentation of the content make it possible to provide intelligent feedback to the student based on performance on exercises and tests. The tracking and feedback mechanisms are implemented within the capabilities of a commercial off-the-shelf development software tool and are written in the Unified Modeling Language to maximize reuse and minimize development cost. The graphical calculator is a standard feature of most college and pre-college algebra and trigonometry courses. Placing this functionality in a Java applet decreases the cost, provides greater capabilities, and provides an opportunity to integrate the calculator with the lessons.

Shelton, Robert O.↗
NASA NTRS2012

Mathematical Simulation for Integrated Linear Fresnel Spectrometer Chip

A miniaturized solid-state optical spectrometer chip was designed with a linear gradient-gap Fresnel grating which was mounted perpendicularly to a sensor array surface and simulated for its performance and functionality. Unlike common spectrometers which are based on Fraunhoffer diffraction with a regular periodic line grating, the new linear gradient grating Fresnel spectrometer chip can be miniaturized to a much smaller form-factor into the Fresnel regime exceeding the limit of conventional spectrometers. This mathematical calculation shows that building a tiny motionless multi-pixel microspectrometer chip which is smaller than 1 cubic millimter of optical path volume is possible. The new Fresnel spectrometer chip is proportional to the energy scale (hc/lambda), while the conventional spectrometers are proportional to the wavelength scale (lambda). We report the theoretical optical working principle and new data collection algorithm of the new Fresnel spectrometer to build a compact integrated optical chip.

Park, Yeonjoon↗
NASA NTRS2012

A Mathematical Analysis of Air Traffic Priority Rules

This paper analyzes priority rules, such as those in Part 91.113 of the Federal Aviation Regulations. Such rules determine which of two aircraft should maneuver in a given conflict scenario. While the rules in 91.113 are well accepted, other concepts of operation for NextGen, such as self separation, may allow for different priority rules. A mathematical framework is presented that can be used to analyze a general set of priority rules and enables proofs of important properties. Specific properties considered in this paper include safety, effectiveness, and stability. A set of rules is said to be safe if it ensures that it is never the case that both aircraft have priority. They are effective if exactly one aircraft has priority in every situation. Finally, a set of rules is called stable if it produces compatible results even under small changes to input data.

Nakawicz, Anthony J.↗
NASA NTRS2013

Mathematical Models of the Common-Source and Common-Gate Amplifiers using a Metal-Ferroelectric-Semiconductor Field effect Transistor

Mathematical models of the common-source and common-gate amplifiers using metal-ferroelectric- semiconductor field effect transistors (MOSFETs) are developed in this paper. The models are compared against data collected with MOSFETs of varying channel lengths and widths, and circuit parameters such as biasing conditions are varied as well. Considerations are made for the capacitance formed by the ferroelectric layer present between the gate and substrate of the transistors. Comparisons between the modeled and measured data are presented in depth as well as differences and advantages as compared to the performance of each circuit using a MOSFET.

Hunt, Mitchell↗
NASA NTRS1993

Mathematical Description of Complex Chemical Kinetics and Application to CFD Modeling Codes

A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.

Bittker, D. A.↗
NASA NTRS2016

A Mathematical Model and Algorithm for Routing Air Traffic Under Weather Uncertainty

A central challenge in managing today's commercial en route air traffic is the task of routing the aircraft in the presence of adverse weather. Such weather can make regions of the airspace unusable, so all affected flights must be re-routed. Today this task is carried out by conference and negotiation between human air traffic controllers (ATC) responsible for the involved sectors of the airspace. One can argue that, in so doing, ATC try to solve an optimization problem without giving it a precise quantitative formulation. Such a formulation gives the mathematical machinery for constructing and verifying algorithms that are aimed at solving the problem. This paper contributes one such formulation and a corresponding algorithm. The algorithm addresses weather uncertainty and has closed form, which allows transparent analysis of correctness, realism, and computational costs.

uncertainty↗
NASA NTRS2017

Surface-Height Determination of Crevassed Glaciers-Mathematical Principles of an Autoadaptive Density-Dimension Algorithm and Validation Using ICESat-2 Simulator (SIMPL) Data

Glacial acceleration is a main source of uncertainty in sea-level-change assessment. Measurement of ice-surface heights with a spatial and temporal resolution that not only allows elevation-change calculation, but also captures ice-surface morphology and its changes is required to aid in investigations of the geophysical processes associated with glacial acceleration.The Advanced Topographic Laser Altimeter System aboard NASAs future ICESat-2 Mission (launch 2017) will implement multibeam micropulse photon-counting lidar altimetry aimed at measuring ice-surface heights at 0.7-m along-track spacing. The instrument is designed to resolve spatial and temporal variability of rapidly changing glaciers and ice sheets and the Arctic sea ice. The new technology requires the development of a new mathematical algorithm for the retrieval of height information.We introduce the density-dimension algorithm (DDA) that utilizes the radial basis function to calculate a weighted density as a form of data aggregation in the photon cloud and considers density an additional dimension as an aid in auto-adaptive threshold determination. The auto-adaptive capability of the algorithm is necessary to separate returns from noise and signal photons under changing environmental conditions. The algorithm is evaluated using data collected with an ICESat-2 simulator instrument, the Slope Imaging Multi-polarization Photon-counting Lidar, over the heavily crevassed Giesecke Braer in Northwestern Greenland in summer 2015. Results demonstrate that ICESat-2 may be expected to provide ice-surface height measurements over crevassed glaciers and other complex ice surfaces. The DDA is generally applicable for the analysis of airborne and spaceborne micropulse photon-counting lidar data over complex and simple surfaces.

Herzfeld, Ute C.↗
NASA NTRS2021

Mathematical Characterization of Battery Models

The purpose of this document is to demonstrate the use of the Extended Kalman Filter as a tool for battery state estimation and the estimation of battery state of charge. The mathematical details based on the equivalent circuit model are presented followed by an electrochemical engineering model. A simplified first-order model is used to demonstrate the procedure followed by second and third-order models. Next a simplified electrochemistry model is presented along with observer development. State observability is calculated for the simpler equivalent circuit models and the simplified electrochemistry model. An outline of the battery model parameter identification method is presented, and model performance based on experimental and flight data is demonstrated.

Battery↗
NASA NTRS2021

Mathematical Model Development and Experimental Verification of Electromagnetic Force Actuators for use in Space Applications

This technical memorandum shows the development of the mathematics needed to model several types of electromagnetic force actuators that may be of interest for use in space applications. The actuators described are capable of providing attractive, repulsive, and longitudinal forces between the actuator and a variety of metal surfaces. Potential applications for these propellant free actuators include spacecraft docking, in-space fabrication, robotic spacecraft inspection and servicing, deflection of metallic debris, and interaction with iron core asteroids (e.g., landing, repelling, and relocating).

Robert C. Youngquist↗
NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗
DOE OSTI2020

A Mathematical Framework for Representing Cyber-Physical System Interdependencies and Resilience

U.S. critical infrastructure is increasingly composed of integrated cyber-physical systems (CPS) whose components are operationally interdependent. These interdependencies can create additional vulnerabilities beyond those that are typically evaluated through independent physical and cyber risk assessments. These additional vulnerabilities, previously undetected at the sub-system and/or component level, could cause cascading effects across both the physical and cyber domains that could lead to infrastructure disruption or failure. This paper will review an initial mathematical framework developed to help understand the dynamics of these interfacing physical and cyber components at a holistic system level. The resulting framework also provides a method for modeling and assessing the resilience of CPS in complex and adaptive systems. It frames the system in terms of mission performance and the potential effects to performance caused by attacks that are cyber, physical, or blended in nature. The framework utilizes a systems-based, state-space modeling approach to reason about risk, resilience, and interdependencies in CPS. Probabilities are applied to each CPS component regarding a threat (both man-made and natural) and the likelihood of that particular component being impacted, along with indirect impact to other interdependent components. These component-level impacts from threats then translate into mission-level impact and systemic state change.

Brigantic, Robert T.↗
DOE OSTI2024

Mathematical methods for neutrino cross-section extraction

Precise modeling of neutrino-nucleus scattering is becoming increasingly important as accelerator-based oscillation experiments seek definitive answers to open questions about neutrino properties. To guide the needed model refinements, a growing number of experimental collaborations are pursuing a wide-ranging program of neutrino interaction measurements at GeV energies. A key step in most such analyses is cross-section extraction, in which measured event counts are corrected for background contamination and imperfect detector performance to yield cross-section results that are directly comparable to theoretical predictions. In this paper, I review the major approaches to cross-section extraction in the literature using representative examples from the MINERvA, MicroBooNE, and T2K experiments. I then present two mathematical techniques, blockwise unfolding and the conditional covariance background constraint, which overcome some limitations of typical cross-section extraction procedures.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

SISTec: Mathematical Calibration of Large Clearance Monitors - 18265

One major path for clearance of large amount of waste arising from the decommission of nuclear power plants is based on measurement with large clearance monitors (also known as free release measurement facilities). These devices utilize multi-detector plastic scintillator arrays (large clearance monitors can consist of up to 24 plastic scintillators) to offer both, extremely low minimum detectable activities (MDA) and short measurement times for waste packages weighing up to one metric ton. However, a major problem with these devices is to obtain nuclide specific efficiencies, especially for geometrically complex large waste packages. Normal procedure for estimating the efficiency is to device dummy waste packages and attach point sources with well-known activities to unfavourable positions in these packages. In accordance with this procedure, calibration factors can be derived in a radiological conservative way. Devising such test dummies is not always possible and the procedure is prone to generating large measurement uncertainties. In this publication, we propose a new method to derive calibration factors by means of the Los Alamos National Laboratory (LANL) simulation tool Monte Carlo N-Particle (MCNP) and a statistical-phenomenological model for the detector characterization. In a multi-step approach, first the detector response for a distribution of activity in a waste package is calculated and subsequently the detectors are mathematically characterized. Applying state of the art statistical and optimizing procedures, parameters for the detector response are derived in a self-consistent way. This also allows to rigorously propagate the uncertainties to the final calculated calibration factors according to the Guide to the Expression of Uncertainty in Measurement (GUM supplement 1). To validate the derived parameters for the detector characterization a minimally invasive experimental setup was devised and installed into the large clearance monitor. It consisted of an aluminum swivel arm which could position point sources to the relevant coordinates. The so collected measurement data not only allowed to investigate the precision of the calculated calibration factors, but also to probe the location of concentrated activity sources in the waste package. Furthermore, data on measurements with dummy waste packages were collected to test the reproducibility of well-known calibration factors. We present the software tool SIStec, which will provide an intuitive user-interface to generate and simulate waste package models and execute the above-mentioned method. Using SIStec, different scenarios for the distribution of activity in the waste package can be probed. This will also allow to optimize the clearance process on various levels. For example, measurement time for pre-measurements can be reduced in exchange for unfavourable calibration factors, which would still allow to meet the regulator limits for clearance. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

R-Functions Method in the Mathematical Modeling of Convective Heat Exchange in an Octahedral Fuel Assembly with 37 Fuel Elements

We consider conjugate boundary-value problems of heat exchange for the cases where a viscous incompressible liquid moves through channels with noncanonical cross section flowing around a bundle of rods. The influence of the type of packing on the velocity and temperature distributions is investigated. For the solution, we use the R-functions method in combination with the Ritz variational method. We consider the cases of cyclic, staggered, and rectangular packing of fuel elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment

Espresso is a beverage brewed using hot, high-pressure water forced through a bed of roasted coffee. Despite being one of the most widely consumed coffee formats, it is also the most susceptible to variation. Here, we report a novel model, complimented by experiment, that is able to isolate the contributions of several brewing variables, thereby disentangling some of the sources of variation in espresso extraction. Under the key assumption of homogeneous flow through the coffee bed, a monotonic decrease in extraction yield with increasingly coarse grind settings is predicted. However, experimental measurements show a peak in the extraction yield versus grind setting relationship, with lower extraction yields at both very coarse and fine settings. This result strongly suggests that inhomogeneous flow is operative at fine grind settings, resulting in poor reproducibility and wasted raw material. With instruction from our model, we outline a procedure to eliminate these shortcomings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Analysis of tumor-immune functional responses in a mathematical model of neoantigen cancer vaccines

Cancer neoantigen vaccines have emerged as a promising approach to stimulating the immune system to fight cancer. We propose a simple model including key elements of cancer-immune interactions and conduct a phase plane analysis to understand the immunological mechanisms of cancer neoantigen vaccines. Analytical results are obtained for two widely used functional forms that represent the killing rate of tumor cells by immune cells: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Using the LMA, our results reveal that a slowly growing tumor can escape the immune surveillance and that there is a unique periodic solution. The LPR offers richer dynamics, in which tumor elimination and uncontrolled tumor growth are both present. We show that tumor elimination requires sufficient number of initial activated T cells in relationship to the malignant cells, which lends support to using the neoantigen cancer vaccine as an adjuvant therapy after the primary tumor is surgically removed or treated using radiotherapy. We also derive a sufficient condition for uncontrolled tumor growth under the assumption of the LPR. Here, the juxtaposition of analyses with these two different choices for the killing rate function highlights their importance on model behavior and biological implications, by which we hope to spur further theoretical and experimental work to understand mechanisms underlying different functional forms for the killing rate.

60 APPLIED LIFE SCIENCES↗