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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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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

A Mathematical Basis for the Safety Analysis of Conflict Prevention Algorithms

In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.

Maddalon, Jeffrey M.↗
DOE OSTI2025

Scalable Unit Commitment with Security Constrained AC Power Flow via ADMM and Hybrid Modeling Strategies

This research introduces a more efficient way to optimize power grid operations, breaking the problem into manageable steps and using advanced mathematical techniques to speed up calculations. By incorporating smart heuristics, improved preprocessing, and contingency analysis, the approach allows operators to make better decisions faster. These innovations enhance our understanding of how to optimize energy generation, making it possible to anticipate failures before they happen, reduce system costs, and improve overall grid performance. Ultimately, this research helps bridge the gap between theoretical models and real-world applications, paving the way for a smarter, more resilient power grid. This research directly benefits the public by making electricity more affordable, reliable, and sustainable. By improving how power grids schedule and distribute electricity, the project helps energy providers reduce operational costs, which can lead to lower electricity prices for consumers. Additionally, the ability to predict and prevent power system failures enhances grid reliability, reducing the likelihood of blackouts that can disrupt homes, businesses, and critical infrastructure such as hospitals. From an environmental perspective, optimizing power generation reduces energy waste and lowers carbon emissions, contributing to cleaner air and a more sustainable energy system. Furthermore, with extreme weather events becoming more frequent, these advancements make the power grid more resilient, ensuring communities are better prepared for emergencies and natural disasters. By strengthening the nation's energy infrastructure, this research plays a crucial role in improving economic stability, public safety, and environmental sustainability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On principles of emergent organization

After more than a century of concerted effort, physics still lacks basic principles of spontaneous organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then an overview of two modern mathematical formulations of organization—intrinsic computation and evolution operators—lays out a way to overcome these challenges. Together, the vantage point they afford shows how to account for the emergence of structured states via a statistical mechanics of systems arbitrarily far from equilibrium. The result is a constructive path forward to principles of organization that builds on mathematical identification of structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Define Minimum Safe Operational Volume for Aerial Vehicles in Upper Class E Airspace

This work presents both analytical and simulation studies for defining the minimum safe operational volume needed for aerial vehicles operating in upper Class E airspace. The analytical study is conducted first to investigate factors that affect the minimum safe operational volume, such as position errors, wake/vortex, vehicle maneuverability, communication and surveillance, control/operator response time. A mathematical approach is developed to compute the boundary of the safe operational volume required by the limited aircraft maneuverability and an analytical sensitivity study is then performed with varying parameters. After the analytical study, simulations are then conducted to verify the results from the analytical study. Simulation results will be included in the final paper.

Separation standard, well-clear definition, upper ↗
DOE OSTI2020

Analysis of Tempered Fractional Operators

Tempered fractional operators are useful in models for subsurface transport and diffusion due to their ability to capture anomalous diffusion: a behavior which the classical partial differential equation models cannot describe. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators in correspondence of a proper choice of nonlocal kernels. Then, we work towards showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Analysis of Tempered Fractional Operators

Tempered fractional operators provide an improved predictive capability for modeling anomalous effects that cannot be captured by standard partial differential equations. These effects include subdiffusion and superdiffusion (i.e. the mean square displacement in a diffusion process is proportional to a fractional power of the time), that often occur in, e.g., geoscience and hydrology. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators by means of a proper choice of the nonlocal kernel. Then, we present a plan for showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Adjoint-Operator Learning For A Neural Network

Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.

Barhen, Jacob↗
NASA NTRS1981

Flight evaluation of a simple total energy-rate system with potential wind-shear application

Wind shears can create havoc during aircraft terminal area operations and have been cited as the primary cause of several major aircraft accidents. A simple sensor, potentially having application to the wind-shear problem, was developed to rapidly measure aircraft total energy relative to the air mass. Combining this sensor with either a variometer or a rate-of-climb indicator provides a total energy-rate system which was successfully applied in soaring flight. The measured rate of change of aircraft energy can potentially be used on display/control systems of powered aircraft to reduce glide-slope deviations caused by wind shear. The experimental flight configuration and evaluations of the energy-rate system are described. Two mathematical models are developed: the first describes operation of the energy probe in a linear design region and the second model is for the nonlinear region. The calculated total rate is compared with measured signals for many different flight tests. Time history plots show the tow curves to be almost the same for the linear operating region and very close for the nonlinear region.

Ostroff, A. J.↗
DOE OSTI2020

Development and Evaluation of Distributed Energy Resource Device Models: Electric Vehicles, Electric Water Heaters, and Commercial Refrigeration Systems

In order to validate distributed energy resource (DER) models operated with grid services in the GMLC 1.4.2 team’s February (GMLC 2019a) and July (GMLC 2019b) reports, a test and measurement program using actual DER devices was conducted by national laboratories for three devices: (1) electric vehicles (EVs), (2) water heaters, and (3) commercial refrigeration. Test procedures were developed and carried out to identify the mathematical models and their parameters that describe the operational function, characterize the physics, and obey transient response of the devices. This report focuses on the experimental results obtained to develop and verify simulations of three specific EV models. This section summarizes elements of the mathematical model and shows the necessity data collected from the EVs while charging and discharging (driving). In the course of the study, we found it necessary to make some modifications to the model to deal with observed transient behavior. Section 1.2 details the model assumptions and equations, Section 1.3 provides details of the EVs tested, Section 1.4 outlines the test procedures developed for the projects, and Section 1.5 presents the experimental results obtained for the three different EVs tested and how these results compare to the models running the same test profiles.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1998

Model Based Autonomy for Robust Mars Operations

Space missions have historically relied upon a large ground staff, numbering in the hundreds for complex missions, to maintain routine operations. When an anomaly occurs, this small army of engineers attempts to identify and work around the problem. A piloted Mars mission, with its multiyear duration, cost pressures, half-hour communication delays and two-week blackouts cannot be closely controlled by a battalion of engineers on Earth. Flight crew involvement in routine system operations must also be minimized to maximize science return. It also may be unrealistic to require the crew have the expertise in each mission subsystem needed to diagnose a system failure and effect a timely repair, as engineers did for Apollo 13. Enter model-based autonomy, which allows complex systems to autonomously maintain operation despite failures or anomalous conditions, contributing to safe, robust, and minimally supervised operation of spacecraft, life support, In Situ Resource Utilization (ISRU) and power systems. Autonomous reasoning is central to the approach. A reasoning algorithm uses a logical or mathematical model of a system to infer how to operate the system, diagnose failures and generate appropriate behavior to repair or reconfigure the system in response. The 'plug and play' nature of the models enables low cost development of autonomy for multiple platforms. Declarative, reusable models capture relevant aspects of the behavior of simple devices (e.g. valves or thrusters). Reasoning algorithms combine device models to create a model of the system-wide interactions and behavior of a complex, unique artifact such as a spacecraft. Rather than requiring engineers to all possible interactions and failures at design time or perform analysis during the mission, the reasoning engine generates the appropriate response to the current situation, taking into account its system-wide knowledge, the current state, and even sensor failures or unexpected behavior.

Kurien, James A.↗
DOE OSTI2022

Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems

Abstract Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1970

Mechanism of operation of the TFE-bonded gas-diffusion electrode

Mathematical analytical model predicts the performance of an electrode as a function of certain measurable physical characteristics. Concept assumes the catalyst particles form porous electrically conductive agglomerates which are completely flooded with electrolyte.

Giner, J.↗
NASA NTRS1973

Minitrack tracking function description, volume 2

The minitrack tracking function is described and specific operations are identified. The subjects discussed are: (1) preprocessor listing, (2) minitrack hardware, (3) system calibration, (4) quadratic listing, and (5) quadratic flow diagram. Detailed information is provided on the construction of the tracking system and its operation. The calibration procedures are supported by mathematical models to show the application of the computer programs.

Englar, T. S.↗
NASA NTRS1972

Precision timing and Very Long Baseline Interferometry (VLBI)

The use of very long baseline interferometry (VLBI) for investigating small angular features in galactic and extragalactic radio sources is discussed. Mathematical models are developed to describe the operation of an interferometer and to show the variations in the resultant fringe frequency. The types of sources to which the interferometer will respond are identified.

Clark, T. A.↗
NASA NTRS1972

GEODYN system support program, volume 4

The GEODYN Orbit Determination and Geodetic Parameter Estimation System consists of a set of computer programs designed to determine and analyze definitive satellite orbits and their associated geodetic and measurement parameters. This manual describes the Support Programs used by the GEODYN System. The mathematics and programming descriptions are detailed. The operational procedures of each program are presented. GEODYN ancillary analysis programs may be grouped into three different categories: (1) orbit comparison - DELTA (2) data analysis using reference orbits - GEORGE, and (3) pass geometry computations - GROUNDTRACK. All of the above three programs use one or more tapes written by the GEODYN program in either a data reduction or orbit generator run.

Mullins, N. E.↗
NASA NTRS1976

Two-photon coherent states of the radiation field

The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.

Yuen, H. P.↗