SEARCH · Search NASA

Results for “theory building”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

DOE OSTI2022

A Glimpse into Photodetachment Spectra of Giant and Nested Fullerene Anions

We focus on the study of the photodetachment of bare, i.e., single-cage (CN)− as well as nested (multi-cage) (CN@CM@…)− singly charged fullerene anions. We calculate the attached electron’s wavefunctions, energies, oscillator strengths and photodetachment cross sections of the C60−, C240−, C540−, (C60@C240)−, (C60@C540)−, (C240@C540)− and (C60@C240@C540)− fullerene anions, where the attached electron is captured into the ground s-state by the resultant external field provided by all fullerene cages in the anion. The goal is to gain insight into the changes in behavior ofphotodetachment of this valence electron as a function of the different geometries and potentials of the various underlying fullerenes or nested fullerenes (fullerene onions) both due to their increasing size and due to “stuffing” of a larger bare fullerene with smaller fullerenes. To meet this goal, we opt for a simple semi-empirical approximation to this problem: we approximate each individual fullerene cage by a rigid potential sphere of a certain inner radius, thickness and potential depth, as in numerous other model studies performed to date. The results reveal a number of rather significant differences in the wavefunctions, oscillator strengths and photodetachment cross sections among these fullerene anions, some of which are completely counter-intuitive. The results obtained can serve as a “zeroth-order-touchstone” for future studies of single-cage and nested fullerene anions by more rigorous theories and/or experiments to build upon this work to assess the importance of interactions omitted in the present study.

Dolmatov, Valeriy K.↗

DOE OSTI2026

Position Operators in Terms of Converging Finite-Dimensional Matrices and Their Intertwining with Geometry, Transport, and Gauge

The position operator 𝑟̂ appears as 𝑖∂ 𝑝 in wave mechanics, while its matrix form (e.g., under a Bloch basis) is well known diverging in diagonals, causing difficulties in basis transformation, observable yielding, etc. We aim to find a convergent r-matrix (CRM) to improve the existing divergent r-matrix (DRM), and investigate its influence at both the conceptual and the application levels. A key modification is increasing the familiar substitution of 𝑟̂ by 𝑖∂ 𝑝 to 𝑖∑ 𝑗 ∂ 𝑘 𝑗 , namely the N-th Weyl algebra. Resolving the divergence makes r-matrix rigorously defined, and we are able to show r-matrix is distinct from a spin matrix in terms of its defining principles, transformation behavior, and the observable it yields. Conceptually, the CRM fills the logical gap between the r-matrix and the Berry connection (this unremarked vagueness has caused the diagonal divergence). In application, we focus on transport, and discover that the Hermitian matrix is not identical with the associative Hermitian operator, i.e., 𝑟 𝑚,𝑛 = 𝑟$^∗_{𝑛,𝑚}$ ⇎ 𝑟̂ = 𝑟̂ † , which subtly affects the celebrated Berry curvature formula for adiabatic current. We also discuss how such a non-representation CRM can contribute to building a unified transport theory.

Weyl algebras↗

NASA NTRS1991

System monitoring and diagnosis with qualitative models

A substantial foundation of tools for model-based reasoning with incomplete knowledge was developed: QSIM (a qualitative simulation program) and its extensions for qualitative simulation; Q2, Q3 and their successors for quantitative reasoning on a qualitative framework; and the CC (component-connection) and QPC (Qualitative Process Theory) model compilers for building QSIM QDE (qualitative differential equation) models starting from different ontological assumptions. Other model-compilers for QDE's, e.g., using bond graphs or compartmental models, have been developed elsewhere. These model-building tools will support automatic construction of qualitative models from physical specifications, and further research into selection of appropriate modeling viewpoints. For monitoring and diagnosis, plausible hypotheses are unified against observations to strengthen or refute the predicted behaviors. In MIMIC (Model Integration via Mesh Interpolation Coefficients), multiple hypothesized models of the system are tracked in parallel in order to reduce the 'missing model' problem. Each model begins as a qualitative model, and is unified with a priori quantitative knowledge and with the stream of incoming observational data. When the model/data unification yields a contradiction, the model is refuted. When there is no contradiction, the predictions of the model are progressively strengthened, for use in procedure planning and differential diagnosis. Only under a qualitative level of description can a finite set of models guarantee the complete coverage necessary for this performance. The results of this research are presented in several publications. Abstracts of these published papers are presented along with abtracts of papers representing work that was synergistic with the NASA grant but funded otherwise. These 28 papers include but are not limited to: 'Combined qualitative and numerical simulation with Q3'; 'Comparative analysis and qualitative integral representations'; 'Model-based monitoring of dynamic systems'; 'Numerical behavior envelopes for qualitative models'; 'Higher-order derivative constraints in qualitative simulation'; and 'Non-intersection of trajectories in qualitative phase space: a global constraint for qualitative simulation.'

Kuipers, Benjamin↗

NASA NTRS2009

A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing

The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.

Takaki, Mitsuo↗

NASA NTRS2016

Global Comparison of CFD and Wind-Tunnel-Derived Force and Moment Databases for the Space Launch System

Recently a very large (739 runs) collection of high-fidelity RANS CFD solutions was obtained for Space Launch System ascent aerodynamics for the vehicle to be used for the first exploratory (unmanned) mission (EM-1). The extensive computations, at full-scale conditions, were originally developed to obtain detailed line and protuberance loads and surface pressures for venting analyses. The line loads were eventually integrated for comparison of the resulting forces and moments to the database that was derived from wind tunnel tests conducted at sub-scale conditions. The comparisons presented herein cover the ranges 0.5 < or = M(infinity) < or = 5, −6deg < or = alpha < or = 6deg, and −6deg < or = beta < or = 6deg. For detailed comparisons, slender-body-theory-based component build-up aero models from missile aerodynamics are used. The differences in the model fit coefficients are shown to be relatively small except for the low supersonic Mach number range, 1.1 < or = M(infinity) < or = 2.0. The analysis is intended to support process improvement and development of uncertainty models.

Hemsch, Michael J.↗

NASA NTRS2018

Advanced Symbolic Analysis Tools for Fault-Tolerant Integrated Distributed Systems

The project aims to develop advanced model-checking algorithms and tools to automate the verification of fault-tolerant distributed systems for avionics. We present a new method called Property-Directed K-Induction (PD-KIND) for synthesizing K-inductive invariants of state-transition systems. PD-KIND builds upon Satifiability Modulo Theories (SMT) to generalize Bradley's IC3 method and its variants. This method is implemented in a new tool called SALLY. Case studies show that PD-KIND can automatically verify fault-tolerant algorithms under a variety of fault models and that SALLY is competitive with other SMT-based model checkers.

Dutertre, Bruno↗

NASA NTRSDate not supplied

Toward Time Synchronization in Delay Tolerant Network based Solar System Internetworking

The expanding presence in space will place an increased dependency on networked communications– a scalable communications infrastructure; that is, the Solar System Internet (SSI). Upcoming developments towards a SSI include NASA’s upcoming LunaNet, or lunar Internet, which provides multi-hop multi-path communications using Delay Tolerant Networking (DTN). DTN has been an active area of research and development, particularly in routing, security, and optimization. DTNs are marked by mobility, disconnection, and a wide variance of latencies (propagation and processing delays). In this paper, we outline progress towards a theory of time synchronization across such a network. An underlying assumption of DTN is that the network is time synchronized already, rather than synchronization being provided as a service. While this is necessary for schedule-based routing, which is necessarily prevalent in DTNs, it is so deeply ingrained as to be built into the primary unit of data in DTNs– the bundle. Indeed, a bundle’s creation timestamp and its time to live (called the lifetime) are based on time, and there are special recommendations for systems that lack accurate clocks. The assumption of time synchronization makes sense when limiting considerations to smaller-scale and more traditional space communication. However, just as end-to-end connectivity cannot be guaranteed in DTNs, neither can access to a reference or authoritative clock. In this more general case, it might be necessary to synchronize over time-varying meshes, and perhaps even to consider relativistic effects. Moreover, by imposing synchronization restrictions in order to sustain a network, the effectiveness of the network to achieve scalability will be necessarily muted. To work towards a time synchronization theory for DTNs, we build upon past successes in modeling DTNs using time-varying graphs and sheaves. This includes error and limitation estimation, which allows one to define domains over which schedule-based routing is possible, up to some threshold sensitivity. Despite the theoretical nature of these results, the approaches taken are also algorithmic, and hence lend themselves to practical implementations. The paper concludes with comparisons of the various methods along with suggestions for future work.

Delay Tolerant Networking↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Update of the ISTP Solar Maximum Mission: ISTP Project Scientist for Theory and Ground-Based Observations

Building upon the numerous successes of the pre-solar maximum International Solar Terrestrial Physics (ISTP) mission, the ISTP Solar Maximum Mission is expected to produce new insights into global flow of energy, momentum, and mass, from the Sun, through the heliosphere, into the magnetosphere and to their final deposition in the terrestrial upper atmosphere/ionosphere system. Of particular interest is the determination of the geo-effectiveness of solar events, principally Coronal Mass Ejections (CMEs). Given the expected increased frequency and strength of CMEs during the Solar Maximum period, a major advance in our understanding of nature of the coupling of CMEs to the magnetosphere-ionosphere-atmosphere system is expected. The roles during this time of the various ISTP assets will be discussed. These assets will include the SOHO, Wind, Polar, and Geotail spacecraft, the ground-based observing networks and the theory tools.

Curtis, Steve↗

DOE OSTI2025

Baryon number violation: from nuclear matrix elements to BSM physics

Processes that violate baryon number, most notably proton decay and $n\bar{n}$ transitions, are promising probes of physics beyond the Standard Model (BSM) needed to understand the lack of antimatter in the Universe. To interpret current and forthcoming experimental limits, theory input from nuclear matrix elements to UV complete models enters. Thus, an interplay of experiment, effective field theory, lattice QCD, and BSM model building is required to develop strategies to accurately extract information from current and future data and maximize the impact and sensitivity of next-generation experiments. Here, we briefly summarize the main results and discussions from the workshop ‘INT-25-91W: Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics,’ held at the Institute for Nuclear Theory, University of Washington, Seattle, WA, 13–17 January 2025.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Controlling extrapolations of nuclear properties with feature selection

Predictions of nuclear properties far from measured data are inherently inaccurate because of uncertainties in our knowledge of nuclear forces and in our treatment of quantum many-body effects in strongly-interacting systems. While the model bias can be directly calculated when experimental data is available, only an estimate can be made in the absence of such measurements. Current approaches to compute the estimated bias quickly lose predictive power when their input variables are taken far from the training region, resulting in uncontrolled uncertainties in applications such as nucleosynthesis simulations. In this letter, we present a novel technique to identify the input variables of machine learning algorithms that can provide robust estimates of model bias. Our process is based on selecting input variables, or features, based on their probability distribution functions across the entire nuclear chart. We illustrate our approach on the problem of quantifying the model bias in nuclear binding energies calculated with Density Functional Theory (DFT). We prove that building model biases with only Z and N as features leads to highly unreliable extrapolations. Conversely, we show that proper feature selection can systematically improve theoretical predictions without increasing uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Precision Computations in Strongly Coupled Conformal Field Theories (Final Technical Report)

Conformal Field Theories (CFTs) are quantum field theories that are invariant under the conformal symmetry group (which includes translations and rotations, but also local rescalings of spacetime). They are building blocks of general quantum field theories, and appear in many areas of physics, including statistical physics, condensed matter physics, particle physics, and quantum gravity. Because of their extra symmetries, the mathematical structure of CFTs is tightly constrained, and this leads to the idea of the ``conformal bootstrap," which is to use these mathematical structures to constrain, and in some cases determine, CFT observables. A new numerical implementation of the conformal bootstrap idea appeared in 2008 with the work of Rattazzi, Rychkov, Tonni, and Vichi. Their observation was that certain bootstrap constraints (conformal symmetry and unitarity) could be combined to yield a convex optimization problem that constraints CFT data. By solving this convex optimization problem on a computer, one could obtain bounds on observables like critical exponents and operator product expansion (OPE) coefficients. Over the course of this award, the PI has improved numerical bootstrap techniques by optimizing known algorithms and finding new ones for performing the required convex optimization computations. The PI has applied these techniques to compute high-precision observables in several important strongly-coupled systems. The PI has also explored both analytical and numerical bootstrap methods for constraining the space of low energy effective field theories of quantum gravity, and developed new analytical techniques for CFT and QFT more broadly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, extended PINNs (XPINNs) based on domain decomposition methods have attracted considerable attention due to their effectiveness in modeling multiscale and multiphysics problems and their parallelization. However, theoretical understanding of their convergence and generalization properties remains unexplored. In this study, we take an initial step towards understanding how and when XPINNs outperform PINNs. Specifically, for general multilayer PINNs and XPINNs, we first provide a prior generalization bound via the complexity of the target functions in the PDE problem and a posterior generalization bound via the posterior matrix norms of the networks after optimization. Moreover, based on our bounds, we analyze the conditions under which XPINNs improve generalization. Concretely, our theory shows that the key building block of XPINN, namely, the domain decomposition, introduces a tradeoff for generalization. On the one hand, XPINNs decompose the complex PDE solution into several simple parts, which decreases the complexity needed to learn each part and boosts generalization. On the other hand, decomposition leads to less training data being available in each subdomain, and hence such a model is typically prone to overfitting and may become less generalizable. Empirically, we choose five PDEs to show when XPINNs perform better than, similar to, or worse than PINNs, hence demonstrating and justifying our new theory.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2002

Dynamical Approach Study of Spurious Numerics in Nonlinear Computations

The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.

Yee, H. C.↗

NASA NTRS2016

Theoretical Aeroacoustics: Compiled Mathematical Derivations of Fereidoun 'Feri' Farassat

Dr. Fereidoun 'Feri' Farassat was a theoretical aero-acoustician at the National Aeronautics and Space Administration (NASA) Langley Research Center. This book contains technical derivations, notes, and classes that Dr. Farassat produced during his professional career. The layout of the book has been carefully crafted so that foundational ideas through advanced theories, which altered the technical discipline of aeroacoustics, build upon one another. The book can be used to understand the theories of acoustics and learn one contemporary aeroacoustic prediction approach made popular by Dr. Farassat. Most importantly, this book gives the general reader insight into how one of NASA's best aeroacoustics theoreticians thought, constructed, and solved problems throughout his career.

Miller, Steven A. E.↗

NASA NTRS2008

The Gravity Probe B Experiment

This presentation briefly describes the Gravity Probe B (GP-B) Experiment which is designed to measure parts of Einstein's general theory of relativity by monitoring gyroscope orientation relative to a distant guide star. To measure the miniscule angles predicted by Einstein's theory, it was necessary to build near-perfect gyroscopes that were approximately 50 million times more precise than the best navigational gyroscopes. A telescope mounted along the central axis of the dewar and spacecraft provided the experiment's pointing reference to a guide star. The telescope's image divide precisely split the star's beam into x-axis and y-axis components whose brightness could be compared. GP-B's 650-gallon dewar, kept the science instrument inside the probe at a cryogenic temperature for 17.3 months and also provided the thruster propellant for precision attitude and translation control. Built around the dewar, the GP-B spacecraft was a total-integrated system, comprising both the space vehicle and payload, dedicated as a single entity to experimentally testing predictions of Einstein's theory.

Kolodziejczak, Jeffrey↗

DOE OSTI2020

Circumnavigating collinear superspace

In this paper, we extend the collinear superspace formalism to include the full range of N = 1 supersymmetric interactions. Building on the effective field theory rules developed in a companion paper — Navigating Collinear Superspace — we construct collinear superspace Lagrangians for theories with non-trivial F- and D-term auxiliary fields. For (massless) Wess-Zumino models, the key ingredient is a novel type of Grassmann-valued supermultiplet whose lowest component is a (non-propagating) fermionic degree of freedom. For gauge theories coupled to charged chiral matter, the key ingredient is a novel type of vector superfield whose lowest component is a non-propagating gauge potential. This unique vector superfield is used to construct a gauge-covariant derivative; while such an object does not appear in the standard full superspace formalism, it is crucial for modeling gauge interactions when the theory is expres sed on a collinear slice. This brings us full circle, by showing that all types of N = 1 theories in four dimensions can beconstructed in collinear superspace from purely infrared considerations. We speculate that supersymmetric theories with N > 1 could also be implemented using similar collinear superspace constructions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗