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Results for “complexity theory”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description

Methods for development of logic design together with algorithms for failure testing, a method for design of logic for ultra-large-scale integration, extension of quantum calculus to describe the functional behavior of a mechanism component-by-component and to computer tests for failures in the mechanism using the diagnosis algorithm, and the development of an algorithm for the multi-output 2-level minimization problem are discussed.

Roth, J. P.↗
NASA NTRS1969

On the shell equations in complex form.

Linear thin shell theory in complex dependent variable form for determining fourth order partial differential equations, considering elastic shells with edge loads

Sanders, J. L., Jr.↗
DOE OSTI2025

Cation-π Bonding in Actinides: UO x + (Benzene) ( x = 0, 1, 2) Complexes Studied with Threshold Photodissociation Spectroscopy and Theory

Cation-π complexes of the form UO x + (benzene) (x = 0, 1, 2) are produced by laser vaporization and cooled in a supersonic molecular beam. These ions are mass selected and studied with UV–visible laser photodissociation spectroscopy. Each of these complexes photodissociates by elimination of the benzene ligand. Above an energetic threshold, the absorption and photodissociation are continuous, indicating a high density of strongly coupled electronic states. The thresholds for the dissociation of each of these three complexes are measured and assigned as their respective bond dissociation energies. The bond energies determined [U + –(benzene): 42.5 ± 0.3 kcal/mol; UO + –(benzene): 41.0 ± 0.3 kcal/mol; UO 2 + –(benzene): 39.7 ± 0.3 kcal/mol] are comparable to those of transition metal ion-benzene complexes. Computational studies at the DFT/B3LYP level complement the experiments, predicting dissociation energies in reasonably good agreement with the experiments. Experiments and theory agree that the U+(benzene) complex is more strongly bound than its corresponding oxide ions. This new thermochemistry on actinide cation-π bonding should stimulate higher-level computational studies on these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Impact Testing Theories and Techniques Employed at the TA-III Mechanical Shock Complex

We present theories and techniques to support safe, predictable, and efficient impact testing at the Sandia National Laboratories TA-III Mechanical Shock Complex (MSC), located in Building 6570. The two testing instruments used at the MSC are the 20-inch actuator, which is a launcher that propels sleds down an indoor track, and an indoor 6-in bore compressed-gas powered cannon. The theories and techniques presented derive from basic mechanical engineering principles but are significantly informed and validated by testing experience at the MSC.

42 ENGINEERING↗
DOE OSTI2025

Operator origin of anomalous dimensions in de Sitter space

The late-time limit of the power spectrum for heavy (principal series) fields in de Sitter (dS) space yields a series of polynomial terms with complex scaling dimensions. Such scaling behavior is expected to result from an associated operator with a complex dimension. In a free theory, these complex dimensions are known to match the constraints imposed by unitarity on the space of states. Yet, perturbative corrections to the scaling behavior of operators are naively inconsistent with unitary evolution of the quantum fields in dS space. This paper demonstrates how to compute one-loop corrections to the scaling dimensions that appear in the two-point function from the field theory description in terms of local operators. We first show how to evaluate these anomalous dimensions using Mellin space, which has the feature that it naturally accommodates a scaleless regulator. We then explore the consequences for the soft de Sitter effective theory (SdSET) description that emerges in the long wavelength limit. Carefully matching between the UV and SdSET descriptions requires the introduction of novel nondynamical “operators” in the effective theory. This is not only necessary to reproduce results extracted from the Källén-Lehmann representation (that use the space of unitary states directly), but it is also required by general arguments that invoke positivity. Published by the American Physical Society 2025

Cohen, Timothy↗
DOE OSTI2025

Quantum graph learning and algorithms applied in quantum computer sciences and image classification

Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1974

Electron detachment in low-energy collisions of H/-/ and D/-/ with He

The applicability of the complex-potential theory to H(-)-He collisions is investigated. Measurements are conducted of the elastic differential cross section for H(-)-He collisions, taking into account energies in the range from 5 to 120 eV. A preliminary determination is made of the energy spectrum of detached electrons. The results are interpreted in terms of the complex-potential theory. The crossing point is determined together with the general shape of the HeH(-) potential curve.

Lam, S. K.↗
NASA NTRS1996

Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

Reuther, James↗
NASA NTRS1974

Subsonic potential aerodynamics for complex configurations - A general theory

A general theory of subsonic potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the velocity potential is obtained for both supersonic and subsonic flow. Under the small perturbation assumption, the potential at any point in the field depends only upon the values of the potential and its normal derivative on the surface of the body. On the surface of the body, this representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface. The theory is applied to finite-thickness wings in subsonic steady and oscillatory flows.

Morino, L.↗
NASA NTRS1992

Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence

The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.

Non-NASA Center↗
NASA NTRS1990

Removing spurious reflections from CFD solutions by using the Complex Cepstrum

The Complex Cepstrum is shown to remove spurious reflections from artificial boundaries in computational fluid dynamic (CFD) solutions. First, the Complex Cepstrum theory is presented. A model time sequence consisting of a direct signal and reflections is analyzed theoretically with the Complex Cepstrum, and it is shown that the direct signal uncontaminated by reflections may be recovered in the time domain. Next, the Complex Cepstrum is applied to one- and three-dimensional CFD solutions, and spurious reflections from the boundary conditions are removed. By eliminating spurious reflections introduced by artificial boundary conditions, the applicability of CFD methods to aeroacoustic problems is greatly enhanced.

Meadows, Kristine R.↗
NASA NTRS1988

Application of transonic slender body theory to bodies of varying complexity

Transonic flows over several bodies of varying complexity including a simple wing-body combination and the Shuttle Orbiter have been modeled with the use of slender body theory. Flows with various angles of attack have been considered. Also some off-body flow calculations were conducted. For attached flows, the calculations predicted the pressure results with good accuracy.

Rajagopal, Karunamurthy↗
NASA NTRS1981

An extension of the local momentum theory to a distorted wake model of a hovering rotor

The local momentum theory is based on the instantaneous balance between the fluid momentum and the blade elemental lift at a local station in the rotor rotational plane. Therefore, the theory has the capability of evaluating time wise variations of air loading and induced velocity distributions along a helicopter blade span. Unlike a complex vortex theory, this theory was developed to analyze the instantaneous induced velocity distribution effectively. The boundaries of this theory and a computer program using this theory are discussed. A concept introduced into the theory is the effect of the rotor wake contraction in hovering flight. A comparison of this extended local momentum theory with a prescribed wake vortex theory is also presented. The results indicate that the extended local momentum theory has the capability of achieving a level of accuracy similar to that of the prescribed wake vortex theory over wide range variations of rotor geometrical parameters. It is also shown that the analytical results obtained using either theory are in reasonable agreement with experimental data.

Kawachi, K.↗
NASA NTRS2004

Network Theory: A Primer and Questions for Air Transportation Systems Applications

A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.

Holmes, Bruce J.↗