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At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Noncommutative-geometry model for closed bosonic strings

It is shown how Witten's (1986) noncommutative geometry may be extended to describe the closed bosonic string. For closed strings, an explicit representation is provided of the integral operator needed to construct an action and of an associative product on string fields. The proper choice of the action of the integral operator and the associative product in order to give rise to a reasonable theory is explained, and the consequences of such a choice are discussed. It is shown that the ghost numbers of the operator and associative product can be chosen arbitrarily for both open and closed strings, and that this construct can be used as an action for interacting closed bosonic strings.

Sen, Siddhartha↗
NASA NTRS1993

Generation and exploration of aggregation abstractions for scheduling and resource allocation

This paper presents research on the abstraction of computational theories for scheduling and resource allocation. The paper describes both theory and methods for the automated generation of aggregation abstractions and approximations in which detailed resource allocation constraints are replaced by constraints between aggregate demand and capacity. The interaction of aggregation abstraction generation with the more thoroughly investigated abstractions of weakening operator preconditions is briefly discussed. The purpose of generating abstract theories for aggregated demand and resources includes: answering queries about aggregate properties, such as gross feasibility; reducing computational costs by using the solution of aggregate problems to guide the solution of detailed problems; facilitating reformulating theories to approximate problems for which there are efficient problem-solving methods; and reducing computational costs of scheduling by providing more opportunities for variable and value-ordering heuristics to be effective. Experiments are being developed to characterize the properties of aggregations that make them cost effective. Both abstract and concrete theories are represented in a variant of first-order predicate calculus, which is a parameterized multi-sorted logic that facilitates specification of large problems. A particular problem is conceptually represented as a set of ground sentences that is consistent with a quantified theory.

Lowry, Michael R.↗
DOE OSTI2017

Macdonald index and chiral algebra

For any 4dN = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. Here, we conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A 1 , A 2n ) and (A 1 , D 2n+1 ) where the chiral algebras are given by Virasoro and $ˆ\atop{su}$(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Quantitative Predictive Theories through Integrating Quantum, Statistical, Equilibrium, and Nonequilibrium Thermodynamics

Today's thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially on the Onsager Theorem as a separate branch of thermodynamics developed in 1930s. Between them, quantum mechanics was invented and was quantitatively solved in terms of density functional theory (DFT) in 1960s. Furthermore, these three scientific domains operate based on different principles and are very much separated from each other. In analogy to the parable of the blind men and the elephant articulated by Perdew, they individually represent different portions of a complex system and thus are incomplete by themselves alone, resulting in the lack of quantitative agreement between their predictions and experimental observations. Over the last two decades, the author's group has developed a multiscale entropy approach (recently termed as zentropy theory) that integrates DFT-based quantum mechanics and Gibbs statistical mechanics and is capable of accurately predicting entropy and free energy of complex systems. Furthermore, in combination with the combined law for nonequilibrium systems developed by Hillert, the author developed the theory of cross phenomena beyond the phenomenological Onsager Theorem. The zentropy theory and theory of cross phenomena jointly provide quantitative predictive theories for systems from electronic to any observable scales as reviewed in the present work.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Constraints on dark matter annihilation to fermions and a photon

Here, we consider Majorana dark matter annihilation to fermion-anti-fermion pair and a photon in the effective field theory paradigm, by introducing dimension 6 and dimension 8 operators in the Lagrangian. For a given value of the cut-off scale, the latter dominates the annihilation process for heavier dark matter masses. We find a cancellation in the dark matter annihilation to a fermion-anti-fermion pair when considering the interference of the dimension 6 and the dimension 8 operators. Constraints on the effective scale cut-off is derived while considering indirect detection experiments and the relic density requirements and they are compared to the bound coming from collider experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

We study ’t Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the “anomaly cocycle” using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group H^3(G,U(1)) × H^2(G,U(1)) H 3 ( G , U ( 1 ) ) × H 2 ( G , U ( 1 ) ) . The first factor captures the anomaly in the internal symmetry group G, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving G and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

Physics↗
NASA NTRS1989

Numerical studies of identification in nonlinear distributed parameter systems

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

Banks, H. T.↗
DOE OSTI2022

MIONet: Learning Multiple-Input Operators via Tensor Product

As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all the existing neural operators are only designed to learn operators defined on a single Banach space; i.e., the input of the operator is a single function. Here, for the first time, we study the operator regression via neural networks for multiple-input operators defined on the product of Banach spaces. We first prove a universal approximation theorem of continuous multiple-input operators. We also provide a detailed theoretical analysis including the approximation error, which provides guidance for the design of the network architecture. Based on our theory and a low-rank approximation, we propose a novel neural operator, MIONet, to learn multiple-input operators. MIONet consists of several branch nets for encoding the input functions and a trunk net for encoding the domain of the output function. Here, we demonstrate that MIONet can learn solution operators involving systems governed by ordinary and partial differential equations. In our computational examples, we also show that we can endow MIONet with prior knowledge of the underlying system, such as linearity and periodicity, to further improve accuracy.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Derivation and experimental verification of clock synchronization theory

The objective of this work is to validate mathematically derived clock synchronization theories and their associated algorithms through experiment. Two theories are considered, the Interactive Convergence Clock Synchronization Algorithm and the Mid-Point Algorithm. Special clock circuitry was designed and built so that several operating conditions and failure modes (including malicious failures) could be tested. Both theories are shown to predict conservative upper bounds (i.e., measured values of clock skew were always less than the theory prediction). Insight gained during experimentation led to alternative derivations of the theories. These new theories accurately predict the clock system's behavior. It is found that a 100% penalty is paid to tolerate worst case failures. It is also shown that under optimal conditions (with minimum error and no failures) the clock skew can be as much as 3 clock ticks. Clock skew grows to 6 clock ticks when failures are present. Finally, it is concluded that one cannot rely solely on test procedures or theoretical analysis to predict worst case conditions. conditions.

INTERACTIVE CONVERGENCE CLOCK↗
DOE OSTI2025

The three-point form factor of Tr ϕ 3 to six loops

We study the three-point form factor of the length-three half-BPS operator (Tr ϕ 3 ) in planar $\mathcal{N}$ = 4 Super-Yang-Mills theory, using analyticity and integrability methods. We find that the functions describing the form factor in perturbation theory live in the same restrictive space of multiple polylogarithms as the one describing the form factor of the stress-tensor operator (Tr ϕ 2 ). Furthermore, we find that the leading-order data in the collinear limit provided by the form factor operator product expansion (FFOPE) is enough to fix the form factor uniquely, at least through six loops. We perform various tests of our results using the subleading FFOPE corrections. We also analyze the form factor in the Regge limit where two Mandelstam invariants are large; we obtain a compact representation for the form factor in this limit which is valid to all orders in the coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

Raman lidar system for the measurement of water vapor and aerosols in the earth's atmosphere

A nighttime operating Raman lidar system that is designed for the measurement of high vertical and temporal resolution profiles of the water vapor mixing ratio and the aerosol backscattering ratio is described. The theory of the measurements is presented. Particular attention is given to operational problems that have been solved during the development of the system. Data are presented from Sept. 1987 and described in their meteorological context.

Whiteman, D. N.↗
DOE OSTI2023

A duality in string theory on AdS 3

We consider bosonic string theory on AdS 3 supported by Kalb-Ramond flux. It is well known that the α' exact worldsheet theory is described by the SL(2,R) WZW model. In this note we perform checks of an α' exact dual description proposed in [arXiv:2104.07233] involving a winding condensate on a free theory background. We give the explicit map of vertex operators for normalizable states on both sides of the duality and demonstrate the equivalence of their two and three point functions by direct computation. The duality is of strong-weak nature in α' .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Well-Posedness and Spectral Analysis of Integrodifferential Equations Arising in Viscoelasticity Theory

We study the well-posedness of initial-value problems for abstract integrodifferential equations with unbounded operator coefficients in Hilbert spaces and provide a spectral analysis of operator functions that are symbols of the specified equations. These equations represent an abstract form of linear partial integrodifferential equations arising in viscoelasticity theory and other important applications. For the said integrodifferential equations, we obtain well-posedness results in weighted Sobolev spaces of vector functions defined on the positive semiaxis and valued in a Hilbert space. For the symbols of the said equations, we find the localization and the structure of the spectrum.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

On the property of measurements with the PTW microLion chamber in continuous beams

Purpose: The performance of liquid ionization chambers, which may prove to be useful tools in the field of radiation dosimetry, is based on several chamber and liquid specific characteristics. The present work investigates the performance of the PTW microLion liquid ionization chamber with respect to recombination losses and perturbations from ambient electric fields at various dose rates in continuous beams. Methods: In the investigation, experiments were performed using two microLion chambers, containing isooctane (C{sub 8}H{sub 18}) and tetramethylsilane [Si(CH{sub 3}){sub 4}] as the sensitive media, and a NACP-02 monitor chamber. An initial activity of approximately 250 GBq {sup 18}F was employed as the radiation source in the experiments. The initial dose rate in each measurement series was estimated to 1.0 Gy min{sup -1} by Monte Carlo simulations and the measurements were carried out during the decay of the radioactive source. In the investigation of general recombination losses, employing the two-dose-rate method for continuous beams, the liquid ionization chambers were operated at polarizing voltages 25, 50, 100, 150, 200, and 300 V. Furthermore, measurements were also performed at 500 V polarizing voltage in the investigation of the sensitivity of the microLion chamber to ambient electric fields. Results: The measurement results from the liquid ionization chambers, corrected for general recombination losses according to the two-dose-rate method for continuous beams, had a good agreement with the signal to dose linearity from the NACP-02 monitor chamber for general collection efficiencies above 70%. The results also displayed an agreement with the theoretical collection efficiencies according to the Greening theory, except for the liquid ionization chamber containing isooctane operated at 25 V. At lower dose rates, perturbations from ambient electric fields were found in the microLion chamber measurement results. Due to the perturbations, measurement results below an estimated dose rate of 0.2 Gy min{sup -1} were excluded from the present investigation of the general collection efficiency. The perturbations were found to be more pronounced when the chamber polarizing voltage was increased. Conclusions: By using the two-dose-rate method for continuous beams, comparable corrected ionization currents from experiments in low and medium energy photon beams can be achieved. However, the valid range of general collection efficiencies has been found to vary in a comparison between experiments performed in continuous beams of 120 kVp x ray, and the present investigation of 511 keV annihilation photons. At very high dose rates in continuous beams, there are presently no methods that can be used to correct for general recombination losses and at low dose rates the microLion chamber may be perturbed by ambient electric fields. Increasing the chamber polarizing voltage, which diminishes the general recombination effect, was found to increase the microLion chamber sensitivity to ambient electric fields. Prudence is thus advised when employing the microLion chamber in radiation dosimetry, as ambient electric fields of the strength observed in the present work may be found in many common situations. Due to uncertainties in the theoretical basis for recombination losses in liquids, further studies on the underlying theories for the initial and general recombination effect are needed if liquid ionization chambers are to become a viable option in high precision radiation dosimetry.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Chiral effective theory of dark matter direct detection

We present the effective field theory for dark matter interactions with the visible sector that is valid at scales of O(1 GeV). Starting with an effective theory describing the interactions of fermionic and scalar dark matter with quarks, gluons and photons via higher dimension operators that would arise from dimension-five and dimension-six operators above electroweak scale, we perform a nonperturbative matching onto a heavy baryon chiral perturbation theory that describes dark matter interactions with light mesons and nucleons. This is then used to obtain the coefficients of the nuclear response functions using a chiral effective theory description of nuclear forces. Our results consistently keep the leading contributions in chiral counting for each of the initial Wilson coefficients.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1973

Study of dynamics of X-14B VTOL aircraft

Research was initiated to investigate certain facets of modern control theory and their integration with a digital computer to provide a tractable flight control system for a VTOL aircraft. Since the hover mode is the most demanding phase in the operation of a VTOL aircraft, the research efforts were concentrated in this mode of aircraft operation. Research work on three different aspects of the operation of the X-14B VTOL aircraft is discussed. A general theory for optimal, prespecified, closed-loop control is developed. The ultimate goal was optimal decoupling of the modes of the VTOL aircraft to simplify the pilot's task of handling the aircraft. Modern control theory is used to design deterministic state estimators which provide state variables not measured directly, but which are needed for state variable feedback control. The effect of atmospheric turbulence on the X-14B is investigated. A maximum magnitude gust envelope within which the aircraft could operate stably with the available control power is determined.

Loscutoff, W. V.↗
NASA NTRS2000

Wind Tunnel Management and Resource Optimization: A Systems Modeling Approach

Time, money, and, personnel are becoming increasingly scarce resources within government agencies due to a reduction in funding and the desire to demonstrate responsible economic efficiency. The ability of an organization to plan and schedule resources effectively can provide the necessary leverage to improve productivity, provide continuous support to all projects, and insure flexibility in a rapidly changing environment. Without adequate internal controls the organization is forced to rely on external support, waste precious resources, and risk an inefficient response to change. Management systems must be developed and applied that strive to maximize the utility of existing resources in order to achieve the goal of "faster, cheaper, better". An area of concern within NASA Langley Research Center was the scheduling, planning, and resource management of the Wind Tunnel Enterprise operations. Nine wind tunnels make up the Enterprise. Prior to this research, these wind tunnel groups did not employ a rigorous or standardized management planning system. In addition, each wind tunnel unit operated from a position of autonomy, with little coordination of clients, resources, or project control. For operating and planning purposes, each wind tunnel operating unit must balance inputs from a variety of sources. Although each unit is managed by individual Facility Operations groups, other stakeholders influence wind tunnel operations. These groups include, for example, the various researchers and clients who use the facility, the Facility System Engineering Division (FSED) tasked with wind tunnel repair and upgrade, the Langley Research Center (LaRC) Fabrication (FAB) group which fabricates repair parts and provides test model upkeep, the NASA and LARC Strategic Plans, and unscheduled use of the facilities by important clients. Expanding these influences horizontally through nine wind tunnel operations and vertically along the NASA management structure greatly increases the complexity of developing a model that can be used for successfully implementing a standardized management planning tool. The objective of this study was to implement an Integrated Wind Tunnel Planning System to improve the operations within the aeronautics testing and research group, in particular Wind Tunnel Enterprise. The study included following steps: Conducted literature search and expert discussions (NASA and Old Dominion University faculty), Performed environmental scan of NASA Langley wind tunnel operations as foundation for problem definition. Established operation requirements and evaluation methodologies. Examined windtunnel operations to map out the common characteristics, critical components, and system structure. Reviewed and evaluated various project scheduling and management systems for implementation, Evaluated and implemented "Theory of Constraints (TOC)" project scheduling methodology at NASA Langley wind tunnel operations together with NASA staff.

Jacobs, Derya, A.↗