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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 1,045 records · Page 58
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

On gauge amplitudes first appearing at two loops

We study scattering amplitudes in massless non-abelian gauge theory where all outgoing gluons have positive helicity. It has been argued recently by Costello that for a particular fermion representation (8 fundamentals plus one antisymmetric-tensor representation in SU(N)) the one-loop amplitudes vanish identically. We show that this vanishing leads to previously-observed identities among one-loop color-ordered partial amplitudes. We then turn to two loops, where Costello has computed the all-plus amplitudes for this theory, as rational functions of the kinematics for any number of gluons using the celestial chiral algebra (CCA) bootstrap. We show that in dimensional regularization, these two-loop amplitudes are not rational, and they are not even finite as ϵ → 0. However, the finite remainder for four gluons agrees with the formula by Costello. In addition, we provide a mass regulator for the infrared-divergent loop integrals; with this regulator, the CCA bootstrap formula is recovered exactly. Finally, we use the CCA bootstrap to compute the double-trace terms in the theory at two loops for an arbitrary number of gluons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

On gauge amplitudes first appearing at two loops

We study scattering amplitudes in massless non-abelian gauge theory where all outgoing gluons have positive helicity. It has been argued recently by Costello that for a particular fermion representation (8 fundamentals plus one antisymmetric-tensor representation in SU(N)) the one-loop amplitudes vanish identically. We show that this vanishing leads to previously-observed identities among one-loop color-ordered partial amplitudes. We then turn to two loops, where Costello has computed the all-plus amplitudes for this theory, as rational functions of the kinematics for any number of gluons using the celestial chiral algebra (CCA) bootstrap. We show that in dimensional regularization, these two-loop amplitudes are not rational, and they are not even finite as ϵ → 0. However, the finite remainder for four gluons agrees with the formula by Costello. In addition, we provide a mass regulator for the infrared-divergent loop integrals; with this regulator, the CCA bootstrap formula is recovered exactly. Finally, we use the CCA bootstrap to compute the double-trace terms in the theory at two loops for an arbitrary number of gluons.

Dixon, Lance J↗
NASA NTRS1986

Navier-Stokes computations for circulation controlled airfoils

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Pulliam, T. H.↗
NASA NTRS1987

Navier-Stokes computations for circulation control airfoils

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Pulliam, Thomas H.↗
DOE OSTI2015

Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence

Herein, we use the 3d–3d correspondence together with the DGG construction of theories T n [ M ] labelled by 3-manifolds M to define a non-perturbative state-integral model for \({SL(n,\mathbb{C})}\) Chern–Simons theory at any level k , based on ideal triangulations. The resulting partition functions generalize a widely studied k = 1 state-integral, as well as the 3d index, which is k = 0. The Chern–Simons partition functions correspond to partition functions of T n [ M ] on squashed lens spaces L ( k , 1). At any k , they admit a holomorphic-antiholomorphic factorization, corresponding to the decomposition of L ( k , 1) into two solid tori, and the associated holomorphic block decomposition of the partition functions of T n [ M ]. A generalization to L ( k , p ) is also introduced. Convergence of the state integrals, for any k , requires triangulations to admit a positive angle structure; we propose that this is also necessary for the DGG gauge theory T n [ M ] to flow to a desired IR SCFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Conjugacy Analysis of the Finite-Difference Equations of the Method of Characteristics on the Basis of a Linear-Algebraic Formulation

A linear-algebraic form of the equations of the method of characteristics, which is used to approximate the neutron transport equation, is obtained. It is shown on the basis of the obtained linear-algebraic form that the discrete form of the conjugate equation differs from the algebraically discrete problem constructed by linear-algebraic transformations of the discrete form of the normal problem. The reason for the discrepancy lies in the approximation of the volumes of the spatial cells in covering the working region by a network of characteristics. It is shown by means of test calculations that when the network of characteristics is refined the solution of the conjugate transport equation converges to the solution of the algebraically conjugate problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Reconstructing householder vectors from Tall-Skinny QR

The Tall-Skinny QR (TSQR) algorithm is more communication efficient than the standard Householder algorithm for QR decomposition of matrices with many more rows than columns. However, TSQR produces a different representation of the orthogonal factor and therefore requires more software development to support the new representation. Further, implicitly applying the orthogonal factor to the trailing matrix in the context of factoring a square matrix is more complicated and costly than with the Householder representation. We show how to perform TSQR and then reconstruct the Householder vector representation with the same asymptotic communication efficiency and little extra computational cost. We demonstrate the high performance and numerical stability of this algorithm both theoretically and empirically. The new Householder reconstruction algorithm allows us to design more efficient parallel QR algorithms, with significantly lower latency cost compared to Householder QR and lower bandwidth and latency costs compared with Communication-Avoiding QR (CAQR) algorithm. Experiments on supercomputers demonstrate the benefits of the communication cost improvements: in particular, our experiments show substantial improvements over tuned library implementations for tall-and-skinny matrices. Furthermore, we also provide algorithmic improvements to the Householder QR and CAQR algorithms, and we investigate several alternatives to the Householder reconstruction algorithm that sacrifice guarantees on numerical stability in some cases in order to obtain higher performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

AMG Preconditioners based on parallel hybrid coarsening and multi-objective graph matching

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package \texttt{PSCToolkit} to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter $\lambda$. We compute the matching by a parallel $2/3-\varepsilon$-approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter $\lambda$ we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

D'Ambra, Pasqua↗
DOE OSTI2018

Abstract Algebra Basics

To understand the mathematics behind Uncertainty Quantification (UQ), one first needs to become familiar with orthogonal polynomials, which in turn requires a grasp of abstract algebra. This note covers some of the basics of abstract algebra.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

A feedback control model for network flow with multiple pure time delays

A control model describing a network flow hindered by multiple pure time (or transport) delays is formulated. Feedbacks connect each desired output with a single control sector situated at the origin. The dynamic formulation invokes the use of differential difference equations. This causes the characteristic equation of the model to consist of transcendental functions instead of a common algebraic polynomial. A general graphical criterion is developed to evaluate the stability of such a problem. A digital computer simulation confirms the validity of such criterion. An optimal decision making process with multiple delays is presented.

Press, J.↗
NASA NTRS1982

Linear-Algebra Programs

The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

Lawson, C. L.↗
NASA NTRS1989

A comparative study of Navier-Stokes codes for high-speed flows

A comparative study was made with four different codes for solving the compressible Navier-Stokes equations using three different test problems. The first of these cases was hypersonic flow through the P8 inlet, which represents inlet configurations typical of a hypersonic airbreathing vehicle. The free-stream Mach number in this case was 7.4. This 2-D inlet was designed to provide an internal compression ratio of 8. Initial calculations were made using two state-of-the-art finite-volume upwind codes, CFL3D and USA-PG2, as well as NASCRIN, a code which uses the unsplit finite-difference technique of MacCormack. All of these codes used the same algebraic eddy-viscosity turbulence model. In the experiment, the cowl lip was slightly blunted; however, for the computations, a sharp cowl leading edge was used to simplify the construction of the grid. The second test problem was the supersonic (Mach 3.0) flow in a three-dimensional corner formed by the intersection of two wedges with equal wedge angles of 9.48 degrees. The flow in such a corner is representative of the flow in the corners of a scramjet inlet. Calculations were made for both laminar and turbulent flow and compared with experimental data. The three-dimensional versions of the three codes used for the inlet study (CFL3D, USA-PG3, and SCRAMIN, respectively) were used for this case. For the laminar corner flow, a fourth code, LAURA, which also uses recently-developed upwind technology, was also utilized. The final test case is the two-dimensional hypersonic flow over a compression ramp. The flow is laminar with a free-stream Mach number of 14.1. In the experiment, the ramp angle was varied to change the strength of the ramp shock and the extent of the viscous-inviscid interaction. Calculations were made for the 24-degree ramp configuration which produces a large separated-flow region that extends upstream of the corner.

Rudy, David H.↗
NASA NTRS1991

Spatial operator approach to under-actuated manipulator kinematics and dynamics

A study is made of the kinematics and dynamics of under-actuated manipulators. The presence of passive hinges causes the kinematics and dynamics of these manipulators to be considerably more complex when compared with fully actuated manipulators. Techniques from the spatial operator algebra are used to develop expressions for the generalized Jacobian, the mass matrix, and an efficient inverse dynamics computational algorithm.

Jain, A.↗
NASA NTRS1992

Hybrid analytical technique for the nonlinear analysis of curved beams

The application of a two-step hybrid technique to the geometrically nonlinear analysis of curved beams is used to demonstrate the potential of hybrid analytical techniques in nonlinear structural mechanics. The hybrid technique is based on successive use of the perturbation method and a classical direct variational procedure. The functions associated with the various-order terms in the perturbation expansion of the fundamental unknowns, and their sensitivity derivatives with respect to material and geometric parameters of the beam, are first obtained by using the perturbation method. These functions are selected as coordinate functions (or modes) and the classical direct variational technique is then used to compute their amplitudes. The potential of the proposed hybrid technique for nonlinear analysis of structures is discussed. The effectiveness of the hybrid technique is demonstrated by means of numerical examples. The symbolic computation system Mathematica is used in the present study. The tasks performed on Mathematica include: (1) generation of algebraic expressions for the perturbation functions of the different response quantities and their sensitivity derivatives: and (2) determination of the radius of convergence of the perturbation series.

Noor, A. K.↗
NASA NTRS1994

High level language-based robotic control system

This invention is a robot control system based on a high level language implementing a spatial operator algebra. There are two high level languages included within the system. At the highest level, applications programs can be written in a robot-oriented applications language including broad operators such as MOVE and GRASP. The robot-oriented applications language statements are translated into statements in the spatial operator algebra language. Programming can also take place using the spatial operator algebra language. The statements in the spatial operator algebra language from either source are then translated into machine language statements for execution by a digital control computer. The system also includes the capability of executing the control code sequences in a simulation mode before actual execution to assure proper action at execution time. The robot's environment is checked as part of the process and dynamic reconfiguration is also possible. The languages and system allow the programming and control of multiple arms and the use of inward/outward spatial recursions in which every computational step can be related to a transformation from one point in the mechanical robot to another point to name two major advantages.

Rodriguez, Guillermo↗