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At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory

The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3 , ζ 5 to the cusp anomalous dimension.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1983

Transition to turbulence in plane channel flow

A numerical simulation of the final stages of transition to turbulence in plane channel flow is reported. Three dimensional, incompressible Navier-Stokes equations are numerically integrated to obtain the time-evolution of two and three dimensional finite amplitude disturbances. Computations are performed on the CYBER-203 vector processor for a 32x51x32 grid. Results are presented for no-slip boundary conditions at the solid walls as well as for periodic suction-blowing to simulate active control of transition by mass transfer. Solutions indicate that the method is capable of simulating the complex character of vorticity dynamics during the various stages of transition and final breakdown. In particular, evidence points to the formation of a lambda-shape vortex and the subsequent system of horseshoe vortices inclined to the main flow direction as the main elements of transition. Calculations involving suction-blowing indicate that interference with a wave of suitable phase and amplitude reduces the disturbance growth rates.

Biringen, S.↗

NASA NTRS1987

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗

NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

Hall, Kenneth C.↗

NASA NTRS1977

Flutter of articulated pipes at finite amplitude

The plane motion of an articulated pipe made of two segments is examined and the flow velocity at which flutter manifests itself is sought. The pressure in the reservoir feeding the pipe is kept constant. In contrast to previous works, the flow velocity is not taken as a prescribed parameter of the system but is left to follow the laws of motion. This approach requires a nonlinear formulation of the problem and the equations of motion are solved using Krylov-Bogoliubov's method. A graph of the amplitude of the limit cycles, as a function of the fluid-system mass ratio, is presented and conclusions are drawn as to the necessity of considering nonlinearities in the analysis.

Rousselet, J.↗

NASA NTRS1975

Effect of Nozzle Nonlinearities upon Nonlinear Stability of Liquid Propellant Rocket Motors

A three dimensional, nonlinear nozzle admittance relation is developed by solving the wave equation describing finite amplitude oscillatory flow inside the subsonic portion of a choked, slowly convergent axisymmetric nozzle. This nonlinear nozzle admittance relation is then used as a boundary condition in the analysis of nonlinear combustion instability in a cylindrical liquid rocket combustor. In both nozzle and chamber analyses solutions are obtained using the Galerkin method with a series expansion consisting of the first tangential, second tangential, and first radial modes. Using Crocco's time lag model to describe the distributed unsteady combustion process, combustion instability calculations are presented for different values of the following parameters: (1) time lag, (2) interaction index, (3) steady-state Mach number at the nozzle entrance, and (4) chamber length-to-diameter ratio. In each case, limit cycle pressure amplitudes and waveforms are shown for both linear and nonlinear nozzle admittance conditions. These results show that when the amplitudes of the second tangential and first radial modes are considerably smaller than the amplitude of the first tangential mode the inclusion of nozzle nonlinearities has no significant effect on the limiting amplitude and pressure waveforms.

Padmanabhan, M. S.↗

NASA NTRS1994

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Tam, Christopher K. W.↗

NASA NTRS1994

A method of measuring the amplitude-modulated vacuum field near a conducting mirror

Electromagnetic fields of the vacuum mode near a conducting mirror are modified with respect to those in free space, with their amplitudes having a sinusoidal spatial dependence from the mirror. Therefore if we combine this spatially amplitude-modulated vacuum field mode and intense coherent light with a beam splitter, we may detect this fluctuation of the vacuum mode in a homodyne detection scheme. It will give a new method to produce squeezed states of light with a single mirror placed close to an unused port of a beam splitter. We show that the amplitude fluctuation of the combined light can be reduced by a factor of 2 below that of the coherent light. We also discuss the limitations due to the finite line width of the laser and the effective absorption length of the photodiodes.

Youn, Sun-Hyun↗

DOE OSTI2020

A Dynamic Amplitude-Correcting Gradient Estimation Technique to Align X-ray Focusing Optics

High-brightness X-rays, as produced at synchrotrons and X-ray free electron laser (XFEL) facilities, are used to characterize materials in a variety of scientific experiments. In most cases, effective use of the high-energy light requires precisely-aligned focusing optics; one example being a compound refractive lens (CRL). To align a CRL, the position and rotation must be optimized along four axes. In practice, this is a labor-intensive, time-consuming manual process that can monopolize scarce experimental time at the necessary X-ray facilities. Models of the expected Xray transmission function suggest that this task can be automated; however, the temporally-varying intensity at X-ray free electron laser facilities preclude the direct use of standard implementations of optimization solvers such as steepest descent algorithms. In this paper, we propose a novel technique to estimate the gradient of noisy functions with temporally-varying amplitudes. We construct this dynamicamplitude correction by systematically sampling a fixed central location within the standard finite difference stencil, accounting for the observed changes in time, and normalizing the difference quotients against those fluctuations. In addition to a rigorous error analysis of the sampling technique, we demonstrate its efficacy in stochastic descent optimization methods. Further, we demonstrate how this approach may be implemented to optimize X-ray focusing optics at synchrotrons or XFEL facilities

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Detecting isolated resonance curves using fixed frequency voltage control tests

Isolated resonance curves, or isolas, are resonance branches of the harmonically forced system that exist separately from the main nonlinear forced response curve, leading to excessive vibrations. Traditional stepped or swept sine simulations and tests rely on continuation along the frequency parameter, typically resulting in a jump phenomenon along the primary resonance branch, prior to the disconnected isola. The main objective of this research is to propose an approach to identify isolated resonance curves by performing continuation along the input amplitude that initializes the response from a low-amplitude solution in the linear regime. Furthermore, this is achieved with the open-loop fixed frequency voltage control method that continues along the shaker voltage parameter and measures the so-called S-curves, which are theoretically a continuous solution branch that connect to the isola. The methodology is demonstrated on a fixture-wing-pylon assembly with a vibro-impact nonlinearity localized in a pylon subcomponent attachment. Multi-harmonic balance simulations are deployed to compute both the nonlinear forced response curves and S-curves to demonstrate the isola detection strategy on a reduced-order finite element model of the nonlinear system. Swept sine and fixed frequency voltage control tests are then conducted on the physical structure to demonstrate the isola detection experimentally, revealing the existence of the large amplitude vibrations that are undetected in the forces levels and frequencies measured with traditional frequency sweeping.

Characterization and Analytical Technique↗

NASA NTRS1992

The NASA/Industry Design Analysis Methods for Vibrations (DAMVIBS) Program - Boeing helicopters airframe finite element modeling

Finite-element modeling of the airframe vibration of the Army/Boeing CH-47D helicopter is conducted with comparisons to experimental data in an effort to improve the design process. A NASTRAN FEM is developed that is fully representative of the test configuration and includes the support fixture, shakers, and the aircraft/shaker suspension system. The analysis is conducted with specific attention given to the prediction of reasonable forced amplitudes throughout the airframe. Reasonable correlation is noted between the FEM and experimental results, although improved correlation can be obtained by including more accurate damping values and secondary effects such as stringer shear loading. It is shown that the general stress model does not provide an adequate dynamic analysis on which to base design improvements. A more detailed model is required that emphasizes highly detailed helicopter elements and employs a finer mesh particularly in the description of the mass distribution.

Gabel, R.↗

NASA NTRS2005

Convection in Ice I with Composite Newtonian/Non-Newtonian Rheology: Application to the Icy Galilean Satellites

Ice I exhibits a complex rheology at temperature and pressure conditions appropriate for the interiors of the outer ice I shells of Europa, Ganymede, and Callisto. We use numerical methods to determine the conditions required to trigger convection in an ice I shell with a stress-, temperature-, and grain-size-dependent rheology measured in laboratory experiments by Goldsby and Kohlstedt [2001] (henceforth GK2001). Triggering convection from an initially conductive ice shell with a non-Newtonian rheology for ice I requires that a finite-amplitude temperature perturbation be issued to the ice shell [2]. Here, we characterize the amplitude and wavelength of temperature perturbation required to initiate convection in the outer ice I shells of Europa, Ganymede, and Callisto using the GK2001 rheology for a range of ice grain sizes.

Barr, Amy C.↗

DOE OSTI2025

First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order

We compute the conservative and radiation-reaction contributions to classical observables in the gravitational scattering between a spinning and a spinless black hole to the fourth order in spin and third order in the gravitational constant. The conservative results are obtained from two-loop amplitudes for the scattering process of a massive scalar with a massive spin-𝑠 field (𝑠=0, 1, 2) minimally coupled to gravity, employing the recently introduced spin interpolation method to resolve all spin-Casimir terms. The two-loop amplitude exhibits a spin-shift symmetry in both probe limits, which we conjecture to be a sign of yet unknown integrability of Kerr orbits through the quartic order in spin and to all orders in the gravitational constant. We obtain the radial action from the finite part of the amplitude and use it to compute classical observables, including the impulse and spin kick. This is done using the recently introduced covariant Dirac brackets, which allow for the computation of classical scattering observables for general (nonaligned) spin configurations. Finally, employing the radiation-reaction amplitude proposed by Alessio and Di Vecchia, together with the Dirac brackets, we obtain radiation-reaction contributions to observables at all orders in spin and beyond the aligned-spin limit. We find agreement with known results up to the quadratic order in spin for both conservative and radiation-reaction contributions. Our results advance the state of the art in the understanding of spinning binary dynamics in general relativity and demonstrate the power and simplicity of the Dirac bracket formalism for relating scattering amplitudes to classical observables.

general relativity↗

NASA NTRS1996

Free-Surface and Contact Line Motion of Liquid in Microgravity

This project involves fundamental studies of the role of nonlinearity in determining the motion of liquid masses under the principal influences of surface tension, viscosity and inertia. Issues to be explored are relevant to aspects of terrestrial processes, as well as being immediately applicable to fluid management in a low-gravity environment. Specific issues include: (1) the mechanic's of liquid masses in large-amplitude motions, (2) the influence of bounding surfaces on the motion, and (3) the ability of such surfaces to control liquid motion by wetting forces, especially when they are augmented by various surface treatments. Mathematical techniques include asymptotic analysis of the governing equations, for problem simplification, and numerical simulation, using both boundary-element and finite-difference methods. The flow problem is divided into an 'outer' or inviscid potential-flow region and one or more inner, or viscous dominated, regions. Relevant to one inner region, the vicinity of the contact line, we discuss time-dependent simulation of slow droplet motion, on a surface of variable wettability, using the lubrication approximation. The simulation uses a disjoining pressure model and reproduces realistic wetting-dewetting behavior.

Schwartz, Leonard W.↗

DOE OSTI2025

Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description

Here, this work applies a reduced basis method to study the continuum physics of a finite quantum system—either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schrödinger equation and train the emulators against the equation's bound-state-like solutions at complex energies. The emulators rapidly and accurately interpolate and extrapolate the matrix elements of the Hamiltonian resolvent operator (Green's function) across a parameter space that includes both complex energy and other real-valued physical inputs in the Schrödinger equation. The spectra, discretized and compressed as the result of emulation, and the associated resolvent matrix elements (or amplitudes), have the defining characteristics of non-Hermitian quantum mechanics calculations, featuring complex eigenenergies with negative imaginary parts and branch cuts moved below the real axis in the complex energy plane. Therefore, one now has a method that extracts continuum physics from bound-state-like calculations and emulates those extractions in the input parameter space. Building on a prior Letter [Zhang, Phys. Rev. Lett. 135, 242501 (2025)], this article provides the full theoretical details, a comprehensive analysis of the method's performance, and a brief discussion of how it can be coupled with existing continuum approaches to perform emulations in their input parameter spaces.

ab initio calculations↗

NASA NTRS1969

Wave propagation in a random medium

A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.

Lee, R. W.↗

NASA NTRS1974

Combustion instability with partial length acoustic liners

The development of analytical techniques and numerical methods for the prediction of the stability behavior of liquid propellant rocket combustors is discussed. The studies involved nonlinear wave propagation effects and nonlinear combustion zone, liner, and nozzle responses. A second primary extension of the basic theory was directed at the inclusion of the effects of injector face baffles. Attention was restricted to the linear (small amplitude) problem, finite Mach numbers, three dimensional oscillations, and distributed combustion effects.

Mitchell, C. E.↗

NASA NTRS1977

Three-dimensional modelling in magnetotelluric and magnetic variational sounding

The Galerkin finite-element method is used to obtain approximate solutions for the three-dimensional induction problem. A rectangular conductive prism is considered as an example, and solutions are obtained for linear and circularly polarized incident plane-wave fields. Magnetotelluric tensor impedances and magnetic transfer functions are computed. Polar diagrams of the tensor impedances and magnetic transfer functions along with their amplitude contour maps are presented. The dimensionality parameter, skew, is contoured at the surface of the earth. It is shown that the relative amplitudes and shapes of the additional and principal impedance polar diagrams can be used to determine the dimensionality of geoelectrical structures. Stations with skew values greater than 0.2 are significantly influenced by the three-dimensionality of the geoelectric structure. The amplitudes of the magnetic transfer function and the orientations of its polar diagrams exhibit large anomalies in the vicinity of the intersection of the lateral contacts.

Reddy, I. K.↗