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At least 1,351 records · Page 75

Flutter calculations in three degrees of freedom

The present paper is a continuation of the general study of flutter published in NACA reports nos. 496 and 685. The paper is mainly devoted to flutter in three degrees of freedom (bending, torsion, and aileron) for which a number of selected cases have been calculated and presented in graphical form. The results are analyzed and discussed with regard to the effects of structural damping, of fractional-span ailerons, and of mass-balancing. The analysis shows that more emphasis should be put on the effect of structural damping and less on mass-balancing. The conclusion is drawn that a definite minimum amount of structural damping, which is usually found to be present, is essential in the calculations for an adequate description of the flutter case. Theoretical flutter predictions are thus brought into closer agreement with the facts of experience. A brief discussion is included of a particular biplane that had experienced flutter at about 200 miles per hour. Some simplifications have been achieved in the method of calculation. (author)

Theodorsen, Theodore↗

A Rb-Sr and Sm-Nd Isotope Geochronology and Trace Element Study of Lunar Meteorite LaPaz Icefield 02205

Rubidium-strontium and samarium-neodymium isotopes of lunar meteorite LaPaz Icefield (LAP) 02205 are consistent with derivation of the parent magma from a source region similar to that which produced the Apollo 12 low-Ti olivine basalts followed by mixing of the magma with small amounts (1 to 2 wt%) of trace element-enriched material similar to lunar KREEP-rich sample SaU 169. The crystallization age of LAP 02205 is most precisely dated by an internal Rb-Sr isochron of 2991+/-14 Ma, with an initial Sr-87/Sr-88 at the time of crystallization of 0.699836+/-0.000010. Leachable REE-rich phosphate phases of LAP 02205 do not plot on a Sm-Nd mineral isochron, indicating contamination or open system behavior of the phosphates. Excluding anomalous phases from the calculation of a Sm-Nd isochron yields a crystallization age of 2992+/-85 (initial Epsilon Nd-143 = +2.9+/-0.8) that is within error of the Rb-Sr age, and in agreement with other independent age determinations for LAP 02205 from Ar-Ar and U-Pb methods. The calculated Sm-147/Nd-144 source ratios for LAP 02205, various Apollo 12 and 15 basalts, and samples with strong affinities to KREEP (SaU 169, NWA 773, 15386) are uncorrelated with their crystallization ages. This finding does not support the involvement of a common KREEP component as a heat source for lunar melting events that occurred after crystallization of the lunar magma ocean.

Rankenburg, K.↗

Classical and quantum computing of shear viscosity for ( 2 + 1 ) D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for ( 2 + 1 )-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density η s is consistent with a well-known holographic result 1 4 π at several temperatures on a 4 × 4 honeycomb lattice with the local electric representation truncated at j max = 1 2 . We also find the ratio of the spectral function and frequency ρ x y ( ω ) ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond j max = 1 2 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including j max truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Renormalization group improvement of the effective potential: an EFT approach

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A non-intrusive optical (NIO) approach to characterize heliostats in utility-scale power tower plants: Sensitivity study

Power towers, a type of concentrating power tower technology, use a large number of heliostats to concentrate sunlight and produce renewable energy. Optical errors of heliostats can cause drastic losses in the efficiency of power-tower plants. Accurately measuring optical errors is crucial to assessing and improving plant performance. This analysis discusses an innovate non-intrusive optical (NIO) approach to measure slope, canting, and tracking errors by detecting distortions in the reflected tower structure in heliostat images. Further in this work a sensitivity study is carefully conducted to determine the uncertainty requirements to allow the method to calculate slope errors with an accuracy of 0.25 mrad. Measurement uncertainty sources include camera resolution and position uncertainty, tower position uncertainty, and number of collected images. Each uncertainty source is investigated to determine its impact on the accuracy of the slope-error calculation. A combination of theoretical results and experimental results obtained from data collected on a heliostat at Sandia National Laboratories is used to determine and validate uncertainty requirements. The analysis shows that a measurement uncertainty of 0.25 mrad can be realized by realistically controlling uncertainty sources when implementing the NIO method. It demonstrates the superior performance of NIO in performing in-situ optical characterization.

14 SOLAR ENERGY↗

Axial-flow compressor turning angle and loss by inviscid-viscous interaction blade-to-blade computation

A method for computation of the flow field around an arbitrary airfoil cascade on an axially symmetric blade-to-blade surface was developed which takes into account the development and separation of the blade surface boundary layers and mixing in the wake. The method predicts the overall fluid turning and total pressure loss in the context of an inviscid-viscous interaction scheme. The inviscid flow solution is obtained from a compressible flow matrix method. The viscous flow is obtained from a differential boundary layer method which calculates laminar, transitional and turbulent boundary layers. Provisions for the calculation of laminar and turbulent separation regions were added to the viscous scheme. The combined inviscid-viscous interaction scheme described yields results which are quantitatively consistent with experimental data. This suggests that the physical basis for the interactive system is correct and justifies continued exploration and use of the method.

Hansen, E. C.↗

The elastic energy and character of quakes in solid stars and planets

The quadrupolar mechanical energy of a rotating axially symmetric solid planet (with or without a liquid interior) is calculated using methods previously developed for neutron stars in which an elastic reference tensor is introduced to describe the build-up of elastic energy in the star. The basic parameters of the theory (the gravitational energy A and elastic energy B) depend upon the internal structure of the planet and may be calculated from specific planetary models. Explicit expressions are obtained for the Love numbers, and for the planetary wobble frequency. The theory provides a simple relationship between changes in shape or axis of figure of the planet and elastic energy release. The theory is extended to describe the Earth by taking into account isostasy, triaxiality and the observed lithospheric configuration.

Pines, D.↗

Spacecraft mass estimation, relationships and engine data: Task 1.1 of the lunar base systems study

A collection of scaling equations, weight statements, scaling factors, etc., useful for doing conceptual designs of spacecraft are given. Rules of thumb and methods of calculating quantities of interest are provided. Basic relationships for conventional, and several non-conventional, propulsion systems (nuclear, solar electric and solar thermal) are included. The equations and other data were taken from a number of sources and are not at all consistent with each other in level of detail or method, but provide useful references for early estimation purposes.

Source record↗

Monte Carlo Simulation of Alloy Design Techniques: Fracture and Welding Studied Using the BFS Method for Alloys

Large-scale simulations of dynamic processes at the atomic level have developed into one of the main areas of work in computational materials science. Until recently, severe computational restrictions, as well as the lack of accurate methods for calculating the energetics, resulted in slower growth in the area than that required by current alloy design programs. The Computational Materials Group at the NASA Lewis Research Center is devoted to the development of powerful, accurate, economical tools to aid in alloy design. These include the BFS (Bozzolo, Ferrante, and Smith) method for alloys (ref. 1) and the development of dedicated software for large-scale simulations based on Monte Carlo- Metropolis numerical techniques, as well as state-of-the-art visualization methods. Our previous effort linking theoretical and computational modeling resulted in the successful prediction of the microstructure of a five-element intermetallic alloy, in excellent agreement with experimental results (refs. 2 and 3). This effort also produced a complete description of the role of alloying additions in intermetallic binary, ternary, and higher order alloys (ref. 4).

Bozzolo, Guillermo H.↗

Soft x-ray spectrum unfold of K-edge filtered x-ray diode arrays using cubic splines

Cubic spline interpolation is able to recover temporally and spectrally resolved soft x-ray flux from an array of K-edge filtered x-ray diodes without the need for a priori assumptions about the spectrum or the geometry of the emitting volume. The mathematics of the cubic spline interpolation is discussed in detail. The analytic nature of the cubic spline solution allows for analytical error propagation, and the method of calculating the error for radiation temperature, spectral power, and confidence intervals of the unfolded spectrally resolved flux is explained. An unfold of a blackbody model demonstrates the accuracy of the cubic spline unfold. Tests of cubic spline performance using spectrally convolved detailed atomic model simulation results have been performed to measure the method's ability to conserve spectral power to within a factor of 2 or better in line-dominated regimes. The unfold is also demonstrated to work when information from the x-ray diode array is limited due to high signal-to-noise ratios or lack of signal due to over-attenuation or over-filtration of the x-ray diode signal. Here, the robustness of the unfold with respect to background subtraction and raw signal processing, signal alignment between diode traces, limited signal information, and initial conditions is discussed. Results from an example analysis of a halfraum drive are presented to demonstrate the capabilities of the unfold in comparison with previously established methods.

47 OTHER INSTRUMENTATION↗

On decoupling the integrals of cosmological perturbation theory

ABSTRACT Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher order corrections by integration over linear statistics of the density fields weighted by kernels resulting from recursive solution of the fluid equations. These integrals quickly become high dimensional and naively require increasing computational resources the higher the order of the corrections. Here, we show how to decouple the integrands that often produce this issue, enabling PT corrections to be computed as a sum of products of independent 1D integrals. Our approach is related to a commonly used method for calculating multiloop Feynman integrals in quantum field theory, the Gegenbauer Polynomial x-Space Technique. We explicitly reduce the three terms entering the 2-loop power spectrum, formally requiring 9D integrations, to sums over successive 1D radial integrals. These 1D integrals can further be performed as convolutions, rendering the scaling of this method Nglog Ng with Ng the number of grid points used for each fast Fourier transform. This method should be highly enabling for upcoming large-scale structure redshift surveys where model predictions at an enormous number of cosmological parameter combinations will be required by Monte Carlo Markov Chain searches for the best-fitting values.

Slepian, Zachary↗

Evaluation of several modal methods for transient structural analysis

The convergence properties of three modal methods for solving structural transient response (STR) problems are examined by comparing the accuracy of the total number of modes used to represent the responses. The goal is to identify a method which involves as few degrees of freedom as possible. Two mode superposition methods, the mode displacement method (MDM) and the mode acceleration method (MAM), are fitted with equivalent expressions for damped response. An error norm is employed to compare the accuracies of the methods in calculating displacements, moments, and shear forces for a viscously-damped cantilevered beam experiencing several dynamic loading conditions and levels of damping. The MAM converges quicker and uses fewer dof, mainly because it has a pseudo-static response term which accounts for some of the flexibility of higher modes. A third method, which integrates the convolution integral iteratively over time, generates a higher order approximation to the STR with a reduced number of modes. It converges fastest among the three, but requires definition of an appropriate forcing function. Finally, the MAM and MDM models are applied to study the effects of the forcing frequency and the initial conditions.

Camarda, Charles J.↗

Rapid calculation of terrain parameters for radiation modeling from digital elevation data

Digital elevation models are now widely used to calculate terrain parameters to determine incoming solar and longwave radiation for use in surface climate models, interpretation of remote-sensing data, and parameters in hydrologic models. Because of the large number of points in an elevation grid, fast algorithms are useful to save computation time. A description is given of rapid methods for calculating slope and azimuth, solar illumination angle, horizons, and view factors for radiation from sky and terrain. Calculation time is reduced by fast algorithms and lookup tables.

Dozier, Jeff↗

Three-dimensional plasma diffusion in a very strong magnetic field.

The thermal equilibrium coefficient of spatial diffusion transverse to a strong uniform dc magnetic field is calculated for a fully ionized plasma. The particles are assumed to move transverse to the field only as a consequence of the E x B drift, but to move freely parallel to it. The particles interact only electrostatically. The calculation is done at large, but fixed and finite, plasma volume. It is shown that, as magnetic field density approaches infinity, the leading term of the coefficient of transverse spatial diffusion falls off in a prescribed manner, but contains a multiplicative factor which goes to zero as the plasma volume becomes infinite. The method of calculation fails for unbounded plasmas.

Montgomery, D.↗

Numerical techniques for solving nonlinear instability problems in smokeless tactical solid rocket motors

The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.

Baum, J. D.↗

Design of spur gears for improved efficiency

A method to calculate spur gear system power loss for a wide range of gear geometries and operating conditions is used to determine design requirements for an efficient gearset. The effects of spur gear size, pitch, ratio, pitch-line-velocity and load on efficiency are shown. A design example is given to illustrate how the method is to be applied. In general, peak efficiencies were found to be greater for larger diameter and fine pitched gears and tare (no-load) losses were found to be significant.

Anderson, N. E.↗

Navier-Stokes calculations of hovering rotor flowfields

Unsteady, thin-layer Navier-Stokes equations written in rotor coordinates are solved using a partially flux-split, implicit numerical algorithm to calculate the flowfields of a hovering rotor blade at subsonic and transonic conditions. Numerical results are in good agreement with experimental data for both nonlifting and lifting rectangular blades. For the lifting case, the rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blades. Alternate methods of calculating the hovering rotor flowfields in blade-fixed mode that have the same circulation distribution as a hovering blade are explored. All of the results presented in this paper were computed on a Cray-2 supercomputer.

Srinivasan, G. R.↗

Diagnosing the sensitivity of grounding-line flux to changes in sub-ice-shelf melting

Abstract. Using a numerical ice flow model, we study changes in ice shelf buttressing and grounding-line flux due to localized ice thickness perturbations, a proxy for localized changes in sub-ice-shelf melting. From our experiments, applied to idealized (MISMIP+) and realistic (Larsen C) ice shelf domains, we identify a correlation between a locally derived buttressing number on the ice shelf, based on the first principal stress, and changes in the integrated grounding-line flux. The origin of this correlation, however, remains elusive from the perspective of a theoretical or physically based understanding. This and the fact that the correlation is generally much poorer when applied to realistic ice shelf domains motivate us to seek an alternative approach for predicting changes in grounding-line flux. We therefore propose an adjoint-based method for calculating the sensitivity of the integrated grounding-line flux to local changes in ice shelf geometry. We show that the adjoint-based sensitivity is identical to that deduced from pointwise, diagnostic model perturbation experiments. Based on its much wider applicability and the significant computational savings, we propose that the adjoint-based method is ideally suited for assessing grounding-line flux sensitivity to changes in sub-ice-shelf melting.

54 ENVIRONMENTAL SCIENCES↗