Search NASA⌕ Search

SEARCH · Search NASA

Results for “Wave setup”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Solid-state platform for cooperative quantum dynamics driven by correlated emission

While traditionally regarded as an obstacle to quantum coherence, recent breakthroughs in quantum optics have shown that the dissipative interaction of a qubit with its environment can be leveraged to protect quantum states and synthesize many-body entanglement. Inspired by this progress, here we set the stage for the—as yet uncharted—exploration of analogous cooperative phenomena in hybrid solid-state platforms. We develop a comprehensive formalism for the quantum many-body dynamics of an ensemble of solid-state spin defects interacting with the magnetic field fluctuations of a common solid-state reservoir. Our framework applies to any solid-state reservoir whose fluctuating spin, pseudospin, or charge degrees of freedom generate magnetic fields. To understand whether correlations induced by dissipative processes can play a relevant role in a realistic experimental setup, we apply our model to a qubit array interacting via the spin fluctuations of a ferromagnetic bath. Our results show that the low-temperature collective relaxation rates of the qubit ensemble can display clear signatures of super- and subradiance, i.e., forms of cooperative dynamics traditionally achieved in atomic ensembles. We find that the solid-state analog of these cooperative phenomena is robust against spatial disorder in the qubit ensemble and thermal fluctuations of the magnetic reservoir, providing a route for their feasibility in near-term experiments. Finally, our work lays the foundation for a multiqubit approach to quantum sensing of solid-state systems and the direct generation of many-body entanglement in spin-defect ensembles. Furthermore, we discuss how the tunability of solid-state reservoirs opens up novel pathways for exploring cooperative phenomena in regimes beyond the reach of conventional quantum optics setups.

NV centers↗
DOE OSTI2023

Thermalization of Interacting Quasi-One-Dimensional Systems

Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intrachain interactions and the weak interchain coupling. When the intrachain interactions are integrable, weak interchain couplings play a crucial part in thermalizing the system. Here, we develop a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and apply it to develop a quantitative theory of relaxation in coupled Bose gases in the experimentally relevant Newton's cradle setup. Here we find that relaxation involves a broad spectrum of timescales. We provide evidence that the Markov process governing relaxation at late times is gapless; thus, the approach to equilibrium is generally nonexponential, even for spatially uniform perturbations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2012

Note: Silicon Carbide Telescope Dimensional Stability for Space-based Gravitational Wave Detectors

Space-based gravitational wave detectors are conceived to detect gravitational waves in the low frequency range by measuring the distance between proof masses in spacecraft separated by millions of kilometers. One of the key elements is the telescope which has to have a dimensional stability better than 1 pm Hz(exp −1/2) at 3 mHz. In addition, the telescope structure must be light, strong, and stiff. For this reason a potential telescope structure consisting of a silicon carbide quadpod has been designed, constructed, and tested. We present dimensional stability results meeting the requirements at room temperature. Results at −60 C are also shown although the requirements are not met due to temperature fluctuations in the setup.

LISA-like↗
NASA NTRSDate not supplied

Toward Relating Open- and Closed-Test Section Microphone Phased Array Aeroacoustic Measurements

Aeroacoustic measurements utilizing microphone phased arrays are becoming more commonplace in large-scale wind tunnels. However, for such costly tests it is difficult to assess the influence of a given facility's configuration on the acquired data. One such opportunity has recently arisen in the NASA Langley Research Center 14- by 22-Foot Subsonic Tunnel, where the High-Lift configuration of the Common Research Model was tested in both open-jet and closed wall configurations. Acoustic data were acquired on the same model with the same specific hardware at the same Mach number; and for similar model angles of attack, array apertures, and array angles relative to the model location. Initial deconvolution comparisons using DAMAS appear poor. The closed test section results show contamination likely due to background noise and reflections. The open-jet results show severe blurring due to the decorrelation of acoustic waves passing through a turbulent free shear layer. However, accounting for image sources in the DAMAS grid reduces visual artifacts in the closed test section results, and a preliminary coherence correction technique mitigates the blurring in the open-jet results. Qualitatively, both tests identify similar source behavior. Quantitatively, summed spectra of the slat noise agree in some frequency bands but differ in others. Proposals that may mitigate the difference are given for each configuration, such as correcting for the array protective cover and applying background subtraction in the closed wall configuration, and further developing the coherence loss correction for deconvolution methods in the open-jet setup.

microphone array↗
NASA NTRS2001

All-Optical Micro Motors Based on Moving Gratings in Photosensitive Media

An all-optical micromotor with a rotor driven by a traveling wave of surface deformation of a stator being in contact with the rotor is being studied. Instead of an ultrasonic wave produced by an electrically driven piezoelectric actuator as in ultrasonic motors, the wave is a result of a photo-induced surface deformation of a photosensitive material produced by an incident radiation. A thin piezoelectric polymer will deform more easily LiNbO3 or metal when irradiated with light. The type of photosensitive material studied are piezoelectric polymers with and without coatings for connecting electrodes. In order to be considered as a possible candidate for micromotors, the material should exhibit surface deformation produced by a laser beam of the order of 10 microns. This is compared to the deformations produced by static holographic gratings studied in photorefractive crystals of LiNbO3 using high vertical resolution surface profilometer Dektak 3 and surface interferometer WYKO. An experimental setup showing the oscillations has been developed. The setup uses a chopped beam from an Argon ion laser to produce the deformation while a probe beam is reflected by the thin film into a fiber which is then detected on an oscilloscope. A ramp voltage signal generator will drive the piezoelectric film in another experiment to determine the resonance of the film. A current is generated when light is incident upon the film and this current can be measured. The reverse process has already been demonstrated in other piezoelectric actuators. Changing voltage, polarity, and frequency of the signal can easily generate vibrations similar to those when light is incident on the film. This can be compared to the effects of laser interaction with light absorbing fluids such as solutions of 2,9,16,23-Tetrakis(phenylthio)-29H, 31 H-phthalocyanine in chlorobenzene in capillary tubes, The possibility of using a liquid with the piezoelectric film would be a novel idea for a micromotor since the interaction of a single low power focused laser beam at 633 nm with such fluid produced an intensive circular motion.

Curley, M.↗
NASA NTRS2017

Portable Laser Spectrometer for Airborne and Ground-Based Remote Sensing of Geological CO2 Emissions

A 24 kilogram, suitcase-sized, CW (Continuous Wave) Laser Remote Sensing Spectrometer (LARSS) with an approximately 2-kilometer range has been developed. It has demonstrated its flexibility in measuring both atmospheric CO2 from an airborne platform and terrestrial emission of CO2 from a remote mud volcano, Bledug Kuwu, Indonesia, from a ground-based sight. This system scans the CO2 absorption line with 20 discrete wavelengths, as opposed to the typical two-wavelength online-offline instrument. This multi-wavelength approach offers an effective quality control, bias control, and confidence estimate of measured CO2 concentrations via spectral fitting. The simplicity, ruggedness, and flexibility in the design allow for easy transportation and use on different platforms with a quick setup in some of the most challenging climatic conditions. While more refinement is needed, the results represent a stepping stone towards widespread use of active one-sided gas remote sensing in the earth sciences.

_______________________↗
DOE OSTI2020

Development and Test of High Temperature Surface Acoustic Wave Gas Sensors

The demand for sensors in hostile environments, such as power plant environments, aerospace environments, oil and gas extraction, and high-temperature metallurgy environments, has risen over the past decades in a continuous attempt to increase process control, improve energy and process efficiency in production, reduce operational and maintenance costs, increase safety, and perform condition-based maintenance in equipment and structures operating in high-temperature harsh-environment conditions. The increased reliability, improved performance, and development of new sensors and networks with a multitude of components, especially wireless networks, are the target for operation in harsh environments. Gas sensors, in particular H2 sensors, operating above 200 C are required in the instrumentation, process control and general safety of a number of industries including coal, natural gas, and nuclear power generation facilities, the aerospace and automotive industries, metallurgical production and defense-related applications. The surface acoustic wave (SAW) platform is a particularly promising option for high-temperature, harsh-environment gas sensing applications since the platform exhibits advantages, such as battery-free and wireless operation, small size, possibility for scale production using well-developed technologies from the semiconductor industry, and low cost of installation and operation. In this work, one-port SAW resonators (SAWRs) operating along five different orientations on a commercially available langasite (LGS) wafer employing Pt-Al2O3 electrodes and reflectors were designed, fabricated, and used as high-temperature H2 sensors. Two of the selected orientations were predicted and confirmed to have temperature-compensated operation above 150 C. A gas sensor test setup was developed, capable of gas cycling between N2, O2 and N2/H2 mixtures under extended high-temperature periods (up to 650 C for over 20 hours). Thin film Pt-Al2O3 was used as the electrode material for the transducers and reflectors capable of high-temperature operation, and also as H2 sensing film. In addition, yttria-stabilized zirconia (YSZ) thin films with Pt decoration were tested as sensing films aimed to enhance the SAWR sensor response to H2. The SAW devices were monitored in excess of 1700 hours in real-time during gas cycling sequences up to 600 C, leading to the following findings: i) the Pt-Al2O3 electrodes performed better for H2 sensing than the Pt-decorated YSZ sensing film, showing as much as 50% higher frequency variation response in the 200 C to 400 C range; ii) different crystallographic orientations operating on the same LGS wafer experienced different responses to H2 exposures up to 500 C; iii) the surface oxidation state of the SAWR sensors was shown to have an important impact on subsequent H2 exposure responses. In addition, a sensor system employing two LGS SAWRs, aligned along two different orientations, has been developed to simultaneously determine H2 presence and temperature. Finally, wireless interrogation of a SAWR sensor was successful within the gas cycling test fixture, and successful wireless H2 detection was achieved above 400 C.

Ayes Moncada, Armando↗
DOE OSTI2023

Development and experimental verification of an active noise cancellation (ANC) method for non-invasive sensing

Ultrasonic wave propagation may be used in non-invasive sensing to identify the properties of a fluid in a container. An ultrasonic excitation can be coupled into the liquid or the gas through the walls of the container and detected by a receiver on the other side. However, in addition to this fluid path, another signal will also propagate through the structure and is referred as noise in this study. For most materials, this structural noise will be of higher amplitude compared to the fluid signal due to the large acoustic impedance difference between the solid container and the fluid. In this paper, an active noise cancellation (ANC) method is developed and demonstrated on an experimental setup. It was shown that this method cancels more than 90% of the noise signal in a given time window of interest. A sequential version of this cancellation method is also proposed, and it was shown that its performance improves as the number of canceling excitations is increased. The performance was found to be independent of the location of canceling transducers and position of the silence window but dependent on the width of the silence window. As an example, the ANC method was applied to noise cancellation of a signal travelling through water in a stainless-steel container. The signal-to-noise ratio (SNR) of the water signal in the window of interest was increased by 148% from 13.98 dB to 34.68 dB by using the proposed ANC method.

42 ENGINEERING↗
DOE OSTI2020

Simulations of Sweeping Wave Propagation in a Boron Carbide Plate

In February 2020, experiments were conducted at Los Alamos National Laboratory measuring the propagation of a sweeping wave through a plate of boron carbide which was induced by detonating an adjacent charge of high explosive. Six such shots were red and in each case progress of the wave along the exposed surface of the plate was tracked using photon doppler velocimetry (PDV). In this report we discuss calculations performed using the Lagrangian hydrocode FLAG to model data taken from these experiments. We discuss the models chosen for the different experimental components, the choice of mesh (focusing on, both, two- and three-dimensional geometries), and compare the results from these calculations to experimentally-extracted PDV traces. Notably, we find that the PDV traces for this experiment are most faithfully reproduced using the full three-dimensional geometry, even when the mesh resolution for the three-dimensional calculations was significantly lower than the resolution for the corresponding two-dimensional calculations. We attribute this to the geometry of the experimental setup. Moreover, we find only negligible differences for the PDV traces obtained using the sesame table equation of state for boron carbide and the Gruneisen equation of state.

36 MATERIALS SCIENCE↗
DOE OSTI2025

High-power test of a C-band linear accelerating structure with an RFSoC-based LLRF system

Normal conducting linear particle accelerators consist of multiple rf stations with accelerating structure cavities. Low-level rf (LLRF) systems are employed to set the phase and amplitude of the field in the accelerating structure and to compensate for the pulse-to-pulse fluctuation of the rf field in the accelerating structures with a feedback loop. The LLRF systems are typically implemented with analog rf mixers, heterodyne-based architectures, and discrete data converters. There are multiple rf signals from each of the rf stations, so the number of rf channels required increases rapidly with multiple rf stations. With a large number of rf channels, the footprint, component cost, and system complexity of the LLRF hardware will increase significantly. To meet the design goals of being compact and affordable for future accelerators, we have designed the next-generation LLRF (NG-LLRF) with a higher integration level based on RFSoC technology. The NG-LLRF system samples rf signals directly and performs rf mixing digitally. Further, the NG-LLRF has been characterized in loopback mode to evaluate the performance of the system and has also been tested with a standing-wave accelerating structure, a prototype for the Cool Copper Collider (C 3 ) with a peak rf power level up to 16.45 MW. The loopback test demonstrated amplitude fluctuation below 0.15% and phase fluctuation below 0.15°, which are considerably better than the requirements of C 3 . The rf signals from the different stages of the accelerating structure at different power levels are measured by the NG-LLRF, which will be critical references for the control algorithm designs. The NG-LLRF also offers flexibility in waveform modulation, so we have used rf pulses with various modulation schemes, which could be useful for controlling some of the rf stations in accelerators. In this paper, the high-power test results at different stages of the test setup will be summarized, analyzed, and discussed.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Passive Islanding Detection of Inverter-Based Resources in a Noisy Environment

Islanding occurs when a load is energized solely by local generators and can result in frequency and voltage instability, changes in current, and poor power quality. Poor power quality can interrupt industrial operations, damage sensitive electrical equipment, and induce outages upon the resynchronization of the island with the grid. This study proposes an islanding detection method employing a Duffing oscillator to analyze voltage fluctuations at the point of common coupling (PCC) under a high-noise environment. Unlike existing methods, which overlook the noise effect, this paper mitigates noise impact on islanding detection. Power system noise in PCC measurements arises from switching transients, harmonics, grounding issues, voltage sags and swells, electromagnetic interference, and power quality issues that affect islanding detection. Transient events like lightning-induced traveling waves to the PCC can also introduce noise levels exceeding the voltage amplitude by more than seven times, thus disturbing conventional detection techniques. The noise interferes with measurements and increases the nondetection zone (NDZ), causing failed or delayed islanding detection. The Duffing oscillator nonlinear dynamics enable detection capabilities at a high noise level. The proposed method is designed to detect the PCC voltage fluctuations based on the IEEE standard 1547 through the Duffing oscillator. For the voltages beyond the threshold, the Duffing oscillator phase trajectory changes from periodic to chaotic mode and sends an islanded operation command to the inverter. The proposed islanding detection method distinguishes switching transients and faults from an islanded operation. Experimental validation of the method is conducted using a 3.6 kW PV setup.

Energy & Fuels↗
DOE OSTI2023

Inference of the optical depth to reionization τ from Planck CMB maps with convolutional neural networks

The optical depth to reionization, τ, is the least constrained parameter of the cosmological Λ cold dark matter (ΛCDM) model. To date, its most precise value is inferred from large-scale polarized cosmic microwave background (CMB) power spectra from the High Frequency Instrument (HFI) aboard the Planck satellite. These maps are known to contain significant contamination by residual non-Gaussian systematic effects, which are hard to model analytically. Therefore, robust constraints on τ are currently obtained through an empirical cross-spectrum likelihood built from simulations. In this paper, we present a likelihood-free inference of τ from polarized Planck HFI maps which, for the first time, is fully based on neural networks (NNs). NNs have the advantage of not requiring an analytical description of the data and can be trained on state-of-the-art simulations, combining the information from multiple channels. By using Gaussian sky simulations and Planck SRoll2 simulations, including CMB, noise, and residual instrumental systematic effects, we trained, tested, and validated NN models considering different setups. We inferred the value of τ directly from Stokes Q and U maps at ~4° pixel resolution, without computing angular power spectra. On Planck data, we obtained τ NN = 0.0579 ± 0.0082, which is compatible with current EE cross-spectrum results but with a ~30% larger uncertainty, which can be assigned to the inherent nonoptimality of our estimator and to the retraining procedure applied to avoid biases. While this paper does not improve on current cosmological constraints on τ, our analysis represents a first robust application of NN-based inference on real data, and highlights its potential as a promising tool for complementary analysis of near-future CMB experiments, also in view of the ongoing challenge to achieve the first detection of primordial gravitational waves.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2011

Validation and Simulation of Ares I Scale Model Acoustic Test - 2 - Simulations at 5 Foot Elevation for Evaluation of Launch Mount Effects

The Ares I Scale Model Acoustics Test (ASMAT) is a series of live-fire tests of scaled rocket motors meant to simulate the conditions of the Ares I launch configuration. These tests have provided a well documented set of high fidelity measurements useful for validation including data taken over a range of test conditions and containing phenomena like Ignition Over-Pressure and water suppression of acoustics. Expanding from initial simulations of the ASMAT setup in a held down configuration, simulations have been performed using the Loci/CHEM computational fluid dynamics software for ASMAT tests of the vehicle at 5 ft. elevation (100 ft. real vehicle elevation) with worst case drift in the direction of the launch tower. These tests have been performed without water suppression and have compared the acoustic emissions for launch structures with and without launch mounts. In addition, simulation results have also been compared to acoustic and imagery data collected from similar live-fire tests to assess the accuracy of the simulations. Simulations have shown a marked change in the pattern of emissions after removal of the launch mount with a reduction in the overall acoustic environment experienced by the vehicle and the formation of highly directed acoustic waves moving across the platform deck. Comparisons of simulation results to live-fire test data showed good amplitude and temporal correlation and imagery comparisons over the visible and infrared wavelengths showed qualitative capture of all plume and pressure wave evolution features.

Strutzenberg, Louise L.↗
DOE OSTI2024

Protocols for x-ray transient grating pump/optical probe experiments at x-ray free electron lasers

Abstract Transient grating spectroscopy is a specialized application of the four-wave-mixing methodology and constitutes a versatile technique for investigating the dynamics of vibrational, magnetic and electronic degrees of freedom of matter in a background-free fashion. Recent developments in free-electron laser sources have enabled the extension of this technique into the extreme ultraviolet range. Ongoing efforts to expand transient grating spectroscopy into the x-ray regime promise numerous advantages: (1) substantial penetration depths that allow for probing bulk material properties, (2) element specificity via specific core-excited states, and (3) short wavelengths that allow for excitation gratings with higher momentum transfer and improved spatial resolution. In this study, we comprehensively outline the procedures for conducting x-ray transient grating pump/optical probe experiment. The process encompasses the design and alignment of the experimental setup, as well as the subsequent steps involved in data acquisition and analysis. This paper is intended as a comprehensive guide for researchers interested in implementing x-ray transient grating spectroscopy, providing valuable insights into the intricacies of the experimental workflow required for this novel technique. Furthermore, we discuss the potential for extending this methodology to an x-ray pump/x-ray probe scheme, envisioning a future direction that holds promise for enhancing the capabilities and scope of x-ray transient grating spectroscopy, opening new opportunities for studying ultrafast processes with unprecedented temporal and spatial resolutions.

Optics↗
NASA NTRS2005

Thrust Augmentation Measurements for a Pulse Detonation Engine Driven Ejector

Thrust augmentation results of an ongoing study of pulse detonation engine driven ejectors are presented and discussed. The experiments were conducted using a pulse detonation engine (PDE) setup with various ejector configurations. The PDE used in these experiments utilizes ethylene (C2H4) as the fuel, and an equi-molar mixture of oxygen and nitrogen as the oxidizer at an equivalence ratio of one. High fidelity thrust measurements were made using an integrated spring damper system. The baseline thrust of the PDE engine was first measured and agrees with experimental and modeling results found in the literature. Thrust augmentation measurements were then made for constant diameter ejectors. The parameter space for the study included ejector length, PDE tube exit to ejector tube inlet overlap distance, and straight versus rounded ejector inlets. The relationship between the thrust augmentation results and various physical phenomena is described. To further understand the flow dynamics, shadow graph images of the exiting shock wave front from the PDE were also made. For the studied parameter space, the results showed a maximum augmentation of 40%. Further increase in augmentation is possible if the geometry of the ejector is tailored, a topic currently studied by numerous groups in the field.

Pal, S.↗
DOE OSTI2025

Engineering long-lived entanglement through dissipation in quantum hybrid solid-state platforms

Spin squeezing, a form of many-body entanglement, is a crucial resource in quantum metrology and information processing. While experimentally viable protocols for generating stable spin squeezing have been proposed in quantum optics setups, there is growing interest in quantum hybrid solid-state systems as alternative platforms for both engineering and exploring many-body quantum phenomena. In this work, we propose a scheme to generate long-lived spin squeezing in an ensemble of solid-state qubits interacting with electromagnetic noise emitted by a squeezed solid-state bath. We identify the conditions under which quantum correlations within the bath can be transferred to the qubit array, driving it into an entangled state independently of its initial configuration. To assess the experimental feasibility of our approach, we analyze the dynamics of an array of solid-state spin defects coupled to a common ferromagnetic bath, which is driven into a non-equilibrium squeezed state through its interaction with a surface acoustic wave mode. Our results demonstrate that the ensemble can exhibit steady-state spin squeezing under suitable conditions, opening new pathways for the generation of robust many-body entanglement in solid-state spin ensembles.

NV centers↗
DOE OSTI2022

Investigating growth to detonation in vapor-deposited hexanitrostilbene and pentaerythritol tetranitrate films using high-throughput methods

In this work, a high-throughput experimental setup was used to characterize initiation threshold and growth to detonation in the explosives hexanitrostilbene (HNS) and pentaerythritol tetranitrate (PETN). The experiment sequentially launched an array of laser-driven flyers to shock samples arranged in a 96-well microplate geometry, with photonic Doppler velocimetry diagnostics to characterize flyer velocity and particle velocity at the explosive–substrate interface. Vapor-deposited films of HNS and PETN were used to provide numerous samples with various thicknesses, enabling characterization of the evolution of growth to detonation. One-dimensional hydrocode simulations were performed with reactions disabled to illustrate where the experimental data deviate from the predicted inert response. Prompt initiation was observed in 144 μm thick HNS films at flyer velocities near 3000 m/s and in 125 μm thick PETN films at flyer velocities near 2400 m/s. This experimental setup enables rapid quantification of the growth of reactions in explosive materials that can reach detonation at sub-millimeter length scales. These data can subsequently be used for parameterizing reactive burn models in hydrocode simulations, as discussed in Paper II [D. E. Kittell, R. Knepper, and A. S. Tappan, J. Appl. Phys. 131, 154902 (2022)].

36 MATERIALS SCIENCE↗
DOE OSTI2021

Design and Testing of a Water-Cooled Rotating Detonation Combustor at Elevated Operating Pressures - Abstract

This is an extended abstract being submitted for consideration that briefly describes the material that will be included in the final paper. This study will detail the design and testing of a water-cooled Rotating Detonation Combustor (RDC) that permits operation for extended periods of time ensuring that the device has reach a stable operating temperature. Extended run times also provides an opportunity to consider transient behaviors that occur as a result of altering the operating conditions such as equivalence ratio. The experimental setup is also unique in that it consists of a ducted exhaust with a downstream high-temperature valve that can control the pre-combustion pressure in the RDC independent of the combustor annulus and exit geometry. This paper will examine the results from the extended operation of the water-cooled RDC over a range of both transient and steady state equivalence ratios (0.5 - 1.0), pre-combustion operating pressures (0 - 207 kPa), mass flow rates (0.42 – 0.5 kg/sec) and air inlet throat area to combustor channel area ratios (0.09 – 0.32). All tests were performed while operating on hydrogen in air at a nominal air inlet temperature of 340 – 350 K. Limited data obtained at an elevated inlet air temperature of 480 K will also be discussed. Results suggest that under certain conditions the operating mode of the detonation wave can vary as it approaches a stable operating temperature. For the RDC tested, a stable operating temperature is not achieved until approximately 8-10 seconds of run time.

Ferguson, Donald↗