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NASA NTRS2014

Precision Control of Thermal Transport in Cryogenic Single-Crystal Silicon Devices

We report on the diffusive-ballistic thermal conductance of multi-moded single-crystal silicon beams measured below 1 K. It is shown that the phonon mean-free-path is a strong function of the surface roughness characteristics of the beams. This effect is enhanced in diffuse beams with lengths much larger than, even when the surface is fairly smooth, 510 nm rms, and the peak thermal wavelength is 0.6 microns. Resonant phonon scattering has been observed in beams with a pitted surface morphology and characteristic pit depth of 30 nm. Hence, if the surface roughness is not adequately controlled, the thermal conductance can vary significantly for diffuse beams fabricated across a wafer. In contrast, when the beam length is of order, the conductance is dominated by ballistic transport and is effectively set by the beam cross-sectional area. We have demonstrated a uniformity of +/-8% in fractional deviation for ballistic beams, and this deviation is largely set by the thermal conductance of diffuse beams that support the micro-electro-mechanical device and electrical leads. In addition, we have found no evidence for excess specific heat in single-crystal silicon membranes. This allows for the precise control of the device heat capacity with normal metal films. We discuss the results in the context of the design and fabrication of large-format arrays of far-infrared and millimeter wavelength cryogenic detectors.

multi-moded single-crystal silicon beams↗

NASA NTRSDate not supplied

An Expanded Role for Python in Expediting System Simulation Development

The Python programming language has traditionally been used as a “scripting” language and is not generally recognized as a language for building system simulations, where C++, Java, and other compiled languages are typically used. While very powerful and gaining favor for a large set of programming tasks, Python is generally regarded as not having the speed to directly do the extensive numeric computations required in large-scale simulation. This paper aims to present an approach, supported by case studies, to re-think this assertion. Directly using Python in this new role has the potential to expedite an agile, spiral cycle of development of design-test-modify for systems simulation.

programming language↗

NASA NTRS2006

Lunar Dust Activation and Related Studies

The primary objective of the presentation is to identify a set of experiments to activate the lunar dust and monitor the mode of deactivation process using various analytical methods. To satisfy the objective, a large set of experiments will be carried out using lunar dust stimulant (JSC-1a-vf obtained from Dr. V. Carter from University of Texas at Dallas) to optimize the methodology. After refining the methodology to carry out the experiments using the simulant, real lunar dust will be used to obtain the necessary results. The secondary objective of the presentation is to identify a set of experiments to assess the potential toxicity of the dust using cellular systems. One of the cell lines that we identified is WI-38 human lung cell line.

Jeevarajan, Antony↗

NASA NTRS2007

Rapid Geometry Creation for Computer-Aided Engineering Parametric Analyses: A Case Study Using ComGeom2 for Launch Abort System Design

ComGeom2, a tool developed to generate Common Geometry representation for multidisciplinary analysis, has been used to create a large set of geometries for use in a design study requiring analysis by two computational codes. This paper describes the process used to generate the large number of configurations and suggests ways to further automate the process and make it more efficient for future studies. The design geometry for this study is the launch abort system of the NASA Crew Launch Vehicle.

Hawke, Veronica↗

NASA NTRSDate not supplied

Impact Ice Microstructure Segmentation Using Transfer Learned Model

A process of using machine learning to segment impact ice microstructure is presented and analyzed. The segmentation was conducted with the goal of obtaining average grain size estimations. The model was trained on a set of micrographs of impact ice grown at NASA Glenn’s Icing Research Tunnel. The model leveraged a model pre-trained on a large set of micrographs of various materials as a starting point. Post-processing of the segmented images was done to connect broken boundaries. An automatic method of determining grain size following an ASTM standard was implemented. Segmentation results using different training sets as well as different encoder and decoder pairs are presented. Calculated sizes are compared to manual grain size measurement methods. Results show promise in accuracy as well as a possible improvement in repeatability and consistency. Next steps for improving the model are suggested.

Machine learning↗

NASA NTRS2016

Statistical Analysis of Periodic Oscillations in LASCO Coronal Mass Ejection Speeds

A large set of coronal mass ejections (CMEs, 3463) has been selected to study their periodic oscillations in speed in the Solar and Heliospheric Observatory (SOHO) missions Large Angle and Spectrometric Coronagraph (LASCO) field of view. These events, reported in the SOHOLASCO catalog in the period of time 19962004, were selected based on having at least 11 height-time measurements. This selection criterion allows us to construct at least ten-point speed distance profiles and evaluate kinematic properties of CMEs with a reasonable accuracy. To identify quasi-periodic oscillations in the speed of the CMEs a sinusoidal function was fitted to speed distance profiles and the speed time profiles. Of the considered events 22 revealed periodic velocity fluctuations. These speed oscillations have on average amplitude equal to 87 kms(exp -1) and period 7.8R /241 min (in distance-time). The study shows that speed oscillations are a common phenomenon associated with CME propagation implying that all the CMEs have a similar magnetic flux-rope structure. The nature of oscillations can be explained in terms of magnetohydrodynamic (MHD) waves excited during the eruption process. More accurate detection of these modes could, in the future, enable us to characterize magnetic structures in space (space seismology).

Michalek, G.↗

NASA NTRS2010

Algorithms for Learning Preferences for Sets of Objects

A method is being developed that provides for an artificial-intelligence system to learn a user's preferences for sets of objects and to thereafter automatically select subsets of objects according to those preferences. The method was originally intended to enable automated selection, from among large sets of images acquired by instruments aboard spacecraft, of image subsets considered to be scientifically valuable enough to justify use of limited communication resources for transmission to Earth. The method is also applicable to other sets of objects: examples of sets of objects considered in the development of the method include food menus, radio-station music playlists, and assortments of colored blocks for creating mosaics. The method does not require the user to perform the often-difficult task of quantitatively specifying preferences; instead, the user provides examples of preferred sets of objects. This method goes beyond related prior artificial-intelligence methods for learning which individual items are preferred by the user: this method supports a concept of setbased preferences, which include not only preferences for individual items but also preferences regarding types and degrees of diversity of items in a set. Consideration of diversity in this method involves recognition that members of a set may interact with each other in the sense that when considered together, they may be regarded as being complementary, redundant, or incompatible to various degrees. The effects of such interactions are loosely summarized in the term portfolio effect. The learning method relies on a preference representation language, denoted DD-PREF, to express set-based preferences. In DD-PREF, a preference is represented by a tuple that includes quality (depth) functions to estimate how desired a specific value is, weights for each feature preference, the desired diversity of feature values, and the relative importance of diversity versus depth. The system applies statistical concepts to estimate quantitative measures of the user s preferences from training examples (preferred subsets) specified by the user. Once preferences have been learned, the system uses those preferences to select preferred subsets from new sets. The method was found to be viable when tested in computational experiments on menus, music playlists, and rover images. Contemplated future development efforts include further tests on more diverse sets and development of a sub-method for (a) estimating the parameter that represents the relative importance of diversity versus depth, and (b) incorporating background knowledge about the nature of quality functions, which are special functions that specify depth preferences for features.

Wagstaff, Kiri L.↗

NASA NTRS2019

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

NASA NTRS2013

Data Mining for Understanding and Improving Decision-making Affecting Ground Delay Programs

Weather↗

NASA NTRS2013

Data Mining for Understanding and Impriving Decision-Making Affecting Ground Delay Programs

The continuous growth in the demand for air transportation results in an imbalance between airspace capacity and traffic demand. The airspace capacity of a region depends on the ability of the system to maintain safe separation between aircraft in the region. In addition to growing demand, the airspace capacity is severely limited by convective weather. During such conditions, traffic managers at the FAA's Air Traffic Control System Command Center (ATCSCC) and dispatchers at various Airlines' Operations Center (AOC) collaborate to mitigate the demand-capacity imbalance caused by weather. The end result is the implementation of a set of Traffic Flow Management (TFM) initiatives such as ground delay programs, reroute advisories, flow metering, and ground stops. Data Mining is the automated process of analyzing large sets of data and then extracting patterns in the data. Data mining tools are capable of predicting behaviors and future trends, allowing an organization to benefit from past experience in making knowledge-driven decisions. The work reported in this paper is focused on ground delay programs. Data mining algorithms have the potential to develop associations between weather patterns and the corresponding ground delay program responses. If successful, they can be used to improve and standardize TFM decision resulting in better predictability of traffic flows on days with reliable weather forecasts. The approach here seeks to develop a set of data mining and machine learning models and apply them to historical archives of weather observations and forecasts and TFM initiatives to determine the extent to which the theory can predict and explain the observed traffic flow behaviors.

data mining↗

NASA NTRS2016

Scattering and Diffraction of Electromagnetic Radiation: An Effective Probe to Material Structure

Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ̶ the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than ~106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.

Xu, Yu-Lin↗

NASA NTRS2017

Semi-Supervised Learning of Lift Optimization of Multi-Element Three-Segment Variable Camber Airfoil

This chapter describes a new intelligent platform for learning optimal designs of morphing wings based on Variable Camber Continuous Trailing Edge Flaps (VCCTEF) in conjunction with a leading edge flap called the Variable Camber Krueger (VCK). The new platform consists of a Computational Fluid Dynamics (CFD) methodology coupled with a semi-supervised learning methodology. The CFD component of the intelligent platform comprises of a full Navier-Stokes solution capability (NASA OVERFLOW solver with Spalart-Allmaras turbulence model) that computes flow over a tri-element inboard NASA Generic Transport Model (GTM) wing section. Various VCCTEF/VCK settings and configurations were considered to explore optimal design for high-lift flight during take-off and landing. To determine globally optimal design of such a system, an extremely large set of CFD simulations is needed. This is not feasible to achieve in practice. To alleviate this problem, a recourse was taken to a semi-supervised learning (SSL) methodology, which is based on manifold regularization techniques. A reasonable space of CFD solutions was populated and then the SSL methodology was used to fit this manifold in its entirety, including the gaps in the manifold where there were no CFD solutions available. The SSL methodology in conjunction with an elastodynamic solver (FiDDLE) was demonstrated in an earlier study involving structural health monitoring. These CFD-SSL methodologies define the new intelligent platform that forms the basis for our search for optimal design of wings. Although the present platform can be used in various other design and operational problems in engineering, this chapter focuses on the high-lift study of the VCK-VCCTEF system. Top few candidate design configurations were identified by solving the CFD problem in a small subset of the design space. The SSL component was trained on the design space, and was then used in a predictive mode to populate a selected set of test points outside of the given design space. The new design test space thus populated was evaluated by using the CFD component by determining the error between the SSL predictions and the true (CFD) solutions, which was found to be small. This demonstrates the proposed CFD-SSL methodologies for isolating the best design of the VCK-VCCTEF system, and it holds promise for quantitatively identifying best designs of flight systems, in general.

Intelligent Systems↗

NASA NTRS2021

Potential origin of the state-dependent hard tail in the black hole microquasar Cygnus X-1 as seen with INTEGRAL

Context.0.1–10 MeV observations of the black hole microquasar Cygnus X-1 have shown the presence of a spectral feature in the form of a power law in addition to the standard black body (0.1–10 keV) and Comptontonization (10–200 keV) components usually seen in all black hole X-ray binaries. This so-called “high-energy tail” has recently been shown to be strong in the hard spectral state and has been interpreted as high-energy part of the emission from a compact jet. Aims. This result was, however, obtained from a data set largely dominated by hard state observations. In the soft state, only upper limits on the presence and hence the potential parameters of a hard tail could be derived. Using an extended data set we aim at obtaining better constraints on the properties of this spectral component in both states. Methods. We make use of data obtained from about 15 years of observations with the INTEGRAL satellite. The data set is separated into the different states and we analyse stacked state-resolved spectra obtained from both the gamma-ray Imager and the Spectrometer onboard. Results. A high-energy component is detected in both states, confirming its earlier detection in the hard state and its suspected presence in the soft state as seen in a much smaller SPI data set. We first characterize the hard tail components in the two states through a model-independent, phenomenological analysis. We then apply physical models based on hybrid Comptonization (eqpair and belm). The spectra are well modeled in all cases, with a similar goodness of the fit. The spectral properties of the tails in the two states are, however, quite different. This might indicate that the emission originates from different media in the two cases. Our results are compatible with a compact jet origin in the hard state and hybrid Comptonization in the soft state.

F. Cangemi↗

NASA NTRS2021

Potential origin of the state-dependent high-energy tail in the black hole microquasar Cygnus X-1 as seen with INTEGRAL

Context. 0.1–10 MeV observations of the black hole microquasar Cygnus X-1 have shown the presence of a spectral feature in the form of a power law in addition to the standard black body (0.1–10 keV) and Comptonization (10–200 keV) components observed by INTEGRAL in several black-hole X-ray binaries. This so-called “high-energy tail” was recently shown to be strong in the hard spectral state of Cygnus X-1, and, in this system, has been interpreted as the high-energy part of the emission from a compact jet. Aims. This result was nevertheless obtained from a data set largely dominated by hard state observations. In the soft state, only upper limits on the presence and hence the potential parameters of a high-energy tail could be derived. Using an extended data set, we aim to obtain better constraints on the properties of this spectral component in both states. Methods. We make use of data obtained from about 15 years of observations with the INTEGRAL satellite. The data set is separated into the different states and we analyze stacked state-resolved spectra obtained from the X-ray monitors, the gamma-ray imager, and the gamma-ray spectrometer (SPI) onboard. Results. A high-energy component is detected in both states, confirming its earlier detection in the hard state and its suspected presence in the soft state with INTEGRAL, as seen in a much smaller SPI data set. We first characterize the high-energy tail components in the two states through a model-independent, phenomenological analysis. We then apply physical models based on hybrid Comptonization (eqpair and belm). The spectra are well modeled in all cases, with a similar goodness of the fits. While in the semi-phenomenological approach the high-energy tail has similar indices in both states, the fits with the physical models seem to indicate slightly different properties. Based on this approach, we discuss the potential origins of the high-energy components in both the soft and hard states, and favor an interpretation where the high-energy component is due to a compact jet in the hard state and hybrid Comptonization in either a magnetized or nonmagnetized corona in the soft state.

accretion↗

NASA NTRS1988

Imaging and spectroscopy of Comet P/Halley

The goals of this investigation are the analysis of a large set of high-resolution echelle/reticon spectra, and the reduction and analysis of a set of narrow-band-filtered charge coupled device (CCD) images of Comet Halley taken during the preperihelion period at Oak Ridge Observatory by Dr. R. E. McCrosky. The scientific objectives associated with these goals are the determination of the spatial distributions of several important radicals, atoms and ions in the coma. These include C2, CN, C3, H2O(+) and CO(+) from the image data. The analysis of the neutral species distribution with Monte Carlo models will aid in the understanding of their production and decay mechanisms as well as serve as an important indicator of the physical conditions in the inner coma. The spatial distributions of the ions will serve as a guide to constrain the complex model necessary for understanding the interaction of the solar wind and the cometary ions. Work during this past year has been devoted largely to the reduction of the standard star photometry for the CCD image data set, as well as the re-flat-fielding of a number of the comet images. We are pleased to report that despite a number of setbacks and the small effort devoted to this work (2 1/2 months for the PI and a generous share of completely unsupported time by Dr. McCrosky) that this portion of the work has been successfully completed. The goals for the upcoming final year of this project (under a new project number) are to complete the calibration of the CCD image data for inclusion in the IHW archive, to analyze a select portion of the neutral radical images with our Monte Carlo models, and to present the results of the 6300/region spectra as a guide to low-resolution spectral observers in order to yield the unambiguous separation of the contributions of cometary O(1D), airglow O(1D), and the numerous NH2 lines in that region of the spectrum.

Combi, Michael R.↗

NASA NTRS1993

Stationary eddies in the Mars general circulation as simulated by the NASA-Ames GCM

Quasistationary eddies are prominent in a large set of simulations of the Mars general circulation performed with the NASA-Ames GCM. Various spacecraft observations have at least hinted at the existence of such eddies in the Mars atmosphere. The GCM stationary eddies appear to be forced primarily by the large Mars topography, and (to a much lesser degree) by spatial variations in the surface albedo and thermal inertia. The stationary eddy circulations exhibit largest amplitudes at high altitudes (above 30-40 km) in the winter extratropical regions. In these regions they are of planetary scale, characterized largely by zonal wavenumbers 1 and 2. Southern Hemisphere winter appears to be dominated by a very strong wave 1 pattern, with both waves 1 and 2 being prominent in the Northern Hemisphere winter regime. This difference seems to be basically understandable in terms of differences in the topography in the two hemispheres. The stationary eddies in the northern winter extratropics are found to increase in amplitude with dust loading. This behavior appears to be at least partly associated with changes in the structure of the zonal-mean flow that favor a greater response to wave 1 topographic forcing. There are also strong stationary eddy circulations in the tropics and in the summer hemisphere. The eddies in the summer subtropics and extratropics arc substantially stronger in southern summer than in northern summer. The summer hemisphere stationary circulations are relatively shallow and are characterized by smaller zonal scales than those in the winter extratropics.

Barnes, J. R.↗

NASA NTRS2012

Wide-Field Imaging Interferometry Spatial-Spectral Image Synthesis Algorithms

Developed is an algorithmic approach for wide field of view interferometric spatial-spectral image synthesis. The data collected from the interferometer consists of a set of double-Fourier image data cubes, one cube per baseline. These cubes are each three-dimensional consisting of arrays of two-dimensional detector counts versus delay line position. For each baseline a moving delay line allows collection of a large set of interferograms over the 2D wide field detector grid; one sampled interferogram per detector pixel per baseline. This aggregate set of interferograms, is algorithmically processed to construct a single spatial-spectral cube with angular resolution approaching the ratio of the wavelength to longest baseline. The wide field imaging is accomplished by insuring that the range of motion of the delay line encompasses the zero optical path difference fringe for each detector pixel in the desired field-of-view. Each baseline cube is incoherent relative to all other baseline cubes and thus has only phase information relative to itself. This lost phase information is recovered by having point, or otherwise known, sources within the field-of-view. The reference source phase is known and utilized as a constraint to recover the coherent phase relation between the baseline cubes and is key to the image synthesis. Described will be the mathematical formalism, with phase referencing and results will be shown using data collected from NASA/GSFC Wide-Field Imaging Interferometry Testbed (WIIT).

Lyon, Richard G.↗

NASA NTRS2012

Turbulent Statistics from Time-Resolved PIV Measurements of a Jet Using Empirical Mode Decomposition

Empirical mode decomposition is an adaptive signal processing method that when applied to a broadband signal, such as that generated by turbulence, acts as a set of band-pass filters. This process was applied to data from time-resolved, particle image velocimetry measurements of subsonic jets prior to computing the second-order, two-point, space-time correlations from which turbulent phase velocities and length and time scales could be determined. The application of this method to large sets of simultaneous time histories is new. In this initial study, the results are relevant to acoustic analogy source models for jet noise prediction. The high frequency portion of the results could provide the turbulent values for subgrid scale models for noise that is missed in large-eddy simulations. The results are also used to infer that the cross-correlations between different components of the decomposed signals at two points in space, neglected in this initial study, are important.

Dahl, Milo D.↗