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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Mass dependence of halo baryon fractions from the kinetic Sunyaev–Zeldovich effect

ABSTRACT We detect the kinetic Sunyaev–Zeldovich imprint of peculiar motions of galaxy groups and clusters, using the photometric Dark Energy Spectroscopic Instrument Legacy Surveys together with cosmic microwave background (CMB) maps from the Atacama Cosmology Telescope (ACT). We develop a comprehensive forward model based on the AbacusSummit cosmological simulations: Mock galaxy group catalogues and synthetic kinetic Sunyaev–Zeldovich (kSZ) maps are generated, together with a reconstructed peculiar velocity field that allows for photo-z errors, redshift-space distortions, and survey masks. We investigate possible contamination from the cosmic infrared background (CIB), finding that CIB effects are subdominant to the kSZ signal in the relevant ACT frequency channel. We then predict the kSZ signal expected when stacking CMB temperature maps around groups, taking account of their estimated radial velocities. Comparing the model with observations, we are able to constrain the total baryon fraction within haloes, as well as their internal gas profiles. We find evidence for mass dependence of the halo baryon fraction within the virial radius. The gas fraction in massive groups is consistent with the universal baryon fraction, but low-mass groups ($10^{12.5} \lesssim M\, /\, h^{-1}\, \mathrm{M}_\odot \lesssim 10^{14}$) are depleted to $0.38 \pm 0.11$ times the universal baryon fraction. We find this low virial baryon fraction to be consistent with an extended gas profile, for which the total baryon content reaches the universal value well beyond the virial radius. This conclusion is consistent with previous analyses using X-ray, kSZ, and weak lensing, and plausibly reflects energetic feedback processes from the galaxies in these haloes.

Roper, Finn A [Institute for Astronomy, University↗
DOE OSTI2023

Measuring the streaming motion in the Milky Way disc with Gaia EDR3+

We map the 3D kinematics of the Galactic disc out to 3.5 kpc from the Sun, and within 0.75 kpc from the mid-plane of the Galaxy. To this end, we combine high-quality astrometry from Gaia EDR3, with heliocentric line-of-sight velocities from Gaia DR2, and spectroscopic surveys including APOGEE, GALAH, and LAMOST. We construct an axisymmetric model for the mean velocity field, and subtract this on a star-by-star basis to obtain the residual velocity field in the Galactocentric components (V Φ , V R , V z ), and V los . The velocity residuals are quantified using the power spectrum, and we find that the peak power (A/[km s –1 ]) in the mid-plane (|z| < 0.25 kpc) is (A Φ , A R , A Z , A los ) = (4.2,8.5,2.6,4.6), at 0.25 < |z|/[kpc] < 0.5, is (A Φ , A R , A Z , A los ) = (4.0,7.9,3.6,5.3), and at 0.5 < |z|/[kpc] < 0.75, is (A Φ , A R , A Z , A los ) = (1.9,6.9,5.2,6.4). Our results provide a sophisticated measurement of the streaming motion in the disc and in the individual components. We find that streaming is most significant in VR, and at all heights (|Z|) probed, but is also non-negligible in other components. Additionally, we find that patterns in velocity field overlap spatially with models for spiral arms in the Galaxy. Our simulations show that phase-mixing of disrupting spiral arms can generate such residuals in the velocity field, where the radial component is dominant, just as in real data. Furthermore, we also find that with time evolution, both the amplitude and physical scale of the residual motion decrease.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2006

Electron Velocity Distribution Function in Magnetic Clouds in the Solar Wind

We present a study of the kinetic properties of the electron velocity distribution functions within magnetic clouds, since they are the dominant thermal component. The study is based on high time resolution data from the GSFC WIND/SWE electron spectrometer and the Berkeley 3DP electron plasma instruments. Recent studies on magnetic clouds have shown observational evidence of anti-correlation between the total electron density and electron temperature, which suggest a polytrope law P(sub e) = alpha(Nu(sub e) (sup gamma)) for electrons with the constant gamma approximates 0.5 < 1. This anti-correlation and small polytropic gamma-values is interpreted in the context of the presence of highly non-Maxwellian electron distributions (i.e. non-thermal) within magnetic clouds. These works suggested that the non-thermal electrons can contribute as much as 50% of the total electron pressure within magnetic clouds. We have revisited some of the magnetic cloud events previously studied and attempted to quantify the nature of the non-thermal electrons by modeling the electron velocity distribution function using a kappa distribution function to characterize the kinetic non-thermal effects. If non-thermal tail effects are the source for the anti-correlation between the moment electron temperature and density and if the kappa distribution is a reasonable representative model of non-thermal effects, then the electron velocity distribution within magnetic clouds should show indication for small K-values when gamma < 1.

Nieves-Chinchil, Teresa↗
NASA NTRS1995

Grain formation around carbon stars. 1: Stationary outflow models

Asymptotic giant branch (AGB) stars are known to be sites of dust formation and undergo significant mass loss. The outflow is believed to be driven by radiation pressure on grains and momentum coupling between the grains and gas. While the physics of shell dynamics and grain formation are closely coupled, most previous models of circumstellar shells have treated the problem separately. Studies of shell dynamics typically assume the existence of grains needed to drive the outflow, while most grain formation models assume a constant veolcity wind in which grains form. Furthermore, models of grain formation have relied primarily on classical nucleation theory instead of using a more realistic approach based on chemical kinetics. To model grain formation in carbon-rich AGB stars, we have coupled the kinetic equations governing small cluster growth to moment equations which determine the growth of large particles. Phenomenological models assuming stationary outflow are presented to demonstrate the differences between the classical nucleation approach and the kinetic equation method. It is found that classical nucleation theory predicts nucleation at a lower supersaturation ratio than is predicted by the kinetic equations, resulting in significant differences in grain properties. Coagulation of clusters larger than monomers is unimportant for grain formation in high mass-loss models but becomes more important to grain growth in low mass-loss situations. The properties of the dust grains are altered considerably if differential drift velocities are ignored in modeling grain formation. The effect of stellar temperature, stellar luminosity, and different outflow velocities are investigated. The models indicate that changing the stellar temperature while keeping the stellar luminosity constant has little effect on the physical parameters of the dust shell formed. Increasing the stellar luminosity while keeping the stellar temperature constant results in large differences in grain properties. For small outflow velocities, grains form at lower supersaturation ratios and close to the stellar photosphere, resulting in larger but fewer grains. The reverse is true when grains form under high outflow velocities, i.e., they form at higher supersaturation ratios, farther from the star, and are much smaller but at larger quantities.

Egan, Michael P.↗
NASA NTRS1924

Tests on a model of the D.F.W. airplane T-29 of the "Deutsche Flugzeug derke" (German airplane works)

Experiments similar to those carried out with the A.E.G (Allgemeine Elektrizitats-Gesellschaft) were made in the small wind tunnel of the Gottingen laboratory on a model of the D.F.W. airplane T-29. Three series of tests were carried out on the model with a velocity head (or dynamic pressure) of 5 kg/sq m (1.02 lb/sq ft), during which one of the movable surfaces was deflected at various angles, while both the others were retained in their central positions. Of special interest among the results of the tests is the different run of the elevating moments. The curves for the A.E.G. model, rising to the right, denote stability with the elevator locked, while the slight inclination to the left with the D.F.W model denotes a slight instability. For the maximum C(sub L) values, the stability of A.E.G. model continues to increase and the instability of the D.F.W. model is converted into stability. The rolling moments shown when the angular deflection of the ailerons is 0 degrees are due, in both series of tests, to the unequal distribution of the air velocity over the cross section of the wind tunnel, rather than to a lack of symmetry in the model.

Molthan, Wilhelm↗
NASA NTRS2000

The nu Andromedae System: Models and Stability

Radial velocity observations of the F8 V star nu Andromedae taken at Lick and at Whipple Observatories have revealed evidence of three periodicities in the line-of-sight velocity of the star. These periodicities have been interpreted as evidence for at least three low-mass companions (LMCs) revolving around nu Andromedae. The mass and orbital parameters inferred for these companions raise questions about the dynamical stability of the system. We report here results from our independent analysis of the published radial velocity data, as well as new unpublished data taken at Lick Observatory. Our results confirm the finding of three periods in the data. Our best fits to the data, on the assumption that these periods arise from the gravitational perturbations of companions in Keplerian orbits, are also generally in agreement but with some differences from the earlier findings. We find that the available data do not constrain well the orbital eccentricity of the middle companion in a three-companion model of the data. We also find that in order for our best-fit model to the Lick data to be dynamically stable over the lifetime of the star (approximately 2 billion years), the system must have a mean inclination to the plane of the sky greater than 13 deg. The corresponding minimum inclination for the best fit to the Whipple data set is 19 deg. These values imply that the maximum mass for the outer companion can be no greater than about 20 Jupiter masses. Our analysis of the stability of the putative systems also places constraints on the relative inclinations of the orbital planes of the companions. We comment on global versus local (i.e., method of steepest descent) means of finding best-fit orbits from radial velocity data sets.

Stepinski, Tomasz F.↗
NASA NTRS1991

Renormalization group analysis of anisotropic diffusion in turbulent shear flows

The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity-scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.

Rubinstein, Robert↗
DOE OSTI2024

The Onset of Nucleate Boiling Prediction in a Mini Channel with the Eulerian Multiphase Flow

The prediction of boiling incipience is a critical issue for a reactor. Vapor lock causes operating instability and undesirable temperature rise, especially for small channels. This study uses the Eulerian multiphase flow boiling model to predict the onset of nucleate boiling in a millimeter scale rectangular channel. Two wall boiling models, namely the RPI (Rensselaer Polytechnic Institute) and the non-equilibrium sub cooled model are applied. Computational fluid dynamics is employed for this study to investigate the impact of operating conditions like liquid flow rate, operating pressure, heat flux, velocity profile, turbulence model, and inlet liquid temperature. Here, the effect of fundamental boiling parameters on the surface wall temperature and vapor volume fraction is also studied. The parameters under consideration are the bubble departure diameter, bubble departure frequency, nucleate site density, quenching time period, and interface heat transfer coefficients. A series of CFD calculations is conducted by varying the considered variables systematically in a wide range of flow conditions covering laminar, transition, and turbulent flows. The sub-component heat fluxes like the liquid convective, the vapor convective, the evaporative, and the quenching terms are monitored to infer the boiling dynamics in the transition region from the single-phase flow to the nucleate boiling zone. It is found that the CFD approach to detecting the boiling incipience point agrees reasonably with available experimental data. However, its limitations, like inaccuracy for lower flow rates and early transition to boiling flow, are also noticed due to the nature of the considered RPI model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1990

Numerical Formulation for the Prediction of Solid/Liquid Change of a Binary Alloy

A computational model is presented for the prediction of solid/liquid phase change energy transport including the influence of free convection fluid flow in the liquid phase region. The computational model considers the velocity components of all non-liquid phase change material control volumes to be zero but fully solves the coupled mass-momentum problem within the liquid region. The thermal energy model includes the entire domain and uses an enthalpy like model and a recently developed method for handling the phase change interface nonlinearity. Convergence studies are performed and comparisons made with experimental data for two different problem specifications. The convergence studies indicate that grid independence was achieved and the comparison with experimental data indicates excellent quantitative prediction of the melt fraction evolution. Qualitative data is also provided in the form of velocity vector diagrams and isotherm plots for selected times in the evolution of both problems. The computational costs incurred are quite low by comparison with previous efforts on solving these problems.

Schneider, G. E.↗
DOE OSTI2024

Backaction-evading receivers with magnetomechanical and electromechanical sensors

Today's mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise originating from the process of measurement itself—the quantum-mechanical backaction of measurement—and go below this ‘standard’ limit, possibly approaching the Heisenberg limit. One of the ways to eliminate this noise is by measuring a quantum nondemolition variable such as the momentum in a free-particle system. Here, we propose and characterize theoretical models for direct velocity measurement that utilize traditional electric and magnetic transducer designs to generate a signal while enabling this backaction evasion. We consider the general readout of this signal via electric or magnetic field sensing by creating toy models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme—voltage or current—for each mechanical detector configuration implies access to either the position or velocity of the mechanical subsystem. This in turn suggests a path forward for key fundamental physics experiments such as the direct detection of dark matter particles. Published by the American Physical Society 2024

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1973

Pilot model expansion tunnel test flow properties obtained from velocity, pressure, and probe measurements

Velocity-profile, pitot-pressure, and supplemental probe measurements were made at the nozzle exist of an expansion tunnel (a modification to the Langley pilot model expansion tube) for a nozzle net condition of a nitrogen test sample with a velocity of 4.5 km/sec and a density 0.005 times the density of nitrogen at standard conditions, both with the nozzle initially immersed in a helium atmosphere and with the nozzle initially evacuated. The purpose of the report is to present the results of these measurements and some of the physical properties of the nitrogen test sample which can be inferred from the measured results. The main conclusions reached are that: the velocity profiles differ for two nozzle conditions; regions of the flow field can be found where the velocity is uniform to within 5 percent and constant for several hundred microseconds; the velocity of the nitrogen test sample is reduced due to passage through the nozzle; and the velocity profiles do not significantly reflect the large variations which occur in the inferred density profiles.

Friesen, W. J.↗
NASA NTRS1998

Structure and Dynamics of the Solar Chromosphere

The problem of chromospheric dynamics and heating consists of two problems: one, concerning the magnetic network on the boundary of supergranulation cells (CB), where the oscillation period is seven minutes, and the other, concerning the cell interior (CI), where the oscillation period is three minutes. The observational data on the oscillations and the emission of radiation can be used to determine the structure and dynamics of the atmosphere provided answers are known to three critical questions, concerning: the nature of the waves powering the bright points, the origin of the observed oscillation periods and the mechanism of chromospheric heating. The recent modeling of the dynamics of the CI, which combines a sophisticated treatment of gas dynamics and radiative transfer in a one-dimensional model with empirical velocity input from the observations, answered the first of these questions: the waves powering K(sub 2upsilon), bright points are propagating acoustic waves. This firm conclusion declares invalid the model of Leibacher & Stein, which explains the observed period with standing acoustic waves in a chromospheric cavity. On the third question, the heating of the chromosphere in the CI, their model predicts that the temperature in the chromosphere is declining in the outward direction up to a height of at least I Mm most of the time, so even the time-average temperature is dropping monotonically in the outward direction, implying that lines formed in the chromosphere up to a height of at least 1 Mm appear in absorption most of the time and everywhere in the CI. The problem of the CI can be resolved with a two-component model, which combines a model for K(sub 2upsilon), bright points with a model for the background. The bright point model has the same aims as the CS94 model, except that the empirical driving from the LRK93 observations is replaced by impulsive excitation, as suggested by the properties of the Klein-Gordon equation.

Kalkofen, Wolfgang↗
NASA NTRS2018

Generating a Grid for Unstructured RANS Simulations of Jet Flows

A study has been performed to determine best practices for generating unstructured grids for Reynolds-Averaged Navier-Stokes (RANS) simulations of jet flows. The Axisymmetric Near-Sonic Jet Case from the Turbulence Modeling Resource was used for this study: a Mach 0.985 flow through the 2-in. diameter Acoustic Reference Nozzle (ARN2). Simulations were run with FUN3D and used the Menter Shear Stress Transport (SST-V), Spalart-Allmaras (S-A), and k-kL turbulence models. The axial velocity and turbulent kinetic energy fields in the jet plume of the unstructured grid solutions were compared to those of the baseline structured grid solution provided by the Turbulence Modeling Resource. Only solutions using grids with structured-like elements in the jet plume showed good agreement with the baseline structured grid solution. Using the SST-V turbulence model, the fully unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. With the S-A turbulence model, the unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. The solutions using the k-kL turbulence model seemed less sensitive to grid topology. Nozzle massflow and thrust performance were also compared for all simulations. Based on the results of this study, it is currently recommended that structured-like grid elements are used in the plumes of jet flows; unstructured grid elements can be used elsewhere.

RANS Simulations; Unstructured Grids; Jet Flows↗
DOE OSTI2021

Sea Ice Collision Risk Assessment for Tidal Turbine Siting in Cook Inlet, Alaska

Cook Inlet has great potential for tidal stream energy development. However, the presence of drifting sea ice could create hazardous collision risks for tidal turbine farms. Before turbines can be installed in Cook Inlet, sites must be surveyed to determine how often sea ice is present, how fast it will be moved by the current, and where the trajectories of drifting sea ice will be concentrated. In this study, we use remotely sensed data to characterize the seasonal sea ice conditions in Cook Inlet, a hydrodynamic model to map the water velocities, and a particle trajectory tracking model to calculate collision risks. The resulting sea ice coverage and collision risk maps will enable tidal energy developers to choose the best locations for the deployment of tidal turbines and other offshore platforms in Cook Inlet.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Comparative study of machine learning techniques for post-combustion carbon capture systems

Computational analysis of countercurrent flows in packed absorption columns, often used in solvent-based post-combustion carbon capture systems (CCSs), is challenging. Typically, computational fluid dynamics (CFD) approaches are used to simulate the interactions between a solvent, gas, and column's packing geometry while accounting for the thermodynamics, kinetics, heat, and mass transfer effects of the absorption process. These simulations can then be used explain a column's hydrodynamic characteristics and evaluate its CO 2 -capture efficiency. However, these approaches are computationally expensive, making it difficult to evaluate numerous designs and operating conditions to improve efficiency at industrial scales. In this work, we comprehensively explore the application of statistical ML methods, convolutional neural networks (CNNs), and graph neural networks (GNNs) to aid and accelerate the scale-up and design optimization of solvent-based post-combustion CCSs. We apply these methods to CFD datasets of countercurrent flows in absorption columns with structured packings characterized by several geometric parameters. We train models to use these parameters, inlet velocity conditions, and other model-specific representations of the column to estimate key determinants of CO 2 -capture efficiency without having to simulate additional CFD datasets. We also evaluate the impact of different input types on the accuracy and generalizability of each model. We discuss the strengths and limitations of each approach to further elucidate the role of CNNs, GNNs, and other machine learning approaches for CO 2 -capture property prediction and design optimization.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2007

Impact of MODIS High-Resolution Sea-Surface Temperatures on WRF Forecasts at NWS Miami, FL

Over the past few years,studies at the Short-term Prediction Research and Transition (SPoRT) Center have suggested that the use of Moderate Resolution Imaging Spectroradiometer (MODIS) composite sea-surface temperature (SST) products in regional weather forecast models can have a significant positive impact on short-term numerical weather prediction in coastal regions. The recent paper by LaCasse et al. (2007, Monthly Weather Review) highlights lower atmospheric differences in regional numerical simulations over the Florida offshore waters using 2-km SST composites derived from the MODIS instrument aboard the polar-orbiting Aqua and Terra Earth Observing System satellites. To help quantify the value of this impact on NWS Weather Forecast Offices (WFOs), the SPoRT Center and the NWS WFO at Miami, FL (MIA) are collaborating on a project to investigate the impact of using the high-resolution MODIS SST fields within the Weather Research and Forecasting (WRF) prediction system. The scientific hypothesis being tested is: More accurate specification of the lower-boundary forcing within WRF will result in improved land/sea fluxes and hence, more accurate evolution of coastal mesoscale circulations and the associated sensible weather elements. The NWS MIA is currently running the WRF system in real-time to support daily forecast operations, using the National Centers for Environmental Prediction Nonhydrostatic Mesoscale Model dynamical core within the NWS Science and Training Resource Center's Environmental Modeling System (EMS) software; The EMS is a standalone modeling system capable of downloading the necessary daily datasets, and initializing, running and displaying WRF forecasts in the NWS Advanced Weather Interactive Processing System (AWIPS) with little intervention required by forecasters. Twenty-seven hour forecasts are run daily with start times of 0300,0900, 1500, and 2100 UTC on a domain with 4-km grid spacing covering the southern half of Florida and the far western portions of the Bahamas, the Florida Keys, the Straights of Florida, and adjacent waters of the Gulf of Mexico and Atlantic Ocean. Each model run is initialized using the Local Analysis and Prediction System (LAPS) analyses available in AWIPS, invoking the diabatic. "hot-start" capability. In this WRF model "hot-start", the LAPS-analyzed cloud and precipitation features are converted into model microphysics fields with enhanced vertical velocity profiles, effectively reducing the model spin-up time required to predict precipitation systems. The SSTs are initialized with the NCEP Real-Time Global (RTG) analyses at l/12 degree resolution (approx. 9 km); however, the RTG product does not exhibit fine-scale details consistent with its grid resolution. SPoRT is conducting parallel WRF EMS runs identical to the operational runs at NWS MIA in every respect except for the use of MODIS SST composites in place of the RTG product as the initial and boundary conditions over water. The MODIS SST composites for initializing the SPoRT WRF runs are generated on a 2-km grid four times daily at 0400, 0700, 1600, and 1900 UTC, based on the times of the overhead passes of the Aqua and Terra satellites. The incorporation of the MODIS SST composites into the SPoRTWRF runs is staggered such that the 0400UTC composite initializes the 0900 UTC WRF, the 0700 UTC composite initializes the 1500 UTC WRF, the 1600 UTC composite initializes the 2100 UTC WRF, and the 1900 UTC composite initializes the 0300 UTC WRF. A comparison of the SPoRT and Miami forecasts is underway in 2007, and includes quantitative verification of near-surface temperature, dewpoint, and wind forecasts at surface observation locations. In addition, particular days of interest are being analyzed to determine the impact of the MODIS SST data on the development and evolution of predicted sea/land-breeze circulations, clouds, and precipitation. This paper will present verification results comparing the NWS MIA forecasts the SPoRT experimental WRF forecasts, and highlight any substantial differences noted in the predicted mesoscale phenomena.

Case, Jonathan L.↗
NASA NTRS2003

Navigation Concepts for the James Webb Space Telescope

This paper evaluates the performance that can be achieved using candidate ground and onboard navigation approaches for operation of the James Webb Space Telescope, which will be in an orbit about the Sun-Earth L2 libration point. The ground navigation approach processes standard range and Doppler measurements from the Deep Space Network The onboard navigation approach processes celestial object measurements and/or ground-to- spacecraft Doppler measurements to autonomously estimate the spacecraft s position and velocity and Doppler reference frequency. Particular attention is given to assessing the absolute position and velocity accuracy that can be achieved in the presence of the frequent spacecraft reorientations and momentum unloads planned for this mission. The ground navigation approach provides stable navigation solutions using a tracking schedule of one 30-minute contact per day. The onboard navigation approach that uses only optical quality celestial object measurements provides stable autonomous navigation solutions. This study indicates that unmodeled changes in the solar radiation pressure cross-sectional area and modeled momentum unload velocity changes are the major error sources. These errors can be mitigated by modeling these changes, by estimating corrections to compensate for the changes, or by including acceleration measurements.

Long, Anne↗
NASA NTRS1985

Model of human visual-motion sensing

A model of how humans sense the velocity of moving images is proposed. The model exploits constraints provided by human psychophysics, notably that motion-sensing elements appear tuned for two-dimensional spatial frequency, and by the frequency spectrum of a moving image, namely, that its support lies in the plane in which the temporal frequency equals the dot product of the spatial frequency and the image velocity. The first stage of the model is a set of spatial-frequency-tuned, direction-selective linear sensors. The temporal frequency of the response of each sensor is shown to encode the component of the image velocity in the sensor direction. At the second stage, these components are resolved in order to measure the velocity of image motion at each of a number of spatial locations and spatial frequencies. The model has been applied to several illustrative examples, including apparent motion, coherent gratings, and natural image sequences. The model agrees qualitatively with human perception.

Watson, A. B.↗