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At least 433 records · Page 24

Thermal expansion of 4H and 6H SiC from 5 K to 340 K

The first thermal expansion measurements of the 4H and 6H polytypes of SiC below room temperature are reported. The measurements were carried out on single-crystal specimens using high-resolution capacitive-based dilatometry. For both polytypes, the thermal expansion coefficient is below 2.4 × 10 -6 1/K near room temperature. No phase transitions are observed over the 5 K to 340 K temperature range of the measurements. The thermal expansion coefficient α of 4H SiC is slightly anisotropic for measurements parallel and perpendicular to the crystallographic c axis with α ∥ about 2.2 × 10 -7 1/K larger than α ⟂ near room temperature. For 6H SiC no discernible anisotropy is observed. The differences in anisotropy can be understood by considering the ratio of hexagonal to cubic bonds of each polytype. Narrow regions with negative thermal expansion that are within the limits of our resolution (~ 1 x 10 -8 ) are observed in the vicinity of 30 K for both specimens. In conclusion, tabulated data, polynomial fits, fit parameters, and comparison to data based on lattice-parameter measurements are provided.

36 MATERIALS SCIENCE↗

Searching for the corner seismic moment in worldwide data

In this paper the existence of the corner frequency value for the seismic moment distribution is investigated, analysing worldwide data. Pareto based distributions, usually considered as the most suitable to this type of data, are fitted to the most recent data, available in a global earthquake catalog. Despite the undeniable finite nature of the seismic moment data, we conclude that no corner frequency can be established considering the available data set.

58 GEOSCIENCES↗

Using Quasiparticle Poisoning To Detect Photons

According to a proposal, a phenomenon associated with excitation of quasiparticles in certain superconducting quantum devices would be exploited as a means of detecting photons with exquisite sensitivity. The phenomenon could also be exploited to perform medium-resolution spectroscopy. The proposal was inspired by the observation that Coulomb blockade devices upon which some quantum logic gates are based are extremely sensitive to quasiparticles excited above the superconducting gaps in their leads. The presence of quasiparticles in the leads can be easily detected via the charge states. If quasiparticles could be generated in the leads by absorption of photons, then the devices could be used as very sensitive detectors of electromagnetic radiation over the spectral range from x-rays to submillimeter waves. The devices in question are single-Cooper-pair boxes (SCBs), which are mesoscopic superconducting devices developed for quantum computing. An SCB consists of a small superconducting island connected to a reservoir via a small tunnel junction and connected to a voltage source through a gate capacitor. An SCB is an artificial two-level quantum system, the Hamiltonian of which can be controlled by the gate voltage. One measures the expected value of the charge of the eigenvectors of this quantum system by use of a radio-frequency single-electron transistor. A plot of this expected value of charge as a function of gate voltage resembles a staircase that, in the ideal case, consists of steps of height 2 e (where e is the charge of one electron). Experiments have shown that depending on the parameters of the device, quasiparticles in the form of "broken" Cooper pairs present in the reservoir can tunnel to the island, giving rise to steps of 1 e. This effect is sometimes called "poisoning." Simulations have shown that an extremely small average number of quasiparticles can generate a 1-e periodic signal. In a device according to the proposal, this poisoning would be turned to advantage. Depending on the wavelength, an antenna or other component would be used to couple radiation into the reservoir, wherein the absorption of photons would break Cooper pairs, thereby creating quasiparticles that, in turn, would tunnel to the island, creating a 1-e signal. On the basis of conservative estimates of device parameters derived from experimental data and computational simulations that fit the data, it has been estimated that the noise equivalent power of a device according to the proposal could be as low as 6 10(exp -22) W/Hz(exp 1/2). It has also been estimated that the spectroscopic resolution (photon energy divided by increment of photon energy) of such a device in visible light would exceed 100.

Echternach, Pierre↗

Spectral Photometric Properties of the Moon

We modeled the solar phase curves of the moon at a series of wavelengths using the full disk telescopic observations [1]. We endeavored to keep the database self-contained, that is, to use the values derived for the solar magnitude and phase curves of the disk-integrated [1]. These observations were made in a suite of 10 narrowband filters between 0.315 microns and 1.06 microns, and in the broad band Johnson UBV filters, as part of a larger program to obtain photoelectric photometry of the larger planets. Two aspects of the lunar observations are unique. First, the observations cover phase angles from 6deg through 120deg. More importantly, the observers used a special 20-mm diameter f/15 fused quartz lens constructed solely for this purpose. The lens reduced the whole lunar image in the focal plane to a size comparable to the planets observed as part of the same program. This image was fed directly into the photometer. Thus, these observations constitute the only existing set of phase curves of the entire lunar disk over a range of wavelengths. Table 1 lists the values of the Hapke model parameters which fit the data. Figure 1 is an example of the model fits to the data.

Dominque, D.↗

Efficient GPU-Accelerated MultiSource Global Fit Pipeline for LISA Data Analysis

The large-scale analysis task of deciphering gravitational-wave signals in the LISA data stream will be difficult, requiring a large amount of computational resources and extensive development of computational methods. Its high dimensionality, multiple model types, and complicated noise profile require a global fit to all parameters and input models simultaneously. In this work, we detail our global fit algorithm, called “Erebor,” designed to accomplish this challenging task. It is capable of analyzing current state-of-the-art datasets and then growing into the future as more pieces of the pipeline are completed and added. We describe our pipeline strategy, the algorithmic setup, and the results from our analysis of the LDC2A Sangria dataset, which contains massive black hole binaries, compact galactic binaries, and a parametrized noise spectrum whose parameters are unknown to the user. The Erebor algorithm includes three unique and very useful contributions: GPU acceleration for enhanced computational efficiency; ensemble Markov Chain Monte Carlo (MCMC) sampling with multiple MCMC walkers per temperature for better mixing and parallelized sample creation; and special online updates to reversible-jump (or transdimensional) sampling distributions to ensure sampler mixing and accurate initial estimates for detectable sources in the data.We recover posterior distributions for all 15 (6) of the injected massive black hole binaries (MBHB) in the LDC2A training (hidden) dataset. We catalog ∼12000 galactic binaries (∼8000 as high confidence detections) for both the training and hidden datasets. All of the sources and their posterior distributions are provided in publicly available catalogs.

LISA↗

Detection of the SO2 atmosphere on Io with the Hubble Space Telescope

Observations of the trailing hemisphere of Io made with the Faint Object Spectrograph of the Hubble Space Telescope (HST) in March 1992 have resulted in the first detection of atmospheric SO2 absorption bands in the ultraviolet. These observations represent only the third positive means of detection of what is widely believed to be Io's primary atmospheric constituent. Below approximately 2130 A the geometric albedo of the satellite is dominated by SO2 gas absorption band signatures, which have been analyzed using models that include the effects of optical thickness, temperature, and spatial distribution. The disk-intergrated HST data cannot resolve the spatial distribution, but it is possible to define basic properties and set constraints on the atmosphere at the time of the observations. Hemispheric atmospheres with average column density N = 6 - 10 x 10(exp 15)/sq sm and T(gas) = 110 - 500 K fit the data, with preference for temperatures of approximately 200 - 250 K. Better fits are found as the atmosphere is spatially confined, with a limit of approximately 8% hemispheric areal coverage and N approximately equal to 3 x 10(exp 17)/sq cm with colder 110 - 250 K temepratures. A dense (N greater than or equal to 10(exp 16)/sq cm), localized component of SO2 gas, such as that possibly associated with active volcanoes, can generate the observed spectral constrast only when the atmosphere is cold (110 K) and an extended component such as Pele is included. The combination of a dense, localized atmosphere with a tenuous component (N less than 10(exp 16)/sq cm, either patchy or extended) also fits the data. In all cases the best fit models imply a disk-averaged column density larger than exospheric but approximately 10 - 30 times less than the previous upper limit from near-UV observations.

Ballester, G. E.↗

Measurements of three-flavor neutrino oscillations from a PISCES two-detector fit to the NOvA Experiment data

NOvA is a long-baseline neutrino oscillation experiment with two functionally identical detectors: a Near Detector (ND) at Fermilab, placed 1 km from the neutrino source, and a Far Detector (FD) located 810 km away from the ND in Minnesota. NOvA s primary physics goals are to measure the neutrino oscillation parameters $\theta_{23}$ and $\Delta m^2_{32}$ with high precision, determine the neutrino mass hierarchy, and constrain the value of $\delta_{CP}$, primarily via the study of muon neutrino to electron neutrino oscillation. Extracting values for oscillation parameters from fits to data usually relies on treating systematic uncertainties as nuisance parameters, a strategy that suffers from poor scalability as the number of uncertainties becomes larger. This work introduces PISCES (Parameter Inference with Systematic Covariance and Exact Statistics), a novel method that circumvents this scalability problem by encoding systematic uncertainties into a covariance matrix. PISCES utilizes a nested minimization in which optimal systematic pulls are first computed using the covariance matrix in an inner minimization step, then the oscillation parameters are profiled over in the outer minimization. PISCES also uses a Poisson Likelihood term, making it ideal for the inclusion of low-statistic samples in the fits. PISCES is a flexible framework that also supports complex fits, such as a joint Near and Far detector fit. In the standard NOvA analysis, oscillation parameters are extracted using an extrapolation technique in which the ND data indirectly constrain the FD prediction via a ratio method. PISCES, on the other hand, enables a simultaneous ND+FD fit, allowing the high-statistics ND data to directly constrain systematic uncertainties across all samples. This thesis presents the full PISCES joint ND+FD fit for the NOvA three-flavor analysis, details its implementation, and evaluates its performance through extensive robustness tests and fake data studies. It also provides a comparison between the PISCES joint ND+FD results and the standard NOvA extrapolation method using the full NOvA 10-year data set. The results demonstrate that PISCES can successfully fit NOvA data while incorporating the constraints from the ND detectors consistently, using physically motivated systematic uncertainties to account for data/MC discrepancies.

Rajaoalisoa, Miriama [Cincinnati U.]↗

Constraints on the four-generation quark mixing matrix from a fit to flavor-physics data

In the scenario with four quark generations, we perform a fit using flavor-physics data and determine the allowed values - preferred central values and errors - of all of the elements of the 4x4 quark-mixing matrix. In addition to the direct measurements of some of the elements, we include in the fit the present measurements of several flavor-changing observables in the K and B systems that have small hadronic uncertainties, and also consider the constraints from the vertex corrections to Z{yields}bb. The values taken for the masses of the fourth-generation quarks are consistent with the measurements of the oblique parameters and perturbativity of the Yukawa couplings. We find that |V-tilde{sub tb}|{>=}0.98 at 3{sigma}, so that a fourth generation cannot account for any large deviation of |V{sub tb}| from unity. The fit also indicates that all the new-physics parameters are consistent with zero, and the mixing of the fourth generation with the other three is constrained to be small: we obtain |V-tilde{sub ub}{sup '}|<0.06, |V-tilde{sub cb}{sup '}|<0.027, and |V-tilde{sub tb}{sup '}|<0.31 at 3{sigma}. Still, this does allow for the possibility of new-physics signals in B{sub d}, B{sub s} and rare K decays.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

New constraints on oscillation parameters from {nu}e appearance and {nu}{mu} disappearance in the NOvA experiment

We present updated results from the NOvA experiment for v(mu) -> v(mu) and v(mu) -> v(e) oscillations from an exposure of 8.85 x 10(20) protons on target, which represents an increase of 46% compared to our previous publication. The results utilize significant improvements in both the simulations and analysis of the data. A joint fit to the data for v(mu) disappearance and v(e) appearance gives the best-fit point as normal mass hierarchy, Delta m(32)(2) = 2.44 x 10(-3) eV(2)/c(4), sin(2) theta(23) = 0.56, and delta(CP) = 1.21 pi. The 68.3% confidence intervals in the normal mass hierarchy are Delta m(32)(2) is an element of[2.37, 2.52] x 10(-3) eV(2)/c(4) , sin(2) theta(23) is an element of [0.43; 0.51] boolean OR [0.52; 0.60], and delta(CP) is an element of [0, 0.21 pi] boolean OR [0.91 pi, 2 pi]. The inverted mass hierarchy is disfavored at the 95% confidence level for all choices of the other oscillation parameters.

Acero, M. A.↗

Consistent lensing and clustering in a low- S 8 Universe with BOSS, DES Year 3, HSC Year 1, and KiDS-1000

ABSTRACT We evaluate the consistency between lensing and clustering based on measurements from Baryon Oscillation Spectroscopic Survey combined with galaxy–galaxy lensing from Dark Energy Survey (DES) Year 3, Hyper Suprime-Cam Subaru Strategic Program (HSC) Year 1, and Kilo-Degree Survey (KiDS)-1000. We find good agreement between these lensing data sets. We model the observations using the Dark Emulator and fit the data at two fixed cosmologies: Planck (S8 = 0.83), and a Lensing cosmology (S8 = 0.76). For a joint analysis limited to large scales, we find that both cosmologies provide an acceptable fit to the data. Full utilization of the higher signal-to-noise small-scale measurements is hindered by uncertainty in the impact of baryon feedback and assembly bias, which we account for with a reasoned theoretical error budget. We incorporate a systematic inconsistency parameter for each redshift bin, A, that decouples the lensing and clustering. With a wide range of scales, we find different results for the consistency between the two cosmologies. Limiting the analysis to the bins for which the impact of the lens sample selection is expected to be minimal, for the Lensing cosmology, the measurements are consistent with A = 1; A = 0.91 ± 0.04 (A = 0.97 ± 0.06) using DES+KiDS (HSC). For the Planck case, we find a discrepancy: A = 0.79 ± 0.03 (A = 0.84 ± 0.05) using DES+KiDS (HSC). We demonstrate that a kinematic Sunyaev–Zeldovich-based estimate for baryonic effects alleviates some of the discrepancy in the Planck cosmology. This analysis demonstrates the statistical power of small-scale measurements; however, caution is still warranted given modelling uncertainties and foreground sample selection effects.

79 ASTRONOMY AND ASTROPHYSICS↗

An analysis of confidence limit calculations used in AAPM Task Group No. 119

Purpose: The report issued by AAPM Task Group No. 119 outlined a procedure for evaluating the effectiveness of IMRT commissioning. The procedure involves measuring gamma pass-rate indices for IMRT plans of standard phantoms and determining if the results fall within a confidence limit set by assuming normally distributed data. As stated in the TG report, the assumption of normally distributed gamma pass rates is a convenient approximation for commissioning purposes, but may not accurately describe the data. Here the authors attempt to better describe gamma pass-rate data by fitting it to different distributions. The authors then calculate updated confidence limits using those distributions and compare them to those derived using TG No. 119 method. Methods: Gamma pass-rate data from 111 head and neck patients are fitted using the TG No. 119 normal distribution, a truncated normal distribution, and a Weibull distribution. Confidence limits to 95% are calculated for each and compared. A more general analysis of the expected differences between the TG No. 119 method of determining confidence limits and a more time-consuming curve fitting method is performed. Results: The TG No. 119 standard normal distribution does not fit the measured data. However, due to the small range of measured data points, the inaccuracy of the fit has only a small effect on the final value of the confidence limits. The confidence limits for the 111 patient plans are within 0.1% of each other for all distributions. The maximum expected difference in confidence limits, calculated using TG No. 119's approximation and a truncated distribution, is 1.2%. Conclusions: A three-parameter Weibull probability distribution more accurately fits the clinical gamma index pass-rate data than the normal distribution adopted by TG No. 119. However, the sensitivity of the confidence limit on distribution fit is low outside of exceptional circumstances.

60 APPLIED LIFE SCIENCES↗

NuSTAR observations of the magnetar 1E 2259+586

We report on new broad band spectral and temporal observations of the magnetar 1E 2259+586, which is located in the supernova remnant CTB 109. Our data were obtained simultaneously with the Nuclear Spectroscopic Telescope Array (NuSTAR) and Swift, and cover the energy range from 0.5-79 keV. We present pulse profiles in various energy bands and compare them to previous RXTE results. The NuSTAR data show pulsations above 20 keV for the first time and we report evidence that one of the pulses in the double-peaked pulse profile shifts position with energy. The pulsed fraction of the magnetar is shown to increase strongly with energy. Our spectral analysis reveals that the soft X-ray spectrum is well characterized by an absorbed double blackbody or blackbody plus power-law model in agreement with previous reports. Our new hard X-ray data, however, suggest that an additional component, such as a power law, is needed to describe the NuSTAR and Swift spectrum. We also fit the data with the recently developed coronal outflow model by Beloborodov for hard X-ray emission from magnetars. The outflow from a ring on the magnetar surface is statistically preferred over outflow from a polar cap.

79 ASTRONOMY AND ASTROPHYSICS↗

Alcock-paczynski cosmological test

In order to test the expansion of the universe and its geometry, we carry out an Alcock-Paczyński cosmological test, that is, an evaluation of the ratio of observed angular size to radial/redshift size. The main advantage of this test is that it does not depend on the evolution of the galaxies but only on the geometry of the universe. However, the redshift distortions produced by the peculiar velocities of the gravitational infall also have an influence, which should be separated from the cosmological effect. We derive the anisotropic correlation function of sources in three surveys within the Sloan Digital Sky Survey (SDSS): galaxies from SDSS-III/Baryon Oscillation Spectroscopic Survey Data Release 10 (BOSS-DR10) and QSOs from SDSS-II and SDSS-III/BOSS-DR10. From these, we are able to disentangle the dynamic and geometric distortions and thus derive the ratio of observed angular size to radial/redshift size at different redshifts. We also add some other values available in the literature. Then we use the data to evaluate which cosmological model fits them. We used six different models: concordance ΛCDM, Einstein-de Sitter, open-Friedman cosmology without dark energy, flat quasi-steady state cosmology, a static universe with a linear Hubble law, and a static universe with tired-light redshift. Only two of the six models above fit the data of the Alcock-Paczyński test: concordance ΛCDM and static universe with tired-light redshift, whereas the rest of them are excluded at a >95% confidence level. If we assume that ΛCDM is the correct one, the best fit with a free Ω {sub m} is produced for Ω{sub m}=0.24{sub −0.07}{sup +0.10}.

79 ASTRONOMY AND ASTROPHYSICS↗

Testing MONDian dark matter with galactic rotation curves

MONDian dark matter (MDM) is a new form of dark matter quantum that naturally accounts for Milgrom's scaling, usually associated with modified Newtonian dynamics (MOND), and theoretically behaves like cold dark matter (CDM) at cluster and cosmic scales. In this paper, we provide the first observational test of MDM by fitting rotation curves to a sample of 30 local spiral galaxies (z ≈ 0.003). For comparison, we also fit the galactic rotation curves using MOND and CDM. We find that all three models fit the data well. The rotation curves predicted by MDM and MOND are virtually indistinguishable over the range of observed radii (∼1 to 30 kpc). The best-fit MDM and CDM density profiles are compared. We also compare with MDM the dark matter density profiles arising from MOND if Milgrom's formula is interpreted as Newtonian gravity with an extra source term instead of as a modification of inertia. We find that discrepancies between MDM and MOND will occur near the center of a typical spiral galaxy. In these regions, instead of continuing to rise sharply, the MDM mass density turns over and drops as we approach the center of the galaxy. Our results show that MDM, which restricts the nature of the dark matter quantum by accounting for Milgrom's scaling, accurately reproduces observed rotation curves.

79 ASTRONOMY AND ASTROPHYSICS↗

Automated identification of 2612 LATE-K and M dwarfs in the lamost commissioning data using classification template fits

We develop a template-fit method to automatically identify and classify late-type K and M dwarfs in spectra from the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST). A search of the commissioning data, acquired in 2009–2010, yields the identification of 2612 late-K and M dwarfs. The template fit method also provides spectral classification to half a subtype, classifies the stars along the dwarf–subdwarf (dM/sdM/esdM/usdM) metallicity sequence, and provides improved metallicity/gravity information on a finer scale. The automated search and classification is performed using a set of cool star templates assembled from the Sloan Digital Sky Survey spectroscopic database. We show that the stars can be efficiently classified despite shortcomings in the LAMOST commissioning data which include bright sky lines in the red. In particular we find that the absolute and relative strengths of the critical TiO and CaH molecular bands around 7000 Å are cleanly measured, which provides accurate spectral typing from late-K to mid-M, and makes it possible to estimate metallicity classes in a way that is more efficient and reliable than with the use of spectral indices or spectral-index based parameters such as ζ{sub TiO/CaH}. Most of the cool dwarfs observed by LAMOST are found to be metal-rich dwarfs (dM). However, we identify 52 metal-poor M subdwarfs (sdM), 5 very metal-poor extreme subdwarfs (esdM) and 1 probable ultra metal-poor subdwarf (usdM). We use a calibration of spectral type to absolute magnitude and estimate spectroscopic distances for all the stars; we also recover proper motions from the SUPERBLINK and PPMXL catalogs. Our analysis of the estimated transverse motions suggests a mean velocity and standard deviation for the UVW components of velocity to be: 〈U〉=−9.8 km s{sup −1}, σ{sub U} = 35.6 km s{sup −1}; 〈V〉=−22.8 km s{sup −1}, σ{sub V}=30.6 km s{sup −1}; 〈W〉=−7.9 km s{sup −1}, σ{sub W} = 28.4 km s{sup −1}. The resulting values are in general agreement with previous reported results, which yields confidence in our spectral classification and spectroscopic distance estimates, and illustrates the potential for using LAMOST spectra of K and M dwarfs for investigating the chemo-kinematics of the local Galactic disk and halo.

79 ASTRONOMY AND ASTROPHYSICS↗

Controlling excited-state contamination in nucleon matrix elements

We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1-flavor ensemble with lattices of size 32 3 × 64 generated using the rational hybrid Monte Carlo algorithm at 𝑎 = 0.081 fm and with 𝑀 𝜋 = 312 MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a 2-state fit to data at multiple values of the source-sink separation 𝑡 sep . We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. Here a detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of 𝑡 sep needed to demonstrate convergence of the isovector charges of the nucleon to the 𝑡 sep → ∞ estimates is presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Mirror twin Higgs cosmology: constraints and a possible resolution to the H$_{0}$ and S$_{8}$ tensions

The mirror twin Higgs model (MTH) is a solution to the Higgs hierarchy problem that provides well-predicted cosmological signatures with only three extra parameters: the temperature of the twin sector, the abundance of twin baryons, and the vacuum expectation value (VEV) of twin electroweak symmetry breaking. These parameters specify the behavior of twin radiation and the acoustic oscillations of twin baryons, which lead to testable effects on the cosmic microwave background (CMB) and large-scale structure (LSS). While collider searches can only probe the twin VEV, through a fit to cosmological data we show that the existing CMB (Planck18 TTTEEE+lowE+lowT+lensing) and LSS (KV450) data already provide useful constraints on the remaining MTH parameters. Additionally, we show that the presence of twin radiation in this model can raise the Hubble constant H$_{0}$ while the scattering twin baryons can reduce the matter fluctuations S$_{8}$, which helps to relax the observed H$_{0}$ and S$_{8}$ tensions simultaneously. This scenario is different from the typical ΛCDM + ΔN$_{eff}$ model, in which extra radiation helps with the Hubble tension but worsens the S$_{8}$ tension. For instance, when including the SH0ES and 2013 Planck SZ data in the fit, we find that a universe with ≳ 20% of the dark matter comprised of twin baryons is preferred over ΛCDM by ~ 4σ. If the twin sector is indeed responsible for resolving the H$_{0}$ and S$_{8}$ tensions, future measurements from the Euclid satellite and CMB Stage 4 experiment will further measure the twin parameters to O(1 - 10%)-level precision. Our study demonstrates how models with hidden naturalness can potentially be probed using precision cosmological data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Improved mapping of radio sources from VLBI data by least-square fit

A method is described for producing improved mapping of radio sources from Very Long Base Interferometry (VLBI) data. The method described is more direct than existing Fourier methods, is often more accurate, and runs at least as fast. The visibility data is modeled here, as in existing methods, as a function of the unknown brightness distribution and the unknown antenna gains and phases. These unknowns are chosen so that the resulting function values are as near as possible to the observed values. If researchers use the radio mapping source deviation to measure the closeness of this fit to the observed values, they are led to the problem of minimizing a certain function of all the unknown parameters. This minimization problem cannot be solved directly, but it can be attacked by iterative methods which we show converge automatically to the minimum with no user intervention. The resulting brightness distribution will furnish the best fit to the data among all brightness distributions of given resolution.

Rodemich, E. R.↗