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At least 973 records · Page 54

A remote sensing method for estimating regional reservoir area and evaporative loss

Evaporation from the water surface of a reservoir can significantly affect its function of ensuring the availability and temporal stability of water supply. Current estimations of reservoir evaporative loss are dependent on water area derived from a reservoir storage-area curve. Such curves are unavailable if the reservoir is located in a data-sparse region or questionable if long-term sedimentation has changed the original elevation-area relationship. In this paper, we propose a remote sensing framework to estimate reservoir evaporative loss at the regional scale. This framework uses a multispectral water index to extract reservoir area from Landsat imagery and estimate monthly evaporation volume based on pan-derived evaporative rates. The optimal index threshold is determined based on local observations and extended to unobserved locations and periods. Built on the cloud computing capacity of the Google Earth Engine, this framework can efficiently analyze satellite images at large spatiotemporal scales, where such analysis is infeasible with a single computer. Our study involves 200 major reservoirs in Texas, captured in 17,811 Landsat images over a 32-year period. The results show that these reservoirs contribute to an annual evaporative loss of 8.0 billion cubic meters, equivalent to 20% of their total active storage or 53% of total annual water use in Texas. At five coastal basins, reservoir evaporative losses exceed the minimum freshwater inflows required to sustain ecosystem health and fishery productivity of the receiving estuaries. Reservoir evaporative loss can be significant enough to counterbalance the positive effects of impounding water and to offset the contribution of water conservation and reuse practices. Our results also reveal the spatially variable performance of the multispectral water index and indicate the limitation of using scene-level cloud cover to screen satellite images. Finally, this study demonstrates the advantage of combining satellite remote sensing and cloud computing to support regional water resources assessment.

58 GEOSCIENCES↗

Bi-Modal Model for Neutron Emissions from PuO{sub 2} and MOX Holdup

The measurement of uranium and plutonium holdup in plants during process activity and for decommissioning is important for nuclear safeguards and material control. The amount of plutonium and uranium holdup in glove-boxes, pipes, ducts, and other containers has been measured for several decades using both neutron and gamma-ray techniques. For the larger containers such as hot cells and glove-boxes that contain processing equipment, the gamma-ray techniques are limited by self-shielding in the sample as well as gamma absorption in the equipment and associated shielding. The neutron emission is more penetrating and has been used extensively to measure the holdup for the large facilities such as the MOX processing and fabrication facilities in Japan and Europe. In some case the totals neutron emission rates are used to determine the holdup mass and in other cases the coincidence rates are used such as at the PFPF MOX fabrication plant in Japan. The neutron emission from plutonium and MOX has 3 primary source terms: 1) Spontaneous fission (SF) from the plutonium isotopes, 2) The (α,n) reactions from the plutonium alpha particle emission reacting with the oxygen and other impurities, and 3) Neutron multiplication (M) in the plutonium and uranium as a result of neutrons created by the first two sources. The spontaneous fission yield per gram is independent of thickness, whereas, the above sources 2) and 3) are very dependent on the thickness of the deposit. As the effective thickness of the deposit becomes thin relative to the alpha particle range, the (α,n) reactions and neutrons from multiplication (M) approach zero. In any glove-box, there will always be two primary modes of holdup accumulation, namely direct powder contact and non-contact by air dispersal. These regimes correspond to surfaces in the glove-box that have come into direct contact with the process MOX powder versus surface areas that have not had direct contact with the powder. The air dispersal of PuO{sub 2} particles has been studied for several decades by health physicists, because the primary health hazard of plutonium is breathing the airborne particles. The air dispersal mechanism results from the smaller particles in the top layer of powder that are lifted into the air by the electrostatic charge buildup from the alpha decay process, and the air convection carries the particles to new more distant locations. If there is open plutonium powder in a glove-box, the surfaces at more distant locations will become contaminated over time. The range of an alpha particle in a solid or powder is a function of the particle energy, the material density, and the atomic number A of the material. The average energy of a plutonium alpha particle is ∼5.2 MeV and the range in air is ∼37 mm. The range in other materials can be estimated via the Bragg-Kleenman equation. For plutonium, A is 94, and the typical density for a single particle is ∼11.5 g/cm{sup 3}, but for a powder, the density would be less because of the air packing fraction. The significance of the small diameter is that the range of the alpha particle is ∼50 μm for powder density 2.5 and significantly less for a single particle with density 11.5, so the thin deposit of separate small particles will have a greatly reduced (α,n) yield. The average alpha transit length to the surface in the isolated MOX particle would be < 2.5 μm; whereas, the range of the alpha particle is much longer. Thus, most of the alpha particles would escape from the MOX particle and be absorbed by the walls and air. The air dispersal particles will have access to a large surface area that includes the walls, whereas, the powder contact surface area will be orders of magnitude smaller. Thus, the vast majority of the glove-box surface area does not produce the full (α,n) reaction neutron yield, even from the O{sub 2} in the PuO{sub 2} as well as any impurity contamination such as H{sub 2}O. To obtain a more quantitative estimate of the neutron (α,n) yields as a function of holdup deposit thickness, we have used MCNPX calculations to estimate the absorption of alpha particles in PuO{sub 2} holdup deposits. The powder thickness was varied from 0.1 μm to 5000 μm and the alpha particle escape probability was calculated. As would be expected, as the thickness approaches zero, the escape probability approaches 1.0, and as the thickness gets much greater than the alpha particle range (∼50 μm), the escape probability becomes small. Typically, the neutron holdup calibration measurement are performed using sealed containers of thick MOX that has all 3 sources of neutrons [SF, (α,n), and M], and no significant impurities. Thus, the calibration counting rates need to include corrections for M and (α,n) yields that are different for the holdup compared with the calibration samples. If totals neutron counting is used for the holdup measurements, the variability of the (α,n) term needs to be considered.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Comparing EGF Methods for Estimating Corner Frequency and Stress Drop from P-wave Spectra

Empirical Green's functions (EGF) are widely applied to correct earthquake spectra for attenuation and other path effects in order to estimate corner frequencies and stress drops, but these source parameter estimates often exhibit poor agreement between different studies. We investigate this issue by analyzing a compact cluster of over 3000 aftershocks of the 1992 Landers earthquake. We apply and compare two different analysis and modeling methods: (1) the spectral decomposition and global EGF fitting approach, and (2) a more traditional EGF method of modeling spectral ratios. We find that spectral decomposition yields event terms that are consistent with stacks of spectral ratios for individual events, but source-parameter estimates nonetheless vary between the methods. The main source of differences comes from the modeling approach used to estimate the EGF. The global EGF-fitting approach suffers from parameter tradeoffs among the absolute stress drop, the stress-drop scaling with moment, and the high-frequency falloff rate, but has the advantage that the relative spectral shapes and stress drops among the different events in the cluster are well-resolved even if their absolute levels are not. The spectral-ratio approach solves for a different EGF for each target event without imposing any constraint on the corner frequency, f c , of the smaller events, and so can produce biased results for target-event f c . Placing constraints on the small-event f c improves the performance of the spectral-ratio method and allows the two methods to yield very similar results.

58 GEOSCIENCES↗

Flux Sensitivity Requirements for the Detection of Lyman Continuum Radiation Drop-ins from Star-forming Galaxies below Redshifts of 3

Flux estimates for ionizing radiation escaping from star-forming galaxies with characteristic UV luminosities (L{sub 1500∗(1+z)}{sup ∗}), derived from GALEX and the VIMOS-VLT Deep Survey, are presented as a function of redshift and assumed escape fraction. These estimates offer guidance to the design of instrumentation and observing strategies, be they spectroscopic or photometric, for attempting to detect LyC escaping star-forming galaxies for redshifts z<3. Examples are given that relate the integrated escape fraction (f {sup e} {sub LyC}) of ionizing photons, obtained by integrating over the entire extreme UV (EUV) bandpass, to the relative escape fraction (f {sup e} {sub 900}) observed just shortward of the ionization edge at 911.8 Å as a function of H i, He i, and He ii column densities. We find that for logN{sub HI}(cm{sup −2})≳17.0, f {sup e} {sub LyC} is significantly greater than f {sup e} {sub 900}. Detection of LyC “drop-ins” in the rest-frame EUV will provide enhanced fidelity to determinations of the integrated fraction of ionizing photons f {sup e} {sub LyC} that escape star-forming galaxies and contribute to the metagalactic ionizing background (MIB).

79 ASTRONOMY AND ASTROPHYSICS↗

Second Generation Toolset for Calculation of Induced Seismicity Risk Profiles

This report describes development and demonstration of Generation 2 of the NRAP toolset for probabilistic analysis of risks from earthquakes that could potentially be induced by CO 2 injection. The capability to carry out hazard estimation at multiple sites and over multiple time periods of interested has been added to the integrated toolset. The capability to carry out hazard runs that utilize multiple simulations, based on random sampling of input parameter distributions, to bound hazard curve uncertainties has also been added. During Generation 2, an innovative method of constructing “nuisance fragility” functions for seismic ground motion has been developed. These functions are combined with seismic hazard curves to estimate of the risk of nuisance from ground shaking. The results described in this report demonstrate the functionality of the toolset based on its application to hypothetical scenarios involving one or two faults. Additional computer program development, including code parallelization, will be needed to bring the toolset up to full functionality. Alternative approaches to implementing the simulation-based approach to probabilistic induced seismicity hazard analysis are also outlined.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Theoretical Prediction of Am(III)/Eu(III) Selectivity to Aid the Design of Actinide-Lanthanide Separation Agents

Selective extraction of minor actinides from lanthanides is a critical step in the reduction of radiotoxicity of spent nuclear fuels. However, the design of suitable ligands for separating chemically similar 4f- and 5f-block trivalent metal ions poses a significant challenge. Furthermore, first-principles calculations should play an important role in the design of new separation agents, but their ability to predict metal ion selectivity has not been systematically evaluated. We examine the ability of several density functional theory methods to predict selectivity of Am(III) and Eu(III) with oxygen, mixed oxygen–nitrogen, and sulfur donor ligands. The results establish a computational method capable of predicting the correct order of selectivities obtained from liquid–liquid extraction and aqueous phase complexation studies. To allow reasonably accurate predictions, it was critical to employ sufficiently flexible basis sets and provide proper account of solvation effects. The approach is utilized to estimate the selectivity of novel amide-functionalized diazine and 1,2,3-triazole ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantifying CO 2 storage efficiency factors in hydrocarbon reservoirs. A detailed look at CO 2 Enhanced Oil Recovery

Carbon dioxide (CO 2 ) enhanced oil recovery (EOR) will likely be the primary means of geologic CO 2 storage during the early stages of commercial-scale carbon capture and storage (CCS) because of the inherent economic incentives as well as the abundant experience and demonstrated success in the United States, where CO 2 EOR has been employed since 1974. The work presented here estimates CO 2 storage efficiency factors in CO 2 EOR operations using a unique industry database of CO 2 EOR sites and 12 different reservoir simulation models. The simulation models encompass fluvial clastic and shallow shelf carbonate depositional environments for reservoir depths of 1219 and 2438 m (4000 and 8000 feet) and 7.6-, 20-, and 64-m (25-, 66-, and 209-foot)-thick pay zones. A novel statistical modeling technique incorporating the Michaelis–Menten function is used to generate empirical percentile estimates of CO 2 storage efficiency factors. West Texas San Andres dolomite water alternating gas (WAG) CO 2 flood performance data were used to derive P10, P50, and P90 CO 2 storage efficiency factors of 0.76, 1.28, and 1.74 Mscf/STB (stock tank barrel) of original oil in place. Median CO 2 storage efficiency factors from continuous CO 2 injection following conventional waterflood varied from 15% to 61% and 8% to 40% for fluvial clastic and shallow shelf carbonate simulation models, respectively, while those from WAG injection varied from 14% to 42% and 8% to 31%, respectively. Variation in the CO 2 storage efficiency factors was largely attributable to reservoir depth (a surrogate for reservoir pressure and temperature) and lithology (clastic versus carbonate). The results of this work provide practical information that can be used to quantify CO 2 storage resource estimates in oil reservoirs during CO 2 EOR operations (as opposed to storage following depletion) and the uncertainty associated with those estimates.

54 ENVIRONMENTAL SCIENCES↗

Assessment of the mechanical performance of the Westinghouse BWR control rod CR 99 at high depletion levels

A long-term program assessing the mechanical performance of the Westinghouse BWR control rod CR 99 at high depletion levels has been performed. The scope of the program has mainly been based on the operation of four CR 99 Generation 2 control rods in demanding positions during 6 and 7 cycles in the Leibstadt Nuclear Power Plant (KKL) and on the detailed visual inspections and blade wing thickness measurements that were performed after the rods were discharged. By correlating statistically the blade wing thickness measurements to the appearance of irradiation-assisted stress corrosion cracking (IASCC), the probability of IASCC appearance as function of the blade wing swelling was estimated. In order to correlate the IASCC probability of a CR 99 to its depletion, the {sup 10}B depletion of the studied rods was calculated in detail on a local level with the stochastic Monte Carlo code MCNP in combination with the Westinghouse nodal code system PHOENIX4/POLCA7. Using this information coupled to the blade wing measurement data, a finite element model describing the blade wing swelling of an arbitrary CR 99 design as function of {sup 10}B depletion could then be generated. In the final step, these relationships were used to quantify the probability of IASCC appearance as function of the {sup 10}B depletion of the CR 99 Generations 2 and 3. Applying this detailed mapping of the CR 99 behavior at high depletion levels and using an on-line core monitoring system with explicit {sup 10}B depletion tracking capabilities will enable a reliable prediction of the probability for IASCC appearance, thus enhancing the optimized design and the sound operation of the CR 99 control rod. Another important outcome of the program was that it was clearly shown that no significant amount of boron leakage did occur through any of the detected IASCC cracks, despite the very high depletion levels achieved. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function

We present a method based on the path integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase δ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to δ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function S(q, ω) of two one-dimensional model systems, harmonic and quartic oscillators, for which S(q, ω) can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Crustal and uppermost mantle structure in the Middle East: assessing constraints provided by jointly modelling Ps and Sp receiver functions and Rayleigh wave group velocity dispersion curves

Seismic velocity models are found, along with uncertainty estimates, for 11 sites in the Middle East by jointly modelling Ps and Sp receiver functions and surface (Rayleigh) wave group velocity dispersion. The approach performs a search for models that satisfy goodness-of-fit criteria guided by a variant of simulated annealing and uses statistical tools to assess these products of searches. These tools, a parameter correlation matrix and marginal posterior probability density (PPD) function, allow us to evaluate quantitatively the constraints that each data type imposes on model parameters and to identify portions of each model that are well-constrained relative to other portions. This joint modelling technique, which we call ‘multi-objective optimization for seismology’, does not require a good starting solution, although such a model can be incorporated easily, if available, and can reduce the computation time significantly. Applying the process described above to broadband seismic data reveals that crustal thickness varies from 15 km beneath Djibouti (station ATD) to 45 km beneath Saudi Arabia (station RAYN). A pronounced low velocity zone for both Vp and Vs is present at a depth of ~12 km beneath station KIV located in northern part of greater Caucasus, which may be due to the presence of a relatively young volcano. Similarly, we also noticed a 6-km-thick low velocity zone for Vp beginning at 20 km depth beneath seismic station AGIN, on the Anatolian plateau, while positive velocity gradients prevail elsewhere in eastern Turkey. Beneath station CSS, located in Cyprus, an anomalously slow layer is found in the uppermost mantle, which may indicate the presence of altered lithospheric material. Crustal P- and S-wave velocities beneath station D2, located in the northeastern portion of central Zagros, range between 5.2–6.2 and 3.2–3.8 km s -1 , respectively. Finally, in Oman, we find a Moho depth of 34.0 ± 1.0 km and 25.0 ± 1.0 to 30.0 ± 1.0 km beneath stations S02 and S04, respectively.

58 GEOSCIENCES↗

Stochastic Averaging of Radiative Transfer Coefficients for Relativistic Electrons

Abstract Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating transfer coefficients that exploits their linear dependence on the electron distribution function, decomposing the distribution function into a sum of parts each of whose emissivity can be calculated easily. We refer to this procedure as stochastic averaging and apply it in two contexts. First, we use it to estimate the emissivity of an isotropicκdistribution function with a high-energy cutoff. The resulting coefficients can be evaluated efficiently enough to be used directly in ray-tracing calculations, and we provide an example calculation. Second, we use stochastic averaging to assess the effect of subgrid turbulence on the volume-averaged emissivity and along the way provide a prescription for a turbulent emissivity. We find that for parameters appropriate to EHT sources turbulence reduces the emissivity slightly. In the infrared, turbulence can dramatically increase the emissivity.

Astronomy & Astrophysics↗

Comparing correlation components and approximations in Hartree–Fock and Kohn–Sham theories via an analytical test case study

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree–Fock (HF) and Kohn–Sham (KS) states as analytical functions of the external potential, Δv, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, Δv} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the “traditional” correlation energy, i.e., the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (45)]. Next, we test the performances of the Liu–Burke and the Seidl–Perdew–Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Further, our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical datasets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecule-surface interaction from van der Waals-corrected semilocal density functionals: The example of thiophene on transition-metal surfaces

Semilocal density functional approximations are widely used. None of them can capture the long-range van der Waals (vdW) attraction between separated subsystems, but they differ remarkably in the extent to which they capture intermediate-range vdW effects responsible for equilibrium bonds between neighboring small closed-shell subsystems. The local density approximation (LDA) often overestimates this effect, while the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) underestimates it. The strongly constrained and appropriately normed (SCAN) meta-GGA often estimates it well. All of these semilocal functionals require an additive nonlocal correction such as the revised Vydrov-Van Voorhis 2010 (rVV10) to capture the long-range part. This work reports adsorption energies and the corresponding geometry of aromatic thiophene (C 4 H 4 S) bound to transition-metal surfaces. The adsorption process requires a genuine interplay of covalent and weak binding and requires a simultaneously accurate description of surface and adsorption energies with the correct prediction of the adsorption site. All these quantities must come from well-balanced short- and long-range correlation effects for a universally applicable method for weak interactions with chemical accuracy. Here, our methods indicate that the correct interplay is not present in any combination of recent meta-GGA's and rVV10. The simple short-range damping of the vdW correction scheme that is practically successful in the combination of GGA's and vdW approximations is less transferable in SCAN+rVV10 or in the revised version, revSCAN+rVV10. In addition, we present accurate random-phase-approximation-quality adsorption energies from a model based on the one of Zaremba and Kohn.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Two-particle correlation functions in cluster perturbation theory: Hubbard spin susceptibilities

Cluster perturbation theory (CPT) is a computationally economic method commonly used to estimate the momentum- and energy-resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. Finally, we benchmark the method with the one-dimensional Fermi-Hubbard model by comparing with known results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Mapping wall-to-wall fractional cover of Arctic tundra plant functional types in Alaska using 20-m spatial resolution satellite imagery and harmonized plot observations

Estimates of fractional cover (fCover) across given land surfaces are used to assess, and often model, vegetation composition and diversity, which are crucial for understanding the health and functioning of terrestrial ecosystems. Remote sensing provides a useful means for scaling local, plot-measured fCover estimates to regional scales. Leveraging a recently synthesized and harmonized plot database, this study generated wall-to-wall maps of fCover for six Alaskan-Arctic plant functional types (PFT), including non-vascular plants, forbs, graminoids, and deciduous and evergreen shrubs, using 20-m satellite data (Sentinel-1, Sentinel-2, ArcticDEM) using a machine learning regression approach, specifically the random forest (RF) algorithm, which is well-suited for handling nonlinear relationships and high-dimensional satellite datasets. This study additionally addressed the spatio-temporal inconsistencies e.g., sampling scale, plot size, and collection year in plot measured fCover by adopting a multivariate outlier detection approach—Cook’s distance—to identify high-quality plots for model training and validation. Our approach achieves high accuracy (R 2 = 0.59–0.93, root mean squared errors = 0.02–0.10 for all PFTs) between plot-observed and satellite-derived fCover when using high-quality plot samples. The mapped fCover characterizes the spatial patterns of different PFTs across the tundra biome at a 20-m resolution, providing key information needed for improved representation of Arctic tundra vegetation in terrestrial biosphere models to better understand climate-vegetation feedback across the Arctic tundra.

Arctic tundra↗

Electronic and optical properties of the LiCdX (X = N, P, As and Sb) filled-tetrahedral compounds with the Tran–Blaha modified Becke–Johnson density functional

Highlights: • Electronic and optical properties of the LiCdX compounds have been predicted. • Tran–Blaha-modified Becke–Johnson functional significantly improves the band gap. • We predict a direct band gap in all of the considered LiCdX compounds. • Origin of the peaks in the optical spectra is determined. - Abstract: The structural, electronic and optical properties of the LiCdN, LiCdP, LiCdAs and LiCdSb filled-tetrahedral compounds have been explored from first-principles. The calculated structural parameters are consistent with the available experimental results. Since DFT with the common LDA and GGA underestimates the band gap, we use a new developed functional able to accurately describe the electronic structure of semiconductors, namely the Tran–Blaha-modified Becke–Johnson potential. The four investigated compounds demonstrate semiconducting behavior with direct band gap ranging from about 0.32 to 1.65 eV. The charge-carrier effective masses are evaluated at the topmost valence band and at the bottommost conduction band. The evolution of the value and nature of the energy band gap under pressure effect is also investigated. The frequency-dependent complex dielectric function and some macroscopic optical constants are estimated. The microscopic origins of the structures in the optical spectra are determined in terms of the calculated energy band structures.

36 MATERIALS SCIENCE↗

Increasing the power of weak lensing data with multipole-based intrinsic alignment estimators

ABSTRACT It has long been known that galaxy shapes align coherently with the large-scale density field. Characterizing this effect is essential to interpreting measurements of weak gravitational lensing, the deflection of light from distant galaxies by matter overdensities along the line of sight, as it also produces coherent galaxy alignments that we wish to interpret in terms of a cosmological model. Existing direct measurements of intrinsic alignments using galaxy samples with high-quality shape and redshift measurements typically use well-understood but sub-optimal projected estimators, which do not make good use of the information in the data when comparing those estimators to theoretical models. We demonstrate a more optimal estimator, based on a multipole expansion of the correlation functions or power spectra, for direct measurements of galaxy intrinsic alignments. We show that even using the lowest order multipole alone increases the significance of inferred model parameters using simulated and real data, without any additional modelling complexity. We apply this estimator to measurements of parameters of the non-linear alignment model using data from the Sloan Digital Sky survey, demonstrating consistent results with a factor of ∼2 greater precision in parameter fits to intrinsic alignments models. This result is functionally equivalent to quadrupling the survey area, but without the attendant costs – thereby demonstrating the value in using this new estimator in current and future intrinsic alignments measurements using spectroscopic galaxy samples.

Astronomy & Astrophysics↗

Learning Functions Varying along a Central Subspace

Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of an s-Hölder function in $R^D$ which varies along a central subspace of dimension $d$ while $d \ll D$. A direct approximation of $f$ in $R^D$ with an accuracy $\varepsilon$ requires the number of samples in the order of $\varepsilon^{-(2s+D)/s}$. In this paper, we analyze the generalized contour regression (GCR) algorithm for the estimation of the central subspace and use piecewise polynomials for function approximation. GCR is among the best estimators for the central subspace, but its sample complexity is an open question. In this paper, we partially answer this questions by proving that if a variance quantity is exactly known, GCR leads to a mean squared estimation error of $O(n^{-1})$ for the central subspace. The estimation error of this variance quantity is also given in this paper. The mean squared regression error of $f$ is proved to be in the order of $(n/\log n)^{-\frac{2s}{2s+d}}$, where the exponent depends on the dimension of the central subspace instead of the ambient space . This result demonstrates that GCR is effective in learning the low-dimensional central subspace. We also propose a modified GCR with improved efficiency. Here, the convergence rate is validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗