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End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations
In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.
Evaluation of 3D Simulation Capabilities within xRAGE using a Suite of Test Problems
This presentation describes a 3D verification and validation suite for xRAGE. Three verification test problems for hydrodynamics are presented: the Kidder ball problem, the Verney shell problem, and a 5-material compression problem. There is excellent agreement between 2D and 3D XRAGE simulation results for these problems, and between the xRAGE results and the benchmark solutions. In addition, two 3D ICF test problems are presented, based on an OMEGA direct drive capsule experiment, and on a NIF indirect drive capsule experiment. These two ICF test problems are used to evaluate two hydrodynamic methods within xRAGE. In addition to hydrodynamics the simulations also include three temperature plasma physics, thermal conduction and radiation diffusion. When simulating either capsule in 3D the newer unsplit hydrodynamic method in xRAGE produces more vorticity relative to the older default method. For the indirect drive capsule the 3D simulations are in reasonable agreement with the experimental values of ion temperature and neutron production. Unstable 3D vortex rings are present near the DT ice/carbon interface which enhance the confinement of the DT ice.
Probing Intra-Halo Light with Galaxy Stacking in CIBER Images
We study the stellar halos of 0.2 ≲ $z$ ≲ 0.5 galaxies with stellar masses spanning $M$* ~ 10 10.5 to 10 12 $M$ ⊙ (approximately $L$* galaxies at this redshift) using imaging data from the Cosmic Infrared Background Experiment (CIBER). A previous CIBER fluctuation analysis suggested that intra-halo light (IHL) contributes a significant portion of the near-infrared extragalactic background light (EBL), the integrated emission from all sources throughout cosmic history. In this work, we carry out a stacking analysis with a sample of ~30,000 Sloan Digital Sky Survey (SDSS) photometric galaxies from CIBER images in two near-infrared bands (1.1 and 1.8 $μ$m) to directly probe the IHL associated with these galaxies. We stack galaxies in five sub-samples split by brightness and detect an extended galaxy profile beyond the instrument point-spread function (PSF) derived by stacking stars. We jointly fit a model for the inherent galaxy light profile plus large-scale one- and two-halo clustering to measure the extended galaxy IHL. We detect nonlinear one-halo clustering in the 1.8 $μ$m band at a level consistent with numerical simulations. Furthermore, by extrapolating the fraction of extended galaxy light, we measure to all galaxy mass scales, we find ~30%/15% of the total galaxy light budget from galaxies is at radius $r$ > 10/20 kpc, respectively. These results are new at near-infrared wavelengths at the $L$* mass scale and suggest that the IHL emission and one-halo clustering could have appreciable contributions to the amplitude of large-scale EBL background fluctuations.
Validating a microphysical prognostic stratospheric aerosol implementation in E3SMv2 using observations after the Mount Pinatubo eruption
Abstract. This paper describes the addition of a stratospheric prognostic aerosol (SPA) capability – developed with the goal of accurately simulating sulfate aerosol formation and evolution in the stratosphere – in the Department of Energy (DOE) Energy Exascale Earth System Model, version 2 (E3SMv2). The implementation includes changes to the four-mode Modal Aerosol Module microphysics in the stratosphere to allow for larger particle growth and more accurate stratospheric aerosol lifetime following the Pinatubo eruption. E3SMv2-SPA reasonably reproduces stratospheric aerosol lifetime, burden, aerosol optical depth, and top-of-atmosphere flux when compared to remote sensing observations. E3SMv2-SPA also has close agreement with the interactive chemistry–climate model CESM2-WACCM (Community Earth System Model version 2–Whole Atmosphere Community Climate Model) – which has a more complete chemical treatment – and the observationally constrained, prescribed volcanic aerosol treatment in E3SMv2. Global stratospheric aerosol size distributions identify the nucleation and growth of sulfate aerosol from volcanically injected SO2 from both major and minor volcanic eruptions from 1991 to 1993. The modeled aerosol effective radius is consistently lower than satellite and in situ measurements (max differences of ∼ 30 %). Comparisons with in situ size distribution samples indicate that this simulated underestimation in both E3SMv2-SPA and CESM2-WACCM is due to overly small accumulation and coarse-mode aerosols 6–18 months post-eruption, with E3SMv2-SPA simulating ∼ 50 % of the coarse-mode geometric mean diameters of observations 11 months post-eruption. Effective radii from the models and observations are used to calculate offline scattering and absorption efficiencies to explore the implications of smaller simulated aerosol size for the Pinatubo climate impacts. Scattering efficiencies at wavelengths of peak solar irradiance (∼ 0.5 µm) are 10 %–80 % higher for daily samples in models relative to observations through 1993, suggesting higher diffuse radiation at the surface and a larger cooling effect in the models due to the smaller simulated aerosol; absorption efficiencies at the peak wavelengths of outgoing terrestrial radiation (∼ 10 µm) are 15 %–40 % lower for daily samples in models relative to observations, suggesting an underestimation in stratospheric heating in the models due to the smaller simulated aerosol. These potential biases are based on aerosol size alone and do not take into account differences in the aerosol number. The overall agreement of E3SMv2-SPA with observations and its similar performance to the well-validated CESM2-WACCM makes E3SMv2-SPA a viable alternative to simulating climate impacts from stratospheric sulfate aerosols.
Effect of Confinement of SIA Cluster Diffusion by Impurities on Radiation Defect Accumulation due to 14MeV neutrons in Tungsten
Impurities acting as traps, reduce the self-interstitial atom (SIA) cluster mobility, thereby increasing recombination and in turn enhancing radiation-resistance of polycrystalline materials. However, at elevated temperatures, depending on SIA-trap (impurity) binding energy, SIA clusters may trap and detrap (detach) numerous times. In tungsten, SIA clusters of all sizes glide one-dimensionally (1D) along their Burgers vector direction. Hence, detrapped SIAs would retrace their path, confining their 1D-glide between traps. However, small SIA clusters can change the direction of their 1D-glide by overcoming a rotation barrier. In addition, impurities or solutes are known to reduce this barrier. A lower rotation barrier can result in detrapped SIA clusters that diffuse in a random 1D direction, effectively leading to 3D (net-3D) diffusion. Here we investigate the effect of two cases of SIA diffusion, namely confined-1D diffusion and net-3D diffusion, on the damage accumulation in polycrystalline tungsten under 14 MeV neutron irradiation using the object kinetic Monte Carlo method. Simulations were performed using cascade debris obtained from molecular dynamics simulations with primary knock-on atom (PKA) energies corresponding to 14 MeV neutrons. In the simulations with net-3D diffusion, SIA clusters of all sizes diffuse in a random 1D direction after the clusters detrap. While for the confined 1D diffusion case, SIA clusters larger than size 5 retain their original direction of 1D-glide. In both types of simulations, trapped vacancies are assumed to be permanently immobilized. Unexpectedly, the damage accumulation was lower with confined 1D diffusion than that with net-3D. We present a systematic comparison of the influence of the two cases of SIA diffusion on the radiation damage accumulation as a function of dose rate, detrapping barrier, and impurity concentration at 1025 K.
Radiation induced athermal diffusivity in uranium mononitride
Uranium mononitride (UN) is one of the ceramic nuclear fuel alternatives to oxide fuel considered for light water reactors and advanced reactor designs. Properties like self- and fission gas diffusivity need to be better understood, given that they influence key fuel performance phenomena such as fission gas swelling and release. In particular, the radiation induced athermal (D 3 ) diffusivity remains challenging to accurately predict and has only been sparsely characterized in UN, despite its importance as it likely governs diffusion at the low temperatures this high-thermal-conductivity fuel form may operate. Molecular Dynamics simulations are used to estimate the mean square displacement induced by a primary knock-on atom (PKA) with a given kinetic energy. These results are combined with the PKA energy distributions obtained from binary collision approximation calculations to obtain the displacement due to a particular fission fragment. Finally, this is combined with experimental fission fragment yields to determine the displacement due to an average fission event and, thus, express the athermal diffusivity as a function of the fission rate density. These results are in excellent agreement with available experimental data. In conclusion, a particular importance is given to the understanding and the quantification of the variability of these results.
Radiation Enhanced Anion Diffusion in Chromia
Cr 2 O 3 is a ubiquitous passivating film on alloys that is vital to their stability and performance in hostile environments. In this study, we directly observe and measure how anion transport through the oxide is affected by 400 keV Ar 2+ ion irradiation as a function of temperature (30–500 °C) and dose (0.33–2.00 dpa) in single-crystal Cr 2 O 3 films using embedded 18 O isotopic tracers and atom probe tomography. Diffusion coefficients are experimentally determined and compared to a chemical rate theory model. Experimental and theoretical results are broadly in agreement, showing anion diffusion increases by at least 4–5 orders of magnitude upon irradiation with a weak dependence on temperature and a stronger dose-driven sink-strength dependence. These results reveal that radiation could significantly reduce the protectiveness of Cr 2 O 3 films when passivity relies upon limited anion diffusivity, even at relatively modest levels of irradiation and low temperatures.
Demystify radiation-enhanced hydrogen isotope diffusion in Fe-Ni-Cr austenitic stainless steels
Understanding and containing hydrogen isotope diffusion is crucial for many nuclear applications. In situ experiments have consistently shown that radiation significantly enhances isotope diffusion in austenitic stainless steels. Despite extensive research, the mechanism behind this phenomenon remains elusive, as most radiation-induced defects (e.g., vacancies, dislocations, and grain boundaries) typically trap hydrogen, thereby slowing diffusion. While grain boundaries may increase in-plane diffusivity and interstitials may enhance diffusion due to material swelling, these effects are relatively minor. Utilizing an Fe-Ni-Cr-H interatomic potential for stainless steels, we conducted extensive molecular dynamics simulations to investigate the origins of radiation-enhanced diffusion. Here, our findings reveal that when a system is resolidified, mimicking defects created by radiation displacements, the resulting structure contains a mixture of phases, boundaries, and dislocation networks. This defective structure significantly increases hydrogen diffusivity, enhancing it by approximately 1.7 times at 900 K. These results suggest that the complex defect structures formed during radiation displacements are the primary drivers of the observed diffusion enhancement, providing valuable insights into the mechanisms underlying radiation-enhanced diffusion in nuclear materials.
Understanding radiation effects in friction stir welded MA956 using ion irradiation and a rate theory model
We report an outstanding challenge in the manufacturing and joining of oxide dispersion strengthened steels is retaining the nanofeatures in the alloy throughout the fabrication and welding process. MA956 was friction stir welded with two different sets of welding parameters, resulting in a medium and high heat input. After welding, 5 MeV Fe ++ ion irradiations were performed at doses ranging from 50 to 200 dpa in the temperature range of 400 to 500°C. Post-irradiation characterization was performed with scanning transmission electron microscopy and energy-dispersive x-ray spectroscopy to investigate the Y-Al-O dispersoids, voids, and dislocations. After welding, the dispersoid microstructure coarsened, resulting in fewer and larger dispersoids regardless of heat input. After irradiation, the dispersoid behavior in the welded material was sensitive to temperature, exhibiting growth behavior attributed to Ostwald coarsening at 500 °C but a mixture of nucleation and more muted growth at 400 and 450 °C, attributed to competing mechanisms of radiation-enhanced diffusion and Ostwald coarsening. Void swelling correlated to heat input; being more prevalent in the welded conditions occurring at lower doses and in higher values relative to the base material. The low values of swelling despite microstructure coarsening caused by welding demonstrate the excellent swelling resistance of MA956, even after welding with the highest swelling values of 0.5% noted in the stir zone high heat input condition at 450 °C, 200 dpa. The dislocation behavior was inconsistent: the strongest trend was that network density was higher for welded versus base material, and an increase in loop diameter with temperature was observed. A rate theory model based on the observed microstructure suggests at high temperature interstitial loss to sinks was more likely to be dominant compared to mutual annihilation via point defect recombination, because of an increase of the radiation diffusion coefficient with temperature regardless of initial welded microstructure.
Radiosensitizing the Vasculature of Primary Brainstem Gliomas Fails to Improve Tumor Response to Radiation Therapy
Diffuse intrinsic pontine gliomas (DIPGs) arise in the pons and are the leading cause of death from brain tumors in children. DIPGs are routinely treated with radiation therapy, which temporarily improves neurological symptoms but generally fails to achieve local control. Because numerous clinical trials have not improved survival from DIPG over standard radiation therapy alone, there is a pressing need to evaluate new therapeutic strategies for this devastating disease. Vascular damage caused by radiation therapy can increase the permeability of tumor blood vessels and promote tumor cell death.
Flux effects in precipitation under irradiation simulation of Fe-Cr alloys
Radiation-enhanced precipitation of Cr-rich α’ in irradiated Fe-Cr alloys, which results in hardening and embrittlement, depends on the irradiating particle and the displacement per atom (dpa) rate. Here, we utilize a Cahn-Hilliard phase-field based approach, that includes simple models for nucleation, irradiating particle and rate dependent radiation-enhanced diffusion and cascade mixing to simulate α’ evolution under neutrons, heavy ions, and electron irradiations. Different irradiating particles manifest very different cascade mixing efficiencies. The model was calibrated using neutron data. For cascade inducing neutron/heavy-ion dpa rates at 300 °C between 10-8 and 10-6 dpa/s the model predicts approximately constant number density, decreasing radius, decreasing α’ Cr composition, and lower α’ volume fraction. The model then predicts a dramatic transition to no α’ formation above approximately 10-5 dpa/s, while electron irradiation, with weak mixing, had little effect at dpa rates up to 10-3 dpa/s. These model predictions are consistent with experiments. We explain the results in terms of the flux dependence of the radiation enhanced diffusion, cascade mixing, and their ratio, which all vary significantly in relevant flux ranges for neutron and cascade inducing ion irradiations. These results show that both cascade mixing and radiation enhanced diffusion must be accounted for when attempting to emulate neutron-irradiation effects using accelerated ion irradiations.
Synthesis, Processing, and Use of Isotopically Enriched Epitaxial Oxide Thin Films
Isotopic engineering has emerged as a key approach to study the nucleation, diffusion, phase transitions, and reactions of materials at an atomic level. It aims to uncover mass transport pathways, kinetics, and operational and failure mechanisms of functional materials and devices. Understanding these phenomena leads to deeper insights into important physical processes, such as the transport of ions in energy conversion and storage devices and the role of active sites and supports during heterogeneous catalytic reactions. Likewise, isotopic engineering is being pursued as a means of modifying functionality to enable future technological applications. In this Account, we summarize our recent work employing isotope labeling (e.g., 18 O 2 and 57 Fe) during thin film synthesis and postgrowth processing to reveal growth mechanisms, defect chemistry, and elemental diffusion under working and extreme conditions. Isotope-resolved analysis techniques with nanometer-scale spatial resolution, such as time-of-flight secondary ion mass spectrometry and atom probe tomography, facilitate the accurate quantification of isotopic placement and concentration in our well-defined heterostructures with precisely positioned, isotope-enriched layers. By measuring the nanometer-scale redistribution between natural abundance and isotopically enriched oxygen layers during the deposition of Fe 2 O 3 and Cr 2 O 3 by molecular beam epitaxy, we identified intermixing processes driven by surface adatoms occurring both at the film growth surface and within the first few layers below the surface. Further insights into synthesis mechanisms were gained by studying the tungsten oxide thin films grown by evaporating WO 3 powder in the presence of background 18 O 2 , revealing minimal incorporation of background oxygen during the film formation process. Thermal and radiation-enhanced diffusion in epitaxial Fe and Cr oxides were precisely tracked using 18 O and 57 Fe tracer layers incorporated into model epitaxial oxide thin films. This approach has allowed us to access thermal diffusion behavior at lower temperatures than previously measured, revealing a potential changeover in diffusion mechanism. Understanding radiation-enhanced diffusion in model oxides that represent the surface layers on the structural components of nuclear reactors informs our understanding of their corrosion behavior under irradiation. Isotopic labeling can also provide unique insights into the surface exchange reactions and defect chemistry of electrocatalysts. For instance, tracking the change in 18 O concentration at the surface of an epitaxial LaNiO 3 thin film after the electrocatalytic oxygen evolution reaction revealed the participation of lattice oxygen, confirming a hypothesis that had been proposed previously. Lastly, we highlight a new direction wherein we perform in situ processing studies utilizing isotopic tracers in conjunction with model epitaxial thin films within the atom probe tomography instrument. Additionally, this Account illustrates the great potential of isotopic engineering to enable fundamental mechanistic insights into physical processes and engineer functional properties in epitaxial films, heterostructures, and superlattices.
Grain Boundary Effects on Radiation Damage and Tritium Diffusion in Li–Al–O Ceramics from Molecular Dynamics and Experiments
Understanding irradiation damage and tritium transport in LiAlO2 ceramics is essential for their deployment in tritium-producing burnable absorber rods (TPBARs). Grain boundaries (GBs) play an important role in governing radiation response and tritium transport in LiAlO2 and its secondary phase LiAl5O8. Using molecular dynamics simulations, we investigated defect evolution and tritium diffusion during displacement cascades in single-crystal and bicrystal LiAlO2 and LiAl5O8 at 600 K. The results reveal that GBs suppress the damage in the LiAlO2 bicrystals as compared to single crystals, via interstitial emission. The effect is more pronounced for Li defects, than for Al and O. In LiAl5O8 the damage reduction due to introduction of GB is less pronounced overall. Tritium diffusion coefficients at GBs are higher by factors of 2–10 relative to diffusion inside grain bulk. The effect is particularly pronounced in LiAlO2, where S5, S17, and S25 GBs promote rapid tritium transport, whereas LiAl5O8 exhibits slower diffusion due to reduced free volume at its GBs. These findings evince a trade-off that while GBs mitigate radiation damage by absorbing interstitials, they simultaneously provide fast pathways for tritium migration which is not desirable for TPBAR application. The mechanistic insights gained here establish a foundation for microstructural design strategies to balance radiation tolerance and tritium retention in ceramic breeder materials.
The response of the Amazon ecosystem to the photosynthetically active radiation fields: integrating impacts of biomass burning aerosol and clouds in the NASA GEOS Earth system model
The Amazon experiences fires every year, and the resulting biomass burning aerosols, together with cloud particles, influence the penetration of sunlight through the atmosphere, increasing the ratio of diffuse to direct photosynthetically active radiation (PAR) reaching the vegetation canopy and thereby potentially increasing ecosystem productivity. In this study, we use the NASA Goddard Earth Observing System (GEOS) model with coupled aerosol, cloud, radiation, and ecosystem modules to investigate the impact of Amazon biomass burning aerosols on ecosystem productivity, as well as the role of the Amazon's clouds in tempering this impact. The study focuses on a 7-year period (2010–2016) during which the Amazon experienced a variety of dynamic environments (e.g., La Niña, normal years, and El Niño). The direct radiative impact of biomass burning aerosols on ecosystem productivity – called here the aerosol diffuse radiation fertilization effect – is found to increase Amazonian gross primary production (GPP) by 2.6 % via a 3.8 % increase in diffuse PAR (DFPAR) despite a 5.4 % decrease in direct PAR (DRPAR) on multiyear average during burning seasons. On a monthly basis, this increase in GPP can be as large as 9.9 % (occurring in August 2010). Consequently, the net primary production (NPP) in the Amazon is increased by 1.5 %, or ~92 Tg C yr -1 – equivalent to ~37 % of the average carbon lost due to Amazon fires over the 7 years considered. Clouds, however, strongly regulate the effectiveness of the aerosol diffuse radiation fertilization effect. The efficiency of this fertilization effect is the highest in cloud-free conditions and linearly decreases with increasing cloud amount until the cloud fraction reaches ~0.8, at which point the aerosol-influenced light changes from being a stimulator to an inhibitor of plant growth. Nevertheless, interannual changes in the overall strength of the aerosol diffuse radiation fertilization effect are primarily controlled by the large interannual changes in biomass burning aerosols rather than by changes in cloudiness during the studied period.
Dynamic substrate reactions during room temperature heavy ion irradiation of CoCrCuFeNi high entropy alloy thin films
Abstract High entropy alloys (HEAs) are promising materials for various applications including nuclear reactor environments. Thus, understanding their behavior under irradiation and exposure to different environments is important. Here, two sets of near-equiatomic CoCrCuFeNi thin films grown on either SiO 2 /Si or Si substrates were irradiated at room temperature with 11.5 MeV Au ions, providing similar behavior to exposure to inert versus corrosion environments. The film grown on SiO 2 had relatively minimal change up to peak damage levels above 500 dpa, while the film grown on Si began intermixing at the substrate–film interface at peak doses of 0.1 dpa before transforming into a multi-silicide film at higher doses, all at room temperature with minimal thermal diffusion. The primary mechanism is radiation-enhanced diffusion via the inverse Kirkendall and solute drag effects. The results highlight how composition and environmental exposure affect the stability of HEAs under radiation and give insights into controlling these behaviors.
From BEYONDPLANCK to COSMOGLOBE: Preliminary WMAP Q -band analysis
We present the first application of the COSMOGLOBE analysis framework by analyzing nine-year WMAP time-ordered observations that uses similar machinery to that of BEYONDPLANCK for the Planck Low Frequency Instrument (LFI). We analyzed only the Q-band (41 GHz) data and report on the low-level analysis process based on uncalibrated time-ordered data to calibrated maps. Most of the existing BEYONDPLANCK pipeline may be reused for WMAP analysis with minimal changes to the existing codebase. The main modification is the implementation of the same preconditioned biconjugate gradient mapmaker used by the WMAP team. Producing a single WMAP Q1-band sample requires 22 CPU-hrs, which is slightly more than the cost of a Planck 44 GHz sample of 17 CPU-hrs; this demonstrates that a full end-to-end Bayesian processing of the WMAP data is computationally feasible. In general, our recovered maps are very similar to the maps released by the WMAP team, although with two notable differences. In terms of temperature, we find a ~2 μK quadrupole difference that most likely is caused by different gain modeling, while in polarization we find a distinct 2.5 μK signal that has been previously referred to as poorly measured modes by the WMAP team. In the COSMOGLOBE processing, this pattern arises from temperature-to-polarization leakage from the coupling between the CMB Solar dipole, transmission imbalance, and sidelobes. No traces of this pattern are found in either the frequency map or TOD residual map, suggesting that the current processing has succeeded in modeling these poorly measured modes within the assumed parametric model by using Planck information to break the sky-synchronous degeneracies inherent in the WMAP scanning strategy.
BEYONDPLANCK X. Planck Low Frequency Instrument frequency maps with sample-based error propagation
We present Planck Low Frequency Instrument (LFI) frequency sky maps derived within the BEYONDPLANCK framework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δg 0 /g 0 = 5 x 10 -5 , which is nominally 40 times smaller than that reported by Planck 2018. However, we also note that the original Planck 2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB) B-mode experiments aiming at nanokelvin precision.