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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Modeling The Effects of Loading Scenario and Thermal Expansion Coefficient on Potential Failure of Cryo-compressed Hydrogen Vessels

A multiscale thermomechanical model for a simplified Type-3 cryogenic compressed hydrogen (H2) storage vessel is developed in this paper. The model accounts for the temperature-dependent elastic-plastic behavior of the vessel carbon/epoxy composite overwrap and aluminum alloy liner. The homogenized thermo-elastic-plastic behavior for the individual laminas of the vessel layup is obtained by an incremental Eshelby-Mori-Tanka approach associated with a micromechanical failure criterion to predict lamina failure while a standard elastic-plastic constitutive model is used to describe the behavior of a typical aluminum alloy assumed for the liner. The vessel response to external loadings is achieved by a finite element method. Four loading scenarios representing four thermomechanical cycles applied to the vessel are analyzed to evaluate constituent and lamina stresses as well as the associate failure criterion during the cycle according to these scenarios. The model can provide helpful guidance to mitigate thermal stresses by an adequate selection of loading scenario, optimizing the layup and by tailoring thermomechanical properties of the resin matrix.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Crystallization Mechanisms of Poly(vinylidene Fluoride- co -chlorotrifluoroethylene): Nucleation Transitions, Growth Kinetics, and Microstructure Evolution

The crystallization kinetics of FK-800, a commercial semicrystalline copolymer of chlorotrifluoroethylene and vinylidene fluoride (poly(CTFE-co-VDF)), dictate its microstructure and functional performance. Crystallization occurs between the glass transition (T g ≈ 31 °C) and melting point (T m ≈ 110 °C), with grain boundaries playing a key role in applications such as memristors, where they regulate filament growth. This study integrates in situ atomic force microscopy (AFM), grazing-incidence wide-angle X-ray scattering (GIWAXS), and differential scanning calorimetry (DSC) to characterize nucleation, growth, and morphology across the full crystallization window. Hot-stage AFM reveals a transition from homogeneous to heterogeneous nucleation near 45 °C and a shift from reaction-limited to diffusion-limited growth above 60 °C. Kinetics are analyzed using Lauritzen–Hoffman, Turnbull–Fisher, and Avrami models to extract surface free energies and activation barriers. A multiscale modeling framework is developed in which nucleation densities and growth rates measured by AFM are used to reconstruct Avrami kinetics, which are then validated against coverage data, and extrapolated to predict bulk crystallization behavior observed by DSC. GIWAXS confirms a primarily flat-on chain orientation at all temperatures, linking orientation to domain morphology. This integrative approach quantitatively connects nanoscale crystallization dynamics with macroscopic phase evolution, establishing a quantitative framework for modeling crystallization across time, temperature, and length scales.

Crystallization↗
DOE OSTI2025

Cross-Scale Catalyst Modeling Applied to H 2 Storage and Release via Formic Acid

Here, we propose the Systems-to-Atoms (S2A) modeling framework that integrates the kinetics of reaction chemistry and structural configurations across various length scales with the aim of establishing a versatile template for multiscale modeling of reactive flow problems and to predict the operando activity of catalyst materials. The approach encompasses a microkinetic model to analyze surface reactions on individual facets of catalyst nanoparticles coupled with the computation of average surface reaction rates for catalyst nanoparticles of specific size distributions. Macro-homogeneous surface reaction kinetics are derived as a function of catalyst loading and used as input parameters for the continuum-scale reactor model. The cross-scale framework enables the optimization of catalyst utilization through reactor design and operating strategy. To demonstrate the framework, we studied the storage and release of hydrogen from formic acid, a promising liquid organic hydrogen carrier (LOHC), over Pd, Pt, and Cu catalysts. The framework predicts observed trends in formic acid dehydrogenation activity for catalysts with comparable weight loadings and metal particle diameters, demonstrating satisfactory quantitative alignment. Finally, the seamless transmission of parameter uncertainties between scales is also discussed.

08 HYDROGEN↗
DOE OSTI2022

Multiscale and multiphysics FEA simulation and materials optimization for laser ultrasound transducers

In this study, the relationship between the nanocomposite design and the laser ultrasound transducer (LUT) characteristics was investigated through simulations in multiple scale levels for material behavior, device response, and acoustic wave propagation in media. First, the effects of the nanoparticle size and concentration on the effective properties of composites were quantitatively investigated with the finite element analysis (FEA) method. Second, the effective properties of the nanocomposite were assigned to the layer, which is modeled as a homogeneous material, in the FEA for the LUT simulating the energy conversion from the incident laser to the acoustic wave. Finally, the ultrasound propagation in the water was calculated by a theoretical wave propagation model. The FEA-based prediction was compared with the experimental data in the literature and a theoretical analysis for LUT based on Thermal-Acoustic coupling. As a result, the ultrasound waves on the transducer surface and at a distance in the water could be predicted. Based on the hierarchically integrated prediction procedure, the optimal conditions of the photoacoustic nanocomposites were investigated through the parametric study with the particle size and concentration as variables. The results guide the material designs optimized for different device characteristics, such as high pressure and broad bandwidth.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Micropolar deep material network

This study extends the Deep Material Network (DMN), a physics-informed machine learning framework, to predict the homogenized mechanical response of composite materials with micropolar (Cosserat-type) constitutive behavior. This extension incorporates microstructure-dependent size effects, enabling accurate, efficient, and size-aware predictions for composites with complex internal architectures. While traditional, direct numerical simulation micropolar models effectively capture size effects by introducing extra local degrees of freedom, they bring significant computational challenges, particularly for multiscale analyses relevant to engineering applications. The micropolar DMN developed in this paper achieves high accuracy while significantly reducing computation time compared to micropolar direct numerical simulations. This advancement enables multiscale analyses and parameter studies that were previously impractical, such as high-cycle fatigue simulations and comprehensive investigations of internal length scale effects notably in size-dependent plastic response and the optimization of lattice structures. By uniting microstructure-sensitive modeling, physics-driven learning, and scalable surrogate modeling, the micropolar DMN paves the way for accelerated material design, large-scale parametric studies, and the reliable incorporation of size-dependent effects across a wide range of engineering applications, including optimization and next-generation composite design.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Understanding the Performance Gap between Polycrystalline and Single-Crystal Nickel-Rich Layered Oxide Cathodes

Singe-crystal (SC) nickel-rich layered oxide cathodes, composed of boundary-free particles with high tap density, offer significant advantages in volumetric energy density and mechanical strength compared with polycrystalline (PC) cathode materials. However, as the nickel content increases (≥80%), SC Ni-rich cathodes often suffer from faster performance degradation than PC cathodes of the same composition, and the underlying causes of this discrepancy remain poorly understood. Herein, we reveal the distinct Ni redox behaviors that govern the electrochemical performance of SC and PC Ni-rich cathodes using multiscale and operando characterization techniques. Our results indicate that the increasingly heterogeneous Ni oxidation process in SC cathodes leads to the additional irreversible oxygen redox activity that deteriorates both the mechanical and chemical structures. In contrast, PC cathodes, despite with more pronounced surface reconstruction, exhibit greater chemomechanical stability due to homogeneous redox reactions during charging. Consequently, we find that bulk degradation, more than surface reactions, ultimately leads to fast capacity decay of SC Ni-rich cathodes during cycling. In conclusion, this work offers a comprehensive view on the impact of Ni redox evolutions on the chemomechanical stability in Ni-rich layered oxide cathodes, providing new insights into the longstanding performance gap between SC and PC cathodes, and guiding the rational design of Ni-rich cathode architectures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multiscale Modeling of the Mechanical Response of Silicon Carbide Composite Within the Accelerated Fuel Qualification Framework

The accelerated fuel qualification (AFQ) framework has been used for the initial development of multiscale modeling of silicon carbide (SiC) fiber reinforced composite (SiC-SiC). The AFQ framework provides a methodology to leverage physics-informed multiscale modeling along with a reduced set of empirical test data to reduce the time and cost of licensing and qualification of new nuclear fuel systems while maintaining the overall nuclear power plant safety case. SiC-SiC is being proposed for in-core applications, most notably fuel cladding, for current and next-generation nuclear reactors because of its high temperature stability, irradiation tolerance, and ability to withstand many accident conditions. As these composites exhibit multiscale architectures and complex microstructure-based fracture mechanics, it is an appealing use case for the AFQ methodology. While the end goal of this work is a single multiscale model that can be used for predictive in-core performance, current focus is on the individual various length scale models. Four individual models have been initially developed from microscale to engineering system level to capture key physics-based effects across different length scales. These models include a microscale homogenized tow model, a mesoscale fast Fourier transform–based weave model that integrates the homogenized tow model, a mesoscale finite element–based weave model, and a system-level BISON fuel performance model. Results of these models have undergone an initial comparison with separate-effects test data showing a good match to experimental results. By using the AFQ framework during model development, several near-term benefits have been secured including a reduction in development time for the SiC-SiC cladding, more targeted irradiation testing, and a better understanding of uncertainty.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

A Continuous-Discontinuous Galerkin Method for Electromagnetic Simulations Based on an All-Frequency Stable Formulation

In this paper, a potential-based partial-differential formulation, called the all-frequency stable formulation, is presented for the accurate and robust simulation of electromagnetic problems at all frequencies. Due to its stability from (near) dc to microwave frequencies, this formulation can be applied to simulate wide-band and multiscale problems without encountering the infamous low-frequency breakdown issue or applying basis function decompositions such as the tree-cotree splitting technique. To provide both efficient and flexible numerical solutions to the electromagnetic formulation, a mixed continuous-discontinuous Galerkin (CDG) method is proposed and implemented. In regions with homogeneous media, the continuous Galerkin method is employed to avoid the introduction of duplicated degrees of freedom (DoFs) on the elemental interfaces, while on the interfaces of two different media, the discontinuous Galerkin method is applied to permit the jump of the normal components of the electromagnetic fields. Numerical examples are provided to validate and demonstrate the proposed numerical solver for problems in a wide electromagnetic spectrum.

Yan, Su↗
DOE OSTI2025

A Poromechanical Framework for Internal Interactions Induced by Solid Inclusions

The framework of poromechanics is generalized to simulate the multiscale behavior of porous media subjected to internal loadings stemming from the growth of solid inclusions. This generalization is designed to enable the study of anisotropic internal stress generation from solid growth within the pores, while recovering isotropic fluid-induced loading as a particular case. For this purpose, a mathematical strategy to define constitutive tensors in a thermodynamically consistent form is proposed, thus offering new opportunities for determining the poromechanical properties of a porous solid through advanced experimentation or micromechanical models. The framework is specialized by means of established elastic solutions for single pore–matrix interaction, as well as through homogenization schemes considering the interaction among congruent pores. In particular, the second Eshelby solution and the Tanaka–Mori–Benveniste homogenization scheme are used to derive a microporoelastic model. At an elemental scale, the model is tested under mixed control conditions by replicating different scenarios of geomaterial testing. In addition, the model characteristics are outlined with reference to inelastic microscopic loadings replicating chemo-mechanical forcing, such as expansive crystal formation. Through a series of parametric analyses, it is shown that the microstructure of the pores significantly influences the properties of porous media. Most notably, it is shown that the effects of a solid forming within the pores depend in a highly nonlinear fashion on the constitutive characteristics of the inhomogeneities and can therefore not be readily quantified or predicted without models capturing the diverse multiscale interactions among pores, inhomogeneities, and matrix.

chemomechanics↗
DOE OSTI2024

Controlled patterning of crystalline domains by frontal polymerization

Materials with hierarchical architectures that combine soft and hard material domains with coalesced interfaces possess superior properties compared with their homogeneous counterparts. These architectures in synthetic materials have been achieved through deterministic manufacturing strategies such as 3D printing, which require an a priori design and active intervention throughout the process to achieve architectures spanning multiple length scales. Here we harness frontal polymerization spin mode dynamics to autonomously fabricate patterned crystalline domains in poly(cyclooctadiene) with multiscale organization. This rapid, dissipative processing method leads to the formation of amorphous and semi-crystalline domains emerging from the internal interfaces generated between the solid polymer and the propagating cure front. The size, spacing and arrangement of the domains are controlled by the interplay between the reaction kinetics, thermochemistry and boundary conditions. Small perturbations in the fabrication conditions reproducibly lead to remarkable changes in the patterned microstructure and the resulting strength, elastic modulus and toughness of the polymer. Furthermore, this ability to control mechanical properties and performance solely through the initial conditions and the mode of front propagation represents a marked advancement in the design and manufacturing of advanced multiscale materials. Drawing inspiration from biological systems in which structural complexity develops through dissipative reaction–diffusion processes, this study explores a transformative synthetic manufacturing strategy aimed at harnessing the principles underpinning morphogenic growth, unlocking new avenues for advanced materials design and fabrication. Synthetic coupled reaction-transport processes offer a versatile yet relatively underexplored method to manipulate the spatial attributes of synthetic materials10. Here we introduce an innovative manufacturing approach based on frontal ring-opening metathesis polymerization (FROMP) that draws parallels with morphogenic growth and development, enabling the formation of patterned microstructures within polymeric materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

The role of moisture in MgCl 2 salt: A multiscale approach to TES performance

This study presents a comprehensive multiscale analysis to evaluate the influence of moisture on the thermal performance of thermal energy storage systems using magnesium chloride (MgCl 2 ) as the phase-changing material. The system uses graphite foam with 90% relative density to enhance thermal conductivity. The analysis includes thermal conductivity calculations and specific heat capacity for different hydrate phases of MgCl 2 : Anhydrous, Mono, Di, Tetra, and Hexa. These properties were evaluated for the first time using the phonon density of states from Density Functional Theory simulations. Results showed that thermal conductivity decreased, while specific heat capacity increased by a factor of two as the phase changed from anhydrous to hexahydrate. Meso-scale models were created to account for the anisotropy of graphite foam and property variations of the MgCl 2 hydrate phases. Asymptotic Expansion homogenization simulations determined the anisotropic thermal conductivity for all phases. This unique methodology improved simulation accuracy, which matched experimental data for anhydrous MgCl 2 . A parametric study examined various operating conditions and their effect on TES performance. It revealed that higher charging temperatures did not enhance exergy efficiency, but increased discharge mass flow rates improved it due to better heat transfer. Thermal performance evaluated by the exergy efficiency remained consistent across hydrate systems under the tested conditions. Furthermore, the study suggests that this uniformity is linked to missing key data, particularly latent heat and melting point for different hydrates. Overall, it highlights the importance of multiscale effects and accurate material properties in designing and optimizing TES systems.

Molten salt degradation↗
DOE OSTI2024

Multiscale Dynamics of Reactive Fronts in the Subsurface

Understanding and predicting flow and reactive transport in rocks (i.e. geologic porous media) is critical to many technologies at the heart of the energy transition, including CO 2 sequestration and H2 storage. However, accurate modeling and prediction of these systems is very complex because physico-chemical processes that occur at very small spatial scales, i.e. in the pores of the rocks, can dramatically control the system performance at the field scale (km). For example, precipitation reactions at the pore-scale can lead to large permeability changes at the field scale and dramatically alter the migration of stored gases. Properly accounting for multi-scale coupling effects is critical to achieve predictivity and confidence in model outputs, which then can guide design and optimization at the system-scale. This can be achieved through the development of rigorous mathematical models that can appropriately account for fine-scale effects at the large scale. The final report of the Early Career award DE-SC0019075 “Multiscale dynamics of reactive fronts in the subsurface” summarizes the mathematical, numerical and experimental advancements to study and predict reactive transport in geologic porous media across scales.

58 GEOSCIENCES↗
DOE OSTI2022

Explicit modeling of pebble temperature in the porous-media model for pebble-bed reactors

In this study, we developed a multiscale model to include an explicit pebble-temperature model nested in the porous-media model for pebble-bed reactor applications. The multiscale solid-phase energy balance model, including the pebble surface energy balance equation and an explicit modeling of pebble temperature, can predict the macroscopic (pebble bed) and microscopic (pebble) temperature distributions under both steady-state and transient conditions. The proposed multiscale model is solved in a fully coupled manner using the Newton- Krylov method, and therefore iterations between the macroscopic (pebble-bed-scale) and microscopic (pebble- scale) model are avoided. Extensive code verifications, validation, and demonstrations have been performed for this newly developed model. By explicitly modeling pebble temperatures, this new model addresses a major deficiency of the basic porous-media model, which assumes homogeneous solid-phase temperature and is not appropriate for pebble-bed reactor design and safety analyses.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Directing Assembly of Mesoscale Multi‐Shell Morphologies of DNA Origami Crystals

Nature builds hierarchically ordered materials, such as seashells, wood, and bones, through spatially and temporally regulated growth. Mimicking such a level of control in synthetic systems remains challenging, particularly in achieving multiscale organizations with prescribed nanoscale arrangements and desired material morphologies. In this study, we introduce a DNA-based self-assembly strategy for constructing diverse multi-shell mesoscale morphologies from nanoscale lattices, enabling prescribed structural, and compositional 3D material patterns. Using DNA origami frames as modular monomers, we direct anisotropic epitaxial growth through addressable DNA frame binding motifs and encapsulate nanoparticles (NPs) in desired 3D patterns. Sequential monomer addition under thermodynamically favorable conditions enables shell growth through heterogeneous nucleation while minimizing unwanted homogeneous nucleation. Here, we demonstrate that DNA-encoded addressability enables epitaxial shell growth along specific lattice directions, yielding crystals with multilayered mesoscale organization, including tube-like (sushi roll) and plate-like (macaron) morphologies. Shell-specific NP configurations and compositions are achieved through addressable and differentiated placement of NPs within each shell, as validated by small-angle x-ray scattering and cross-sectional scanning transmission electron microscopy. We further demonstrate addressable NP release and reveal that shells modulate release kinetics. Together, these findings establish a platform for fabricating DNA origami crystals with programmable mesoscale morphologies, nanoscale structure, composition, and transport properties.

3D patterning↗
DOE OSTI2022

$\mathrm{IH}$-$\mathrm{GAN}$: A conditional generative model for implicit surface-based inverse design of cellular structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry–property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from properties to geometries. Here we further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (R 2 -scores between target properties and properties of generated unit cells >98%) and 2) improve the optimized structural performance over the conventional variable-density single-type structure. In the minimum compliance example, our IH-GAN generated structure achieves a 79.7% reduction in concentrated stress and an extra 3.03% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 86.4% and 79.6% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending.

42 ENGINEERING↗
DOE OSTI2020

Data-driven learning of nonlocal physics from high-fidelity synthetic data

A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. Here, we extract nonlocal models from data, circumventing these challenges and providing data-driven justification for the resulting model form. Extracting data-driven surrogates is a major challenge for machine learning (ML) approaches, due to nonlinearities and lack of convexity — it is particularly challenging to extract surrogates which are provably well-posed and numerically stable. Our scheme not only yields a convex optimization problem, but also allows extraction of nonlocal models whose kernels may be partially negative while maintaining well-posedness even in small-data regimes. To achieve this, based on established nonlocal theory, we embed in our algorithm sufficient conditions on the non-positive part of the kernel that guarantee well-posedness of the learnt operator. These conditions are imposed as inequality constraints to meet the requisite conditions of the nonlocal theory. We demonstrate this workflow for a range of applications, including reproduction of manufactured nonlocal kernels; numerical homogenization of Darcy flow associated with a heterogeneous periodic microstructure; nonlocal approximation to high-order local transport phenomena; and approximation of globally supported fractional diffusion operators by truncated kernels.

42 ENGINEERING↗
DOE OSTI2023

A deep learning upscaling framework: Reactive transport and mineral precipitation in fracture-matrix systems

Pore-scale modeling has limited applicability at large scales due to its high computational cost. One common approach to upscale pore-scale models is the use of effective medium theories, which homogenize small-scale features in a porous structure and characterize the medium by macroscale properties (e.g., permeability) and equations (e.g., Darcy’s law). However, there are classes of physical processes for which effective medium approximations may become inaccurate, e.g., mineral precipitation and clogging during reactive transport. We have developed a deep learning upscaling framework, in which pore-scale modeling is directly employed in macroscale systems, without relying on effective medium approximations. The upscaling framework is first developed for general multiscale systems and then applied to modeling reactive transport with mineral precipitation in the altered layer in fracture-matrix structures. Solute transport from the fractures to the matrix is modeled as a wall boundary condition for the fractures, which, in turn, is predicted by recurrent neural networks using the concentration histories at the fracture-matrix boundary. Specifically, we consider a meter-scale fracture network embedded in sandstones, where the smallest feature is at the micron scale. Here the proposed framework allows us to span five orders of magnitude in length scales by capturing mineral precipitation in the altered layer of the rock matrix at the pore scale across the entire meter-scale fracture network.

42 ENGINEERING↗
DOE OSTI2022

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗