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DOE OSTI2025

Stemflow Hydrodynamics

Stemflow hydrodynamics is the study of water movement along the exterior surface area of plants. Its primary goal is to describe water velocity and water depth along the stem surface area. Its significance in enriching the rhizosphere with water and nutrients is not in dispute. Yet, the hydrodynamics of stemflow have been entirely overlooked. This review seeks to fill this knowledge gap by drawing from thin film theories to seek outcomes at the tree scale. The depth‐averaged conservation equations of water and solute mass are derived at a point. These equations are then supplemented with the conservation of momentum that is required to describe water velocities or relations between water velocities and water depth. Relevant forces pertinent to momentum conservation are covered and include body forces (gravitational effects), surface forces (wall friction), line forces (surface tension), and inertial effects. The inclusion of surface tension opens new vistas into the richness and complexity of stemflow hydrodynamics. Flow instabilities such as fingering, pinching of water columns into droplets, accumulation of water within fissures due to surface tension and their sudden release are prime examples that link observed spatial patterns of stemflow fronts and morphological characteristics of the bark. Aggregating these effects at the tree‐ and storm‐ scales are featured using published experiments. The review discusses outstanding challenges pertaining to stemflow hydrodynamics, the use of dynamic similarity and 3D printing to enable the interplay between field studies and controlled laboratory experiments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Temperature Effects on Droplet Oscillation Decay with Application to Fuel Property Measurement

Observation of oscillation decay in droplets has been shown to be an effective approach in determining physical properties such as viscosity and surface tension for emerging biofuels using μl quantities. Herein this work extends the approach to higher temperatures relevant to fuel injection conditions for internal combustion engines. Experiments are conducted that use high-resolution strobed imaging of moving, heated, μm-sized, fuel droplets to capture shape oscillation decay through image processing and analysis. Two fuels are investigated, iso-butanol and a primary reference fuel (PRF 84), which is a mixture of iso-octane and n-heptane. A piezoelectric droplet generator is used to generate a continuous train of single droplets, which are given an initial perturbation and subsequently undergo damped oscillations, captured using strobed imaging. Surface tension and viscosity calculated at four different temperatures ranging from 30°C-55°C using the frequency and decay time associated with the fundamental mode are found to be within ~ 10% of reference values obtained from the literature. Complementary numerical simulations are performed that utilize a volume-of-fluid approach to track transient droplet oscillation phenomena along with heat and mass transfer in a 2D axisymmetric domain. Simulations, where droplet size and temperature can be independently varied, capture an expected decrease in oscillation frequency and increase in decay time, with increase in fuel temperature. The simulations are further used to study the relative contribution to deviations in surface tension and viscosity predictions due to heat and mass transfer from the droplet, as well as viscous effects violating the inviscid flow assumption in the droplet oscillation theory. Mass loss effects are found to be negligible. Temperature change due to heat transfer is found to have the next highest sensitivity, particularly for the more volatile PRF 84, which has a lower viscosity and associated Ohnesorge number. For isobutanol, which has a higher viscosity and Ohnesorge number, viscous effects contribute the most to deviation in fuel property predictions.

09 BIOMASS FUELS↗

DOE OSTI2023

Experimental measurement of the effective contact angle for solvent/packing interactions in a structured packed column for CO 2 capture

The contact angle is a critical factor for determining the effective mass transfer area for carbon dioxide (CO 2 ) capture via the chemical absorption process in a packed column, and thus the overall capture efficiency of the packed column. Many widely used commercial packings involve microscale features (perforation, corrugation, etc.) that may also affect the wetting behavior. This study proposes a systematic method of using a modified Wilhelmy plate to measure the effective contact angle to characterize the solvent and featured packing interaction. In lieu of computational efforts relying on assumptions guided by semi-informed correlation, the proposed method directly measures the effective contact angle as a function of the solvent and packing thermophysical and hydrodynamic properties. The characterization of the effective contact angle is then integrated in the computational fluid dynamics modeling to reduce uncertainty in the prediction of effective mas transfer area. Experiments were conducted for stainless steel coupons using water and aqueous sodium hydroxide (NaOH) solvent for verification of the proposed experimental protocol. The surface tension of the aqueous NaOH solvent was altered using surfactant and antifoam. The effective contact angle increases with the increased value of the surface tension for flat stainless steel sheets. On the other hand, effective contact angles do not vary in Mellapak coupons for aqueous monoethanolamine (MEA) and NaOH solvent. In this case, surface textures and sheet design play a dominant role in the surface tension of solvents. Furthermore, CO 2 loading has a significant effect on the contact angle for Mellapak coupons. As expected, the contact angle decreases with the increasing temperature of CO 2 capture solvents (MEA, EEMPA). The effective contact angle measurement using the Wilhelmy plate method can provide more accurate and efficient solvents for characterizing the solvent-packing surface interactions. Subsequently, the present method enhances the accuracy of the prediction of the effective mass transfer area in carbon capture by solvent absorption.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Holographic duality for Ising CFT with boundary

We extend the holographic duality between 3d pure gravity and 2d Ising CFT proposed in ref. [1] to CFTs with boundaries. Besides the usual asymptotic boundary, the dual bulk spacetime now has a real cutoff, on which live branes with finite tension, giving Neumann boundary condition on the metric tensor. The strongly coupled bulk theory requires that we dress the well-known semiclassical AdS/BCFT answer with boundary gravitons, turning the partition function into the form of Virasoro characters. Using this duality, we relate the brane tensions to the modular S-matrix elements of the dual BCFT and derive the transformation between gravitational solutions with different brane tensions under modular S action.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

An integrated approach to derive relative permeability from capillary pressure

Surface tension affects all aspects of fluid flow in porous media. Through measurements of surface tension interaction under multiphase conditions, a relative permeability curve can be determined. Relative permeability is a numerical description of the interaction between two or more fluids and the porous media. It is a critical parameter for various tools that characterize subsurface multiphase flow systems, such as numerical simulation for carbon sequestration, oil and gas development, and groundwater contamination remediation. Therefore, it is critical to get a good statistical distribution of relative permeability in the porous media under study. Empirical formula for determining relative permeability from capillary pressure are already well established but do not provide the needed flexibility that is required to match laboratory-derived relative permeability curves. By expanding the existing methods for calculating relative permeability from capillary pressure data, it is possible to create both two and three-phase relative permeability curves. Mercury intrusion capillary pressure (MICP) data from the Morrow 'B' Sandstone coupled with interfacial tension and contact angle measurements were used to create a suite of relative permeability curves. Furthermore, these curves were then calibrated to a small sample of existing laboratory curves to elucidate common fitting parameters for the formation that were then used to create relative permeability curves from MICP data that does not have an associated laboratory-measured relative permeability curve.

58 GEOSCIENCES↗

DOE OSTI2023

Large deformation and brittle failure calculated using the dual-domain material point method

The dual domain material point (DDMP) method is explored as a candidate to be implemented in a general purpose code to perform simulations of materials with complex geometry that undergo large history-dependent deformation and failure. To test its candidacy, we study its mesh convergence, its sensitivity to mesh orientation, and its ability to handle softening and failure of a material. Simulations of large deformation and simulations of mechanical failure are performed using both DDMP and the material point method (MPM). When cell-crossing of material points is not an issue and when there are a sufficient number of material points in each computation cell, the numerical error decreases with the square of the cell size as expected for both MPM and DDMP. DDMP has reduced error compared with MPM when there are many instances of material points crossing cell boundaries due to the continuous nature of the modified gradient of the shape functions. Simulations of a specimen under tension are also performed where the background mesh is aligned and misaligned with the tension direction. MPM displays a significant mesh-dependent stress field, DDMP shows negligible mesh dependency. Despite a mesh orientation-dependent stress field from MPM, the critical tension and failure mode from both MPM and DDMP calculations have negligible mesh dependency when using a non-local failure model. If only the failure mode is important (i.e., local stresses are unimportant), MPM with a non-local failure model is a suitable method for modeling failure with small deformations. However, if local stresses are also important or if there are large deformations with many cell-crossings before failure, DDMP should be the method that is used. A needed improvement for DDMP is identified from our numerical simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Effect of Heave Plate Hydrodynamic Force Parameterization on a Two-Body Wave Energy Converter

Heave plates are one approach to generating the reaction force necessary to harvest energy from ocean waves. In a Morison equation description of the hydrodynamic force, the components of drag and added mass depend primarily on the heave plate oscillation. These terms may be parameterized in three ways: (1) as a single coefficient invariant across sea state, most accurate at the reference sea state, (2) coefficients dependent on the oscillation amplitude, but invariant in phase, that are most accurate for relatively small amplitude motions, and (3) coefficients dependent on both oscillation amplitude and phase, which are accurate for all oscillation amplitudes. We validate a MATLAB model for a two-body point absorber wave energy converter against field data and a dynamical model constructed in ProteusDS. We then use the MATLAB model to evaluate the effect of these parameterizations on estimates of heave plate motion, tension between the float and heave plate, and wave energy converter electrical power output. We find that power predictions using amplitude-dependent coefficients differ by up to 30% from models using invariant coefficients for regular waves ranging in height from 0.5 to 1.9 m. Amplitude- and phase-dependent coefficients, however, yield less than a 5% change when compared with coefficients dependent on amplitude only. This suggests that amplitude-dependent coefficients can be important for accurate wave energy converter modeling, but the added complexity of phase-dependent coefficients yields little further benefit. We show similar, though less pronounced, trends in maximum tether tension, but note that heave plate motion has only a weak dependence on coefficient fidelity. Finally, we emphasize the importance of using experimentally derived added mass over that calculated from boundary element methods, which can lead to substantial under-prediction of power output and peak tether tension.

dynamical model↗

DOE OSTI2020

Dynamic Tensile Response of a Fe–49Co–2V Alloy at Various Strain Rates and Temperatures

Soft ferromagnetic alloys are often utilized in electromagnetic applications due to their desirable magnetic properties. In support of these applications, the ferromagnetic alloys are also required to bear mechanical load under various loading and environmental conditions. In this study, a Fe–49Co–2V alloy was dynamically characterized in tension with a Kolsky tension bar and a Drop–Hopkinson bar at various strain rates and temperatures. Dynamic tensile stress–strain curves of the Fe–49Co–2V alloy were obtained at strain rates ranging from 40 to 230 s -1 and temperatures from - 100 to 100 °C. All dynamic tensile stress–strain curves exhibited an initial linear elastic response to an upper yield followed by Lüders band response and then a nearly linear work-hardening behavior. The yield strength of this material was found to be sensitive to both strain rate and temperature, whereas the hardening rate was independent of strain rate or temperature. The Fe–49Co–2V alloy exhibited a feature of brittle fracture in tension under dynamic loading with no necking being observed.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Coupled loads analysis of a novel shared-mooring floating wind farm

Shared mooring lines are a method to reduce the stationkeeping cost of floating offshore wind farms; however, their impacts on floating array dynamics are not yet well understood. Here this article presents advancements to floating wind farm simulation capabilities that allow the dynamic modeling of shared-mooring floating wind arrays - specifically, platform coupling through shared lines and proper phasing of wave loads across the array. These capabilities are demonstrated on a 10-turbine shared-mooring array featuring two staggered rows of wind turbines. A baseline array design with individually moored turbines is used as a basis for comparison. Coupled analysis using FAST.Farm shows that the shared-mooring design has smaller fluctuations in surge when compared to the baseline design. The mean and maximum platform offsets are highest in normal operating conditions, but the maximum mooring line tensions are highest in 50-year storm conditions. Power spectral density analysis of platform surge and sway motions shows that the shared mooring configuration does not introduce any significant inter-platform resonances. The tower-base bending moment statistics and the line tension damage equivalent loads indicate no consequential differences in turbine loading or mooring fatigue life. Anchor load analysis shows that the total required anchor capacity for the shared-mooring array is decreased by approximately 25% when shared anchors are used. Dynamic simulations of the shared mooring system under line failures show that remaining line tensions stay within bounds and that offsets are significantly smaller when compared to the baseline design. Overall, the results show that shared moorings do not introduce any dynamic response concerns in this floating wind array design.

17 WIND ENERGY↗

DOE OSTI2024

Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Lastly, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.

Compressible neo-Hookean materials↗

DOE OSTI2024

A data-driven multiscale model for reactive wetting simulations

Here, we describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop’s composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material’s wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of “convergence” of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

The anomalous magnetic moment of the muon in the Standard Model: an update

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, a μ , updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the e + e - → π + π - cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a^{SM}_{μ}$ = 116 592 033 (62) x $10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1–6 of E989 at Fermilab, one finds $a^{exp}_{μ} -a^{SM}_{μ}= 38 (63)$ x $10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Electric current-induced precipitation hardening in advanced high-strength steel

Effect of electric current on precipitation hardening for advanced high-strength steel is investigated based on mechanical testing and microscopic observation. Complex-phase steel containing nano-sized Nb-bearing carbides was used. By comparing the flow stress between uniaxial tension with applied electric current (pulsed tension) and without electric current (nonpulsed tension) at various elevated temperatures, the influence of electric current on precipitation hardening was confirmed. A higher values of Vickers hardness and full-width-at-half-maximum were obtained in the pulsed tensile specimen compared to the identically heat treated specimen after the same deformation. Small angle neutron scattering analysis showed that the volume fraction and mean diameter of newly formed precipitates in the pulsed tensile specimen were higher and larger than those in the induction heat treated specimen, respectively. In conclusion, it clearly shows that additional precipitation hardening could be induced by the athermal effect of electric current, which is distinct from the thermal effect of Joule heating.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Learning Coarse-Grained Potentials for Binary Fluids

Even though atomistic and CG models have been used to simulate liquid nanodroplets in vapor, very few rigorous studies of the liquid-liquid interface structure are available, and most of them are limited to planar interfaces. In this work, we evaluate several existing force fields (FF)s, including two atomistic and three CG FFs, with respect to modeling the interface structure and thermodynamic properties of the water-hexane interface. Both atomistic FFs are able to quantitatively reproduce the interfacial tension and the coexisting densities of the experimentally-observed planar interface. We use the atomistic FFs to model water droplets in hexane and use these simulations to test the CG FFs. We found that the tested CG FFs cannot reproduce the interfacial tensions of planar and/or curved interfaces. Finally, we propose a new approach for learning coarse-grained (CG) potentials within the CG SDK (Shinoda-DeVane- Klein) FF framework from atomistic simulation data. We demonstrate that the new potential significantly improves the prediction of both the interfacial tension and structure of water-hexane planar and curved interfaces.

Gao, Peiyuan↗

DOE OSTI2026

Sculpting 2D Crystals via Membrane Contractions before and during Solidification

When phospholipids crystallize within the otherwise fluid membranes of giant unilamellar vesicles, the resulting molecularly thin “2D” solids exhibit great variety in their morphology evolution. For example, within membranes containing moderate amounts of the crystallizing component, crystals grow with a fixed morphology depending on vesicle size. Conversely for membranes containing large amounts of the crystallizing species, we find small compact crystals on vesicles of all sizes. However, on large vesicles, growing crystals sprout flower petals that lengthen progressively. These behaviors result from two combined mechanisms: first, like other 2D solids, the shear rigidity of phospholipid crystals renders them intolerant to morphologies with nonzero Gaussian curvature. As a result and especially at elevated membrane tension, the cost of bending elasticity is reduced at the expense of line energy by the formation of flowers as opposed to compact crystals. Second, the composition-dependent tension rise during cooling relaxes via water permeation of the membrane with a time constant scaling as R2. The amount of crystal formed for a small decrease in temperature determines this composition-dependent increase in stress from thermal contractions versus solidification. Surface Evolver computations were motivated using the predicted tension evolution to develop a processing space that maps to experimental observations for initial and growing crystal morphology. Important variable groups are identified, including a scaled ratio of bending to line energy, a vesicle-size-independent group for membrane contractions, and a time constant for stress relaxation. Though processing stresses ultimately relax, the crystal morphology persists well beyond the processing window.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Hadronic uncertainties versus new physics for the W boson mass and Muon g – 2 anomalies

There are now two single measurements of precision observables that have major anomalies in the Standard Model: the recent CDF measurement of the W mass shows a 7σ deviation and the Muon g – 2 experiment at FNAL confirmed a long-standing anomaly, implying a 4.2σ deviation. Doubts regarding new physics interpretations of these anomalies could stem from uncertainties in the common hadronic contributions. We demonstrate that these two anomalies pull the hadronic contributions in opposite directions by performing electroweak fits in which the hadronic contribution was allowed to float. The fits show that including the g – 2 measurement worsens the tension with the CDF measurement and conversely that adjustments that alleviate the CDF tension worsen the g – 2 tension beyond 5σ. This means that if we adopt the CDF W mass measurement, the case for new physics in either the W mass or muon g – 2 is inescapable regardless of the size of the SM hadronic contributions. Lastly, we demonstrate that a mixed scalar leptoquark extension of the Standard Model could explain both anomalies simultaneously.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Shape-recovering liquids

Binding particles to an interface between immiscible liquids to reduce interfacial tension underpins the emulsification and phase behaviour of composite liquid systems. Nevertheless, we found that the strong binding and two-dimensional assembly of ferromagnetic particles at a liquid–liquid interface not only suppresses emulsification but also increases interfacial tension. Consequently, the particle-stabilized interface in a cylindrical vessel rapidly and reproducibly adopts the shape of a Grecian urn after vigorous agitation. The suppression of emulsification, the rapid formation of a stable, non-planar equilibrium interface shape and the increase in interfacial tension all originate from attractive in-plane dipolar magnetic interactions between the particles.

Raykh, Anthony↗

DOE OSTI2020

Planck 2018 results. VI. Cosmological parameters

In this paper, we present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5 σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ω c h 2 = 0.120 ± 0.001, baryon density Ω b h 2 = 0.0224 ± 0.0001, scalar spectral index n s = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100 θ * = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H 0 = (67.4 ± 0.5) km s –1 Mpc –1 ; matter density parameter Ω m = 0.315 ± 0.007; and matter fluctuation amplitude σ 8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be N eff = 2.99 ± 0.17, in agreement with the Standard Model prediction N eff = 3.046, and find that the neutrino mass is tightly constrained to Σ m ν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2 σ , which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, Ω K = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w 0 = –1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r 0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6 σ , tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.

79 ASTRONOMY AND ASTROPHYSICS↗