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DOE OSTI2014

One-dimensional particle simulations of Knudsen-layer effects on D-T fusion

Particle simulations are used to solve the fully nonlinear, collisional kinetic equation describing the interaction of a high-temperature, high-density, deuterium-tritium plasma with absorbing boundaries, a plasma source, and the influence of kinetic effects on fusion reaction rates. Both hydrodynamic and kinetic effects influence the end losses, and the simulations show departures of the ion velocity distributions from Maxwellian due to the reduction of the population of the highest energy ions (Knudsen-layer effects). The particle simulations show that the interplay between sources, plasma dynamics, and end losses results in temperature anisotropy, plasma cooling, and concomitant reductions in the fusion reaction rates. However, for the model problems and parameters considered, particle simulations show that Knudsen-layer modifications do not significantly affect the velocity distribution function for velocities most important in determining the fusion reaction rates, i.e., the thermal fusion reaction rates using the local densities and bulk temperatures give good estimates of the kinetic fusion reaction rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Active galactic nucleus black hole mass estimates in the era of time domain astronomy

We investigate the dependence of the normalization of the high-frequency part of the X-ray and optical power spectral densities (PSDs) on black hole mass for a sample of 39 active galactic nuclei (AGNs) with black hole masses estimated from reverberation mapping or dynamical modeling. We obtained new Swift observations of PG 1426+015, which has the largest estimated black hole mass of the AGNs in our sample. We develop a novel statistical method to estimate the PSD from a light curve of photon counts with arbitrary sampling, eliminating the need to bin a light curve to achieve Gaussian statistics, and we use this technique to estimate the X-ray variability parameters for the faint AGNs in our sample. We find that the normalization of the high-frequency X-ray PSD is inversely proportional to black hole mass. We discuss how to use this scaling relationship to obtain black hole mass estimates from the short timescale X-ray variability amplitude with precision ∼0.38 dex. The amplitude of optical variability on timescales of days is also anticorrelated with black hole mass, but with larger scatter. Instead, the optical variability amplitude exhibits the strongest anticorrelation with luminosity. We conclude with a discussion of the implications of our results for estimating black hole mass from the amplitude of AGN variability.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Robust Real-Time Modeling of Distribution Systems with Data-Driven Grid-Wise Observability (Final Technical Report)

The overall objective of this project is to leverage existing and emerging sensor measurements to develop data-driven observability enhancement algorithms as well as robust state estimation and parameter identification techniques to enable real-time grid-wise monitoring and modeling of loads and distributed energy resources (DERs). The project resulted in a holistic framework with the following key components: 1) data-driven and machine learning-based grid-edge visibility enhancement, 2) robust branch-current-based state estimation (BCSE), and 3) robust real-time steady-state and dynamic-state modeling of loads and DERs. The research outcomes have provided utility companies better network visibility, higher-fidelity load/DER models, and more accurate assessment of DERs’ impacts, thus, facilitating the integration of renewable energy sources. The synergistic collaborative project among Iowa State University (ISU), Argonne National Laboratory (ANL), Electric Power Research Center (EPRC), SIEMENS Industry, Alliant Energy, Cedar Falls Utilities (CFU), and Maquoketa Valley Electric Cooperative (MVEC) to leverage the team’s extensive expertise and experience in power distribution systems, state estimation, online modeling and identification, and DER integrations. The proposed frameworks have been verified with industry adopted software and attempted integrated with existing tool wherever possible

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2014

Quantum dynamical study of femtosecond photodesorption of CO from TiO{sub 2}(110)

The photodesorption of CO from TiO{sub 2}(110) by femtosecond pulses is investigated with the Surrogate Hamiltonian approach. The aim of the study is to resolve the relaxation mechanism and forecast the lifetime of the exited state based on a microscopic description of the excitation and relaxation processes. The parameters characterizing the system are obtained from ab initio and Density Functional Theory-calculations with one parameter estimated from physical considerations and convergence studies. Two electronic states are considered and the relaxation is assumed to be due to the interaction of the excited adsorbate with electron hole pairs in the surface. Desorption probabilities and velocity distributions of the desorbing molecules are calculated and an exited state lifetime is predicted. Throughout this paper atomic units, i.e., ℏ = m{sub e} = e = a{sub 0} = 1, have been used unless otherwise stated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Development of an ERT‐Based Framework for Bentonite Buffers Monitoring From Laboratory Tests: 2. Quantitative Moisture Dynamics Estimation Model

Abstract The long‐term containment of high‐level radioactive waste in geological disposal repositories relies on Engineered Barrier Systems (EBS), with bentonite clay emerging as a candidate material due to its unique properties. Understanding moisture dynamics within bentonite buffers is crucial for EBS performance, as it directly influences the material's swelling capacity, thermal and hydraulic conductivity, mechanical properties, and long‐term evolution under complex thermal‐hydrological‐mechanical (THM) processes. This study develops an advanced Electrical Resistivity Tomography (ERT)‐based framework to quantitatively monitor moisture dynamics under THM conditions. Our framework extends the Waxman‐Smits model to incorporate the coupled effects of temperature, water content, fluid chemistry, and mechanical changes on bentonite's electrical properties. Utilizing HotBENT‐Lab data from our companion paper, which includes electrical conductivity, CT density, and thermocouple measurements, this study offers a novel methodological framework bridging different scales of the model. Our results show that the extended model can estimate water content from ERT data, capturing spatial and temporal variations in moisture distribution within bentonite columns. However, the model tends to overestimate water content compared to CT density‐derived measurements. We address this discrepancy by incorporating a simplified swelling effect model, which improves agreement between ERT and CT density‐based water content estimates. We also discuss model limitations, including simplified treatment of swelling and micropore effects, and propose a conceptual framework for transitioning from laboratory to field applications, addressing challenges such as parameter scalability, field validation methods, and integration of diverse data sources. This ERT‐based framework can potentially advance real‐world moisture monitoring of bentonite‐based EBS in nuclear waste repositories. Plain Language Summary Safely containing high‐level radioactive waste depends on barriers made from materials like bentonite clay, which is effective because it swells and seals in the waste. To ensure these barriers work well over time, it's important to understand how moisture moves through the clay. Our study developed a new method using ERT to monitor moisture levels in bentonite under conditions that mimic those in actual storage sites, including changes in temperature, water content, and mechanical stress. This study improved an existing model to better account for how these factors affect the clay, allowing us to create more accurate moisture maps. Initially, the proposed model overestimated the amount of water in the clay, but its accuracy was improved by factoring in how the clay swells when wet. This study also identified some limitations of the model and suggested ways to adapt it for use in real‐world waste storage sites. This new approach could lead to better monitoring and safety checks for nuclear waste storage systems, helping to ensure long‐term containment. Key Points This work develops an ERT‐based framework extending the Waxman‐Smits model to monitor bentonite moisture dynamics during coupled THM processes The extended model accurately estimates water content from Electrical Resistivity Tomography data, incorporating swelling effects to improve precision This work proposes a conceptual framework for transitioning from laboratory to field applications, advancing EBS monitoring in nuclear waste repositories

Chen, Hang↗

DOE OSTI2012

Rigorous Kinetic Modeling and Optimization Study of a Modified Claus Unit for an Integrated Gasification Combined Cycle (IGCC) Power Plant with CO{sub 2} Capture

The modified Claus process is one of the most common technologies for sulfur recovery from acid gas streams. Important design criteria for the Claus unit, when part of an Integrated Gasification Combined Cycle (IGCC) power plant, are the ability to destroy ammonia completely and the ability to recover sulfur thoroughly from a relatively low purity acid gas stream without sacrificing flame stability. Because of these criteria, modifications to the conventional process are often required, resulting in a modified Claus process. For the studies discussed here, these modifications include the use of a 95% pure oxygen stream as the oxidant, a split flow configuration, and the preheating of the feeds with the intermediate pressure steam generated in the waste heat boiler (WHB). In the future, for IGCC plants with CO{sub 2} capture, the Claus unit must satisfy emission standards without sacrificing the plant efficiency in the face of typical disturbances of an IGCC plant, such as rapid change in the feed flow rates due to load-following and wide changes in the feed composition because of changes in the coal feed to the gasifier. The Claus unit should be adequately designed and efficiently operated to satisfy these objectives. Even though the Claus process has been commercialized for decades, most papers concerned with the modeling of the Claus process treat the key reactions as equilibrium reactions. Such models are validated by manipulating the temperature approach to equilibrium for a set of steady-state operating data, but they are of limited use for dynamic studies. One of the objectives of this study is to develop a model that can be used for dynamic studies. In a Claus process, especially in the furnace and the WHB, many reactions may take place. In this work, a set of linearly independent reactions has been identified, and kinetic models of the furnace flame and anoxic zones, WHB, and catalytic reactors have been developed. To facilitate the modeling of the Claus furnace, a four-stage method was devised so as to determine which set of linearly independent reactions would best describe the product distributions from available plant data. Various approaches are taken to derive the kinetic rate expressions, which are either missing in the open literature or found to be inconsistent. A set of plant data is used for optimal estimation of the kinetic parameters. The final model agrees well with the published plant data. Using the developed kinetics models of the Claus reaction furnace, WHB, and catalytic stages, two optimization studies are carried out. The first study shows that there exists an optimal steam pressure generated in the WHB that balances hydrogen yield, oxygen demand, and power generation. In the second study, it is shown that an optimal H{sub 2}S/SO{sub 2} ratio exists that balances single-pass conversion, hydrogen yield, oxygen demand, and power generation. In addition, an operability study has been carried out to examine the operating envelope in which both the H{sub 2}S/SO{sub 2} ratio and the adiabatic flame temperature can be controlled in the face of disturbances typical for the operation of an IGCC power plant with CO{sub 2} capture. Impact of CO{sub 2} capture on the Claus process has also been discussed.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2019

Slow-scale split-step tau-leap method for stiff stochastic chemical systems

Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. A motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided, and the obtained results confirm the efficiency of the considered splitting approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Liouvillian dynamics of the open Schwinger model: String breaking and kinetic dissipation in a thermal medium

Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an antifermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. Here in this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal medium, treating the Schwinger model as an open quantum system coupled to a thermal environment. Within the regime of weak coupling between the system and environment, the real-time evolution of the system can be described by a Lindblad evolution equation. We analyze the Liouvillian gaps of this Lindblad equation and the time dependence of the system’s von Neumann entropy. We observe that the late-time relaxation rate decreases as the environment correlation length increases. Moreover, when the environment correlation length is infinite, the system exhibits two steady states, one in each of the sectors with definite charge-conjugation-parity (CP) quantum numbers. For parameter regimes where an initial string breaks in vacuum, we observe a delay of the string breaking in the medium, due to kinetic dissipation effects. Conversely, in regimes where an initial string remains intact in vacuum time evolution, we observe string breaking (melting) in the thermal medium. We further discuss how the Liouvillian dynamics of the open Schwinger model can be simulated on quantum computers and provide an estimate of the associated Trotter errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Regional Assessment of Virtual Battery Potential from Building Loads

Flexibility from building loads can be used for integrating renewable energy and providing different grid services. It is challenging to quantify and compare the flexibility from different classes of building loads due to their diversified characteristics and dynamics. Methodology has been proposed to model building loads as a virtual battery (VB), which is simple and general, yet able to capture physical characteristics of building loads, environmental parameters, human behavior, and other factors. This paper presents a regional assessment of VB technical potential and economic benefits from residential loads and commercial buildings. Housing, population, weather station, and climate zone information have been collected and used to estimate VB technical potential. Energy and ancillary service prices are then used for economic benefits assessment and analysis.

Wu, Di↗

DOE OSTI2022

Transient creep‐fatigue crack growth in creep‐brittle materials: Application to Alloy 718

Abstract This study presents incremental finite element computations of creep‐fatigue crack growth in Alloy 718 at in air. Alloy 718 is representative of creep‐brittle materials, in which viscoplastic deformation is restricted near the tip of a growing crack. The computations predict crack growth using a unique combination of an irreversible cohesive zone formulation and a strain gradient viscoplastic material model based on the Kocks–Mecking formulation. Cohesive zone damage parameters are estimated using sustained loading and constant‐amplitude cyclic loading experiments. Computations of crack extension under three different waveforms containing overloads all predict post‐overload retardation. The amount of retardation depends strongly on the overload ratio, consistent with experiments in the literature using similar waveforms. Analysis of the crack‐tip fields demonstrates retardation is associated with unloading in the highly deformed material near the advancing crack tip. Dynamic recovery and geometrically necessary dislocations are shown to significantly influence post‐overload crack extension.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Surface Composition of (99942) Apophis

On 2029 April 13, near-Earth asteroid (NEA) (99942) Apophis will pass at a distance of ∼6 Earth radii from Earth. This event will provide researchers with a unique opportunity to study the effects of tidal forces experienced by an asteroid during a close encounter with a terrestrial planet. Binzel et al. predicted that close flybys of terrestrial planets by NEAs would cause resurfacing of their regolith due to seismic shaking. In this work, we present the best pre-encounter near-infrared spectra of Apophis obtained so far. These new data were obtained during the 2013 apparition using the NASA Infrared Telescope Facility (IRTF). We found that our spectral data is consistent with previous observations by Binzel et al. but with a much higher signal-to-noise ratio. Spectral band parameters were extracted from the spectra and were used to determine the composition of the asteroid. Using a naïve Bayes classifier, we computed the likelihood of Apophis being an LL chondrite to be >99% based on mol% of Fa versus Fs. Using the same method, we estimated a probability of 89% for Apophis being an LL chondrite based on ol/(ol+px) and Fs. The results from the dynamical model indicate that the most likely source region for Apophis is the ν {sub 6} resonance in the inner main belt. Data presented in this study (especially Band I depth) could serve as a baseline to verify seismic shaking during the 2029 encounter.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

A daily, 250 m and real-time gross primary productivity product (2000–present) covering the contiguous United States

Abstract. Gross primary productivity (GPP) quantifies the amount of carbon dioxide (CO2) fixed by plants through photosynthesis. Although as a key quantity of terrestrial ecosystems, there is a lack of high-spatial-and-temporal-resolution, real-time and observation-based GPP products. To address this critical gap, here we leverage a state-of-the-art vegetation index, near-infrared reflectance of vegetation (NIRV), along with accurate photosynthetically active radiation (PAR), to produce a SatelLite Only Photosynthesis Estimation (SLOPE) GPP product for the contiguous United States (CONUS). Compared to existing GPP products, the proposed SLOPE product is advanced in its spatial resolution (250 m versus >500 m), temporal resolution (daily versus 8 d), instantaneity (latency of 1 d versus >2 weeks) and quantitative uncertainty (on a per-pixel and daily basis versus no uncertainty information available). These characteristics are achieved because of several technical innovations employed in this study: (1) SLOPE couples machine learning models with MODIS atmosphere and land products to accurately estimate PAR. (2) SLOPE couples highly efficient and pragmatic gap-filling and filtering algorithms with surface reflectance acquired by both Terra and Aqua MODIS satellites to derive a soil-adjusted NIRV (SANIRV) dataset. (3) SLOPE couples a temporal pattern recognition approach with a long-term Cropland Data Layer (CDL) product to predict dynamic C4 crop fraction. Through developing a parsimonious model with only two slope parameters, the proposed SLOPE product explains 85 % of the spatial and temporal variations in GPP acquired from 49 AmeriFlux eddy-covariance sites (324 site years), with a root-mean-square error (RMSE) of 1.63 gC m−2 d−1. The median R2 over C3 and C4 crop sites reaches 0.87 and 0.94, respectively, indicating great potentials for monitoring crops, in particular bioenergy crops, at the field level. With such a satisfactory performance and its distinct characteristics in spatiotemporal resolution and instantaneity, the proposed SLOPE GPP product is promising for biological and environmental research, carbon cycle research, and a broad range of real-time applications at the regional scale. The archived dataset is available at https://doi.org/10.3334/ORNLDAAC/1786 (download page: https://daac.ornl.gov/daacdata/cms/SLOPE_GPP_CONUS/data/, last access: 20 January 2021) (Jiang and Guan, 2020), and the real-time dataset is available upon request.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Robust Adaptive Decentralized Dynamic State Estimation with Unknown Control Inputs using Field PMU Measurements

This paper proposes a robust adaptive decentralized dynamic state estimation method for power system with unknown inputs of the highly detailed synchronous machine model. The temporal and spatial correlations among the unknown inputs are used to derive a vector auto-regressive model. The latter is further integrated together with state transition and measurement models for joint state and unknown inputs estimation. Thanks to the consideration of implicit cross-correlations between the states and the unknown inputs, only generator terminal voltage and current phasors are needed. Test results on the US WECC system using the field PMU measurements show that the proposed method is able to track both the system dynamic states and unknown controller inputs. These information could significantly benefit the validation and calibration of generator controller parameters.

Zhao, Junbo↗

DOE OSTI2021

A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction

Here, we put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements for air traffic improvements. Toward emerging applications of digital twins in aviation, the proposed approach allows for constructing a realtime predictive tool for wake-vortex transport and decay systems. We build on the fact that in realistic application, there are uncertainties in initial and boundary conditions, model parameters, as well as measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities, especially for advection-dominated flows with slow decay in the Kolmogorov n-width. In the presented LSTM nudging (LSTM-N) approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate our concept by solving the two-dimensional vorticity transport equation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-N behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity, and offer a huge potential in developing next-generation digital twin technologies for aerospace applications.

42 ENGINEERING↗

DOE OSTI2015

Computational Molecular Simulation of the Oxidative Adsorption of Ferrous Iron at the Hematite (001)-Water Interface

The interaction of Fe(II) with ferric oxide/oxyhydroxide phases is central to the biogeochemical redox chemistry of iron. Molecular simulation techniques were employed to determine the mechanisms and quantify the rates of Fe(II) oxidative adsorption at the hematite (001)-water interface. Molecular dynamics potential of mean force calculations of Fe(II) adsorbing on the hematite surface revealed the presence of three free energy minima corresponding to Fe(II) adsorbed in an outersphere complex, a monodentate innersphere complex, and a tridentate innersphere complex. The free energy barrier for adsorption from the outersphere position to the monodentate innersphere site was calculated to be similar to the activation enthalpy for water exchange around aqueous Fe(II). Adsorption at both innersphere sites was predicted to be unfavorable unless accompanied by release of protons. Molecular dynamics umbrella sampling simulations and ab initio cluster calculations were performed to determine the rates of electron transfer from Fe(II) adsorbed as an innersphere and outersphere complex. The electron transfer rates were calculated to range from 10^-4 to 10^2 s-1, depending on the adsorption site and the potential parameter set, and were generally slower than those obtained in the bulk hematite lattice. The most reliable estimate of the rate of electron transfer from Fe(II) adsorbed as an outersphere complex to lattice Fe(III) was commensurate with the rate of adsorption as an innersphere complex suggesting that adsorption does not necessarily need to precede oxidation.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2019

Utilization of Hydroturbines in Wastewater Treatment Plants

Wastewater treatment plants (WWTPs) are a significant energy consumer, yet there are several opportunities for implementing on-site power generation systems. Within the treatment process, the high flow rate of effluent is produced and discharged to a nearby water body by gravity. Thus, hydroturbines can be utilized to generate power in such an application due to a difference in elevation and high flow rate. This paper presents a case study of introducing a hydroturbine in a WWTP in Wisconsin and evaluating the power output in addition to determining the energy savings. The WWTP considered in this study has an effluent flow rate of 190 MGD (million gallons per day) and elevation difference of 3 m (10 ft) between the final stage of treatment and the discharge point. Based on the parameters above; hubless rim-drive Kaplan type hydroturbine (RDT) is the optimal choice to be used in such an application. The RDT is designed and optimized by using in-house code. A computational fluid dynamics (CFD) software is applied to evaluate the performance of the proposed model, and the system is simulated through homer software to validate the results generated by the CFD. The expected savings is estimated to be 1564 MWh/yr.

Energy & Fuels↗

DOE OSTI2019

Computational Assessment of Hydrodynamic Loads on Rockeries for River Bank Protection

Colorado experienced an extreme flooding event in September of 2013 that ravaged canyon roadways southeast of Estes Park, CO. Central Federal Lands was asked to rebuild SH 34 and CO 43 after the floods. To minimize river encroachments in narrow canyons, roadway fill embankments must be over steepened. Using a rockery to stabilize the roadway embankment rather than traditional vertical, concrete structures was the solution. However, no analytical techniques were available for evaluating the hydraulic stability of such structures. Argonne National Laboratory was employed to estimate the hydrodynamic forces by using advanced, computational fluid dynamics (CFD). An investigation was conducted on a section of a model rockery comprised of large boulders exposed to a variety of hydraulic flow conditions. A repeatable geometric section of a typical rockery structure was modeled and used to create boundaries for the CFD model. The test case matrix covers computer simulations of various rockery and channel geometries. The geometrical parameters taken into account are: rockery height, outside face batter angle of the rockery, rockery base width, river bed width, and the hydraulic parameters are: flow depth, flow velocity, and hydraulic angle of attack. Two failure mechanisms of rockery structures, sliding and overturning, are considered. The existing design equations for both modes are modified by addition of hydrodynamic force terms. The new terms were calculated for a parametric set of geometry and condition variation using the CFD model. Moreover, formulas for dimensionless hydraulic force coefficients are proposed that can be used in the design of new rockeries or in evaluation of existing dry-stack rockeries in river environments.

42 ENGINEERING↗

DOE OSTI2017

Calibrating the Planck Cluster Mass Scale with Cluster Velocity Dispersions

We measure the Planck cluster mass bias using dynamical mass measurements based on velocity dispersions of a subsample of 17 Planck-detected clusters. The velocity dispersions were calculated using redshifts determined from spectra that were obtained at the Gemini observatory with the GMOS multi-object spectrograph. We correct our estimates for effects due to finite aperture, Eddington bias, and correlated scatter between velocity dispersion and the Planck mass proxy. The result for the mass bias parameter, (1−b), depends on the value of the galaxy velocity bias, b{sub v}, adopted from simulations: (1−b)=(0.51±0.09)b{sub v}{sup 3}. Using a velocity bias of b{sub v}=1.08 from Munari et al., we obtain (1−b)=0.64±0.11, i.e., an error of 17% on the mass bias measurement with 17 clusters. This mass bias value is consistent with most previous weak-lensing determinations. It lies within 1σ of the value that is needed to reconcile the Planck cluster counts with the Planck primary cosmic microwave background constraints. We emphasize that uncertainty in the velocity bias severely hampers the precision of the measurements of the mass bias using velocity dispersions. On the other hand, when we fix the Planck mass bias using the constraints from Penna–Lima et al., based on weak-lensing measurements, we obtain a positive velocity bias of b{sub v}≳0.9 at 3σ.

79 ASTRONOMY AND ASTROPHYSICS↗