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At least 721 records · Page 40

High Fidelity Computational Model for Fluidized Bed Experiments (Final Report)

MFiX was integrated with preconditioners and linear solver packages in Trilinos via MFIX, Fortran, C, and C++ wrappers. The MFIX wrapper interpreted the structure of the matrix and vector from MFiX while the Fortran wrapper transfers this information to a low-level language, C. C-wrapper transforms the memory semantic between Fortran and C++ language. C++ wrapper passes the matrix and vector to a Trilinos package and gets the solution. This solution was transferred to MFiX via C++, C, Fortran, MFIX wrapper. The framework is used to integrate first, second and third generation linear solvers in Trilinos with MFiX.

20 FOSSIL-FUELED POWER PLANTS↗

High Fidelity Computational Model for Fluidized Bed Experiments

MFiX was integrated with preconditioners and linear solver packages in Trilinos via MFiX, Fortran, C, and C++ wrappers. The MFiX wrapper interpreted the structure of the matrix and vector from MFiX while the Fortran wrapper transfered this information to a low-level language, C. The C-wrapper transformed the memory semantic between Fortran and C++ language. The C++ wrapper passed the matrix and vector to a Trilinos package and got the solution. This solution was transferred to MFiX via C++, C, Fortran, MFiX wrapper. The framework was used to integrate first, second, and third generation linear solvers in Trilinos with MFiX.

20 FOSSIL-FUELED POWER PLANTS↗

Modelling the complex evaporated gas flow and its impact on particle spattering during laser powder bed fusion

The additive manufacturing (AM) of metals is becoming an increasingly important production process with the potential to replace traditional techniques such as casting. Laser Powder Bed Fusion (LPBF) is used in many applications to print metal parts from powder. The metal powder is heated locally with sufficient laser radiation that the liquid melt easily reaches its boiling temperature, which leads to a metallic vapour jet that can entrain both powder bed particles and molten droplets. The small size of laser-matter interaction site makes a detailed experimental analysis of the process challenging. Synchrotron X-ray imaging experiments are one of the few methods which can capture the dynamic melting and solidification processes. Comparing such experiments with computer simulations of the process is an important approach in order to better understand the manufacturing process and to analyse the influence of process parameters on the evaporated gas jet and the subsequent impact on particle ejection, leading to potentially reduced AM component quality. The melting and solidification of the metal powder is simulated using an Eulerian multiphase approach based on a control volume discretization of powder bed and substrate and a volume of liquid separation from melt and gas phase. The gas phase modelled as an ideal gas reaches velocities up to 100 m/s. Lagrangian particle tracking in the simulation demonstrates that the velocity fields calculated by the Eulerian multi-phase approach in combination with a standard drag-force model lead to particle accelerations in good agreement with those measured experimentally. In order to avoid numerical laborious Lagrangian calculations, a direct method to compare an Eulerian multiphase simulation with synchrotron X-ray experiments was introduced and validated. This approach is used to analyse the influence of process parameters including laser power and laser speed on the maximal acceleration of particles from the melt pool area. While the particle acceleration increases linearly with line energy in the conduction mode, a linear decrease of the acceleration with increasing line energy can be found in the transition mode before the accel-eration increases again with line energy in the keyhole mode.

36 MATERIALS SCIENCE↗

Rapid determination of supercritical CO 2 and brine relative permeability using an unsteady-state flow method

In this study, relative permeability of supercritical CO 2 (scCO 2 ) and brine was determined in reactive and non-reactive rock cores using a combination of unsteady-state methodology and computed tomography. Experiments were conducted using a medical grade CT scanner to determine saturation using a custom Python script. The saturation and differential pressure across the core were then used to derive four empirical constants to calculate relative permeability. This methodology increases temporal efficiency while reducing experimental complexity. Additionally, we show that the method can be used to determine scCO 2 relative permeability in a wide range of lithologies and flow rates, and with the ability to account for matrix dissolution during scCO 2 flooding.

54 ENVIRONMENTAL SCIENCES↗

First-Principles-Based Computational Study on Nucleation and Growth Mechanisms of U on Mo(110) Surface Solvated in an Eutectic LiCl-KCl Molten Salt

In nuclear engineering and industry electrochemical methods have been intensively employed in pyro-processing technology to recycle used nuclear fuels for substantial alleviation of the concern with the safe treatment of high-level radioactive nuclear wastes. Pyro-processing is based on sequential electrochemical reactions at high temperature (typically above 700 K at ambient pressure) to enhance the efficiency for decoupling nuclear fuels from unfavorable fission fragments. Using a molten salt in electrorefining process, at which actinides can be selectively deposited in solid cathode from ionic states, gives several advantages over an aqueous solution: higher thermal conductivity (it is liquid phase at high temperature, molten salt plays a role as medium at high temperature over 773 K in electrochemical reaction, lower kinetic barrier in ionic diffusion mobility and better stability against undesired side reactions with radioactive materials. Therefore, the volume of high-level nuclear wastes to be, otherwise, disposed into secured sites is dramatically reduced. Most of all it conforms to nuclear non-proliferation treaty. Electrochemical reactions in a molten salt medium are, however, much more complicated than in aqueous solution rendering the accurate understanding of thermodynamic and kinetic properties formidably challenging. It is represented by extensive researches in experiments and computations to identify underlying mechanisms on how U and other fission fragments behave in the electrorefining system. Regardless of the researches there is a general agreement that the initial stage of the nucleation and growth process of the U deposit is critical for determining the properties of final product and the electrorefining efficiency. In spite of the focused studies it still remains unclear. Theoretical and computational researches have been often carried out with various empirical parameter for interatomic potential energy, which are unknown variables until numerical fits to experimental measurements or just assumption is made. Thus, empirical simulations sometimes predicted outcomes are inconsistent depending on materials of interest with experimental measurements. This may be largely because the accuracy of an empirical interatomic potential energy models critically depends on the input parameters and thus, can be limited in transferability of the results. Furthermore, it may be devoid of fundamental physics or chemistry. This situation requires special caution when an electrorefining system is studied to recycle spent nuclear fuels because of the extreme difficulty in reliable acquisition of thermodynamic and kinetic data from direct experimental measurements. In this presentation, we extensively utilized first principles density functional theory (DFT) calculations and ab-initio molecular dynamic (AIMD) simulations to figure out underlying mechanisms of the initial stage of nucleation and growth behaviors of U on Mo(110) surface in a eutectic LiCl-KCl molten salt at T = 773 K. To rigorously investigate the effect of the molten salt electrolyte we compared the results with those calculated under vacuum condition.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Exploiting analytics techniques in CMS computing monitoring

The CMS experiment has collected an enormous volume of metadata about its computing operations in its monitoring systems, describing its experience in operating all of the CMS workflows on all of the Worldwide LHC Computing Grid Tiers. Data mining efforts into all these information have rarely been done, but are of crucial importance for a better understanding of how CMS did successful operations, and to reach an adequate and adaptive modelling of the CMS operations, in order to allow detailed optimizations and eventually a prediction of system behaviours. These data are now streamed into the CERN Hadoop data cluster for further analysis. Specific sets of information (e.g. data on how many replicas of datasets CMS wrote on disks at WLCG Tiers, data on which datasets were primarily requested for analysis, etc) were collected on Hadoop and processed with MapReduce applications profiting of the parallelization on the Hadoop cluster. We present the implementation of new monitoring applications on Hadoop, and discuss the new possibilities in CMS computing monitoring introduced with the ability to quickly process big data sets from mulltiple sources, looking forward to a predictive modeling of the system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Bayesian Conavigation: Dynamic Designing of the Material Digital Twins via Active Learning

Scientific advancement is universally based on the dynamic interplay between theoretical insights, modeling, and experimental discoveries. However, this feedback loop is often slow, including delayed community interactions and the gradual integration of experimental data into theoretical frameworks. This challenge is particularly exacerbated in domains dealing with high-dimensional object spaces, such as molecules and complex microstructures. Hence, the integration of theory within automated and autonomous experimental setups, or theory in the loop-automated experiment, is emerging as a crucial objective for accelerating scientific research. The critical aspect is to use not only theory but also on-the-fly theory updates during the experiment. Furthermore, we introduce a method for integrating theory into the loop through Bayesian conavigation of theoretical model space and experimentation. Our approach leverages the concurrent development of surrogate models for both simulation and experimental domains at the rates determined by latencies and costs of experiments and computation, alongside the adjustment of control parameters within theoretical models to minimize epistemic uncertainty over the experimental object spaces. This methodology facilitates the creation of digital twins of material structures, encompassing both the surrogate model of behavior that includes the correlative part and the theoretical model itself. While being demonstrated here within the context of functional responses in ferroelectric materials, our approach holds promise for broader applications, such as the exploration of optical properties in nanoclusters, microstructure-dependent properties in complex materials, and properties of molecular systems.

Microscopy↗

Head-on parallel blade-vortex interaction

An experimental and computational study was carried out to investigate the parallel head-on blade-vortex interaction (BVI) and its noise generation mechanism. A shock tube, with an enlarged test section, was used to generate a compressible starting vortex which interacted with a target airfoil. The dual-pulsed holographic interferometry (DPHI) technique and airfoil surface pressure measurements were employed to obtain quantitative flow data during the BVI. A thin-layer Navier-Stokes code (BV12D), with a high-order upwind-biased scheme and a multizonal grid, was also used to simulate numerically the phenomena occurring in the head-on BVI. The detailed structure of a convecting vortex was studied through independent measurements of density and pressure distributions across the vortex center. Results indicate that, in a strong head-on BVI, the opposite pressure peaks are generated on both sides of the leading edge as the vortex approaches. Then, as soon as the vortex passes by the leading edge, the high-pressure peak suddenly moves toward the low-peak-reducing in magnitude as it moves--simultaneously giving rise to the initial sound wave. In both experiment and computation, it is shown that the viscous effect plays a significant role in head-on BVIs.

Lee, Soogab↗

Development and Experimental Optimization of High-Temperature Modeling Tools and Methods for Concentrated Solar Power Particle - Systems

A novel, open-source radiative modeling toolset was developed to extend the functionality of particle-based modeling software (e.g. discrete element method (DEM)) to environmental conditions relevant to concentrated solar power applications. This toolset was optimized for deployment on desktop workstations instead of high-performance computing systems, to render such tools more accessible to the research community. Both particle-based modeling and radiative exchange modeling are computationally expensive and often require specialized programming expertise, making these methods cumbersome to use. Recent developments in DEM software by DCS Computing have greatly reduced these challenges, providing a graphical-user-interface based platform and modeling optimization for desktop workstations, HPCs, and cloud computing. The University of Dayton leveraged the experience of DCS Computing in developing a user-friendly, open-source radiative heat transfer expansion for DEM modeling. The University of Dayton DEM+ radiative modeling toolset was developed using a combination of fundamental experimental measurements, modeling, and simplified flow experiments over a range of temperatures and flow conditions. The toolset provides researchers with access to multiple radiative models including an accelerated Monte-Carlo Ray Tracing (application agnostic, highly computationally expensive), an expanded database of distance-based approximations (application limited, computationally light), and a weighted blending of the two methods capable of achieving over 90% reduction in computation time with equivalent accuracy compared to Monte-Carlo Ray Tracing. Through a graphical user interface, users can customize the radiative models to match their desired accuracy and available computational resources, improving access to particle based modeling for the research community. Ceramic sintered bauxite proppants were used in modeling and experimentally as a baseline. Both the radiative heat transfer and flow properties for particulate systems were investigated at elevated temperatures up to 800 °C. The major accomplishments for this work include a verified, open-source radiative modeling toolset to be distributed amongst the research community and the fabrication of three small-scale test facilities to investigate particle behavior and tune DEM flow properties for operation up to 800 °C. The findings have been shared with the research community via conference modeling workshops, deployment of the tools in DCS Computing Aspherix®, and open-source access to the developed radiative modeling tool. The development of next-generation CSP facilities and thermal energy storage systems based on ceramic particles requires providing access to computationally efficient and accurate modeling tools. Particles will experience a wide range of environments (20-800 °C) and handling conditions (dilute curtains or dense packing), requiring specially designed and optimized equipment. Optimizing solid particle physics models and establishing best-practices for particle modeling in CSP environments will assist researchers with designing optimized equipment, accelerating the deployment of more economically-competitive CSP facilities.

14 SOLAR ENERGY↗

Progress Towards Fuselage Drag Reduction via Active Flow Control: A Combined CFD and Experimental Effort

A combined computational and experimental effort has been undertaken to study fuselage drag reduction on a generic, non-proprietary rotorcraft fuselage by the application of active ow control. Fuselage drag reduction is an area of research interest to both the United States and France and this area is being worked collaboratively as a task under the United States/France Memorandum of Agreement on Helicopter Aeromechanics. In the first half of this task, emphasis is placed on the US generic fuselage, the ROBIN-mod7, with the experimental work being conducted on the US side and complementary US and French CFD analysis of the baseline and controlled cases. Fuselage simulations were made using Reynolds-averaged Navier-Stokes ow solvers and with multiple turbulence models. Comparisons were made to experimental data for numerical simulations of the isolated fuselage and for the fuselage as installed in the tunnel, which includes modeling of the tunnel contraction, walls, and support fairing. The numerical simulations show that comparisons to the experimental data are in good agreement when the tunnel and model support are included. The isolated fuselage simulations compare well to each other, however, there is a positive shift in the centerline pressure when compared to the experiment. The computed flow separation locations on the rear ramp region had only slight differences with and without the tunnel walls and model support. For the simulations, the flow control slots were placed at several locations around the flow separation lines as a series of eight slots that formed a nearly continuous U-shape. Results from the numerical simulations resulted in an estimated 35% fuselage drag reduction from a steady blowing flow control configuration and a 26% drag reduction for unsteady zero-net-mass flow control configuration. Simulations with steady blowing show a delayed flow separation at the rear ramp of the fuselage that increases the surface pressure acting on the ramp, thus decreasing the overall fuselage pressure drag.

Schaeffler, Norman W.↗

MERRA Analytic Services: Meeting the Big Data Challenges of Climate Science Through Cloud-enabled Climate Analytics-as-a-service

Climate science is a Big Data domain that is experiencing unprecedented growth. In our efforts to address the Big Data challenges of climate science, we are moving toward a notion of Climate Analytics-as-a-Service (CAaaS). We focus on analytics, because it is the knowledge gained from our interactions with Big Data that ultimately produce societal benefits. We focus on CAaaS because we believe it provides a useful way of thinking about the problem: a specialization of the concept of business process-as-a-service, which is an evolving extension of IaaS, PaaS, and SaaS enabled by Cloud Computing. Within this framework, Cloud Computing plays an important role; however, we it see it as only one element in a constellation of capabilities that are essential to delivering climate analytics as a service. These elements are essential because in the aggregate they lead to generativity, a capacity for self-assembly that we feel is the key to solving many of the Big Data challenges in this domain. MERRA Analytic Services (MERRAAS) is an example of cloud-enabled CAaaS built on this principle. MERRAAS enables MapReduce analytics over NASAs Modern-Era Retrospective Analysis for Research and Applications (MERRA) data collection. The MERRA reanalysis integrates observational data with numerical models to produce a global temporally and spatially consistent synthesis of 26 key climate variables. It represents a type of data product that is of growing importance to scientists doing climate change research and a wide range of decision support applications. MERRAAS brings together the following generative elements in a full, end-to-end demonstration of CAaaS capabilities: (1) high-performance, data proximal analytics, (2) scalable data management, (3) software appliance virtualization, (4) adaptive analytics, and (5) a domain-harmonized API. The effectiveness of MERRAAS has been demonstrated in several applications. In our experience, Cloud Computing lowers the barriers and risk to organizational change, fosters innovation and experimentation, facilitates technology transfer, and provides the agility required to meet our customers' increasing and changing needs. Cloud Computing is providing a new tier in the data services stack that helps connect earthbound, enterprise-level data and computational resources to new customers and new mobility-driven applications and modes of work. For climate science, Cloud Computing's capacity to engage communities in the construction of new capabilies is perhaps the most important link between Cloud Computing and Big Data.

Data Analytics↗

Thermal Design and Flight Experience of the Mars Exploration Rover Spacecraft Computer-Controlled, Propulsion Line Heaters

This paper covers the design, thermal testing and flight experiences with the computer-controlled thermostats on the propulsion line heaters. Flight experience revealed heater control behavior with propellant loaded into the system and during thruster firings that was not observable during system level testing. Explanations of flight behavior, lessons learned, and suggestions for improvement of the propellant line heater design are presented in this paper.

propulsion lines↗

Quantifying how the cis/trans ratio of N,N -dimethyl-3,5-dimethylpiperidinium hydroxide impacts the growth kinetics, composition and local structure of SSZ-39

This work integrates experiments and computational methods to quantify how the cis/trans ratio of the OSDA used in SSZ-39 synthesis impacts the crystallization kinetics, material properties, and final product composition. The crystallization kinetics increase by 30% when increasing the trans isomer content from 14% to 80%. Per prior work, in all cases based on the synthesis gel composition and product yield aluminum is the limiting reagent, and the absence of any amorphous material detected in the time resolved PXRD studies leads us to conclude that FAU dissolution is the rate limiting step in the formation of SSZ-39 in this synthesis protocol. The TGA and NMR results suggest that the trans isomer of OSDA is selectively incorporated into the product. The NMR binding studies, and corresponding DFT-based results show that the trans isomer binds to FAU more strongly than the cis isomer, providing one possible explanation for this enhancement in kinetics and preferential uptake of the trans isomer. The EDS analysis indicates that the Si/Al ratios are between 7.7 and 8.6 at low and high trans OSDA content, indicating zeolite composition is mildly sensitive to the trans isomer content. EDS results show this decrease in aluminum content leads to a corresponding decrease in sodium uptake. DFT-based calculations confirm OSDA–sodium interactions cannot explain any decrease in sodium uptake, reinforcing lower aluminum content as the cause of lower sodium uptake. Preliminary cobalt titration experiments show a surprisingly low cobalt uptake but also show a clear dependence of the cobalt uptake on the solution pH.

Cui, Zheng [Tulane University, New Orleans, LA (Un↗

Augmenting a Simulation Campaign for Hybrid Computer Model and Field Data Experiments

The Kennedy and O’Hagan (KOH) calibration framework uses coupled Gaussian processes (GPs) to meta-model an expensive simulator (first GP), tune its “knobs” (calibration inputs) to best match observations from a real physical/field experiment and correct for any modeling bias (second GP) when predicting under new field conditions (design inputs). There are well-established methods for placement of design inputs for data-efficient planning of a simulation campaign in isolation, that is, without field data: space-filling, or via criterion like minimum integrated mean-squared prediction error (IMSPE). Analogues within the coupled GP KOH framework are mostly absent from the literature. Here, in this study, we derive a closed form IMSPE criterion for sequentially acquiring new simulator data for KOH. We illustrate how acquisitions space-fill in design space, but concentrate in calibration space. Closed form IMSPE precipitates a closed-form gradient for efficient numerical optimization. We demonstrate that our KOH-IMSPE strategy leads to a more efficient simulation campaign on benchmark problems, and conclude with a showcase on an application to equilibrium concentrations of rare earth elements for a liquid–liquid extraction reaction.

97 MATHEMATICS AND COMPUTING↗

Data Science and Computation for Rapid and Dynamic Compression Experiment Workflows at Experimental Facilities (Workshop Overview) [Slides]

Motivation for this workshop stems from these items: Compression experiments are important to LANL's core mission. The scientific community is sometimes frustrated at the pace of discovery. Data analytics for other experimental regimes are advancing. Now is the time as facilities are upgraded and coming online. Advances in data analytics and computational resources could push compression experiment discoveries to a new level.

97 MATHEMATICS AND COMPUTING↗

Modeling the influence of nozzle-generated turbulence on diesel sprays

The physical mechanisms governing spray breakup in direct injection engines, such as aerodynamic induced instabilities and nozzle-generated cavitation and turbulence, are not well understood due to the experimental and computational limitations in resolving these processes. Recent x-ray and visible extinction measurements have been con-ducted with a targeted interest in the spray formation region in order to characterize the distribution of droplet sizes throughout the spray. Detailed analysis of these measurements shows promise of yielding insight into likely mechanisms governing atomization, which can inform the improvement of spray models for engine computational fluid dynamic (CFD) codes. In order to investigate potential atomization mechanisms, we employ a joint experimental and computational approach to characterize the structure of the spray formation region using the Engine Combustion Network Spray D injector. X-ray tomography, radiography and ultra-small angle x-ray scattering measurements conducted at the Advanced Photon Source at Argonne National Laboratory quantify the injector geometry, liquid fuel mass and Sauter mean diameter (SMD) distributions under non-vaporizing conditions. Diffused back-illumination imaging measurements, conducted at the Georgia Institute of Technology, characterize the asymmetry of the spray structure. The selected range of injection pressures (50 – 150 MPa) and ambient densities (1.2 – 22.8 kg/m3) allow for the influence of aerodynamic forces on the spray to be studied in a controlled and systematic manner, while isolating the atomization process from the effects of vaporization. In comparison to high ambient density conditions, the spray is observed to be more asymmetric at low ambient density conditions. Although several mechanisms may cause asymmetries in the nozzle exit flow conditions and ultimately the spray distribution, irregularities in the internal nozzle geometry were identified, suggesting an increased sensitivity of the spray structure to internal nozzle surface finish imperfections at such conditions. The presence of these asymmetries may influence the ability to interpret line-of-sight measurements and their derived SMD values and trends from a single viewing angle of the spray. With this consideration in mind, the measured local sensitivities to ambient density suggest that for ambient densities less than 2.4 kg/m3, aerodynamic effects are likely suppressed, allowing the influence of turbulent-induced breakup to be isolated. In concert with the experimental measurements, we utilize three-dimensional, CFD Lagrangian-Eulerian spray simulations in CONVERGE to evaluate the details of the predicted spray structure. In particular, we compare measured and predicted sensitivities of the SMD distribution to changes in injection and ambient conditions from three different atomization models, namely Kelvin Helmholtz (KH), KH Aerodynamics Cavitation Turbulence (KH-ACT), and the newly developed KH-Faeth hybrid model. While none of the existing hybrid spray models were able to replicate the experimentally observed sensitivities, it was found that the scales characterizing the KH-Faeth model show promise of capturing the experimentally observed trends if the effects of secondary droplet breakup are neglected. These results inform recommendations for future experiments and computational studies that can guide the development of an improved spray breakup model.

33 ADVANCED PROPULSION SYSTEMS↗

Computing for the DUNE Long-Baseline Neutrino Oscillation Experiment

This is a talk given at Computers in High Energy Physics in Adelaide, South Australia, Australia in November 2019. It is partially intended to explain the context of DUNE Computing for computing specialists. The DUNE collaboration consists of over 180 institutions from 33 countries. The experiment is in preparation now with commissioning of the first 10kT fiducial volume Liquid Argon TPC expected over the period 2025-2028 and a long data taking run with 4 modules expected from 2029 and beyond. An active prototyping program is already in place with a short test beam run with a 700T, 15,360 channel prototype of single-phase readout at the neutrino platform at CERN in late 2018 and tests of a similar sized dual-phase detector scheduled for mid-2019. The 2018 test beam run was a valuable live test of our computing model. The detector produced raw data at rates of up to ~2GB/s. These data were stored at full rate on tape at CERN and Fermilab and replicated at sites in the UK and Czech Republic. In total 1.2 PB of raw data from beam and cosmic triggers were produced and reconstructed during the six week test beam run. Baseline predictions for the full DUNE detector data, starting in the late 2020's are 30-60 PB of raw data per year. In contrast to traditional HEP computational problems, DUNE's Liquid Argon TPC data consist of simple but very large (many GB) 2D data objects which share many characteristics with astrophysical images. This presents opportunities to use advances in machine learning and pattern recognition as a frontier user of High Performance Computing facilities capable of massively parallel processing.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Advances and Enhancements in the Fabric for Frontier Experiments Project at Fermilab

The FabrIc for Frontier Experiments (FIFE) project within the Fermilab Scientific Computing Division is charged with integrating offline computing components into a common computing stack for the non-LHC Fermilab experiments, supporting experiment offline computing, and consulting on new, novel workflows. We will discuss the general FIFE onboarding strategy, the upgrades and enhancements in the FIFE toolset, and plans for the coming year. These enhancements include: expansion of opportunistic computing resources (including GPU and high-performance computing resources) available to experiments; assistance with commissioning computing resources at European sites for individual experiments; StashCache repositories for experiments; enhanced job monitoring tools; and a custom workflow management service. Additionally we have completed the first phase of a Federated Identity Management system to make it easier for FIFE users to access Fermilab computing resources.

Herner, Kenneth↗