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At least 361 records · Page 20

Fault diagnosis and fault tolerant control for T-S fuzzy stochastic distribution systems subject to sensor and actuator faults

The problem of fault diagnosis (FD) and fault tolerant control (FTC) for a class of Takagi-Sugeno (T-S) fuzzy stochastic distribution control (SDC) systems subject to sensor and actuator faults is discussed in this paper. First, fuzzy logic models are used to approximate the output probability density function (PDF). Next, an adaptive augmented state/fault diagnosis observer is proposed to estimate the system state, sensor and the actuator faults simultaneously. New expected weights based on the sensor fault estimation information and a PI-type fuzzy feedback fault tolerant (FT) controller are designed to compensate the effect of sensor fault and actuator fault simultaneously. When the sensor fault occurs, the expected objective is redesigned to compensate the sensor fault. Meanwhile, the PI controller can compensate the effect of actuator fault, and the output PDF of the system can still track the desired PDF after the fault occurs. Finally, an example of quality distribution control in chemical reaction process is given to confirm the effectiveness of the algorithm.

42 ENGINEERING↗

Herbaceous Feedstock 2022 State of Technology Report

The U.S. Department of Energy promotes production of advanced liquid transportation fuels from lignocellulosic biomass by funding fundamental and applied research that advances the state of technology (SOT). As part of its involvement in this mission, Idaho National Laboratory completes an annual SOT report for nth-plant and 1st-plant herbaceous biomass feedstock logistics. The purpose of the SOT is to provide the status of feedstock supply system technology development for herbaceous biomass to biofuels relative to technical targets and cost goals from specific design cases, based on data and experimental results. Although conventional feedstock supply systems form the backbone of the emerging biofuels industry, they have limitations that restrict widespread implementation on a national scale. To meet the demands of the future industry, the feedstock supply system must shift from the conventional system to what has been termed “advanced” supply systems. In advanced designs, a distributed network of aggregation and processing centers, termed “depots,” are employed near the points of biomass production (i.e., the field or forest) to reduce feedstock variability and produce feedstocks of a uniform format, moving toward biomass commoditization. The 2022 Herbaceous SOT is part of a vision of achieving an implemented advanced feedstock supply system, which produces a stable, tradable commodity at the decentralized distributed depot. It utilizes feedstock fractionation by incorporating technologies that can separate the biomass into its anatomical fractions (leaves, husks, stems and cobs) to reduce impurities and produce fractions that satisfy downstream quality considerations. By using a series of air classification steps, this strategy can reduce the extrinsic ash in corn stover and produce enriched tissue fractions that can be blended to a conversion specification or converted individually in optimized biochemical conversion campaigns. Additionally, a majority of the leaves (which do not meet the quality specification) are separated out early and can be supplied to alternate markets. The 2022 Herbaceous SOT incorporates an advanced biomass fractionation and processing system to produce pellets enriched tissues from three-pass corn stover. The resulting enriched pellets are delivered to the biorefinery individually where they can be blended to a specification or converted in campaigns where the conditions are optimized for each tissue. Unused fractions can be sent to a a midstream market or to a different conversion process that is better suited to their properties to offset the cost of the delivered feedstock. The main benefits from the proposed system can be summarized as: (1) $6.86/dry ton (2016$) lower cost for the air classification due to elimination of the requirement to discard the high ash lights fraction; (2) $1.56/dry ton lower delivered cost by selling the unsuitable leaf fraction into the feed market as a midstream co-product (assuming a selling price that is 11% higher than their cost of production); (3) 0.98% increase in carbohydrate content (from 60.16% to 61.14%); and (4) 0.97% decrease in ash content (from 6.00% to 5.03%) compared to the 2021 Herbaceous SOT. Overall, the 2022 nth-plant Herbaceous SOT predicts a modeled delivered feedstock cost of $78.64/dry ton (2016$) if it is assumed that the enriched leaf fraction is sold at its production cost; this is a slight increase of $0.43/dry ton increase from the 2021 Herbaceous SOT nth-Supply case cost. The increased cost derived from a $0.38/dry ton increase in transportation and handling cost to procure more biomass (to replace the enriched leaf fraction that was not delivered to the biorefinery. The total preprocessing cost was $0.27/dry ton higher than the 2021 result because of updates to energy consumption, purchasing price and dry matter loss data for the rotary shear ($3.00/dry ton increase) and the pelleting mill ($4.52/dry ton increase). The data utilized were generated in pilot-scale tests in the Biomass Feedstock National User Facility (BFNUF) at INL and at Forest Concepts, including tests for rotary shear and pelleting of the air classified fractions. A greenhouse gas emissions analysis was performed by Argonne National Laboratory using the most up to date version of the Greenhouse Gases, Regulated Emissions, and Energy use in Transportation model (GREET®). The analysis showed an increase of 17.34 kg CO2e/dry ton from the 2021 SOT (67.71 kg CO2e/ton in the 2021 Herbaceous SOT to 85.05 kg CO2e/ton in the 2022 Herbaceous SOT). The net increase is primarily attributed to increased energy consumption in pelleting mill.

09 BIOMASS FUELS↗

A stochastic scan strategy for grain structure control in complex geometries using electron beam powder bed fusion

Spatial control of microstructure within a three-dimensional component has been a dream of materials scientists for centuries. However, limitations in traditional manufacturing processes prevent detailed control over the distribution of microstructures in a single part. Here, we demonstrate the ability to control grain structure and crystallographic texture during metal additive manufacturing for arbitrary cross-sections of a practical size, with profound implications for the design and optimization of next-generation products. The key to this advance is a new geometry agnostic scan path algorithm that manipulates the spatial distribution of solidification conditions. Utilizing a fundamental understanding of solidification dynamics and a model of the heat transfer during processing, we have designed this algorithm to manipulate the natural competition between epitaxial dendrite growth and grain nucleation. With this algorithm, we successfully controlled the grain structure of Ni-based superalloy IN718 in the shape of the Mona Lisa.

36 MATERIALS SCIENCE↗

Towards universal unfolding of detector effects in high-energy physics using denoising diffusion probabilistic models

Correcting for detector effects in experimental data, particularly through unfolding, is critical for enabling precision measurements in high-energy physics. However, traditional unfolding methods face challenges in scalability, flexibility, and dependence on simulations. We introduce a novel approach to multidimensional object-wise unfolding using conditional Denoising Diffusion Probabilistic Models (cDDPM). Our method utilizes the cDDPM for a non-iterative, flexible posterior sampling approach, incorporating distribution moments as conditioning information, which exhibits a strong inductive bias that allows it to generalize to unseen physics processes without explicitly assuming the underlying distribution. Our results highlight the potential of this method as a step towards a "universal" unfolding tool that reduces dependence on truth-level assumptions, while enabling the unfolding of a wide range of measured distributions with improved adaptability and accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improving the picture of atomic structure in nonoriented polymer domains using the pair distribution function: A study of polyamide 6

Abstract Investigations of the atomic structures within polyamides started over 80 years ago and continue today. These weakly ordered materials diffract X‐rays poorly and typically require postprocessing to obtain idealized samples for structural studies. An important goal remains to develop techniques to study the local structure in its natural state, with atomic resolution, and with sensitivity to subtle changes due to synthesis conditions or other technologically relevant processing procedures. Here, we compare the structures of as‐produced, nonoriented polyamide 6 ([C 6 H 11 NO] n ) from both hydrolytic and anionic processes. A total scattering pair distribution function approach is used to elucidate information about the atomic bonding, molecular conformation, chain packing, crystallite size, and ratio of ordered to disordered domain content. The results are compared with those from standard analytical methods.

Terban, Maxwell W.↗

Measurement of Charmonium Production in $p + p$ and $p + d$ Interactions in the Fermilab SeaQuest Experiment

The Fermilab SeaQuest experiment has measured dimuon events from the interactions of 120GeV proton beam on liquid hydrogen and deuterium targets with dimuon mass between 2 and 9GeV. These dimuon events contain both the Drell-Yan process and the charmonium ($J/\psi$ and $\psi^\prime$) production. Unlike the Drell-Yan process which probes the antiquark distributions in the nucleons, the charmonium production is sensitive to both quark and gluon distributions. SeaQuest has extracted the $\sigma^{pd}/2\sigma^{pp}$ ratio as well as the differential cross sections for charmonium production in the kinematic region of $0.4 < x_F < 0.9$. The $\sigma^{pd}/2\sigma^{pp}$ ratio for charmonium production are found to be significantly different from that of the Drell-Yan process. The measured differential cross sections for charmonium production are compared with theoretical calculations using Color Evaporation Model and Non-Relativistic QCD model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Physics-Informed Sparse Gaussian Process for Probabilistic Stability Analysis of Large-Scale Power System with Dynamic PVs and Loads

This work proposes a physics-informed sparse Gaussian process (SGP) for probabilistic stability assessment of large-scale power systems in the presence of uncertain dynamic PVs and loads. The differential and algebraic equations considering uncertainties from dynamic PVs and loads are reformulated to a nonlinear mapping relationship that allows the application of SGP. Thanks to the nonparametric characteristic of Gaussian process, the proposed framework does not require distributions of uncertain inputs and this distinguishes it from existing approaches. As the original Gaussian process is not scalable to large-scale systems with high dimensional uncertain inputs, this paper develops the SGP with a stochastic variational inference technique. It leads to approximately two orders of complex reduction. A data pre-processing step is also introduced to tackle the coexistence of stable and unstable cases by sample clustering and constructing separate SGPs. The probabilistic transient stability index is analyzed to assess system stability under different uncertain dynamics loads and PVs. Comparisons are performed with the sampling-based, the polynomial chaos expansion-based, and traditional Gaussian process-based methods on the modified IEEE 118-bus and Texas 2000-bus systems under various scenarios, including different levels of uncertainties and the existence of nonlinear correlations among dynamic PVs. The impacts of data quality and quantity issues are also investigated. It is shown that the proposed SGP achieves significantly improved computational efficiency while maintaining high accuracy with a limited number of data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Conversion of Uranium Metal to Uranyl Sulfate Solution

Experiments involving conversion of uranium (U) metal to U 3 O 8 , followed by dissolution to form uranyl sulfate solution, were performed with batches of up to 300 g of U metal. The focus was to identify major U species formed during the oxidation process, determine the particle size distribution of the uranium oxide product, and identify the size of the dissolution vessel needed to accommodate the exothermic reaction during the conversion of U 3 O 8 to uranyl sulfate using 30% hydrogen peroxide and H 2 SO 4 . The information obtained in this study will be used for designing full-scale processes to convert kilogram quantities of U metal to uranyl sulfate solution with a concentration of 300 g U/L.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Cold Spray Additive Manufacturing For New Pipeline Fabrication In Live, Natural Gas Distribution Mains

ULC Technologies (ULC) and the Penn State University Applied Research Lab (PSU ARL) developed a process and approach for rehabilitating live, natural gas distribution pipelines using Cold Spray Additive Manufacturing (CSAM). Robotic inline fabrication of a new pipe will be performed inside a natural gas main without disrupting customers. The material studied was blended with stainless steel which offers corrosion resistance, high strength and compatibility with hydrogen to enable a robust pipeline system that is future proofed. Stainless steel coatings sprayed and tested in the lab showed excellent strength, ductility, and porosity values. ULC initially sought to use methane as the process gas for compatibility with the host pipe, but after evaluating the field and lab challenges, nitrogen was deemed to be more suitable. Early robotic concepts have been developed that indicate technical feasibility. While the technology development originally targeted natural gas distribution mains, market research showed a broader need. Spot repairs performed in natural gas transmission mains may be a more economical approach for reinforcing distribution and transmission mains compared with full pipe-in-pipe rehabilitation. Additive manufacturing offers custom programming, as well as high accuracy and precision. This means custom contours can be manufactured in situ, offering flexibility in the repair solution, such as fabricating internal full circumferential sleeves. The value of the repair can be high at difficult-to-reach locations and in pipes that need reinforcement before the injection of methane-hydrogen blends.

03 NATURAL GAS↗

Building Large-Scale U.S. Synthetic Electric Distribution System Models

Rapid increases in distributed energy resources on distribution systems are prompting research efforts to improve and evaluate electric power distribution algorithms; however, there is a shortage of realistic, large-scale, U.S.-style test systems for the evaluation of such advanced algorithms. Some available tools to build large-scale test systems are of European style, and their application to studies focused on the United States might not be desirable given very different characteristics between the European and U.S. distribution designs. Motivated by this need, this paper develops detailed algorithms to build large-scale U.S. distribution systems and incorporates them in a new Reference Network Model, RNM-US. The approach starts with information from street maps and a catalog with electric equipment that includes power lines, transformers, voltage regulators, capacitors, and switching devices. The paper presents the algorithms through an illustrative case study of the different steps that comprise the process of building a synthetic distribution grid. Finally, the paper presents a medium- and a large-scale data set covering 10 million electrical nodes and 120,000 km of power lines, demonstrating the applicability of the proposed method to build very large-scale synthetic distribution systems.

27 ARPA - Advanced Research Projects Agency-Energy↗

Multistage distributionally robust mixed-integer programming with decision-dependent moment-based ambiguity sets

We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical ones, respectively. For both sets, we show that the subproblem in each stage can be recast as a mixed-integer linear program (MILP). Moreover, we extend the general moment-based ambiguity set in to the multistage decision-dependent setting, and derive mixed-integer semidefinite programming (MISDP) reformulations of stage-wise subproblems. We develop methods for attaining lower and upper bounds of the optimal objective value of the multistage MISDPs, and approximate them using a series of MILPs. We deploy the Stochastic Dual Dynamic integer Programming (SDDiP) method for solving the problem under the three ambiguity sets with risk-neutral or risk-averse objective functions, and conduct numerical studies on multistage facility-location instances having diverse sizes under different parameter and uncertainty settings. Furthermore, our results show that the SDDiP quickly finds optimal solutions for moderate-sized instances under the first two ambiguity sets, and also finds good approximate bounds for the multistage MISDPs derived under the third ambiguity set. We also demonstrate the efficacy of incorporating decision-dependent distributional ambiguity in multistage decision-making processes.

97 MATHEMATICS AND COMPUTING↗

Sources of stochasticity in the growth of cloud droplets: supersaturation fluctuations versus turbulent transport

The role played by fluctuations of supersaturation in the growth of cloud droplets is examined in this study. The stochastic condensation framework and the three regimes of activation of cloud droplets – namely, mean-dominant, fluctuation-influenced, and fluctuation-dominant, are used for analyzing the data from high-resolution large-eddy simulations of the Pi convection-cloud chamber. Based on a detailed budget analysis the significance of all the terms in the evolution of the droplet size distribution equation is evaluated in all three regimes. The analysis indicates that the mean-growth rate is a dominant process in shaping the droplet size distribution in all three regimes. Turbulence introduces two sources of stochasticity, turbulent transport and particle lifetime, and supersaturation fluctuations. The transport of cloud droplets plays an important role in all three regimes, whereas the direct effect of supersaturation fluctuations is primarily related to the activation and growth of the small droplets in the fluctuation-influenced and fluctuation-dominant regimes. Here, we compare our results against the previous studies (experimental and theory) of the Pi chamber, and discuss the limitations of the existing models based on the stochastic condensation framework. Furthermore, we extend the discussion of our results to atmospheric clouds, and in particular focus on recent adiabatic turbulent cloud parcel simulations based on the stochastic condensation framework, and emphasize the importance of entrainment/mixing and turbulent transport in shaping the droplet size distribution.

54 ENVIRONMENTAL SCIENCES↗

A Grand Challenge "Uncertainty Project" to Accelerate Advances in Earth System Predictability: AI-Enabled Concepts and Applications

This proposal is emerging from GISS ModelE3 ESM development in the area of cloud physics, so we begin with an example of research needs/gaps from that work. Here, some of our greatest development concerns arise where we lack fundamental process-level understanding, as in ice formation. Namely, it is currently unclear what is the main process that is forming the majority of ice crystals in commonly occurring convection, apparently via secondary ice production at warm temperatures. We are keenly awaiting laboratory data for candidate mechanisms, which is not yet in hand to crucially establish their efficiency. Our progress is also hampered by a lack of uncertainty characterization in currently available measurements of ice crystal number size distributions. Furthermore, the same multiplication process may be responsible for a majority of ice crystals in many extratropical mixed-phase clouds, whose variable representation in CMIP6 ESMs may be a leading cause of differences in cloud phase feedback and ECS. Yet we have been required to deliver an ESM with the cloud physics knowledge at hand. The proposed grand challenge project is AI-enabled via application of machine learning (ML) to climate model and observational data streams (focal area 3), and applications include AI-guided observing system design and model/component/parameterization selection (areas 1 and 2). The project is structurally agnostic as to whether model or observing system components use AI approaches or not, but uncertainties must be estimated and propagatable in both.

58 GEOSCIENCES↗

2 Kelvin helium distribution system for the Electron Ion Collider’s 10 o’clock satellite refrigerator

The Electron-Ion Collider (EIC) at Brookhaven National Laboratory (BNL) will involve superfluid helium cooling of superconducting magnets and Superconducting Radio Frequency (SRF) cavities at several sites around the existing Relativistic Heavy Ion Collider (RHIC) accelerator tunnel. While the majority of the cooling power for these loads is provided by BNL’s central cryogenic plant, Jefferson Lab is designing satellite equipment which augments the central plant and enables 2 Kelvin operation. The 2 K cryogenic distribution system for the collider’s 10 o’clock location (Interaction Region 10 or IR10) includes all necessary interfaces to the IR10 Satellite Refrigerator, to the overall EIC cryogenic distribution system, and to 12 SRF cryomodules for the electron and hadron storage rings. In addition to providing the required cooling capacities in all operating modes, the IR10 2 K cryogenic distribution system also stabilizes the supply temperature and enables safe connection and disconnection of individual IR10 cryomodules. Moreover, the layout of the IR10 2 K cryogenic distribution system copes with challenging spatial constraints and adapts to the process configuration and routing of existing RHIC cryogenic distribution components which will be re-used for EIC. This paper gives a full overview of the IR10 satellite cryogenic distribution system design, and highlights some of the challenges encountered.

Laverdure, Nathaniel [Thomas Jefferson National Ac↗

In situ high-temperature 3D imaging of the damage evolution in a SiC nuclear fuel cladding material

Silicon carbide (SiC)-based nuclear fission fuel rod cladding has been considered as one of the possible designs for accident tolerant fuels. It is in the form of a SiC fibre reinforced SiC matrix composite tube (SiC f -SiC m ) with monolithic SiC outer and/or inner coating layers. This study focuses on the deformation and fracture processes in this material using in situ X-ray micro-computed tomography (XCT) at room temperature (RT) and 1200 °C in an inert gas environment in a C-ring compression loading configuration. Prior to testing, local properties and residual stresses were characterised using nanoindentation and Raman spectroscopy since they can impact the mechanical behaviour of the material. The 3D strain distribution, crack formation and propagation processes including the toughening mechanisms (e.g., crack deflection, micro-cracking, crack bridging and bifurcation) are investigated in the coating and underlying composites at RT and 1200 °C. There is no particular sequence which toughening mechanism occurs first – this is very different from the conventional toughening theory in ceramic-matrix composites under uniaxial tension loading. Indeed, no evidence of fibre pull-out or fibre fracture was observed in this SiC f -SiC m nuclear cladding material in the current C-ring compression configuration. The correlation between local measurements and bulk mechanical behaviour are discussed.

3D imaging↗

Barium stars as tracers of s -process nucleosynthesis in AGB stars

Barium (Ba) stars help to verify asymptotic giant branch (AGB) star nucleosynthesis models since they experienced pollution from an AGB binary companion and thus their spectra carry the signatures of the slow neutron capture process (s process). For a large number (180) of Ba stars, we searched for AGB stellar models that match the observed abundance patterns. We aim to uncover any systematic deviations of the sample abundances from the predictions of the nucleosynthesis models. We employed three machine learning algorithms as classifiers: a Random Forest method, developed for this work, and the two classifiers used in our previous study. Compared to that work, we also expanded our observational sample with 11 Ba stars available in the supersolar metallicity range. We studied the statistical behaviour of the different s-process elements in the observational sample to investigate if the AGB models systematically under- or overpredict the abundances observed in the Ba stars and show the results in the form of violin plots of the residuals between spectroscopic abundances and model predictions. We inspected the correlations between the observed [Fe/H], the s-process elemental abundances, and the residuals. We employed the [Zr/Fe] and [Nb/Fe] abundances as a thermometer to constrain the operational temperature that rules the production of these elements in the sample stars, assuming a steady-state s process. We also investigated the mass distribution of the identified polluter AGB stars and the behaviour of the δ parameter, which describes the fraction of accreted AGB material relative to the Ba star envelope. We find a significant trend in the residuals that implies an underproduction of the elements just after the first s-process peak (Nb, Mo, and Ru) in the models relative to the observations. This may originate from a neutron-capture process (e.g. the intermediate neutron-capture process, i process) not yet included in the AGB models of metallicity from solar to roughly 1/5 solar, corresponding to the range of the Ba stars. Correlations are found between the residuals of these peculiar elements, suggesting a common origin for the deviations from the models. In addition, there is a weak metallicity dependence of the residuals of these elements. The s-process temperatures derived with the [Zr/Fe] – [Nb/Fe] thermometer have an unrealistic value for the majority of our stars. The most likely explanation is that at least a fraction of these elements are not produced in a steady-state s process, and instead may be due to processes not included in the AGB models. The mass distribution of the identified models confirms that our sample of Ba stars was polluted by low-mass AGB stars (< 4 M ⊙ ). Most of the matching AGB models require low accreted mass, but a few systems with high accreted mass are needed to explain the observations.

79 ASTRONOMY AND ASTROPHYSICS↗

Understanding extraction limits of plasma cathodes with experiment and simulation

The project is focused on computations for enhanced ionization near the exit orifice of a plasma cathode and how the cathode extraction electrode geometry and stray magnetic field structure influence available extractable current. The computational effort will take place at the Princeton Collaborative Research Laboratory (PCRF). The specific modeling platform to be utilized from PCRF is the electrostatic direct implicit particle in cell (EDIPIC) code. EDIPIC will be used to study ionization processes in the electron extraction region of the cathode. The control of electron energy is a key aspect to minimizing power losses in the plasma. Exiting electrons ionize gas leaving the orifice and in the process produce the dense plasma from which large amounts of current can be extracted. Project activities include studying processes that determine the energy distribution of the exiting electrons thus providing insight into how to optimize the source. The model will be validated and developed using experimental measurements as warranted. The familiarity and expertise of the team at PPPL with this type of plasma and the challenges posed greatly enhances the likelihood of gaining insight into the extraction sheath under the duration of the proposed activity. The effort is expected to shed a great deal of insight into electron extraction processes and pathways for optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

EmSense: A High-Resolution Emulated Sensor for Experiments with the Smart Grid and Distributed Ledger Technology

This work involves the development of a device - EmSense (“Emulated Sensor”) - that emulates a high-resolution sensor for a power grid. The device collects raw current and voltage sensor data which derive from ORNL's signature library. This library is a dataset that ORNL curates from many different sources that include power systems from various utilities. The EmSense packages the data from the library in the form of IEC 61850 Sampled Value (SV) packets and then broadcasts these SV packets on the network. In another mode, EmSense can generate artificial sinusoidal data that appears as waveforms for voltage and current signals. EmSense has an internal algorithm for determining the period of a signal based on the data so that the period can be specified as a variable in the IEC 61850 packets. The purpose of EmSense is to allow for experimentation with the Dark Net Infrastructure where a variety of power line sensors must be represented along with their typical communication traffic. The EmSense device was developed in coordination with the software for receiving and processing the packets in the Distributed Ledger Technology (DLT) framework of the DarkNet Project. This receiving software must have a methodology for dealing with information of high velocity, variety, and volume. Experimenting with EmSense facilitates the development of such software. The results showed that the DLT framework and the trust-anchoring approach managed to process a large flow of traffic even with up to six instances of EmSense device broadcasting data. This was achieved without overfilling packet queues in the memory of the actual hardware of the DLT devices or causing the Central Processing Unit (CPU) of the hardware to be overwhelmed. The DLTs were also able to store the data in a compact and useful form for later analysis and archival purposes.

Werth, Aaron↗