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At least 433 records · Page 24

Support Vector Machines for Classification of Direct Energy Deposition Standoff Distance for Improved Process Control

A critical factor in the implementation of direct energy deposition is the ability to maintain the standoff distance between the nozzle and the build surface, as this influences powder capture efficiency and overall part quality. Due to process-related variations, layer height may vary, causing unintended variation in standoff distance and poor build quality. While prior work has utilized contact probing to qualify standoff distance during processing, in situ methods for qualification of standoff distance are of major interest. The present work seeks to understand efficacy of image-based methods for classifying standoff distance variation in real-time using support vector machines (SVMs). It was hypothesized that the size of the melt pool and the amount of spatter will have significant correlations with deviations in the standoff distance; thus, SVMs were used on a dataset that is comprised of morphological features of melt pool size and image entropy. The SVM model was used to classify melt pool images into categories according to standoff distance variation from nominal. K-folds cross validation was used to find the optimal hyperparameters for the SVM model. To understand the impact of the selected features on the classification performance and inference speed, multiple models were trained with differing numbers of included features. Results for classification score, inference time, and image preprocessing/feature extraction from these data are reported. The present results show that the SVM model was able to predict the standoff distance classification with an accuracy of 97 percent and a speed of 0.122 s per image, making it a viable solution for real-time control of standoff distance.

Klesmith, Zoe↗

Development of Methane Emissions Model to Assess Fuel Recovery Potential at Gas Well Sites Using On Site Compression

The U.S. natural gas production and consumption has increased 85.5% since 2005 primarily due to the unconventional production methods of horizontal drilling and hydraulic fracturing. Natural gas used as a fuel has a lower greenhouse gas (GHG) footprint than coal and petroleum due to lower Carbon Dioxide (CO2) emissions when combusted. However, the “greener” benefit to natural gas may be negated by leaks in production and transmission systems. Methane (CH4), the primary hydrocarbon in natural gas, has an estimated Global Warming Potential (GWP) of 28-36 over 100 years, meaning it can absorb 28-36 more energy than CO2 which has a GWP of 1.0. Natural gas well sites are prone to methane emissions, or leaks and irregular gas releases, vented to atmosphere throughout production and transmission. The U.S. Department of Energy (DOE) and the National Energy Technology Laboratory (NETL) has recently granted West Virginia University (WVU) funding under agreement DE-FOA-0002005, to “Advance technologies to mitigate methane emissions and increase the efficiency of the natural gas transportation infrastructure”. As part of this funding WVU was tasked with identifying and quantifying sources of methane emissions at unconventional well sites, processing this data, and developing a system to recapture these emissions. A 0-D Simulink model was developed, utilizing standardized methodologies, data from previously conducted studies, as well as collected data from well sites in the Marcellus shale play region. The model was developed to predict emission rates from various components at natural gas well sites as well as the potential to utilize these emissions as fuel for the natural gas powered compressor engines on-site. This model was utilized to run high, medium, and low cases for four identified emission sources, engine size, pneumatic controller count, liquid level production which dictates tank emissions, and compressor packing vent emissions. Due to discrepancies in transient tank emission data, a high and low emission factor for tanks was used, resulting in two sets of 81 executed cases, and 162 unique cases of total site emissions and potential for fuel consumption. Each of the cases were run over 86,400 seconds at a 1 Hz, representative of a full 24 hour day of operation. The fuel consumption offset an average of 557% of fuel consumption on an energy density basis across all 81 cases with the high tank emission factor with a maximum offset of 2334%. The fuel consumption offset was an average of 82.9% for all 81 cases with the low tank emission factor with a maximum offset of 337%. This study highlights flaws in the use of publicly available methane number calculations to determine natural gas’s suitability as an engine fuel as well as the lack of public data for transient liquid storage tank emissions.

03 NATURAL GAS↗

Multiobjective Optimal Controlled Variable Selection for a Gas Turbine–Solid Oxide Fuel Cell System Using a Multiagent Optimization Platform

Hybrid gas turbine–fuel cell systems have immense potential for high efficiency in electrical power generation with cleaner emissions compared with fossil-fueled power generation. We report a systematic controlled variable (CV) selection method is deployed for a hybrid gas turbine–fuel cell system in the HyPer (hybrid performance) facility at the U.S. Department of Energy’s National Energy Technology Laboratory (NETL) for maximizing its economic and control performance. A three-stage approach is used for the CV selection comprising a priori analysis, multiobjective optimization, and a posteriori analysis. The a priori analysis helps to screen off several candidate CVs, thus reducing the size of the combinatorial optimization problem for multiobjective CV selection. For optimal CV selection, a transfer function model of the HyPer facility is identified. By considering several candidate models, the final transfer function model is selected using Akaike’s Final Prediction Error criterion. Experimental data from the HyPer facility are used to estimate the noise in the measurement data. For solving the combinatorial multiobjective optimization problem for CV selection, a multiagent optimization platform comprising simulated annealing, genetic algorithm, and efficient ant colony optimization algorithms is used. Pareto-optimal CV sets exhibit a high trade-off between the economic and control objective. The a posteriori analysis is undertaken for several top Pareto-optimal CV sets. An optimal CV set is selected that shows the best compromise between process economics and controllability under both nominal and off-design conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Implementing a Laser Stabilization System for Trapping Ca+ Ions: an Internship Reflection

At Lawrence Livermore National Laboratory, I contributed to a project developing 3D printed micro ion traps for quantum computing. I designed, implemented, and assessed a laser stabilization system that locked lasers to the frequencies required for calibrating our High Finesse WS8-10 wavelength meter and for laser cooling and trapping of Ca+ ions. I also programmed a Python interface for hardware communication, data collection, and statistical analysis. Additionally, I optimized and aligned laser beam paths, and I implemented a closed digital feedback loop using Proportional, Integral, and Derivative (PID) control parameters. I analyzed both the long-term and short-term behavior of our locked lasers and adjusted PID parameters to enhance performance. Furthermore, I used COMSOL to simulate the capacitance of a linear Paul trap design and predict our trap’s performance. The procedures I developed for the interface, analysis, and simulations will continue to support the ion trapping experiment after my appointment. I strengthened my skills in data analysis, Python coding, and optical alignment for laser systems. My confidence as a researcher grew, particularly in communicating my research. This experience taught me the importance of careful planning and consideration in research and solidified my desire to continue exploring novel quantum technology as an undergraduate

42 ENGINEERING↗

Reactivity-initiated accidents in two pressurized water reactor high burnup core designs

Here, this paper presents a safety analysis of two proposed core loadings for 24-month Pressurized Water Reactor (PWR) fuel cycles. This analysis focuses on reactivity-initiated accidents (RIAs) and evaluates core safety performance impacts of rod-averaged burnup limits up to 75 GWD/MTU and less than 7 % enriched UO 2 . The capabilities of Polaris, PARCS, and RELAP5-3D are leveraged to evaluate the core neutronic and thermal–hydraulic behavior for normal-operation, uncontrolled control rod withdrawal (CRW) transients, and control rod ejection (CRE) accidents. The two core designs are compared to identify features of realistic high burnup/extended enrichment core design approaches which have significant safety impact, identify experimental data needs for high-fidelity predictive modeling, and provide recommendations for future high burnup core designs. The first core design evaluated in this study was developed by Southern Nuclear Company and used an ZrB 2 Integral Fuel Burnable Absorber (IFBA) and B 4 C Wet-Annular Burnable Absorber (WABA)-based burnable poison strategy. The second core design assessed in this work used a Gd 2 O 3 -doped UO 2 burnable poison, similar to that used in boiling water reactors or French PWRs. Results indicate that fuel thermal limits are maintained for limiting CRW and hot full power (HFP) CRE transients. Cladding failure is predicted for the highest energy deposition rods in each core during limiting hot zero power (HZP) CRE accidents (where maximum radially averaged enthalpy exceeds 120 cal/g), though licensing may be permissible with a limited number of failed rods. While concerns exist regarding high critical boron concentration during steady state for the IFBA core and large plenum pressures for the gadolinia core design, the analysis demonstrates adequate safety performance during limiting RIA accident scenarios for two representative high burnup core designs. Design changes limiting plenum pressures and implementation of accident tolerant fuel (ATF) cladding features which minimize hydriding and susceptibility to pellet-cladding mechanical interaction (PCMI) are recommended for future high burnup fuel concepts. To support the technical basis for burnup limit increases, high-fidelity fuel performance models are needed to address physical effects not considered in this analysis, and high burnup irradiated fuel tests are required to extend applicability of the fuel failure limits and validate existing and future models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Multi-decadal variation of ENSO forecast skill since the late 1800s

Diagnosing El Niño-Southern Oscillation (ENSO) predictability within operational forecast models is hindered by computational expense and the need for initialization with three-dimensional fields generated by global data assimilation. We instead examine multi-year ENSO predictability since the late 1800s using the model-analog technique, which has neither limitation. We first draw global coupled model states from pre-industrial control simulations, from the Coupled Model Intercomparison Project Phase 6, that are chosen to initially match observed monthly sea surface temperature and height anomalies in the Tropics. Their subsequent 36-month model evolution are the hindcasts, whose 20th century ENSO skill is comparable to twice-yearly hindcasts generated by a state-of-the-art European operational forecasting system. Despite the so-called spring predictability barrier, present throughout the record, there is substantial second-year ENSO skill, especially after 1960. Overall, ENSO exhibited notably high values of both amplitude and skill towards the end of the 19th century, and again in recent decades.

54 ENVIRONMENTAL SCIENCES↗

Imaging of a fluid injection process using geophysical data — A didactic example

In many subsurface industrial applications, fluids are injected into or withdrawn from a geologic formation. It is of practical interest to quantify precisely where, when, and by how much the injected fluid alters the state of the subsurface. Routine geophysical monitoring of such processes attempts to image the way that geophysical properties, such as seismic velocities or electrical conductivity, change through time and space and to then make qualitative inferences as to where the injected fluid has migrated. The more rigorous formulation of the time-lapse geophysical inverse problem forecasts how the subsurface evolves during the course of a fluid-injection application. Using time-lapse geophysical signals as the data to be matched, the model unknowns to be estimated are the multiphysics forward-modeling parameters controlling the fluid-injection process. Properly reproducing the geophysical signature of the flow process, subsequent simulations can predict the fluid migration and alteration in the subsurface. The dynamic nature of fluid-injection processes renders imaging problems more complex than conventional geophysical imaging for static targets. This work intents to clarify the related hydrogeophysical parameter estimation concepts.

58 GEOSCIENCES↗

Machine-Guided Design of Oxidation-Resistant Superconductors for Quantum Information Applications

Decoherence in superconducting qubits has long been attributed to two-level systems arising from the surfaces and interfaces present in real devices. A recent significant step in reducing decoherence was the replacement of superconducting niobium by superconducting tantalum, resulting in a tripling of transmon qubit lifetimes (T1). The identity, thickness, and quality of the native surface oxide, is thought to play a major role, as tantalum only has one oxide whereas niobium has several. Here we report the development of a thermodynamic metric to rank materials based on their potential to form a well-defined, thin, surface oxide. We first computed this metric for known binary and ternary metal alloys using data available from the Materials Project and experimentally validated the strengths and limits of this metric through the preparation and controlled oxidation of eight known metal alloys. Then we trained a convolutional neural network to predict the value of this metric from atomic composition and atomic properties. This allowed us to compute the metric for materials that are not present in the Materials Project, including a large selection of known superconductors, and, when combined with Tc, allowed us to identify new candidate superconductors for quantum information science and engineering (QISE) applications. We tested the oxidation resistance of a pair of these predictions experimentally. Our results are expected to lay the foundation for the tailored and rapid selection of improved superconductors for QISE.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Evaluation of High-Temperature Martensitic Steels for Heavy-Duty Diesel Piston Applications

Five different commercially available high-temperature martensitic steels were evaluated for use in a heavy-duty diesel engine piston application and compared to existing piston alloys 4140 and microalloyed steel 38MnSiVS5 (MAS). Finite element analyses (FEA) were performed to predict the temperature and stress distributions for severe engine operating conditions of interest, and thus aid in the selection of the candidate steels. Complementary material testing was conducted to evaluate the properties relevant to the material performance in a piston. The elevated temperature strength, strength evolution during thermal aging, and thermal property data were used as inputs into the FEA piston models. Additionally, the long-term oxidation performance was assessed relative to the predicted maximum operating temperature for each material using coupon samples in a controlled-atmosphere cyclic-oxidation test rig. A current commercial steel piston alloy, quenched and tempered martensitic steel 4140, was tested in a single-cylinder research engine for a baseline oxidation and mechanical performance assessment using an abbreviated (50h) durability test plan. The predicted suitability of a candidate piston material in an engine is primarily based on its elevated temperature strength, oxidation resistance, and the complex influence of thermal conductivity, the latter of which is substantially lower for the candidate materials considered in this research relative to the traditional alloys. Although the lower thermal conductivity causes the candidate alloys to operate in higher temperature ranges under identical engine operating conditions and piston geometries, increasing the likelihood of partially or completely negating their strength and oxidation resistance advantages relative to 4140 and MAS steels, this evaluation indicates that several of the candidate piston alloys are predicted to enable improved oxidation resistance under more severe engine operating conditions relative to the current piston materials. However, further evaluation is required to determine if the elevated temperature fatigue strength and durability of these alloys are suitable for more severe engine conditions.

36 MATERIALS SCIENCE↗

Responsible Adoption of Artificial Intelligence (AI) in Electric Grid Operations

The future of the grid will be powered by AI—or undermined by it. Artificial intelligence is rapidly reshaping grid operations, improving fault detection, forecasting accuracy, and real-time optimization. As AI systems move closer to operational decision loops, however, they introduce new consequence pathways: expanded attack surfaces, model integrity risks, regulatory exposure, and human-automation challenges. This talk presents a consequence-driven framework for deploying AI responsibly in the electric grid. Attendees will gain practical strategies to strengthen resilience, boost reliability, and deploy AI securely — ensuring the grid of the future is not only smarter but safer.

25 - ENERGY STORAGE↗

Comparison of structurally diverse simulation models for prediction of epidemic outcomes caused by a long-distance dispersed pathogen

Long-distance dispersal (LDD) pathogens pose substantial challenges for epidemic control due to their ability to generate new infection foci at great distances. While various modeling approaches have been developed to understand and manage such outbreaks, little work has compared how models of different structures behave under shared conditions. Here, in this study, we compare four structurally distinct epidemiological models — EPIMUL, GEMF, PoPS, and Warwick — each adapted to simulate the spread of wheat stripe rust (WSR), a wind-dispersed LDD pathogen, under identical epidemiological parameters and dispersal kernel. Using data from a controlled field experiment, we evaluate the ability of each model to replicate disease prevalence under nine intervention scenarios that vary in timing and culling area. While the models differ substantially in design — ranging from spatial grid-based to network-based and raster-based frameworks — the shared dispersal kernel allowed for close alignment in their predictions. All models accurately captured general epidemic trends, particularly the strong effect of early intervention on disease suppression. We qualitatively compared their behavioral responses across scenarios and also evaluated an ensemble prediction by averaging across model outputs. Our findings highlight how integrating shared epidemiological components into distinct modeling frameworks can improve consistency and accuracy, while reinforcing the importance of early culling in managing LDD pathogen outbreaks.

Dispersal kernel↗

Integrative teaching of metabolic modeling and flux analysis with interactive python modules

Abstract The modeling of rates of biochemical reactions—fluxes—in metabolic networks is widely used for both basic biological research and biotechnological applications. A number of different modeling methods have been developed to estimate and predict fluxes, including kinetic and constraint‐based (Metabolic Flux Analysis and flux balance analysis) approaches. Although different resources exist for teaching these methods individually, to‐date no resources have been developed to teach these approaches in an integrative way that equips learners with an understanding of each modeling paradigm, how they relate to one another, and the information that can be gleaned from each. We have developed a series of modeling simulations in Python to teach kinetic modeling, metabolic control analysis, 13C‐metabolic flux analysis, and flux balance analysis. These simulations are presented in a series of interactive notebooks with guided lesson plans and associated lecture notes. Learners assimilate key principles using models of simple metabolic networks by running simulations, generating and using data, and making and validating predictions about the effects of modifying model parameters. We used these simulations as the hands‐on computer laboratory component of a four‐day metabolic modeling workshop and participant survey results showed improvements in learners' self‐assessed competence and confidence in understanding and applying metabolic modeling techniques after having attended the workshop. The resources provided can be incorporated in their entirety or individually into courses and workshops on bioengineering and metabolic modeling at the undergraduate, graduate, or postgraduate level.

Kaste, Joshua A. M.↗

Leveraging artificial intelligence and advanced food processing techniques for enhanced food safety, quality, and security: a comprehensive review

Artificial intelligence is emerging as a transformative force in addressing the multifaceted challenges of food safety, food quality, and food security. This review synthesizes advancements in AI-driven technologies, such as machine learning, deep learning, natural language processing, and computer vision, and their applications across the food supply chain, based on a comprehensive analysis of literature published from 1990 to 2024. AI enhances food safety through real-time contamination detection, predictive risk modeling, and compliance monitoring, reducing public health risks. It improves food quality by automating defect detection, optimizing shelf-life predictions, and ensuring consistency in taste, texture, and appearance. Furthermore, AI addresses food security by enabling resource-efficient agriculture, yield forecasting, and supply chain optimization to ensure the availability and accessibility of nutritious food resources. This review also highlights the integration of AI with advanced food processing techniques such as high-pressure processing, ultraviolet treatment, pulsed electric fields, cold plasma, and irradiation, which ensure microbial safety, extend shelf life, and enhance product quality. Additionally, the integration of AI with emerging technologies such as the Internet of Things, blockchain, and AI-powered sensors enables proactive risk management, predictive analytics, and automated quality control. By examining these innovations' potential to enhance transparency, efficiency, and decision-making within food systems, this review identifies current research gaps and proposes strategies to address barriers such as data limitations, model generalizability, and ethical concerns. These insights underscore the critical role of AI in advancing safer, higher-quality, and more secure food systems, guiding future research and fostering sustainable food systems that benefit public health and consumer trust.

AI↗

Review of rotating wing dynamic stall: Experiments and flow control

Dynamic stall has been a technical challenge and a fluid dynamical subject of interest for more than fifty years; but in the last decade significant advances have been made in the understanding, prediction, modeling, and control of dynamic stall on rotors. This paper provides a summary of the state of the art of dynamic stall experiments and future directions in the understanding of dynamic stall on rotors. Experimental data sets are discussed, as well the direction of future research for control of dynamic stall. Coordinated testing between airfoils and rotating blades, as well as close integration between computational and experimental studies were found to be productive approaches. Advanced analysis methods, including statistical methods, modal representations, and artificial intelligence methods have led to significant advances in the understanding of dynamic stall. Investigations of dynamic stall control devices have allowed many useful targeted investigations of the transition to separated flow, but have not yet resulted in a commercially implemented device.

42 ENGINEERING↗

Phosphoproteomics Modifications in Women with Rheumatoid Arthritis─Application of Web-Based Software to Enhance Data Visualization

Individuals with rheumatoid arthritis (RA) are at increased risk of functional disability, cardiovascular disease, and obesity, all of which are influenced by dysregulated skeletal muscle. Here, this pilot study aims to identify phosphoproteomics changes in RA skeletal muscle and visualize modifications through development of a web-based app designed to promote user-friendly data interpretation and visualization. NanoLC–MS/MS analysis was performed on vastus lateralis biopsies from three women with RA and matched healthy controls. Differential analysis was performed using the Limma R package. Kinase substrate enrichment analysis (KSEA) predicted changes in kinase activity. RA muscle displayed 35 upregulated and 60 downregulated phosphosites, including the cytoskeletal proteins TTN (Ser33201, Ser33013, Ser20925), NEB (Ser2219, Thr254, Ser33013, Ser20925), FLNA (Ser1459), and LASP1 (Ser146). Compared to healthy controls, KSEA predicted decreased activity of several kinases in RA muscle, including PRKACA and CDKs. All such changes were visualized by use of our web-based app. Overall, phosphoproteome analysis reveals signaling alterations in RA skeletal muscle linked to cytoskeletal proteins, representing candidate disease biomarkers; these modifications can be explored through use of our web-based software.

phosphoproteomics↗

Biogeochemistry of upland to wetland soils, sediments, and surface waters across Mid-Atlantic and Great Lakes coastal interfaces

Transferable and mechanistic understanding of cross-scale interactions is necessary to predict how coastal systems respond to global change. Cohesive datasets across geographically distributed sites can be used to examine how transferable a mechanistic understanding of coastal ecosystem control points is. To address the above research objectives, data were collected by the EXploration of Coastal Hydrobiogeochemistry Across a Network of Gradients and Experiments (EXCHANGE) Consortium – a regionally distributed network of researchers that collaborated on experimental design, methodology, collection, analysis, and publication. The EXCHANGE Consortium collected samples from 52 coastal terrestrial-aquatic interfaces (TAIs) during Fall of 2021. At each TAI, samples collected include soils from across a transverse elevation gradient (i.e., coastal upland forest, transitional forest, and wetland soils), surface waters, and nearshore sediments across research sites in the Great Lakes and Mid-Atlantic regions (Chesapeake and Delaware Bays) of the continental USA. The first campaign measures surface water quality parameters, bulk geochemical parameters on water, soil, and sediment samples, and physicochemical parameters of sediment and soil.

54 ENVIRONMENTAL SCIENCES↗

Knowledge-Informed Uncertainty-Aware Machine Learning for Time Series Forecasting of Dynamical Engineered Systems

The high complexity and multiscale nature of many engineered systems—such as those in nuclear power plants—make representing and forecasting their dynamic behavior challenging. Physics-based models can be overly complex and computationally intractable, whereas machine learning (ML) tools are often data-hungry and prone to unphysical solutions. This study proposes a knowledge-informed ML-aided hybrid residual modeling approach that offers accurate and efficient time series forecasting for the operation of dynamical engineered systems. Hybrid residual modeling entails a baseline solution from domain knowledge and known physics expressions about the system dynamics integrated with an ML model to capture undiscovered information from the mismatch (i.e., residuals) between true states from measurements and baseline-predicted outputs. This study further quantifies the ML model uncertainty to provide trustworthy solutions. Real-time operational data from thermal-hydraulic flow loops of the cryogenic moderator system in Oak Ridge National Laboratory’s Spallation Neutron Source facility were used to demonstrate the potential of knowledge-informed uncertainty-aware ML in real-world applications. The state variables of the cryogenic helium loop were modeled with (1) first principles–based system identification (sysID), (2) long short-term memory (LSTM) neural network, and (3) hybrid sysID (baseline) + LSTM (residual). The superior predictive capability of the sysID+LSTM model versus stand-alone sysID and LSTM is confirmed by average performance metrics and individual data points across different prediction horizons. By creating a robust representation of the underlying physical system, the widely applicable hybrid residual modeling approach will enable the future development of digital twins for performance prediction, prognostics, and operation control.

Zhao, Xingang↗

Real-Time Optimization Workflow Status Update

Economically optimal and safe operation of integrated energy systems (IES) requires optimization at many different time scales. A real-time optimization (RTO) workflow will attempt to maximize revenue and minimize operational costs on a time scale of minutes to hours. Such a workflow requires the use of a digital twin (DT), which is a virtual representation of a physical system. The DT is updated using real-time data from the physical system, and serves as a model in an optimization framework. The optimization results are then sent back to the physical system to complete the loop. This report details the progress made in developing building blocks for a DT/RTO framework. The Risk Analysis Virtual Environment (RAVEN) platform within the Framework for Optimization of Resources and Economics (FORCE) tool suite can perform many of the tasks required for building a DT and performing RTO. The first item of this report details RAVEN enhancements that enable RAVEN workflows to be run in various environments. Data communication between the physical system and its DT is essential for successful RTO. This includes preprocessing real-time data, loading data into a data warehouse, and querying the stored data. The second section of this report describes the progress made in implementing an adapter in Python in order for Deep Lynx to handle the data communication. Typical dispatch optimization frameworks are built on linear programming (LP). The prototype RTO workflow developed in this report uses an LP problem as a part of a receding-horizon- or economic model predictive control (EMPC) based optimization. The third section of this report details the framework of an RTO workflow in which the system consists of a simple electrical storage device. A DT can be built from a reduced-order model (ROM). Integrating a ROM into a typical LP optimization framework has been challenging because most optimization packages require the user to write algebraic expressions for the system model. The final section of this report shows how an externally built RAVEN ROM can be integrated in an RTO framework by using the Python package Pyomo. This demonstrates the RTO workflow capability from a software-only perspective and is an important step in demonstrating the capability to implement an RTO workflow for a physical system.

97 MATHEMATICS AND COMPUTING↗