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At least 127 records · Page 7

Distributed Magnetic Field and Temperature Monitoring for Superconducting Radio Frequency Cavities

The overall objective of the proposed Phase I program was to design, construct and demonstrate a fiber optic sensing system capable of providing temperature and magnetic field measurements with an enhanced spatial resolution that can be implemented over a large surface area (cryomodules) to survey superconducting radio frequency cavities and magnets. A magnetic field sensor capable of detecting fluxes on the order of 1 μT is required to detect the distribution of trapped flux on the cavity surface. A unique distributed magnetic field sensor was successfully designed and constructed to demonstrate the detection of magnetic fluxes less than 500 nT. The sensor leveraged the ultra-high sensitivity of Sentek’s picoDAS to measure the magnetostriction induced vibrations in a commercially available Metglas 2605 SC ribbon that was in physical contact with sensing fiber. Static magnetic fields were detected by applying an alternating current a copper wire proximate to the Metglas 2605SC ribbon to create an AC bias magnetic field. In an alternative approach, an AC bias magnetic field was applied to a special magnetic field sensing fiber with Metglas 2605SC cladding successfully detect a magnetic field flux of a 3 μT. Exhaustive testing was performed to characterize the dependency of sensor response on the direction of the applied magnetic field. Although the special sensing fiber based magnetic field sensor did not exhibit an observable dependence on the direction of the magnetic field, the Metglas 2605SC ribbon sensor exhibited a clear directional dependence. A wide variety of polymer materials were evaluated to enhance the temperature response of an FBG based sensor at cryogenic temperatures. The processing and performance challenges provided the motivation to develop a new simple cryogenic temperature sensor that uses a commercially available fiber optic splice protector. The EVA hot melt tube that becomes adhered to the optical fiber and the polyolefin outer tube that shrinks upon heating in the fusion splicer heater provide the high thermal expansion coefficient necessary to impart a significant strain on the FBG when exposed to cryogenic temperatures. The temperature sensitivity (Δ𝜆𝐵𝑟𝑎𝑔𝑔~ 62 𝑝𝑝𝑚/℃) of the FBG-based sensor was on par with the best reported to date. The simple design, use of readily available cost-effective materials, and well-established processing techniques lends this approach to the creation of hundreds to thousands of temperature sensors on one single optical fiber length. The inherently small form factor also allows for co-location with the distributed magnetic field sensor. In preparation for field testing of the prototype sensing system at the Jefferson Labs in potential Phase II program, several different cable designs were evaluated to package the sensors. The preliminary successful demonstration of fully functional sensing cables provides the foundation for subsequent development efforts to advance the Technology Readiness Level of the technology. The technical feasibility of the proposed approach was successfully demonstrated in this Phase I effort.

43 PARTICLE ACCELERATORS↗

An Evaluation and Qualification of U.S.-Based Research Reactors for Irradiation Capabilities Supporting Advanced Nuclear Systems

Irradiation experiments are a prerequisite for evaluating nuclear reactor system designs, analyzing the performance of these systems, and obtaining licenses. Likewise, irradiation facilities are necessary for producing the radioisotopes used in industrial and medical applications. Recent developments in modeling and simulation capabilities and advancements in computational resources have further enabled the design of irradiation experiments for evaluating radiation-induced phenomena and determining nuclear fuel, material, and system design and safety criteria pertaining to both normal and accident scenarios. These computational tools and models require comprehensive experimental datasets acquired under prototypic radiation conditions—for exploring material and system performance under the uniquely harsh environments found in nuclear reactors—to enable verification and validation for qualification and licensing purposes. However, qualification of irradiation experimental facilities, primarily research and test reactors (RTRs), necessitates that their performance be evaluated based on the irradiation environment (e.g. flux, power, testing capabilities) using an appropriate scoring matrix. Although many university campus RTRs are available for research and development (R&D) activities and initiatives, this study focuses on evaluating and qualifying the irradiation facilities (mostly RTRs) within the United States that are suitable for advanced nuclear fuel, material, and system irradiation experiments aimed at establishing operational-performance limits and informing component and fuel designs so as to improve operational efficiencies and mitigate proliferation vulnerabilities, as well as for radioisotope production aimed at multipurpose applications. As a result, the findings of the present study support the acceleration of nuclear fuel and material qualifications, thus hastening new and advanced nuclear energy system demonstrations and radioisotope production efforts by using extended R&D.

irradiation experiment↗

Integrity Enhancing Protocols: Performance and Recommendations for Nuclear Systems

In today’s communication landscape there are multiple technologies and protocols used for communication between end devices. Within security paradigms for these protocols, integrity management is a common goal of system designers. Communication protocols focused on maintaining message integrity can provide assurance that some received data has not been altered or tampered with. While integrity is often coupled with confidentiality in protocol design, this analysis focuses on an evaluation of only integrity protocols. This report outlines various ways message integrity may be preserved with respect to high performance operational technology (OT) systems. It describes a series of experiments and an evaluation framework used to evaluate the performance of the identified integrity approaches regarding common system design goals. Finally, it addresses the testing environment utilized and closes the report with a summary of experimental results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Evaluation of Machine Learning Models for Automated Data Analysis in In-Service Nuclear Power Plant Inspections

The commercial nuclear power industry is facing a potential shortage of certified nondestructive evaluation (NDE) analysts to meet future in-service inspection demands. Automated data analysis (ADA) currently supports human inspectors in tasks such as eddy current evaluations for steam generator examinations. Machine learning (ML) systems are nearing the capability to pass performance demonstration tests for ultrasonic testing (UT) inspections of reactor pressure vessel upper head penetrations in nuclear power plants (NPPs). Current research and development is focused on assisted analysis (AA) of ADA versus fully automated examinations. This presentation will cover assessment of ML flaw detection on dissimilar metal weld (DMW) piping joints.

36 MATERIALS SCIENCE↗

2023 T120 Horizon and Slim Posthole Seismometer Exploratory Evaluation

Sandia National Laboratories has tested and evaluated a suite of four T120 broadband seismometers designed and manufactured by Nanometrics. Specifically, two T120 Horizon V2 sensors, one T120 Horizon V1 sensor and one T120 Slim Posthole (PH) sensor were evaluated. The purpose of this seismometer evaluation is to measure performance characteristics in areas such as power consumption, sensitivity, frequency response, full scale, self-noise, dynamic range, calibration system response, and passband. The T120 model of sensors are being evaluated to explore the potential for a future seismometer Type Approval process in the International Monitoring System (IMS) of the Comprehensive Nuclear-Test-Ban Treaty (CTBT).

47 OTHER INSTRUMENTATION↗

Evaluating inkjet dispenser/liquid vortex capture-mass spectrometry for single-cell metabolomics in Hep G2 steatosis caused by tamoxifen

Single-cell mass spectrometry (MS) is advancing our understanding of metabolic pathways in heterogeneous cell populations; however, many techniques are slow or require disruptive sample preparations. This study evaluated coupling a modified HP D100 single-cell inkjet dispenser with liquid vortex capture-mass spectrometry (D100/LVC-MS). The D100 is a single-cell inkjet dispenser capable of titrating solutions and isolating single cells via disposable cassettes equipped with microfluidic channels and an impedance sensor. The LVC-MS enables high-throughput capture, lysis, and ionization of analytes for mass spectrometric analysis. The D100/LVC-MS system was characterized through titration and single-cell experiments. Propranolol titration demonstrated linearity across a broad concentration range using the D100/LVC-MS system. Additionally, Hep G2 hepatocarcinoma cells and Chlamydomonas reinhardtii algae were used to showcase the D100’s high-throughput or low-buffer-volume single-cell dispensing strategies. The D100/LVC-MS system’s performance was validated by evaluating tamoxifen-induced steatosis in Hep G2 cells. Tamoxifen, associated with nonalcoholic fatty liver disease in breast cancer patients following long-term use, was tested in Hep G2 cells at 20 µM for 72 h against DMSO-treated controls. High-throughput analysis of 500 cells per condition, completed in 25 min per run, demonstrated the system’s efficiency. The D100/LVC-MS system simultaneously quantified tamoxifen and measured triglycerides and phosphatidylcholines. Triglycerides were upregulated in the tamoxifen-treated cells and the results indicated two distinct cell populations, differing in tamoxifen and phosphatidylcholines levels, suggesting heterogeneity within the treated population. In conclusion, these findings highlight the D100/LVC-MS system as a cost-effective, high-throughput platform for single-cell metabolomics and lipidomics, with significant potential for evaluating metabolic alterations.

Chromatography↗

Experimental Investigation of Steel-Borne Acoustic Pulses for Fault Pinpointing in Pipe-Type Cable Systems: A Scaled-Down Model Approach

Pipe-type cable systems, including high-pressure fluid-filled (HPFF) and high-pressure gas-filled cables, are widely used for underground high-voltage transmission. These systems consist of insulated conductor cables within steel pipes, filled with pressurized fluids or gases for insulation and cooling. Despite their reliability, faults can occur due to insulation degradation, thermal expansion, and environmental factors. As many circuits exceed their 40-year design life, efficient fault localization becomes crucial. Fault location involves prelocation and pinpointing. Therefore, a novel pinpointing approach for pipe-type cable systems is proposed, utilizing accelerometers mounted on a steel pipe to capture fault-induced acoustic signals and employing the time difference of arrival method to accurately pinpoint the location of the fault. The experimental investigations utilized a scaled-down HPFF pipe-type cable system setup, featuring a carbon steel pipe, high-frequency accelerometers, and both mechanical and capacitive discharge methods for generating acoustic pulses. The tests evaluated the propagation velocity, attenuation, and pinpointing accuracy with the pipe in various embedment conditions. The experimental results demonstrated accurate fault pinpointing in the centimeter range, even when the pipe was fully embedded, with the acoustic pulse velocities aligning closely with the theoretical values. These experimental investigation findings highlight the potential of this novel acoustic pinpointing technique to improve fault localization in underground systems, enhance grid reliability, and reduce outage duration. Further research is recommended to validate this approach in full-scale systems.

Moutassem, Zaki↗

Scaled melter testing of alternative reductants for Low-Activity Waste vitrification: Melter feed properties and processing behavior

This study examines the use of boron nitride (BN) and coke dust as alternative reductants for low-activity waste vitrification in scaled melter systems, intended to enhance operational flexibility at the Hanford Waste Treatment and Immobilization Plant. The baseline reductant, sucrose, while widely considered advantageous for glass production rates, produces challenging off gas emissions during processing. Early crucible-scale testing indicated that BN and coke effectively control foaming and glass redox, while significantly reducing acetonitrile emissions. Both real tank waste and simulant waste melter feeds were tested with BN and coke in this study. Rheological properties for melter feeds with both reductants were within operational limits, although the particle size of coke should be controlled and sufficient agitation is necessary to ensure smooth operations. While promising for handling and reduction of emissions, both simulant melter feeds demonstrated lower average glass production rates in the simulant melter system compared with sucrose. In the radioactive system, the rates were more comparable to previously measured low activity waste feeds on the order of 1285 kg m 2 day −1 for BN and 1671 kg m −2 day −1 for coke. Further scale-up testing is required to interpret the processing rates in the context of the full scale melter systems and evaluate the cost-benefit impact of these reductants on efficiency and sustainability.

Rigby, Jessica C. [Pacific Northwest National Labo↗

Balance of Plant Modeling and Real-Time Hardware-in-the-Loop Integration with the Microreactor Automated Control System

The advent of novel microreactor technology has driven a focused effort to explore safety and efficiency improvements that can be achieved through the use of automated system control. Development of control strategies, especially for initial demonstration, requires an adequate surrogate environment to safely research failure modes and control integration with realistic hardware delay. However, efficiency gains from control strategies are improved when the scope of controller action is expanded to include system-level dynamics such as downstream heat extraction and mass flow. For this reason, a balance-of-plant (BOP) model of a representative microreactor system has been developed using the TRANsient Simulation Framework of Reconfigurable Models library in Modelica. This model captures a reactor and primary NaK coolant loop that represent corresponding system components of the Microreactor Applications Research Validation and EvaLuation (MARVEL) design as well as a secondary coolant loop and heat extraction representative of the Microreactor Agile Non-Nuclear Experimental Test Bed (MAGNET). This model configuration allows for hardware-in-the-loop (HIL) integration with microreactor automated control system (MACS) hardware in real time through a Python-based gRPC client. Real-time simulation of model performance with emulated hardware and communication delay suggests that under independent proportional-integral-derivative control of BOP model drum dynamics and downstream heat extraction, stable power load following is achievable. A slight delay in load following, filtering of high-frequency dynamics, and localized temperature fluctation suggest room for improvement through the development of higher-level control strategies. The simulated coupling of the MAGNET facility lays the groundwork for future digital twin analysis with a coupled MACS-MAGNET HIL demonstration.

McConnell, Jono [ORNL] (ORCID:0000000238984741)↗

Advancing the HERO WEC Through Integrated Modeling, Testing, and Field Deployments: Preprint

The Hydraulic and Electric Reverse Osmosis Wave Energy Converter (HERO WEC) was developed by the National Laboratory of the Rockies as a modular platform for advancing wave-powered desalination technologies. Designed to operate in either a hydraulic or electric configuration, the system enables direct comparison of mechanical-to-water and electrical-to-water conversion pathways using a single hardware architecture. Deployments at the Jennette's Pier test site in 2022 and 2024 demonstrated freshwater production between 60 and 300 gallons per day, including successful operation in wave heights as low as 0.25 m. A structured evaluation approach combining numerical modeling of hydrodynamic and PTO response, controlled laboratory testing, and in-ocean field deployments has been used to characterize and refine system performance. Insights from these efforts are now informing the second-generation HERO WEC (V2), which incorporates improved drivetrain components, refined geometry, enhanced control systems, and design updates aimed at increasing robustness and long-duration survivability. The HERO WEC platform continues to serve as an open-access research asset supporting broader marine energy and desalination development.

16 TIDAL AND WAVE POWER↗

Geometry Optimization of Cable-Based Actuation for Small-Scale Model Testing of a Floating Marine Turbine: Preprint

This research aims to apply combined wave and tidal current loads to a small-scale floating marine current turbine in a wave tank, where an actuation system applies hydrodynamic and mooring forces on the hardware based on results from a simulation. We use a real-time hybrid test setup with physical wave forcing from the wave tank and simulated current and mooring forces implemented through a tensioned cable array. For this paper, we developed an optimization algorithm that adjusts the hardware geometry of the cable array to achieve more efficient tension allocation across the cables for the loads that need to be actuated. By adjusting the points where the cables are attached to the floating platform and the angles between the platform and the winches, an optimal cable geometry can be found to minimize tension variations in the lines, maintain the desired pretension, and prevent excessive tensions. We present the optimization problem formulation, the actuation system evaluation approach, and optimization results that show effective cable actuation setups that are being considered for implementation in the wave tank tests.

cable-based actuation↗

Development of a Test-Bed for Testing and Refining EarthEn’s Supercritical CO 2 Based Energy Storage System

EarthEn’s energy storage concept leverages supercritical carbon dioxide (sCO 2 ) as a working fluid and relies on compact, high-performance components operating at elevated pressures and temperatures. To accelerate component development and reduce technical risk prior to larger-scale demonstrations, Oak Ridge National Laboratory (ORNL) developed a 100 kW-scale sCO 2 test-bed under a Cooperative Research and Development Agreement with EarthEn (CRADA NO. NFE-24-10050). The objective of the work was to design and construct a flexible experimental facility capable of reproducing key thermodynamic state points and heat-transfer conditions relevant to EarthEn’s thermal energy storage (TES) cycle, with particular emphasis on enabling development and evaluation of next-generation heat exchangers and TES concepts. The test-bed consists of a closed-loop sCO 2 circulation system housed within an open-topped enclosure. In its as-installed configuration, dense-phase sCO 2 is recirculated through a printed circuit recuperator, an electrically heated section, a throttling device used to simulate turbine expansion, and a water-cooled printed circuit heat exchanger that rejects heat to the building chilled-water system before returning to the pump. The pump is driven by a variable frequency drive, enabling controlled adjustment of flow and operating point. A comprehensive instrumentation suite was integrated to support both safe operation and high-quality data collection. Installed sensors include Coriolis flow meters for sCO 2 flow rate and density, resistance temperature detectors and thermocouples distributed throughout the loop (including the heated section and key heat exchanger ports), and pressure transducers for absolute and differential pressure measurements. The facility was designed to support high-pressure (19 MPa nominal) and high-temperature (575°C nominal) operation with credited overpressure protection provided by a rupture disk. Nominal operating conditions were selected to support 100 kW-class testing while maintaining flexibility for non-heated and heated shakedown, control development, and future integration of advanced TES test sections. In parallel with facility development, a system-level thermal-hydraulic model was created using Modelica-based tools to support component sizing, anticipate performance over targeted test conditions, and establish a framework for future model calibration against experimental data. At the conclusion of the project performance period, the facility was in final assembly, and the pressure boundary was nearly completed. However, several practical challenges associated with high-pressure/high-temperature systems and specialized component procurement impacted schedule and prevented initial pump-driven operation and full commissioning within the available resources. This report documents the as-built design, operating capabilities, and instrumentation, and it summarizes key lessons learned related to heater fabrication and testing, first-of-a-kind assembly factors, specialty flange supply constraints, and fill pump corrective actions. Finally, it outlines a phased plan for future commissioning and experimental campaigns, including control and instrumentation shakedown, heater characterization, model calibration, and testing at state points representative of EarthEn’s TES cycle.

25 ENERGY STORAGE↗

Calculating Critical Inertia of a Power System

The increasing integration of renewable energy sources in modern power systems has led to a decline in system inertia, raising concerns about frequency stability following large disturbances. Determining critical inertia is essential to prevent excessive frequency decline and ensure grid stability. This paper evaluates four different methods for calculating critical inertia, using the Electric Reliability Council of Texas (ERCOT) system as a test case. The results highlight the importance of employing multiple methodologies to capture the full spectrum of inertia requirements.

Hakim sneha, Fariha [University of Tennessee, Knox↗

Atmospheric-river-induced precipitation in California as simulated by the regionally refined Simple Convective Resolving E3SM Atmosphere Model (SCREAM) Version 0

Abstract. Using the regionally refined mesh (RRM) configuration of the US Department of Energy's Simple Cloud-Resolving Energy Exascale Earth System Model (E3SM) Atmosphere Model (SCREAM), we simulate and evaluate four meteorologically distinct atmospheric river events over California. We test five different RRM configurations, each differing in terms of the areal extent of the refined mesh and the resolution (ranging from 800 m to 3.25 km). We find that SCREAM RRM generally has a good representation of the AR-generated precipitation in CA, even for the control simulation which has a very small 3 km refined patch, and is able to capture the fine-scale regional distributions that are controlled largely by the fine-scale topography of the state. It is found that SCREAM generally has a wet bias over topography, most prominently over the Sierra Nevada mountain range, with a corresponding dry bias on the lee side. We find that refining the resolution beyond 3 km (specifically 1.6 km and 800 m) has virtually no benefit towards reducing systematic precipitation biases but that improvements can be found when increasing the areal extent of the upstream refined mesh. However, these improvements are relatively modest and only realized if the size of the refined mesh is expanded to the scale where employing RRM no longer achieves the substantial cost benefit it was intended for.

54 ENVIRONMENTAL SCIENCES↗

Experimental Investigation on Cooling performance of A Thermoelectric Freezer

Thermoelectric heat pumps (TEHPs) have found widespread use in the electronics cooling industry and portable refrigerators. However, there has been a lack of extensive research on the application of TEHPs in low-temperature refrigeration settings. To address this gap, various configurations of TEHPs were fabricated to assess their suitability for freezer applications. Key parameters such as cooling capacity and system performance of the TEHPs were crucial in evaluating these configurations. Three configurations, each with different numbers of cooling units and fan arrangements, were tested using a 300-liter freezer prototype under typical room conditions (21°C). A cooling unit is comprised of two-stage thermoelectric modules, an aluminum plate fin heat exchanger sink with fans positioned either on top or directing airflow through the center, and a cooling block with circulating icy water for heat dissipation. Across all configurations, the minimum temperature inside the freezer cabinet reached -16.0°C. The cooling capacity peaked at 74.7 W, with the thermoelectric coefficient of performance (COP) reaching a maximum of 0.45. System COP ranged from 0.23 to 0.28. Minimum TE power consumption was recorded at 138.8 W, with TE system power consumption at 174.4 W, indicating feasibility for practical residential freezer applications. This investigation lays the foundation for integrating TE freezers with ice thermal storage systems.

Hu, Yifeng↗

Standard Operating Procedure for Optimal Deployment of Meteorological Instrumentation Within the Solar Radiation Research Laboratory: 2024 Edition

The objective of the National Renewable Energy Laboratory's (NREL's) Solar Radiation Research Laboratory (SRRL) is to collect and use high-quality solar radiation data sets for research leading to the widespread adoption of solar technologies. To appropriately populate and track the diverse array of instruments at the NREL-SRRL, NREL has established a Standard Operating Procedure (SOP) for optimal instrument deployment within the SRRL for both the Baseline Measurement System (BMS) and the Research Measurement System (RMS). Using best practices methodologies, the NREL-SRRL maintains a varied and extensive array of solar monitoring equipment to test, evaluate, and characterize the solar sensors used by federal and international agencies as well as the solar industry to determine the solar resource. The SOP provides the industry with guidance for solar resource assessment and is used for procedures in the long-term continuous monitoring of legacy instruments alongside state-of-the-art instruments. Based on the SOP, instruments are annually evaluated for continued deployment. Instruments that do not meet the SOP criteria are decommissioned, and new instruments that meet the criteria are deployed. Streamlining and optimizing the use of this facility ensures that the lab continues to be a world-leading solar calibration and measurement facility. This 2024 edition includes updates to the appendices to reflect the instrument changes from one year to another.

14 SOLAR ENERGY↗

Performance Evaluation of an Additively Manufactured ultra-High Operating Temperature SiC Solar-Thermal Air Receiver (HOTSSTAR) Test Module

Increasing operating temperatures of solar receivers is paramount to the efficiency of concentrated solar thermal and solar power systems. GE Aerospace Research in collaboration with Heliogen Inc and Sandia National Laboratories (SNL) is engaged in the development of ultra-High Operating Temperature SiC-matrix Solar Thermal Air Receiver (HOTSSTAR) enabled by additive manufacturing. HOTSSTAR goal is to demonstrate SiC receiver with air exit temperatures up to 1100oC. We discuss fabrication and on-sun test results of a prototype 50kWth test module. The receiver architecture is based on a radial airflow design and consists of a series of radial SiC receiver sectors organized around central absorber. These components were fabricated using binder-jet printed SiC followed by melt-infiltration reaction bonding process. To enhance the thermo-mechanical reliability of SiC test articles in thermal gradient/ shock environment of the application, the components were laminated with GE’s MI SiC CMC. A dedicated test facility was constructed at SNL Solar Tower to evaluate the operational performance of HOTSSTAR module under solar fluxes >200 W/cm2. We report on our final 50kW test module fabrication, integration at the test facility at Sandia, and discuss on-sun test results. We compare the performance of HOTSSTAR module relative to our model predictions.

14 SOLAR ENERGY↗

Improving the User Interface of the DeepLynx Data Warehouse

DeepLynx is an open-source ontology-based data warehouse created by INL to support the creation and life cycle of digital engineering projects, with a particular emphasis on digital twins [1]. Digital twins are systems that represent physical assets and process in a real-time digital environment [1]. Most well-known commercial data warehouses use Graphical User Interfaces (GUIs) for users to interact with their systems [3]. Limited publications have addressed the design of these interfaces and understanding of their target users. The current users and development team acknowledge the need to improve the current UI, not just for aesthetics but to improve functionality and workflow of DeepLynx. Traditional data warehouse users are developers, data scientists and business analysts [2]. DeepLynx users have a vast range of experience using data warehouses, and diverse roles, including engineers, scientists and management positions. Because there is a broader audience of target users for DeepLynx than a typical data warehouse, it is essential that DeepLynx has a useable and intuitive user interface. To achieve this the team performed human-computer interaction methods, including a Heuristic Evaluation of current UI using Neilsen’s Usability Heuristic, create personas based on current users by designing a user survey, data analysis and develop of personas. Followed by a redesign of the UI following using Neilsen’s Usability Heuristic and Norman’s Principles of Interactive Design in industry standard software Figma. Lastly a Heuristic Evaluation of new UI design, using Neilsen’s Usability Heuristic and User testing of redesign UI and have a group of users complete a Thinking Aloud Test of the new UI. Preliminary results of the Heuristic Evaluation of current UI arise issue with Consistency and Standards, Visibility of System Status, Match System and Real World and Recognition Rather than Recall. These issues were addressed in the proposed redesign by applying Neilsen’s Usability Heuristic and Norman’s Principles of Interactive Design. Next steps include formalized list of lessons learned and design implications for future publications.

97 MATHEMATICS AND COMPUTING↗