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SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High- temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes ad- vantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High-temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Alternative Technologies Adopters Outreach Survey Report

Brookhaven National Laboratory (BNL), in collaboration with Ioanna Iliopulos and Christopher Boyd (independent contractors), conducted quantitative and qualitative surveys to document views and opinions of scientists and researchers with firsthand experience operating x-ray devices for a wide range of research applications. The goal of the study was to fill critical information gaps and identify misconceptions widely held among the research community regarding the transition from Cesium-137 irradiators to x-ray devices. The survey instrument focused on three distinct yet interrelated areas that impact users' experience: operational impacts, including infrastructure needs, workflow, personnel management, and training, and regulatory compliance; research design and investigation impacts, including calibration, dosimetry, continuity of previous studies, development of new research agendas, and the outcomes for both; and funding impacts, specifically how grant sources and opportunities have responded to the transition.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Considerations for Introducing Artificial Intelligence into Nuclear Power Plants

Advanced computational tools and techniques such as artificial intelligence and machine learning (AI/ML) can transform the nuclear power industry. This is necessary given that the economic viability of the existing fleet is in jeopardy and its labor-centric approach to operations and maintenance. Currently, AI/ML research is being undertaken for reactor system design and analysis including fault and accident prognosis, nuclear risk analysis such as plant safety and security evaluation, and plant operations and maintenance including predictive maintenance. Applications include both existing and advanced reactor technologies with the aim of improving operational and business efficiencies. Most every aspect of the organization can benefit, from instrumentation and control, to work planning, to human-machine interactions and business management. AI/ML in nuclear can simplify complex problems and produce more effective decision-making. Nonetheless, careful consideration must be given to the implementation of an AI/ML initiative. The aims of this research are to 1) review barriers to AI/ML adoption within the nuclear power industry, and 2) suggest potential solutions. These barriers are organized along five distinct categories (Figure 1) that are interconnected. The first are historical barriers that track the industry’s development over the decades including worldwide nuclear events that shaped public perceptions. The resulting federal scrutiny and intense safety culture that emerged are discussed. Technical barriers to AI/ML adoption are considerable, and include data privacy concerns, data governance, and the current lack of AI/ML expert knowledge at the plants. The main business case barrier remains cost, but an absence of an industry-wide vision and wide-scale adoption also produces reluctance. Stakeholder readiness is reviewed with special attention given to regulatory readiness. The 5-year strategic plan for AI readiness recently published by the U.S. Nuclear Regulatory Commission is highlighted. Last, adoption barriers at the user level are addressed including the importance of user experience and explainable AI. The AI adoption barriers described here are inter-related and ideally should be addressed in a holistic fashion.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Advances on CHP District Energy and Microgrids Deployment: Simplified Tool for Rapidly Deploying Feasibility Analytics for the Non-Technical User (Final Technical Report)

Community energy systems have proven to have the potential to improve cost efficiency, resilience, and decarbonize. However, investing in community energy systems such as community microgrids or district energy systems is a complex decision due to the high initial investment and the uncertainties associated with the long development time and lifecycle of the project. Tools that make feasibility assessments accessible to non-technical users like investors, policymakers, and other stakeholders will result in more feasibility analyses completed, more candidate projects identified, and more community energy systems deployed. The pilot tool developed under this award is named Energy Fellow. Energy Fellow allows technical and non-technical users to complete feasibility analyses for district energy systems and community microgrids. This is the first software tool of its kind designed for non-technical users and available at no cost. Its scope was adjusted to a 25x25-mile region within the Houston area in Texas to make its development compatible with the funding available. However, the findings and models developed make this pilot tool easily scalable to the US. The lessons learned during the design, implementation, and testing stages have helped find trade-off solutions to software and hardware challenges related to implementing 3D models in online tools. Green software strategies has been successfully applied to the design and operations of the tool, and the team has researched the aspects of the (non-technical) user experience that will make commercial developments of this tool even more impactful.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A Conceptual Design for a Desktop Application to Support Inventory Reconciliation Activities

This paper describes desktop software being developed at Oak Ridge National Laboratory (ORNL) to empower users to reconcile observations about items at nuclear facilities more accurately, reliably, and quickly. Inventory activities at nuclear facilities are often conducted using pen and paper, which can be time-consuming, tedious, and susceptible to reading or transcription errors. The proposed inventory assistant would be a replacement for the paper-based process that could be used by International Atomic Energy Agency (IAEA) inspectors, nuclear facility operators, or treaty verification monitors to conduct an inventory of nuclear and non-nuclear items in a more timely and accurate manner. Garner, McGirl, and Whitaker previously reported their work about a conceptual design for a mobile app to assist users in the field. In general, the inventory assistant would ingest an inventory list, distribute assigned items from the inventory list to one or more mobile devices, enable inventory teams to record their observations in the field, and then enable an inventory lead to integrate and reconcile the observations to produce a final report. The assistant consists of two software components - one for the inventory teams to record observations in the field (In-Field Observations App [IFOA]) and one for the inventory lead to (1) distribute the inventory list to each team, (2) integrate the observations from each team, and (3) reconcile the inventory list with observations (Distribution, Integration, and Reconciliation Application [DIRA]). This paper reviews the inventory assistant workflow and describes the DIRA user experience in more detail. As an example, the authors have chosen to follow the use case of IAEA inspectors conducting item counting and tag checking activities of UF 6 cylinders at a gas centrifuge enrichment plant with a large number of UF 6 cylinders (e.g., thousands). These activities can currently require 30 - 40 person-days of inspection to complete. The authors believe an inventory assistant could allow the IAEA to complete item counting and tag checking using the global identifier or the operator’s barcode in 8 - 10 person-days of inspection. We would expect other users (e.g., facility operators or treaty verification monitors) to also benefit from significant time savings.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The Galaxy platform for accessible, reproducible, and collaborative data analyses: 2024 update

Galaxy (https://galaxyproject.org) is deployed globally, predominantly through free-to-use services, supporting user-driven research that broadens in scope each year. Users are attracted to public Galaxy services by platform stability, tool and reference dataset diversity, training, support and integration, which enables complex, reproducible, shareable data analysis. Applying the principles of user experience design (UXD), has driven improvements in accessibility, tool discoverability through Galaxy Labs/subdomains, and a redesigned Galaxy ToolShed. Galaxy tool capabilities are progressing in two strategic directions: integrating general purpose graphical processing units (GPGPU) access for cutting-edge methods, and licensed tool support. Engagement with global research consortia is being increased by developing more workflows in Galaxy and by resourcing the public Galaxy services to run them. The Galaxy Training Network (GTN) portfolio has grown in both size, and accessibility, through learning paths and direct integration with Galaxy tools that feature in training courses. Code development continues in line with the Galaxy Project roadmap, with improvements to job scheduling and the user interface. Environmental impact assessment is also helping engage users and developers, reminding them of their role in sustainability, by displaying estimated CO 2 emissions generated by each Galaxy job.

97 MATHEMATICS AND COMPUTING↗

2020 Exascale Computing Project Annual Meeting (Executive Summary Report)

The Exascale Computing Project (ECP) delivers specific applications, software products, and outcomes on DOE computing facilities. Integration across these elements for specific hardware technologies for exascale system instantiations is fundamental to ECP success. The outcome of the ECP is the delivery of a capable exascale computing ecosystem to provide breakthrough solutions addressing our most critical challenges in scientific discovery, energy assurance, economic competitiveness, and national security. This outcome is not a matter of ensuring more powerful computing systems. The ECP is designed to create more valuable and rapid insights from a wide variety of applications (“capable”), which requires a much higher level of inherent efficacy in all methods, software tools, and ECP-enabled computing technologies to be acquired by DOE laboratories (“ecosystem”). The ECP annual meeting provides a unique opportunity for the core technical expertise in the United States focused on achieving this next plateau of computational science and computing performance to engage in direct discussions on project execution. Face-to-face gatherings in technical communities like this are common and needed for the exchange of scientific ideas and technical performance. The ECP annual meeting stands apart from other technical conferences and meetings in the computing community as it is uniquely and solely focused on the execution of the ECP and the integration of technical activities leading to the creation of the exascale computing ecosystem for the future. The direct interaction of key critical technical staff, who are leaders in their respective fields, and the resulting give-and-take between software, applications, and hardware and the technical co-design therein, is unique and essential to the effective execution of the ECP. The first annual meeting was held in Knoxville, Tennessee, January 31 – February 2, 2017 and brought together, for the first time, a diverse collection of researchers from 16 DOE national laboratories as well as university computer and computational science researchers to discuss shared problems and joint solutions for the development of a capable exascale computing ecosystem. These interactions resulted in focused technical plans and an energized community centered on advances for ECP. The second annual meeting was held in Knoxville, Tennessee, February 5–9, 2018. It included 643 individual thought leaders and performers in application development, software research and deployment, and hardware research and integrators, all of whom are part of the multifaceted, billion dollar HPC community. This meeting provided a platform to discuss and disseminate numerous examples where researchers with common goals and synergistic solutions came together for the first time to deliver tangible results. Additionally, at the 2018 meeting, ECP researchers had the opportunity to digest all US HPC vendor R&D product roadmaps pointing to exascale – not only to learn how their research can play a role, but, more importantly, to influence those roadmaps to ensure successful delivery on DOE applications that will contribute to (if not solve) problems of national interest in national security, science, energy, and health, as well as growing security threats. The third annual meeting was held in Houston, Texas, January 14–17, 2019. With a 19% increase in the number of registrations (768 people), and the change in location, the third annual meeting was considered the most impactful of the three at the time. The new website provided a better platform for the dissemination of the content, the new venue as a meeting hotel instead of a conference center facilitated interactions and discussions after event hours, and the addition of an award-winning mobile event conference app (Whova) transformed dramatically the attendee experience at the event. This fourth annual meeting was held in Houston, Texas, February 3-7, 2020. This meeting had an increase in the number of attendees for a total of 824 people registered (782 attendees) and included numerous enhancements based on feedback and lessons learned from previous meetings, some of which are listed here: Improved quality of the sessions, their material and the whole program.; Had more industry participation and addition of external collaborators from overseas.; Published the full agenda earlier to better accommodate attendance and travel plans based on schedule.; Centralized all sessions in one venue.; Provided additional hotels and room blocks for the attendees.; Improved communication with the audience (links, material, directions, notifications, etc.) to go paperless.; Enhanced side meeting scheduling, management and user experience.; Made available additional space and tables for impromptu meetings and side discussions.; Improved IT and A/V solutions for speakers. In addition, our final survey captured the following points as opportunities for improvement in future meetings: consider a different meeting location that is more pedestrian friendly, reduce talks during working meals to allow more collaboration and informal time, adapt the agenda to acknowledge attendees from different timezones, consider recording some of the tutorials and/or sessions to share broadly with the HPC community, have a larger poster room, provide additional power strips, and improve the WiFi.

97 MATHEMATICS AND COMPUTING↗

Bridging the Gap Between Modern UX Design and Particle Accelerator Control Room Interfaces

Accelerator control systems often represent relatively complex and safety-sensitive human-machine interfaces within process control industries. These systems are technically robust and reflect the cumulative integration of solutions built and adapted across decades. One of the regular, unfortunate casualties of provisional accelerator control system updates is their human-system interfaces (HSIs) which often lag behind modern usability and design standards. An additional challenge is that although there is a multitude of established human factors (HF), and user experience (UX) principles for everyday digital applications, there are very few (if any) established principles for complex and safety-critical applications for an accelerator. This paper argues for the importance of established HF and UX principles (herein referred to as human-centered design principles) into the development of accelerator HSIs, emphasizing the need for clarity, consistency, responsiveness, and cognitive accessibility. Drawing from HF/UX best practices and human-centered design, this paper discusses how these approaches can enhance operator performance, reduce human error, and improve accelerator personnel collaboration. Case studies from Accelerator Control Operations Research Network (ACORN) at Fermilab are explored to demonstrate how interfaces built with human-centered design principles can scale with system complexity while remaining intuitive and efficient for diverse user roles including operators, machine experts, and engineers. By bridging the gap between traditional control system design and modern human-centered design methods, this paper provides a roadmap for evolving accelerator HSIs into more usable, maintainable, and effective tools.

Hill, Rachael [Idaho Natl. Lab.]↗

time-resolved spectroscopy fit (trspecfit) v0.01

Analyze 2D time- and energy-resolved data, such as from a pump-probe spectroscopy experiment. User can select and input different peak shapes/ functions and background types to first fit a ground state/ unperturbed spectrum. This would be similar to how standard spectroscopy data is fit. Subsequently, to describe the time domain, users can choose functions that describe the temporal dynamics of one or more spectral features, such as a peak amplitude, peak position, etc. These time dynamics functions can be added or convoluted (e.g. describing an instrument response function) with each other. Functionality to integrate implicit variables leading to distributions of certain parameters/ functions is in development. Alternatively, 2D data can be analyzed one time step at a time to get an idea of the time dynamics of the system before deploying the global 2D fit described above. Typically people write custom software for this purpose. During my PhD I've seen five internal LBL and external researchers write one-off code in different languages to analyze time- and energy-resolved spectra. While this was specifically was for a laser pump - X-ray probe spectroscopy experiment, I'm trying to write a general package for the time-resolved spectroscopy community.

Mahl, Johannes [Lawrence Berkeley National Laborat↗

Enhancement of PyARC for Westinghouse Electric Company’s Lead Fast Reactor Design and Modeling (Final TCF Report)

Westinghouse Electric Company is a nuclear reactor vendor headquartered in the U.S. that is developing advanced reactor technology for the U.S. and global markets. Westinghouse has been relying on the neutronics Argonne Reactor Codes (ARC) executed through the NEAMS Workbench and its PyARC module that are developed under the DOE-NE Nuclear Energy Advanced Modeling and Simulation (NEAMS) and Advanced Reactor Technology (ART) – Fast Reactor programs. Through this user experience, Westinghouse identified several enhancements that would benefit the ARC codes’ usability by the US industry and therefore its commercialization potential. The enhancements were proposed to deliver both improvements in workflow and analysis capabilities to better support effective fast reactor core design and analysis to the nuclear industry. The PyARC workflow was extended in this project by integrating non-neutronic ARC codes DASSH and NUBOW-3D. The Ducted Assembly Steady-State Heat equation (DASSH) code is developed at ANL to perform steady-state thermal hydraulic sub-channel analysis in liquid metal fast reactor assemblies to determine optimized coolant flow and temperature distributions, which in this project was updated and validated for lead fast reactor (LFR) applications. The interface between REBUS and NUBOW-3D were improved in this project to assess the impact of the core restraint design and thermal induced expansion effects on the reactivity of the core, and to model the deformations of the fuel assemblies induced by temperature and irradiation. Finally, the ARC models that were extensively verified and validated through various SFR-based modeling benchmarks are extended in this project through code-to-code comparison on relevant LFR-specific neutronics benchmarks against Monte-Carlo neutronic solutions. Overall, this work enables verification of the capability of the ARC codes for a wide range of Generation-IV reactor designs. The outcome of this project is the release of a comprehensive modeling toolkit of validated, robust and efficient codes, as well as their user interface, that enables industry to perform a wide range of fast reactor analyses for design and licensing of their concepts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

In-device Battery Failure Analysis

Lithium-ion batteries are indispensable power sources for a wide range of modern electronic devices. However, battery lifespan remains a critical limitation, directly affecting the sustainability and user experience. Conventional battery failure analysis in controlled lab settings may not capture the complex interactions and environmental factors encountered in real-world, in-device operating conditions. Here, this study analyzes the failure of commercial wireless earbud batteries as a model system within their intended usage context. Through multiscale and multimodal characterizations, the degradations from the material level to the device level are correlated, elucidating a failure pattern that is closely tied to the specific device configuration and operating conditions. The findings indicate that the ultimate failure mode is determined by the interplay of battery materials, cell structural design, and the in-device microenvironment, such as temperature gradients and their fluctuations. This holistic, in-device perspective on environmental influences provides critical insights for battery integration design, enhancing the reliability of modern electronics.

36 MATERIALS SCIENCE↗

Preparation of a 73 As source sample for application in an offline ion source

For the generation of beams with the offline ion source at the Facility for Rare Isotope Beams (FRIB), suitable source samples are required. Arsenic-73 is a frequently requested user beam due to its significance in nuclear structure studies and astrophysics. In this work, we outline the process of preparing a 73 As source sample, containing (5.76 ± 0.37)∗10 14 atoms of 73 As, which was successfully used to generate a 73 As beam for a multi-day user experiment. Silver arsenate was chosen as the chemical form, due to its favorable volatility within the designated operating temperature range. We refined the precipitation method using stable arsenic prior to its application with the 73 As sample, resulting in precipitation yields of (99.4 ± 4.5)%.

As-73↗

Visual feedback and guided balance training in an immersive virtual reality environment for lower extremity rehabilitation

Balance training is essential for physical rehabilitation procedures, as it can improve functional mobility and enhance cognitive coordination. However, conventional balance training methods may have limitations in terms of motivation, real-time objective feedback, and personalization, which a virtual reality (VR) setup may provide a better alternative. In this work, we present an immersive VR training environment for lower extremity balance rehabilitation with real-time guidance and feedback. The VR training environment immerses the user in a 3D ice rink model where a virtual coach (agent) leads them through a series of balance poses, and the user controls a trainee avatar with their own movements. Here we developed two coaching styles: positive-reinforcement and autonomous-supportive, and two viewpoints of the trainee avatar: first-person and third-person. The proposed environment was evaluated in a user study with healthy, non-clinical participants (n = 16, 24.4 ± 5.7 years old, 9 females). Our results show that participants showed stronger performance in the positive-reinforcement style compared to the autonomous-supportive style. Additionally, in the third-person viewpoint, the participants exhibited more stability in the positive-reinforcement style compared to the autonomous-supportive style. For viewpoint, participants exhibited stronger performance in the first-person viewpoint compared to third-person in the autonomous-supportive style, while they were comparable in the positive-reinforcement style. We observed no significant effects on the foot height and number of mistakes. Furthermore, we report the analysis of user performance with balance training poses and subjective measures based on questionnaires to assess the user experience, usability, and task load. The proposed VR balance training could offer an interactive, adaptive, and engaging environment and open new potential research directions for lower extremity rehabilitation.

97 MATHEMATICS AND COMPUTING↗

Improving operational flexibility of integrated energy system with uncertain renewable generations considering thermal inertia of buildings

Insufficient flexibility in system operation caused by traditional "heat-set" operating modes of combined heat and power (CHP) units in winter heating periods is a key issue that limits renewable energy consumption. In order to reduce the curtailment of renewable energy resources through improving the operational flexibility, a novel optimal scheduling model based on chance-constrained programming (CCP), aiming at minimizing the lowest generation cost, is proposed for a small-scale integrated energy system (IES) with CHP units, thermal power units, renewable generations and representative auxiliary equipments. In this model, due to the uncertainties of renewable generations including wind turbines and photovoltaic units, the probabilistic spinning reserves are supplied in the form of chance-constrained; from the perspective of user experience, a heating load model is built with consideration of heat comfort and inertia in buildings. To solve the model, a solution approach based on sequence operation theory (SOT) is developed, where the original CCP-based scheduling model is tackled into a solvable mixed-integer linear programming (MILP) formulation by converting a chance constraint into its deterministic equivalence class, and thereby is solved via the CPLEX solver. We report the simulation results on the modified IEEE 30-bus system demonstrate that the presented method manages to improve operational flexibility of the IES with uncertain renewable generations by comprehensively leveraging thermal inertia of buildings and different kinds of auxiliary equipments, which provides a fundamental way for promoting renewable energy consumption.

30 DIRECT ENERGY CONVERSION↗

The new Batch Mode Ion Source for stand-alone operation at the Facility for Rare Isotope Beams (FRIB)

Gas stoppers have been used for a long-standing successful science program at Michigan State University with stopped and rare-isotope beams produced by projectile fragmentation. The National Superconducting Cyclotron Laboratory’s Coupled Cyclotron Facility has recently transitioned into the Facility for Rare Isotope Beams (FRIB) laboratory to provide rare isotopes using a high-power superconducting linear accelerator and new production facilities. To allow the science program with stopped and reaccelerated beams to continue during the transition period, a stand-alone capability was added. The Batch Mode Ion Source (BMIS) was built and has been providing beams of long-lived and stable isotopes of a variety of elements for successful user experiments. Finally, the BMIS system is described and results from the production of various beams are presented.

47 OTHER INSTRUMENTATION↗

3.0 - MOOSE: Enabling massively parallel multiphysics simulations

The development of MOOSE has kept accelerating since the last release, with over 2,100 pull requests merged over the last 30 months that involved nearly fifty contributors across close to a dozen institutions internationally. The growth in MOOSE's capabilities and downstream applications is reflected in the growth of the community. User support provided on the GitHub discussions forum has steadily increased to nearly 50 daily interactions. New simulation projects, notably to model advanced nuclear reactor and fusion devices, are driving a significant expansion of the capabilities. This paper reports on these developments, with several major released features, new physics modules, and key improvements to the user experience and simulation workflow.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Optimal experimental design using eigenvalue-based criteria with Pyomo.DoE

New developments in automated optimal experimental design within the PSE+ software ecosystem. Advancements in user experience (to reduce the time taken to perform optimal experiment design) and computational capabilities (allowing more diverse experimental design) are shown with an example relevant to critical minerals and materials. Also, a small tutorial on science-based optimal experimental design and novel contributions therein are presented.

97 MATHEMATICS AND COMPUTING↗