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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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559 records · Page 16

Heliostat sizing methodology for concentrating solar thermal industrial process heat projects

This study presents a method to obtain a heliostat size that minimizes the levelized cost of heat (LCOH) of a heliostat-based concentrating solar thermal system for applications of solar heating for industrial processes at operating temperatures from 565 to 1550°C. The method extends prior work by embedding a routine for system design that obtains near-optimal subsystem sizes, increasing the fidelity of drive cost functions, and adding an optical performance model to supplement the previously developed cost models, which we update to reflect current pricing trends. An illustrative business case is developed for Daggett, California, targeting specified annual thermal energy outputs of 50 to 400 GWh th . Optical performance is modeled using verified estimates from the literature. A surrogate heliostat cost model, derived from commercial heliostat designs and scaled for production volume, installation, and operations and maintenance costs, is used to develop cost functions. Results show that heliostat size strongly affects the LCOH, producing a characteristic U-shaped trend with a robust near-optimal window of 7-20 m 2 ; the heliostat size producing the lowest project cost in our study grows slightly as the project size increases, and is reduced as the operating temperature increases. The findings in this study are consistent with the general trend of smaller heliostats being deployed at existing projects for high-temperature industrial process heat and reflect the significant reduction in power electronics and other per-heliostat costs. The methodology we propose is general and can be tailored to revised cost curves as the technology continues to evolve.

14 SOLAR ENERGY

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING

The Benard Problem: A Comparison of Finite Difference and Spectral Collocation Eigen Value Solutions

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2 nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2 nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

J Raymond Lee Skarda

Analysis of Surface and Bulk Behavior in Ni-Pd Alloys

The most salient features of the surface structure and bulk behavior of Ni-Pd alloys have been studied using the BFS method for alloys. Large-scale atomistic simulations were performed to investigate surface segregation profiles as a function of temperature, crystal face, and composition. Pd enrichment of the first layer was observed in (111) and (100) surfaces, and enrichment of the top two layers occurred for (110) surfaces. In all cases, the segregation profile shows alternate planes enriched and depleted in Pd. In addition, the phase structure of bulk Ni-Pd alloys as a function of temperature and composition was studied. A weak ordering tendency was observed at low temperatures, which helps explain the compositional oscillations in the segregation profiles. Finally, based on atom-by-atom static energy calculations, a comprehensive explanation for the observed surface and bulk features will be presented in terms of competing chemical and strain energy effects.

Ordering

Manufacturing Process Development of a Carbon Fiber Reinforced Polymer Composite Shaft for Electric Motors

Electric aircraft applications require electric motors with increased specific power and efficiency. Composite structural components in motors are a potential solution for reducing motor mass, reducing magnetic losses, and limiting undesired conduction paths for fault, electromagnetic interference, or common-mode currents. In this report, manufacturing trials for a high-speed carbon fiber reinforced polymer composite motor shaft are presented. Four prototype shafts were produced using a hybrid biaxial/triaxial fabric that was circumferentially wrapped onto an additively manufactured high-temperature washout mandrel. An additional traditional overbraid approach was also evaluated and shows promise for high-rate, high-performance parts using automated manufacturing. This paper discusses the shaft design, manufacturing methods explored, material selection, the manufacturing trials, and the lessons learned. The results of this manufacturing investigation show feasibility for manufacturing composite shafts for electric motors.

Electric moto shaft

Machine Learning for Predicting Multipactor Susceptibility in Planar RF Structures

Multipactor discharge is a persistent challenge in high-power microwave (HPM) and accelerator systems, where secondary electron avalanches can cause heating, vacuum degradation, and failure. This work presents the first supervised machine learning (ML) framework for multipactor prediction, trained on high-fidelity 3D Particle-in-Cell (PIC) simulation data in planar geometries. The model maps operational, geometric, and material-dependent secondary electron yield (SEY) parameters to the time-averaged electron growth rate, enabling rapid reconstruction of susceptibility charts. Among the models evaluated, tree-based ensemble methods such as Random Forest and Extra Trees demonstrate superior generalization to unseen materials compared to neural networks such as multilayer perceptron (MLP). Performance metrics, including Intersection over Union (IoU), Structural Similarity Index Measure (SSIM), and Pearson correlation, show close agreement with simulation benchmarks. Principal Component Analysis attributes generalization limits to material feature-space disjointedness.

43 PARTICLE ACCELERATORS

Carbon Fiber Composite Processing Using Isothermal Resins

To meet future demand for single-aisle composite aircraft production, manufacturing rates are expected to increase by up to six times current production rates. Resin infusion is a manufacturing method that has potential to enable fabrication of structures at the desired rates. However, production cycle times with currently available commercial infusion resins cannot support the rates needed for an estimated 80 aircraft per month. Recently, rapid-curing isothermal resins were developed that can reduce the overall processing time. These resins can be infused, cured, and demolded at a single temperature below 100 °C, thereby eliminating the need for time consuming temperature ramps and shortening the overall cure time. In addition, the low temperatures enable use of low-cost tooling during production. This presentation will discuss the use of resin transfer molding to produce composites with rapid-curing isothermal resins, manufacturing considerations, and performance characteristics of the composites.

John M Gardner

Converting Second‐Order Saddle Points to Transition States: New Principles for the Design of 4π Photoswitches

Abstract Molecular photoswitches have demonstrated potential for storing solar energy at the molecular level, with power densities comparable to commercial batteries and hydroelectric energy storage. However, development of efficient photoswitches is hindered by limitations in cyclability and optical properties of existing materials. We here demonstrate that certain limitations in photoswitches based on electrocyclizations stem from the issue of controlling competition between Woodward‐Hoffmann allowed and forbidden pathways. Our approach moves beyond the traditional view of activation barriers and reveals that second‐order saddle points are crucial in dictating the competition between disrotatory and conrotatory pathways. These insights suggest new opportunities to manipulate the competition between these pathways through geometric constraints, fundamentally altering the connectivity of the potential energy surface. Our study also emphasizes the necessity of multi‐reference methods and the need to conduct higher‐dimensional explorations for competing pathways beyond photoswitch design.

Chemistry

Impact of Crystalline Phases on Low-Activity Waste Glass Durability: Insights from PCT and VHT

During vitrification of nuclear wastes, slow cooling along the container centerline promotes crystalline phase formation, which can alter residual glass composition and reduce chemical durability. This study investigates the effects of crystalline phases on the chemical durability of low-activity waste (LAW) borosilicate glasses using the product consistency test (PCT) and vapor hydration test (VHT) on container centerline cooled (CCC) samples. A preliminary model (R2 = 0.88) was developed to predict CCC PCT responses based on glass composition, PCT data from quenched glasses, and measured crystal fractions. Using the latest LAW glass dataset, the feasibility of predictive modeling is evaluated, limitations in current data and methods are identified, and challenges for improving model accuracy are discussed to guide future data collection and model development.

borosilicate glass

Manufacturing Research in Support of Saturn V

Research achievements applicable to the production of Saturn V components a r e described in this report. Leakage at the mechanical connections in high-pressure lines has been minimized or eliminated through the use of precisely flared tubes. Flaring to close tolerance is done with a n orbital flaring adapter, and the forming operation is precisely controlled with an electronic control console. A technique of “aging” or heat-treatment hardening of aluminum materials has been used to form cylindrical-tank segments and double-contoured gore segments precisely, and to remove weld distortions). The control of weld porosity has been improved as a result of research which demonstrated the close correlation between electrical energy input per inch of weld and weld porosity and metallurgical quality. Based on this information, the gas metallic arc method has been used successfully for two-pass welding, and thinner gage aluminum has been welded (LOX tunnel to fuel bulkhead) with an MSFC designed gas metallic arc unit.

COMPOSITE MATERIAL

A Predictive Bubble Point Pressure Model for Porous Liquid Acquisition Device Screens

This article presents a simplified model for porous screen channel liquid acquisition devices based on a maximum bubble point pressure method from Adamson and Gast (1997). To validate the model, three 304 stainless steel (325 × 2300, 450 × 2750, and 510 × 3600) mesh samples were tested in methanol, acetone, isopropyl alcohol, and water. Screen pores are estimated based on analysis from scanning electron microscopy, historical data, and current test data. Results show that the bubble point pressure is proportional to the surface tension of the fluid only when accounting for nonzero contact angles. The previous assumption that bubble point pressure scales inversely with effective pore diameter is shown to be invalid, as the second finest 450 × 2750 produced the highest bubble point of the three screens. The simplified bubble point model can be used to make predictions for any pure fluid when pore diameters are based on bubble point tests and not SEM analysis.

Liquid Acquisition Device

ARCTRON: A Rapid Experimental Proving Ground for TPS Experiments and Arcjet Technology Development

Innovation in high-enthalpy facilities is fundamentally limited by the cost and risk of experimentation. New concepts for plasma control, diagnostics, facility components, and plasma-material interaction often require repeated iterations that are impractical to perform in production arcjets. As a result, promising ideas may remain unexplored or reach operational facilities only after significant development effort. ARCTRON is being developed as a rapid experimental proving ground where new ideas in plasma science, arcjet engineering, diagnostics, and material response can be conceived, tested, and quantitatively evaluated before transition to large-scale facilities. The platform combines radio-frequency (RF) and DC arc plasma generation, externally applied magnetic fields, configurable gas composition, reduced-pressure operation, laser heating, electrical biasing, and modular diagnostic access. These capabilities permit the plasma source, applied forcing, test article, and measurement configuration to be modified independently, allowing individual physical mechanisms to be isolated more readily than in a traditional test environment. One class of investigations addresses fundamental plasma-surface interaction physics. Conventional material tests often expose a specimen simultaneously to convective heating, reactive species, pressure, shear, radiation, and surface-current effects. The resulting material response may be measured accurately, while the contribution of each mechanism remains difficult to identify. ARCTRON is designed to vary these effects selectively. Plasma chemistry can be changed independently through configurable gas mixtures; magnetic fields and electrical biasing can modify charged-particle transport; laser heating can provide a non-plasma thermal input; and pressure, flow, and discharge mode can be varied over a broad operating space. This enables controlled tests of hypotheses involving surface catalycity, reactive-species transport, plasma-assisted oxidation, electromagnetic effects, shear, and the relative contributions of thermal and chemical loading. A second class of investigations enabled by this approach concerns the engineering of high-enthalpy facilities themselves. Arc-heated facilities are limited by electrode erosion, unstable arc attachment, localized heating, and damage to nozzles and other plasma-facing components. ARCTRON provides a lower-cost environment for testing concepts intended to mitigate these limitations. Candidate investigations include the use of applied magnetic fields to alter current paths and reduce plasma interaction with nozzle walls, ExB forcing to introduce controlled plasma rotation, magnetic or geometric approaches for distributing arc attachment, and alternative electrode or discharge configurations intended to reduce erosion and improve stability. Because the platform is reconfigurable, these concepts can be evaluated through repeated design--build--test cycles before they are considered for implementation in operational facilities. The platform also supports the development and validation of diagnostics that may be difficult to introduce initially into a large arcjet. Current and planned measurements include spatially resolved optical emission spectroscopy, electrostatic probes, fast imaging, pyrometry, calorimetry, laser-induced fluorescence, and absorption spectroscopy. These diagnostics are intended not merely to document a nominal operating condition, but to constrain the local plasma state and its relationship to component or material response. The modular facility geometry allows diagnostic concepts to be tested, calibrated, and compared under repeatable conditions before deployment in more demanding environments. ARCTRON is also supported by an integrated software suite. Automated control and data acquisition allow discharge parameters, gas composition, magnetic fields, diagnostic timing, and test configuration to be recorded as part of each experiment (STARDAC - Software for Testing, Analysis, Research Data, and Control). The Backend for Experiment Analysis, Storage, and Traceability (BEAST) is a database that provides the infrastructure needed to associate heterogeneous measurements with facility configuration, specimen identity, calibration state, geometry, and analysis provenance. This backend is particularly important for exploratory campaigns, in which many related configurations may be tested, and the value of an individual experiment depends on its connection to earlier and subsequent iterations. Complementary analysis capabilities, including computer-vision-based transient response measurements (arcjetCV), three-dimensional surface reconstruction (STARSCAN), and model-based Bayesian inference (SHIELD), and tomography data analysis (TOMATO, PuMA) can be incorporated when required by a specific hypothesis without becoming the focus of every campaign. The central objective of ARCTRON is therefore not to maximize heat flux or reproduce a complete flight environment. Its purpose is to reduce the cost and time required to ask consequential questions about plasma behavior, plasma-facing materials, diagnostics, and arcjet technology. By providing a controlled environment for rapid reconfiguration, mechanism isolation, quantitative measurement, and iterative engineering, ARCTRON can help mature concepts that would otherwise remain too speculative or too risky for evaluation in production facilities. The resulting knowledge can then guide the design of material models, focus test objectives in larger arcjets, reduce facility-development risk, and improve the physical basis of high-enthalpy ground testing. This work will present the ARCTRON architecture, operating modes, diagnostic suite, and digital experimental workflow. Initial experimental results from the first integrated operation of the facility will be presented, including flow characterization, power limitations, and deployment of the initial diagnostic suite. Ongoing development efforts aimed at catalycity characterization, magnetic plasma control, and advanced optical diagnostics will also be discussed, illustrating how the platform supports rapid iteration from concept to experiment.

experimental diagnostics

ARCTRON: A Rapid Experimental Proving Ground for TPS Experiments and Arcjet Technology Development

Innovation in high-enthalpy facilities is fundamentally limited by the cost and risk of experimentation. New concepts for plasma control, diagnostics, facility components, and plasma-material interaction often require repeated iterations that are impractical to perform in production arcjets. As a result, promising ideas may remain unexplored or reach operational facilities only after significant development effort. ARCTRON is being developed as a rapid experimental proving ground where new ideas in plasma science, arcjet engineering, diagnostics, and material response can be conceived, tested, and quantitatively evaluated before transition to large-scale facilities. The platform combines radio-frequency (RF) and DC arc plasma generation, externally applied magnetic fields, configurable gas composition, reduced-pressure operation, laser heating, electrical biasing, and modular diagnostic access. These capabilities permit the plasma source, applied forcing, test article, and measurement configuration to be modified independently, allowing individual physical mechanisms to be isolated more readily than in a traditional test environment. One class of investigations addresses fundamental plasma-surface interaction physics. Conventional material tests often expose a specimen simultaneously to convective heating, reactive species, pressure, shear, radiation, and surface-current effects. The resulting material response may be measured accurately, while the contribution of each mechanism remains difficult to identify. ARCTRON is designed to vary these effects selectively. Plasma chemistry can be changed independently through configurable gas mixtures; magnetic fields and electrical biasing can modify charged-particle transport; laser heating can provide a non-plasma thermal input; and pressure, flow, and discharge mode can be varied over a broad operating space. This enables controlled tests of hypotheses involving surface catalycity, reactive-species transport, plasma-assisted oxidation, electromagnetic effects, shear, and the relative contributions of thermal and chemical loading. A second class of investigations enabled by this approach concerns the engineering of high-enthalpy facilities themselves. Arc-heated facilities are limited by electrode erosion, unstable arc attachment, localized heating, and damage to nozzles and other plasma-facing components. ARCTRON provides a lower-cost environment for testing concepts intended to mitigate these limitations. Candidate investigations include the use of applied magnetic fields to alter current paths and reduce plasma interaction with nozzle walls, ExB forcing to introduce controlled plasma rotation, magnetic or geometric approaches for distributing arc attachment, and alternative electrode or discharge configurations intended to reduce erosion and improve stability. Because the platform is reconfigurable, these concepts can be evaluated through repeated design--build--test cycles before they are considered for implementation in operational facilities. The platform also supports the development and validation of diagnostics that may be difficult to introduce initially into a large arcjet. Current and planned measurements include spatially resolved optical emission spectroscopy, electrostatic probes, fast imaging, pyrometry, calorimetry, laser-induced fluorescence, and absorption spectroscopy. These diagnostics are intended not merely to document a nominal operating condition, but to constrain the local plasma state and its relationship to component or material response. The modular facility geometry allows diagnostic concepts to be tested, calibrated, and compared under repeatable conditions before deployment in more demanding environments. ARCTRON is also supported by an integrated software suite. Automated control and data acquisition allow discharge parameters, gas composition, magnetic fields, diagnostic timing, and test configuration to be recorded as part of each experiment (STARDAC - Software for Testing, Analysis, Research Data, and Control). The Backend for Experiment Analysis, Storage, and Traceability (BEAST) is a database that provides the infrastructure needed to associate heterogeneous measurements with facility configuration, specimen identity, calibration state, geometry, and analysis provenance. This backend is particularly important for exploratory campaigns, in which many related configurations may be tested, and the value of an individual experiment depends on its connection to earlier and subsequent iterations. Complementary analysis capabilities, including computer-vision-based transient response measurements (arcjetCV), three-dimensional surface reconstruction (STARSCAN), and model-based Bayesian inference (SHIELD), and tomography data analysis (TOMATO, PuMA) can be incorporated when required by a specific hypothesis without becoming the focus of every campaign. The central objective of ARCTRON is therefore not to maximize heat flux or reproduce a complete flight environment. Its purpose is to reduce the cost and time required to ask consequential questions about plasma behavior, plasma-facing materials, diagnostics, and arcjet technology. By providing a controlled environment for rapid reconfiguration, mechanism isolation, quantitative measurement, and iterative engineering, ARCTRON can help mature concepts that would otherwise remain too speculative or too risky for evaluation in production facilities. The resulting knowledge can then guide the design of material models, focus test objectives in larger arcjets, reduce facility-development risk, and improve the physical basis of high-enthalpy ground testing. This work will present the ARCTRON architecture, operating modes, diagnostic suite, and digital experimental workflow. Initial experimental results from the first integrated operation of the facility will be presented, including flow characterization, power limitations, and deployment of the initial diagnostic suite. Ongoing development efforts aimed at catalycity characterization, magnetic plasma control, and advanced optical diagnostics will also be discussed, illustrating how the platform supports rapid iteration from concept to experiment.

experimental diagnostics

Impact of Advances in Anion Exchange Membranes and Ionomers on Alkaline Fuel Cells

Abstract The operation of low‐temperature electrochemical energy conversion systems (fuel cells, electrolyzers) at high pH values is of perennial interest due to the possibility of moving away from expensive platinum group metal catalysts and reducing cost. Historically, the anion exchange membranes (AEMs) and ionomers have been hampered by performance (ionic conductivity, mechanical strength) and chemical stability issues. In this context, select developments over the past decade in alternate AEM chemistries, water management methods, and production of membrane electrode assemblies (MEAs) that have enabled a significant leap in performance of alkaline fuel cells are examined. These developments are linked to performance improvements in alkaline H 2 /O 2 fuel cells and also consider developments in alkaline fuel cells using nitrogen‐containing fuels (ammonia, hydrazine), carbon‐containing fuels (alcohols, glycols), and boron‐containing fuels (sodium borohydride, ammonia borane). Finally, current challenges and bottlenecks are identified, and potential solutions are proposed.

Chemistry

BLEECAM™ (Benchmarking Life Cycle Environmental, Economic, and Social Metrics for Critical and Advanced Minerals and Materials) [SWR-25-125]

The National Laboratory of the Rockies' (NLR) Benchmarking Life Cycle Environmental, Economic, and Social Metrics for Critical and Advanced Minerals and Materials (BLEECAM™) is an open-source, integrated decision-support tool for evaluating the impacts, risks, and trade-offs across U.S. and global materials supply chains. Funded by the U.S. Department of Energy, BLEECAM supports supply chain and market analysis. The tool integrates multi-objective supply chain optimization, system dynamics, network design, lifecycle assessment, techno-economic modeling, and social impact assessment methods to evaluate how supply chains evolve over time, geography, and deployment scenarios. BLEECAM also supports analysis related to energy infrastructure, data centers and digital infrastructure, advanced manufacturing, and other sectors that depend on critical materials.

Khalifa, SherifA. [National Laboratory of the Rock

X-ray tomography of damage dynamics in advanced materials using a laser wakefield accelerator

Additively manufactured (AM) metals offer the potential for customizable, cost-effective components, but qualification and certification are crucial. Key to this process is understanding pore dynamics under stress, typically analyzed using micro-computed tomography. This study introduces laboratory-scale “betatron” x-rays from laser wakefield acceleration as a high-throughput alternative for x-ray tomography of advanced materials, such as AM AlSi10Mg alloys. Coupled with 3D finite element modeling, this method provides detailed insights into stress-porosity interactions. The approach delivers high-resolution scans, revealing that pore shape and local triaxiality significantly influence fracture dynamics, supporting advanced material characterization. This work also demonstrates the potential and versatility of laser-betatron x-ray μCT for generating large datasets to accelerate our understanding of the stochastic, process-specific nature of pore formation in AM alloys.

Senthilkumaran, Vigneshvar

Automated Resupply of Consumables: Enhancement of Space Commercialization Opportunities

This paper addresses work performed at Rockwell International's Space Systems Division to investigate the feasibility of, and develop concepts for, automated and/or robotic resupply of consumables on orbit. The work focuses on the resupply of satellites and is described in five sections. First, the various problems relating the resupply on orbit are discussed: for example, economic concerns, fuel handling problems, and safety issues. Next major methods of effecting fuel transfer on orbit are summarized, together with their advantages and disadvantages. Direct fuel exchange is emphasized as the most feasible technique. Third, guidelines are developed for automated/robotic refueling mechanisms to accomplish on-orbit consumable resupply. For example, the guidelines cover safety, reliability, maintainability, alignment, induced loads, thermal protection, leaks, extravehicular activity (EVA) interface, and so on. The fourth part of the paper covers the development of design concepts for satellite resupply robotic interfaces that comply with the guidelines. Concepts include servicer fluid transfer system and satellite propulsion system, and a combined docking/umbilical device. Last, future technical development in these areas are discussed.

Davoud Manouchehri

The cluster decomposition of the configurational energy of multicomponent alloys

Abstract The cluster expansion method (CEM) is a widely used lattice-based technique in the study of multicomponent alloys. Despite its prevalent use, a clear understanding of expansion terms is lacking. We present a modern mathematical formalism of the CEM and introduce thecluster decomposition—a unique and basis-independent decomposition for functions of the atomic configuration in a crystal. We identify the cluster decomposition as an invariant ANOVA decomposition; and demonstrate how functional analysis of variance and sensitivity analysis can be used to interpret interactions among species. Furthermore, we show how the mathematical structure of the cluster decomposition enables numerical evaluation that scales with the number of clusters and is independent of the number of species. Overall, our work enables rigorous interpretations of interactions among species, provides opportunities to explore parameter estimation beyond linear regression, introduces a numerical efficient implementation, and enables analysis of cluster expansions based on established mathematical and statistical principles.

Chemistry