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370 records · Page 7

Pre- and post-processing of cluster galaxies out to 5 × R 200: the extreme case of A2670

ABSTRACT We study galaxy interactions in the large-scale environment around A2670, a massive (M200 = $8.5 \pm 1.2~\times 10^{14} \, \mathrm{{M}_{\odot }}$) and interacting galaxy cluster at z = 0.0763. We first characterize the environment of the cluster out to 5× R200 and find a wealth of substructures, including the main cluster core, a large infalling group, and several other substructures. To study the impact of these substructures (pre-processing) and their accretion into the main cluster (post-processing) on the member galaxies, we visually examined optical images to look for signatures indicative of gravitational or hydrodynamical interactions. We find that ∼21 per cent of the cluster galaxies have clear signs of disturbances, with most of those (∼60 per cent) likely being disturbed by ram pressure. The number of ram-pressure stripping candidates found (101) in A2670 is the largest to date for a single system, and while they are more common in the cluster core, they can be found even at >4 × R200, confirming cluster influence out to large radii. In support of a pre-processing scenario, most of the disturbed galaxies follow the substructures found, with the richest structures having more disturbed galaxies. Post-processing also seems plausible, as many galaxy–galaxy mergers are seen near the cluster core, which is not expected in relaxed clusters. In addition, there is a comparable fraction of disturbed galaxies in and outside substructures. Overall, our results highlight the complex interplay of gas stripping and gravitational interactions in actively assembling clusters up to 5 × R200, motivating wide-area studies in larger cluster samples.

Astronomy & Astrophysics

The Slow Demise of the Long-Lived Sn 2005ip

The Type IIn supernova (SN IIn) 2005ip is one of the most well-studied and long-lasting examples of an SN interacting with its circumstellar environment. The optical light curve plateaued at a nearly constant level for more than five years, suggesting ongoing shock interaction with an extended and clumpy circumstellar medium (CSM). Here, we present continued observations of the SN from ∼1000 to 5000 d post-explosion at all wavelengths, including X-ray, ultraviolet, near-infrared (NIR), and mid-infrared. The UV spectra probe the pre-explosion mass loss and show evidence for CNO processing. From the bolometric light curve, we find that the total radiated energy is in excess of 10 50 erg, the progenitor star’s pre-explosion mass-loss rate was >~ 1 × 10 −2 Mꙩ yr −1 , and the total mass lost shortly before explosion was >~1Mꙩ, though the mass lost could have been considerably larger depending on the efficiency for the conversion of kinetic energy to radiation. The ultraviolet through NIR spectrum is characterized by two high-density components, one with narrow high-ionization lines, and one with broader low-ionization H I, He I, [OI], Mg II, and Fe II lines. The rich Fe II spectrum is strongly affected by Lyα fluorescence, consistent with spectral modelling. Both the Balmer and He I lines indicate a decreasing CSM density during the late interaction period. We find similarities to SN 1988Z, which shows a comparable change in spectrum at around the same time during its very slow decline. These results suggest that, at long last, the shock interaction in SN 2005ip may finally be on the decline.

stars

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING

Controls for Electrified Aircraft Propulsion

Advanced electrified aircraft propulsion (EAP) concepts with integrated power, propulsion, and thermal systems require the development of equally sophisticated controllers to fly safe and efficient missions. Hybrid electric aircraft utilize electric machines mechanically coupled to the engine shafts to extract and insert power for a variety of purposes. Additionally, electric machines may drive propulsive fans pulling from a combination of on-board energy storage devices and engine extracted power. NASA’s investment in hybrid electric aircraft hardware-in-the-loop testing enables controls research on representative engine models using a novel emulation and scaling methodology. High-voltage, high-power electrical powertrain presents several technical risks at altitude. High-power requires high efficiency to minimize losses. Superconducting electric machines and power distribution research at NASA has identified key challenges with potential controls solutions. These risks necessitate the development of controllers robust to model uncertainty, disturbances, and fault conditions. System health management and fault detection schemes play an important role in a multi-layer controls approach that utilizes a supervisor which oversees inner loops for the highly coupled power, propulsion, and thermal systems. Such a supervisory controller enables coordinates energy transfer between engines, energy storage devices, electric machines, propulsors, and heat exchangers. Existing methods have shown an improvement in engine operability using the hybrid electric powertrain.

Halle E Buescher

Extreme confinement of hydrogen gas within fullerenelike nanoporous carbon

Nanoporous carbons and carbon nanostructures can store hydrogen at cryogenic temperatures but lack the volumetric and gravimetric capacity to be industrially significant. Recent inelastic neutron scattering experiments suggest a highly dense phase of hydrogen at temperatures well above the melting point of solid hydrogen. However, it remains unclear how pore geometry and intermolecular interactions enable these dense phases to exist, with dispersion (van der Waals) or electrostatic/induction suggested to be the key effects in slit and curved pores but their relative contributions have yet to be quantified. In this paper, we perform benchmark electronic structure calculations allowing the interactions between planar and curved aromatic molecules with hydrogen to be accurately determined. Dispersion was found to dominate over electrostatic and inductive effects with some many-body charge transfer (Dobson type-A) effects needed to capture the most highly curved structures. Density functional methods that include type-A many-body effects were found to accurately describe the intermolecular interactions at a fraction of the cost of coupled-cluster simulations and these approaches were used to calculate the energies inside large carbon bowl and slit pores. The interaction energies inside the bowl pores were found to depend on the orientation of the hydrogen molecule. This rotational barrier, modeled as a quantum hindered rotor, could reproduce the peak splitting observed in inelastic neutron scattering experiments, with weak splitting arising from bowl-like fullerene pores and strong splitting from highly confining nanotubelike pores. Increasing the fraction of such curved pores in nanoporous carbons may therefore offer a pathway to enhance their hydrogen-storage capacity. Moreover, the preferential adsorption of ortho hydrogen on nanotubelike pores could enable the storage of high-density hydrogen without the need to remove heat produced during the ortho-para hydrogen conversion.

36 MATERIALS SCIENCE

Test Data Analysis of the Thermodynamic Vent System-Augmented Top Spray Injector Liquid Nitrogen Transfer Experiments

Traditionally, a cryogenic tank must be pre-chilled to some “target” temperature before the main vent valve can be closed to attempt a non-vented fill (NVF) of cryogenic liquid propellant. This methodology is particularly attractive for performing in-space transfer of cryogens due to the unknown location of the liquid/vapor interface in microgravity and the high likelihood of venting liquid if the vent valve is opened during transfer. This paper presents in-depth test data analysis of a Thermodynamic Vent System (TVS) augmented injector used for cryogenic tank chilldown and fill experiments of a thin-walled Titanium tank. Eight tests were conducted using liquid nitrogen across a range of inlet conditions and boundary conditions, and three different chilldown/fill methods. For four of the tests, the injector sprays liquid into the tank as normal, but also uses a TVS heat exchanger to cool the metallic injector itself as well as the main incoming liquid stream. Results show that using the TVS augmented injector simplifies transfer operation via enhanced condensation at the injector surface at the cost of sacrificing only a small amount of propellant.

Thermodynamic Vent System

Gaseous Optical Contamination of the Spacecraft Environment: A Review

Interactions between the ambient atmosphere and orbiting spacecraft, sounding rockets, and suborbital vehicles, and with their effluents, give rise to optical (extreme UV to LWIR) foreground radiation which constitutes noise that raises the detection threshold for terrestrial and celestial radiations, as well as military targets. Researchers review the current information on the on-orbit optical contamination. Its source species are created in interaction processes that can be grouped into three categories: (1) Reactions in the gas phase between the ambient atmosphere and desorbates and exhaust; (2) Reactions catalyzed by exposed ram surfaces, which occur spontaneously even in the absence of active material releases from the vehicles; and (3) Erosive excitative reactions with exposed bulk (organic) materials, which have recently been identified in the laboratory though not as yet observed on spacecraft. Researchers also assess the effect of optical pumping by earthshine and sunlight of both reaction products and effluents.

Tran, N. H.

Time-Resolved Stochastic Dynamics of Quantum Thermal Machines

Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing an exchange of finite quanta with the environment. Here, in this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles classified as enginelike, coolinglike, or idle. We analyze the statistics of individual cycle types and their durations, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of a given type. Central to our analysis is the notion of intermittency, which captures the operational consistency of the machine by assessing the frequency and distribution of idle cycles. Our framework offers a novel approach to characterizing thermal machines, with significant relevance to experiments involving mesoscopic transport through quantum dots.

full counting statistics

Monte Carlo modeling of atomic oxygen attack of polymers with protective coatings on LDEF

Characterization of the behavior of atomic oxygen interaction with materials on the Long Duration Exposure Facility (LDEF) will assist in understanding the mechanisms involved, and will lead to improved reliability in predicting in-space durability of materials based on ground laboratory testing. A computational simulation of atomic oxygen interaction with protected polymers was developed using Monte Carlo techniques. Through the use of assumed mechanistic behavior of atomic oxygen and results of both ground laboratory and LDEF data, a predictive Monte Carlo model was developed which simulates the oxidation processes that occur on polymers with applied protective coatings that have defects. The use of high atomic oxygen fluence-directed ram LDEF results has enabled mechanistic implications to be made by adjusting Monte Carlo modeling assumptions to match observed results based on scanning electron microscopy. Modeling assumptions, implications, and predictions are presented, along with comparison of observed ground laboratory and LDEF results.

Bruce A. Banks

Solar Heat for Industrial Processes: Integration with Chemical Reactors

The integration of solar thermal systems with chemical reactors has been proposed as part of a larger effort to develop and deploy solar heat for industrial processes (SHIP) technologies. A strong motivation for SHIP processes and technologies is the potential for high thermal efficiency coupled with low-cost thermal energy storage (TES) which can enable commercial deployment of such systems. While there are different ways to categorize SHIP technologies, one important such distinction is between directly irradiated systems and indirect off-sun process driven by a SHIP system. While directly irradiated systems can provide high thermal efficiencies and high fluxes, they usually require complex engineering solutions due to the need for redesigning the established processes and unit operations. In most cases, it is also more challenging to couple such a process to a TES system, losing some of the benefits of SHIP. On the other hand, using a SHIP system to drive an industrial process off-sun can allow better integration with existing process chains, easier TES capabilities, and potential for more applications fitting a specific SHIP technology. However, the integration of SHIP systems with the industrial processes is not fully explored in detail, especially in the case of high-temperature processes such as reforming, cracking, cement manufacturing, and iron/steelmaking. Many of these systems require heating fluxes of >50 kW/m^2, supplied via combustion of hydrocarbons in a fire box and benefitting from radiative heat transfer between the flue gases and the reaction zones. As such, using SHIP systems for such processes is more complex than providing the same thermal input in the form of a heat transfer medium (HTM) entering the reactor, kiln, or furnace. Moreover, in case convective heat transfer using SHIP is envisioned, for example using supercritical CO2 as the HTM from a particle receiver, the thermal integration might be more challenging than initially envisioned: lower heat transfer coefficients and limited approach temperature might require large flow rates, causing a mismatch between the process thermal requirements and the thermal capacity of the SHIP system. In addition, even if the heat exchange between SHIP and reactor is effective, there is still a cold leg HTM at the reaction temperature or slightly below it. Chemical plants usually include a set of heat exchangers, heat recovery steam generators, and even power generation units - in a tightly integrated design - to recover the flue gases which are eventually vented. With SHIP systems mostly operating on a closed HTM loop, bottoming the cold leg is crucial. In this talk, we will present different modeling results for a variety of syngas production reactions, using catalytic and chemical looping processes, and discuss some of the challenges and design considerations for off-sun chemical reactors using SHIP systems.

14 SOLAR ENERGY

The NASA Inductrack Model Rocket Launcher at the Lawrence Livermore National Laboratory

The Inductrack magnetic levitation system, developed at the Lawrence Livermore National Laboratory, is being studied for its possible use for launching rockets. Under NASA sponsorship, a small model system is being constructed at the Laboratory to pursue key technical aspects of this proposed application. The Inductrack is a passive magnetic levitation system employing special arrays of high-field permanent magnets (Halbach arrays) on the levitating carrier, moving above a "track" consisting of a close-packed array of shorted coils with which are interleaved with special drive coils. Halbach arrays produce a strong spatially periodic magnetic field on the front surface of the arrays, while canceling the field on their back surface. Relative motion between the Halbach arrays and the track coils induces currents in those coils. These currents levitate the carrier cart by interacting with the horizontal component of the magnetic field. Pulsed currents in the drive coils, synchronized with the motion of the carrier, interact with the vertical component of the magnetic field to provide acceleration forces. Motional stability, including resistance to both vertical and lateral aerodynamic forces, is provided by having Halbach arrays that interact with both the upper and the lower sides of the track coils. In its completed form the model system that is under construction will have a track approximately 100 meters in length along which the carrier cart will be propelled up to peak speeds of Mach 0.4 to 0.5 before being decelerated. Preliminary studies of the parameters of a full-scale system have also been made. These studies address the problems of scale-up, including means to simplify the track construction and to reduce the cost of the pulsed-power systems needed for propulsion.

L S Tung

Research Reports: 2001 NASA/ASEE Summer Faculty Fellowship Program

For the thirty-seventh consecutive year, a NASA/ASEE (American Society for Engineering Education) Summer Faculty Fellowship Program was conducted at Marshall Space Flight Center (MSFC). The program was conducted by The University of Alabama in Huntsville and MSFC during the period May 29 - August 3, 2001. Operated under the auspices of the American Society for Engineering Education, the MSFC program, as well as those at other NASA Centers, was sponsored by the University Affairs Office, NASA Headquarters, Washington, DC. The basic objectives of the programs, which are in the thirty-seventh year of operation nationally, are (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate an exchange of ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA Centers. The Faculty Fellows spent ten weeks at MSFC engaged in a research project compatible with their interests and background and worked in collaboration with a NASA MSFC colleague. This document is a compilation of Fellows' reports on their research during the summer of 2001.

Avionics

Influence of controlled disorder on the dipolar spin-ice state of Ho-based pyrochlores

Pyrochlore magnets of the form 𝑅 2 ⁢𝐵 2 ⁢O 7 , in which rare-earth ions on the 𝑅 site form a three-dimensional network of corner-sharing tetrahedra, provide a canonical setting for geometrical frustration. Ho-based pyrochlores host a dipolar spin-ice ground state, characterized by Ising moments constrained by the ice rules and elementary excitations analogous to magnetic monopoles. Here, in this work, we examine how controlled chemical disorder influences this state by introducing site mixing on the nonmagnetic 𝐵 site in two compounds. Ho 2⁢ GaSbO 7 contains only Ga 3+ /Sb 5+ charge disorder, whereas Ho 2 ⁢ScSbO 7 exhibits both charge and substantial size disorder arising from the large ionic-radius mismatch between Sc 3+ and Sb 5+ . Although both materials retain the pyrochlore structure, neutron-scattering measurements reveal a reduced correlation length for the 𝑅/𝐵-site cation ordering and enhanced local structural distortions in Ho 2 ⁢ScSbO 7 . Despite these structural differences, bulk thermodynamic measurements and magnetic diffuse scattering demonstrate that both systems exhibit the defining signatures of a dipolar spin-ice state. Low-energy inelastic neutron spectroscopy further uncovers broad magnetic excitations that develop within the dipolar spin-ice regime, a feature absent in pristine Ho pyrochlores and indicative of disorder-induced splitting of the non-Kramers ground-state doublet. Together, these results show that controlled disorder generates tunable transverse-field-driven quantum fluctuations in Ho-based pyrochlores, although the dipolar spin-ice state is remarkably robust to this disorder.

magnetic anisotropy

Adsorption of hydroxamic acid ligands for improved extraction of rare earth elements from monazite ores

Efficient separation of rare earth element (REE) ores via froth flotation requires the development of novel ligands with enhanced adsorption capacity and selectivity. To realize these advances, understanding the mechanisms underlying interactions between the ligand and mineral surfaces is essential. This study systematically evaluates the adsorption behavior of alkyl- and aromatic alkyl-substituted hydroxamic acid ligands on monazite surfaces using complementary spectroscopic techniques, including UV–visible (UV–vis) spectroscopy, Raman spectroscopy, infrared spectroscopy, and vibrational sum frequency generation (SFG) spectroscopy, together with the ab initio molecular dynamics (AIMD) simulations. Among the studied ligands, octanohydroxamic acid (OHA) and 4-ethoxy-N,2-dihydroxybenzamide (EDHBA) exhibit high adsorption capacity under basic pH (8–10) by forming multilayers on the surface. OHA has a higher equilibrium adsorption capacity compared to EDHBA, but it forms a less stable multilayer susceptible to disruption in the presence of interfering ions. AIMD results show that OHA adopts a single stable chelating geometry, while EDHBA exhibits multiple binding modes involving distinct interactions with La surface atoms and phosphate-bound oxygens, resulting in more complex adsorption kinetics. The variations in surface binding and intermolecular interactions observed between alkyl and aromatic molecules influence the differences in adsorption kinetics, equilibrium adsorption capacities on the mineral surface, and their flotation performance. This work provides valuable insight into the adsorption mechanism of ligands at mineral interfaces, which is crucial for guiding the design of new ligands with enhanced separation performance.

Zhou, Muchu [ORNL] (ORCID:0000000182650215)

Machine Learning for Predicting Team Functioning in HERA Missions

Team functioning is integral to success in future long term space exploration missions. Proactively detecting declines in team functioning can mitigate conflict and ensure mission success. This project developed a speech-based artificial intelligence (AI) system that unobtrusively predicts degradation in team functioning, including performance and cohesion, in the Human Exploration Research Analog (HERA) Campaigns 4 and 5. The AI system conducted automated analysis of the prosodic (tone of voice) and linguistic (language content) components of speech, modeling interpersonal dynamics at both the turn-taking and day-wide levels. We investigated team functioning via observing structured interactions (i.e., multi-mission space exploration vehicle-extra vehicular activity [MMSEV-EVA], team interaction battery [TIB]) and unstructured interactions before the MMSEV-EVA task. We developed machine learning models to predict team functioning (objective task accuracy, self reported team efficacy and self reported team cohesion) by analyzing OpenSmile acoustic features, linguistic descriptors extracted via the linguistic inquiry and word count (LIWC) dictionary, and semantic embeddings. In the TIB, static models using logistic regression and random forests were not able to predict task accuracy, but predicted team efficacy and cohesion during both the decision making and relational tasks to a moderate level (60-70%). Majority voting on the individual turns to predict day long team efficacy further increased accuracies (70-80%). Finally, long short-term memory (LSTM) models showed the best performance across all variables (80-91%), including task performance. In the MMSEV-EVA, static models achieved an accuracy of 60% with majority voting, which increased to 80% through the incorporation of mission day as a variable, accounting for the learning effect. A key finding across both tasks was the "team-dependent" nature of these interactions; models achieved much higher accuracy when trained on prior days of the same team's data rather than attempting to generalize across entirely different teams, with even 1-2 days of prior data per team achieving 5-15% improvement over team-independent models. In addition, the incorporation of pre-task data from the same team also improves model performance, e.g., incorporating data from the decision-making task of the TIB, which preceded the relational task, improved the prediction of team efficacy and cohesion during the latter. We compared model performance when trained on machine-generated data compared to data that had been further corrected by human annotators. Overall, models trained on human-corrected data exhibited a modest improvement in performance, particularly when acoustic features were used. We found no significant correlation between word error rate (WER) and model accuracy (r(55) = -0.08, p = 0.51), but model’s accuracy was significantly higher for medium/high quality transcription (0.74 (SD = 0.48)) compared to the low-quality group (0.64 (SD = 0.36)) (t(63)=2.82, p = 0.006). Based on these, several design recommendation emerge, that could inform Standards at NASA. Models predicting team functioning should incorporate at least one to two days of historical interaction data, include brief pre-task discussions, and explicitly model temporal learning effects, especially for longer operational tasks. Minimum quality standards for automated speech-processing pipelines are needed, given the performance gains observed with manually corrected acoustic data. Finally, systems should leverage both acoustic features and language embeddings in complementary ways, with modality choices and fusion strategies tailored to mission context, task demands, and data quality requirements.

Shrivatsa Mishra

Signatures of a spin-active interface and a locally enhanced Zeeman field in a superconductor-chiral material heterostructure

A localized Zeeman field, intensified at heterostructure interfaces, could play a crucial role in a broad area including spintronics and unconventional superconductors. Conventionally, the generation of a local Zeeman field is achieved through magnetic exchange coupling with a magnetic material. However, magnetic elements often introduce defects, which could weaken or destroy superconductivity. Alternatively, the coupling between a superconductor with strong spin-orbit coupling and a nonmagnetic chiral material could serve as a promising approach to generate a spin-active interface. Here, we leverage an interface superconductor, namely, induced superconductivity in noble metal surface states, to probe the spin-active interface. Our results unveil an enhanced interface Zeeman field, which selectively closes the surface superconducting gap while preserving the bulk superconducting pairing. The chiral material, i.e., trigonal tellurium, also induces Andreev bound states (ABS) exhibiting spin polarization. The field dependence of ABS manifests a substantially enhanced interface Landég-factor (g eff ~ 12), thereby corroborating the enhanced interface Zeeman energy.

Science & Technology - Other Topics

Tensorized Interior Radiative Heat Transfer for a Scalable and Calibrated Building Energy Simulator

Building energy simulation is a critical tool for developing and testing advanced control strategies, such as Reinforcement Learning (RL), to provide demand flexibility and affordable energy costs. The recently introduced Smart Buildings Control Suite (sbsim) provides a lightweight, scalable, and data-calibrated simulation environment based on a 2D finite-difference model. However, the initial model primarily focused on conductive and convective heat transfer, neglecting the significant impact of long-wave radiative heat exchange between interior surfaces. This paper presents a significant extension to the sbsim framework by incorporating a physically-grounded model for interior radiative heat transfer. Our primary contribution is the development and integration of a fully tensorized radiative heat transfer module, which preserves the computational efficiency and scalability of the original simulator. This was achieved by developing a pipeline for view factor calculation, including an algorithm to identify directly seeing surfaces within complex floor plans, and formulating the net radiation equations for efficient execution on modern hardware accelerators. We validate the numerical accuracy of our tensorized implementation by comparing its results against a traditional iterative approach, demonstrating identical outcomes. This enhancement increases the physical fidelity of sbsim, enabling more accurate training of RL agents for building energy optimization.

Ham, Sang woo

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