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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Onset of instabilities in rotating flows by direct numerical simulation

A rotating disk is the canonical experiment for measuring surface reaction rates in geochemical and electrochemical systems. Using the similarity solution for laminar flow around an infinite disk, the mass transfer coefficient can be simply related to the intrinsic reaction rate at the surface. However, measurements of mass transfer rates use a finite-size disk within a larger container of solution; here the flow is no longer strictly laminar, but there must always be some recirculation. Our interest was initially in the assumption of a uniform radial concentration field, how this breaks down near the perimeter of the disk, and what effect that might have on the measured mass transfer rates. However, our numerical simulations suggest that the flow around a finite-size disk becomes time dependent at Reynolds number ($\textit{Re}$) below 1000, which is much smaller than the typical values in mass-transfer measurements ($\textit{Re}$~10 4 ). In this work, we observe the formation of coherent structures in the flow, which suggest a non-uniform mass transfer at the disk surface. The rotating-disk flow follows a similar sequence of instabilities to the Taylor–Couette flow: a centrifugal instability leading an axisymmetric, time-invariant flow, followed by a Hopf bifurcation to a time-periodic flow. To minimise the possibility that our results are a numerical artefact, we have also simulated the instability in the stationary boundary layer of a rotor–stator flow, comparing with self-similar solutions at low $\textit{Re}$ and with spectral methods near the critical Reynolds number.

42 ENGINEERING↗
DOE OSTI2024

Reynolds-number scaling of wall-pressure–velocity correlations in wall-bounded turbulence

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range$Re_\tau \approx 550\unicode{x2013}5200$. Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of$\lambda _x/y \approx 14$(and$\lambda _x/y \approx 8$for the wall-normal velocity). When extending the analysis to both homogeneous directions in$x$and$y$, the peak coherence is centred at$\lambda _x/\lambda _z \approx 2$and$\lambda _x/\lambda _z \approx 1$for$p_w$and$u$, and$p_w$and$v$, respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of$Re_\tau \approx 2$k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of$\approx$0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.

Mechanics↗
DOE OSTI2025

Asymptotic coefficients of the attached-eddy model derived from an adiabatic atmosphere

The attached-eddy model (AEM) predicts that the mean streamwise velocity and streamwise velocity variance profiles follow a logarithmic shape, while the vertical velocity variance remains invariant with height in the overlap region of high Reynolds number wall-bounded turbulent flows. Moreover, the AEM coefficients are presumed to attain asymptotically constant values at very high Reynolds numbers. Here, the AEM predictions are examined using sonic anemometer measurements in the near-neutral atmospheric surface layer, with a focus on the logarithmic behaviour of the streamwise velocity variance. Utilizing an extensive 210-day dataset collected from a 62 m meteorological tower located in the Eastern Snake River Plain, Idaho, USA, the inertial sublayer is first identified by analysing the measured momentum flux and mean velocity profiles. The logarithmic behaviour of the streamwise velocity variance and the associated ‘−1’ scaling of the streamwise velocity energy spectra are then investigated. The findings indicate that the Townsend–Perry coefficient (A 1 ) is influenced by mild non-stationarity that manifests itself as a Reynolds number dependence. After excluding non-stationary runs, and requiring the bulk Reynolds number defined using the atmospheric boundary layer height to be larger than 4 × 10 7 , the inferred A 1 converges to values ranging between 1 and 1.25, consistent with laboratory experiments. Furthermore, nine benchmark cases selected through a restrictive quality control reveal a close relation between the ‘−1’ scaling in the streamwise velocity energy spectrum and the logarithmic behaviour of streamwise velocity variance. However, additional data are required to determine whether the plateau value of the pre-multiplied streamwise velocity energy spectrum is identical to A 1 .

atmospheric flows↗
DOE OSTI2026

Modulation induced by very-large-scale motions on the inclination angle of wall-attached eddies: an atmospheric surface layer experiment

The forward leaning inclination angle, 𝛾, of coherent turbulent structures is a well-known feature of wall-bounded turbulent flows. Although invariant across friction Reynolds numbers within the range 𝑅𝑒 𝜏 =10 3 −10 6 , 𝛾 can vary significantly across turbulent scales within a high-Reynolds-number flow. Very-large-scale motions (VLSMs) are known to induce significant changes in the instantaneous shear profile, which is a conditioning event that could trigger variability in the inclination angle of smaller coherent turbulent structures. Although this aspect has been extensively studied via numerical and laboratory experiments, few studies have explored this feature for a very-high-Reynolds-number atmospheric flow. In this work, the inclination angle of turbulent structures within the atmospheric surface layer at a very high Reynolds number (𝑅𝑒 𝜏 =7.9 ×10 5 ) is investigated by deploying a scanning Doppler light detection and ranging and a super large particle image velocimetry (SLPIV) apparatus. The inclination angle of wall-attached eddies is inferred either from the two-point correlation of streamwise velocity (𝛾 =41.1∘) or with a scale-dependent approach through the spectral linear stochastic estimator (SLSE). The SLSE (and, thus, the scale-dependent inclination angle) is conditionally evaluated based on the high- and low-momentum events induced by VLSMs, both in the streamwise (𝑢′𝑉𝐿𝑆𝑀) and in the vertical (𝑤′ 𝑉𝐿𝑆𝑀) velocity components. As a result, lower inclination angles (𝛾 =30° −50°) are found for 𝑢$^{'}_{VLSM}$ >0 (𝑤$^{'}_{VLSM}$ <0), while higher values (50° −85°) are ascribed to 𝑢$^{'}_{VLSM}$ <0 (𝑤$^{'}_{VLSM}$ >0). This result emphasises the primary role that VLSMs play in shaping the wall-attached eddy geometry, which, in turn, is crucial to determine the Reynolds stress balance within the wall-attached eddy range.

42 ENGINEERING↗
DOE OSTI2022

Discovery of peculiar radio morphologies with ASKAP using unsupervised machine learning

Abstract We present a set of peculiar radio sources detected using an unsupervised machine learning method. We use data from the Australian Square Kilometre Array Pathfinder (ASKAP) telescope to train a self-organizing map (SOM). The radio maps from three ASKAP surveys, Evolutionary Map of Universe pilot survey (EMU-PS), Deep Investigation of Neutral Gas Origins pilot survey (DINGO), and Survey With ASKAP of GAMA-09 + X-ray (SWAG-X), are used to search for the rarest or unknown radio morphologies. We use an extension of the SOM algorithm that implements rotation and flipping invariance on astronomical sources. The SOM is trained using the images of all ‘complex’ radio sources in the EMU-PS which we define as all sources catalogued as ‘multi-component’. The trained SOM is then used to estimate a similarity score for complex sources in all surveys. We select 0.5% of the sources that are most complex according to the similarity metric and visually examine them to find the rarest radio morphologies. Among these, we find two new odd radio circle (ORC) candidates and five other peculiar morphologies. We discuss multiwavelength properties and the optical/infrared counterparts of selected peculiar sources. In addition, we present examples of conventional radio morphologies including: diffuse emission from galaxy clusters, and resolved, bent-tailed, and FR-I and FR-II type radio galaxies. We discuss the overdense environment that may be the reason behind the circular shape of ORC candidates.

Astronomy & Astrophysics↗
DOE OSTI2020

Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer

Here, we report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers, and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants, viz. the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in a critically balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Hamiltonian reduction of Vlasov–Maxwell to a dark slow manifold

In this work, we show that non-relativistic scaling of the collisionless Vlasov–Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov–Maxwell phase space. Vlasov–Maxwell dynamics restricted to the slow manifold recovers the Vlasov–Poisson and Vlasov–Darwin models as low-order approximations, and provides higher-order corrections to the Vlasov–Darwin model more generally. The slow manifold may be interpreted to all orders in perturbation theory as a collection of formal Vlasov–Maxwell solutions that do not excite light waves, and are therefore ‘dark’. We provide a heuristic lower bound for the time interval over which Vlasov–Maxwell solutions initialized optimally near the slow manifold remain dark. We also show how the dynamics on the slow manifold naturally inherits a Hamiltonian structure from the underlying system. After expressing this structure in a simple form, we use it to identify a manifestly Hamiltonian correction to the Vlasov–Darwin model. The derivation of higher-order terms is reduced to computing the corrections of the system Hamiltonian restricted to the slow manifold.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via the momentum map. We numerically demonstrate this time invariance of the momentum map and its usefulness in establishing precise initial conditions with a desired initial electric field and fixed background charge. The restriction of this canonical, finite element Poisson structure to the 1X2P $1\frac {1}{2}$ -dimensional phase space is also considered and simulated numerically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Finite orbit width effects in large aspect ratio stellarators

New orbit-averaged equations for low collisionality neoclassical fluxes in large aspect ratio stellarators with mirror ratios close to unity are derived. The equations retain finite orbit width effects by employing the second adiabatic invariant $J$ as a velocity-space coordinate and they have been implemented in the orbit-averaged neoclassical code KNOSOS (Velasco et al. , J. Comput. Phys. , vol. 418, 2020, 109512; Velasco et al. , Nucl. Fusion , vol. 61, 2021, 116013). The equations are used to study the $1/\nu$ regime and the lower collisionality regimes. For generic large aspect ratio stellarators with mirror ratios close to unity, as the collision frequency decreases, the $1/\nu$ regime transitions directly into the $\nu$ regime, without passing through a $\sqrt {\nu }$ regime. An explicit formula for the neoclassical fluxes in the $\nu$ regime is obtained. The formula includes the effect of particles that transition between different types of wells. While these transitions produce stochastic scattering independent of the value of the collision frequency in velocity space, the diffusion in real space remains proportional to the collision frequency. The $\sqrt {\nu }$ regime is only recovered in large aspect ratio stellarators close to omnigeneity: large aspect ratio stellarators with large mirror ratios and optimized large aspect ratio stellarators with mirror ratios close to unity. Neoclassical transport in large aspect ratio stellarators with large mirror ratios can be calculated with the orbit-averaged equations derived by Calvo et al. ( Plasma Phys. Control. Fusion , vol. 59, 2017, 055014). In these stellarators, the $\sqrt {\nu }$ regime exists in the collisionality interval $(a/R) \ln (R/a) \ll \nu _{ii} R a/\rho _i v_{ti} \ll R/a$ . In optimized large aspect ratio stellarators with mirror ratios close to unity, the $\sqrt {\nu }$ regime occurs in an interval of collisionality that depends on the deviation from omnigeneity $\delta$ : $\delta ^{2} |\ln \delta | \ll \nu _{ii} R a/\rho _i v_{ti} \ll 1$ . Here, $\nu _{ii}$ is the ion–ion collision frequency, $\rho _i$ and $v_{ti}$ are the ion gyroradius and thermal speed, and $a$ and $R$ are the minor and major radii.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Detecting shearless phase-space transport barriers in global gyrokinetic turbulence simulations with test particle map models

In magnetically confined fusion plasmas, the role played by zonal 𝐸 x 𝐵 flow shear layers in the suppression of turbulent transport is relatively well understood. However, less is understood about the role played by the weak shear regions that arise in the non-monotonic radial electric field profiles often associated with these shear layers. In electrostatic simulations from the global total-𝑓 gyrokinetic particle-in-cell code XGC, we demonstrate how shearless regions with non-zero flow curvature form zonal ‘jets’ that, in conjunction with neighbouring regions of shear, can act as robust barriers to particle transport and turbulence spreading. By isolating quasi-coherent fluctuations radially localised to the zonal jets, we construct a map model for the Lagrangian dynamics of gyrokinetic test particles in the presence of drift waves. We identify the presence of shearless invariant tori in this model and verify that these tori act as partial phase-space transport barriers in the simulations. We also demonstrate how avalanches impinging on these shearless tori cause eddy detachment events that form ‘cold/warm core ring’ structures analogous to those found in oceanic jets, facilitating transport across the barriers without destroying them completely. We discuss how shearless tori may generically arise from tertiary instabilities or other types of discrete eigenmodes, suggesting their potential relevance to broader classes of turbulent fluctuations.

fusion plasma↗
DOE OSTI2021

Antiferromagnetic Order and Linear Magnetoresistance in Fe-Substituted Shandite Co 3 In 2 S 2

Co 3 In 2 S 2 is a shandite phase closely related to the ferromagnetic Weyl semimetal Co 3 Sn 2 S 2 and contains Co atoms on an ideal kagome net. Elemental substitutions in Co 3 Sn 2 S 2 have been shown to invariably suppress its magnetism, and it remains a rare example of a shandite phase with magnetic order. Here, we report a new magnetic shandite compound discovered by substituting Fe into Co 3 In 2 S 2 . Single crystals of (Co 1–x Fe x ) 3 In 2 S 2 were grown, and neutron diffraction, ac and dc magnetization, and heat capacity measurements reveal long-range antiferromagnetic order with an interesting noncollinear structure and transition temperatures from 11 to 17 K. Partially substituting Fe for Co was inspired by calculated electronic structures, which suggest that Co 3 In 2 S 2 is near a magnetic instability and shows a peak in the density of states that can be approached by hole doping. While the focus of the present work is primarily on magnetism, there is a nodal ring below the Fermi energy in Co 3 In 2 S 2 that may also provide interest from a topological perspective. Potentially related to this, we find large, linear, nonsaturating magnetoresistance in this compound. Furthermore, this work expands the scope of magnetic topological materials among shandites and motivates similar chemical manipulation studies to reveal hidden magnetic instabilities in this important family and other topological systems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Electrolyte-Induced Restructuring of Acid-Stable Oxygen Evolution Catalysts

Crystalline metal oxide catalysts operating under oxygen evolution reaction (OER) conditions invariably restructure, resulting in active sites with hydroxo/oxo species in an amorphous environment. An increase in the population of terminal hydroxo/oxo species (i.e., edge sites) facilitates proton-coupled electron-transfer (PCET) kinetics for oxygen generation and thus improves catalyst competency. While amorphous films benefit from a greater density of active sites, they suffer from diminished charge transport as compared to that of extended crystalline lattices. Managing this amorphous–crystalline dichotomy is essential when designing OER catalysts, which we highlight with the examination of electrodeposited PbO x materials, which historically are very poor OER catalysts. Along these lines, the presence of phosphate during PbO x electrodeposition truncates the growth of an extended lattice owing to its strong bonding to oxide surfaces to afford an amorphous catalyst film (A-PbO x ) with significant charge-transfer resistance (138 ± 42 Ω) and poor OER kinetics (420 ± 105 mV dec –1 Tafel slope). Conversely, electrodeposition of Pb 2+ in the presence of less coordinating electrolytes such as nitrate affords crystalline β-PbO2 with improved charge-transfer resistance (42.6 ± 1.1 Ω), though still poor OER kinetics (134 ± 36 mV dec –1 Tafel slope). By operating amorphous A-PbOx in less coordinating electrolytes, however, a new partially crystalline material can be generated (μc-PbO x ) with further reduced charge-transfer resistance (33.0 ± 1.4 Ω) and improved OER kinetics (70 ± 15 mV dec –1 Tafel slope). The enhanced OER activity of μc-PbO x is the result of coupling the high edge-site population of an amorphous PbOx phase with crystalline-like charge transport properties. Finally, the ability to use an electrolyte to induce OER activity in an inactive amorphous form of PbO x highlights the benefits of optimizing the amorphous–crystalline phase compositions in the design of active OER catalysts.

catalysts↗
DOE OSTI2022

Synergistic Enhancement of Lead and Selenate Uptake at the Barite (001)–Water Interface

The interactions of heavy metals with minerals influence the mobility and bioavailability of toxic elements in natural aqueous environments. The sorption of heavy metals on covalently bonded minerals is generally well described by surface complexation models (SCMs). However, understanding sorption on sparingly soluble minerals is challenging because of the dynamically evolving chemistry of sorbent surfaces. The interpretation can be even more complicated when multiple metal ions compete for sorption. In the present study, we observed synergistically enhanced uptake of lead and selenate on the barite (001) surface through two sorption mechanisms: lattice incorporation that dominates at lower coverages and two-dimensional monolayer growth that dominates at higher coverages. Further, we also observed a systematic increase in the sorption affinity with increasing co-sorbed ion coverages, different from the assumption of invariant binding constants for individual adsorption processes in classical SCMs. Computational simulations showed thermodynamically favorable co-incorporation of lead and selenate by simultaneously substituting for barium and sulfate in neighboring sites, resulting in the formation of molecular clusters that locally match the net dimension of the substrate lattice. These results emphasize the importance of ion–ion interactions at mineral–water interfaces that control the fate and transport of contaminants in the environment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Investigation of Mass Transfer and Sorption in CO 2 /Brine/Rock Systems via In Situ FT-IR

CO 2 geological storage in deep saline formations is considered a promising method to mitigate anthropogenic CO 2 emissions and, thereby, minimize changes to the Earth’s atmosphere. A fundamental understanding of CO 2 mass transfer and sorption phenomena in brine-saturated reservoir formations is necessary to understand the long-term fate of injected CO 2 as it is subjected to different (physical, dissolution, and mineral) trapping mechanisms. In this work, we investigate CO 2 sorption in brine-saturated and dry Mt. Simon sandstone samples via in-situ Fourier Transform infrared spectroscopy (FT-IR) at elevated pressures, ranging from 0.3 MPa to 8.3 MPa, at a temperature of 50 ⁰C. The FT-IR spectra of bulk-phase CO 2 were simultaneously recorded under the same conditions. For bulk-phase CO 2 , we observed, in agreement with past studies, a doublet peak at 2361 cm -1 and 2336 cm -1 and another peak (ν 2 bending mode) at 667 cm -1 . With increasing pressure, the position of the peak at 667 cm -1 remains invariant, however, when crossing into the supercritical region the doublet peak degenerates onto a single peak at 2336 cm -1 with a barely visible shoulder at 2361 cm -1 . The bulk CO 2 data provide a perfect fit for Beer’s law for the whole range of pressure conditions. For the dry sample, the IR spectrum is experimentally indistinguishable from the bulk CO 2 spectrum, signifying that if physical adsorption occurs to any significant extent, the adsorbed CO 2 molecules are not substantially more rotationally constrained than the dense bulk CO 2 molecules. For the brine-saturated sample, we observe a strong band centered at 2342 cm -1 and a small companion peak at 2360-2361 cm -1 that degenerates into a barely visible shoulder peak at the higher pressures. The 2342 cm -1 band has been previously observed by other investigators for CO 2 dissolved in bulk water/brine as well during its adsorption on a variety of other wet natural porous media. We observe no peaks corresponding to bicarbonate or carbonate bulk species, which correlates well with the prior literature on similar low-pH aqueous solutions. The integrated peak area for the CO 2 sorbed in the brine-saturated sample correlates linearly with its solubility in the same bulk brine, as measured separately via a PVT-cell approach. Here, this validates the accuracy of both techniques, and the potential of the FT-IR method to be used in the study of mass transfer and adsorption in such systems. To that effect, a simple mathematical model is presented to analyze the FT-IR data to determine the CO 2 effective diffusivity in the brine-saturated sandstone sample.

58 GEOSCIENCES↗
DOE OSTI2022

Four-Coordinate Fe N 2 and Imido Complexes Supported by a Hemilabile NNC Heteroscorpionate Ligand

Inspired by mechanistic proposals for N 2 reduction at the nitrogenase FeMo cofactor, we report herein a new, strongly σ-donating heteroscorpionate ligand featuring two weak-field pyrazoles and an alkyl donor. This ligand supports four-coordinate Fe(I)-N 2 , Fe(II)-Cl, and Fe(III)-imido complexes, which we have characterized using a variety of spectroscopic and computational methods. Structural and quantum mechanical analysis reveal the nature of the Fe–C bonds to be essentially invariant between the complexes, with conversion between the (formally) low-valent Fe-N 2 and high-valent Fe-imido complexes mediated by pyrazole hemilability. This presents a useful strategy for substrate reduction at such low-coordinate centers and suggests a mechanism by which FeMoco might accommodate the binding of both π-acidic and π-basic nitrogenous substrates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Periodic Trends within Actinyl(VI) Nitrates and Their Structures, Vibrational Spectra, and Electronic Properties

In this work, a series of actinyl(VI) nitrate salts of the form MAnO 2 (NO 3 ) 3 , where M = NH 4 + K + , Rb + , Cs + , and Me 4 N + and AnO 2 2+ = U, Np, Pu, and AnO 2 (NO 3 ) 2 (H 2 O) 2 ·H 2 O, and the uranyl tetranitrates M 2 UO 2 (NO 3 ) 4 have been synthesized from aqueous solution and their structures determined using single-crystal X-ray diffraction. Together, these complexes represent an isostructural series of actinide complexes among the salts crystallized with the same charge-compensating cation and have been studied using vibrational spectroscopy including Raman and Fourier-transform infrared. Periodic trends in both the structural properties of these complexes and their vibrational spectra are presented and discussed, in particular the invariant nature of the O≡An≡O asymmetric stretching frequencies observed across the actinyl series. Electronic structure calculations were performed at a variety of levels of theory to aid in the interpretation of the vibrational data and to correlate trends in the data with the underlying electronic properties of these molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Commutative Algebra Modeling in Materials Science – A Case Study on Metal–Organic Frameworks (MOFs)

Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract algebra that has been rarely applied in data and material sciences. We introduce the first ever commutative algebra modeling and prediction in materials science. Specifically, category-specific commutative algebra (CSCA) is proposed as a new framework for MOF representation and learning. It integrates element-based categorization with multiscale algebraic invariants to encode both local coordination motifs and global network organization of MOFs. These algebraically consistent, chemically aware representations enable compact, interpretable, and data efficient modeling of MOF properties such as Henry’s constants and uptake capacities for common gases. Compared to traditional geometric and graph-based approaches, CSCA achieves comparable or superior predictive accuracy while substantially improving interpretability and stability across data sets. By aligning commutative algebra with the chemical hierarchy, the CSCA establishes a rigorous and generalizable paradigm for understanding structure and property relationships in porous materials and provides a nonlinear algebra-based framework for data-driven material discovery.

Khaemba, Caleb S.↗
DOE OSTI2023

Accurate calculation of many-body energies in water clusters using a classical geometry-dependent induction model

We incorporate geometry-dependent distributed multipole and polarizability surfaces into an induction model that is used to describe the 3- and 4-body terms of the interaction between water molecules. The expansion is carried out up to hexadecapole with the multipoles distributed on the atom sites. Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole distributed polarizabilities are used to represent the response of the multipoles to an electric field. We compare the model against two large databases consisting of 43,844 3-body terms and 3,603 4-body terms obtained from high level ab initio calculations previously used to fit the MB-pol and q-AQUA interaction potentials. The classical induction model with no adjustable parameters reproduces the ab-initio 3- and 4-body terms contained in these teo Databases with a Root-Mean-Square-Error (RMSE) of 0.104/0.058 and a Mean-Absolute-Error (MAE) of 0.054/0.026 kcal/mol, respectively, results that are on a par with those obtained 1 by fitting the same data using tens of thousands of Permutationally Invariant Polynomials (PIPs). This demonstrates the accuracy of this physically motivated model in describing the 3- and 4-body terms in the interactions between water molecules with no adjustable parameters. The triple-dipole-dispersion energy was included in the 3-body energy and was found to be small but not quite negligible. The model represents a practical, efficient and transferable approach for obtaining accurate non-additive interactions for multi-component systems without the need of performing tens of thousands of high level electronic structure calculations and fitting them with tens of thousands of PIPs.

molecular analysis water, aqueous↗