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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A transport-based framework for solidification cracking in Ni-based superalloys processed by laser powder bed fusion

Solidification cracking remains a persistent barrier to laser powder bed fusion (LPBF) processing of solid-solution-strengthened (SSS) Ni-based superalloys and is commonly attributed to carbide formation, liquation-type failure, or elemental segregation. In this work, the cracking behavior of three SSS Ni-based superalloys—Inconel 625 (625), Inconel 617 (617), and Haynes 230 (230)—is examined under comparable LPBF conditions to evaluate the origins of their cracking susceptibility. Carbides were present in both 625 and 230, yet cracking behavior differed significantly. MC-type carbides in 625 remain discrete and preserve liquid connectivity, whereas Cr-rich M23C6 carbides in 230 form at cellular triple junctions that bottleneck the interdendritic liquid network, influencing cracking through liquid connectivity rather than as an independent cause. Alloy 617 exhibited anomalous segregation without resolvable secondary phases yet cracked mildly, indicating that extensive carbide formation is not a prerequisite for cracking. To rationalize these observations, a transport-limited framework is proposed in which cracking occurs when terminal-liquid feeding cannot accommodate solidification-induced strain; among the mechanisms evaluated, this framework is most consistent with the physical constraints imposed by LPBF solidification. Transport-based crack-susceptibility indexes incorporating permeability, viscosity, and solidification kinetics distinguish the alloy hierarchy; permeability ratios Krat increased from approximately 7 (625) to 11.5 (617) and 14.5 (230), with corresponding increases in the μ-weighted mushy zone risk index (CSIMZRM). These results are consistent with transport-limited liquid feeding as a rate-limiting contributor to solidification cracking in LPBF-processed SSS Ni-based superalloys, providing a physically grounded basis for alloy and process design.

Hyer, Holden [ORNL] (ORCID:0000000343915561)↗
DOE OSTI2026

Electronic transport, thermal transport, thermal expansion, and magnetization in the strongly correlated metal LaNi⁢O 3

Perovskite structured LaNiO 3 is a strongly correlated metal with intriguing thermal and magnetic properties. The volume dependence of calculated and measured physical properties can add additional critical information to develop a more in-depth understanding of this strongly correlated phenomenon. Taking advantage of recent single crystal LaNiO 3 growth using the floating-zone method, we have measured the thermal expansion, the magnetostriction, and the pressure dependence of the magnetic susceptibility, which then allows derivation of the Grüneisen parameters γ e = $\frac{dlnN(E_F)}{d lnV}$, γ χ = $\frac{dlnχ}{d lnV}$, as well as of electric and thermal transport properties. We simulate the volume dependence of structural and magnetic properties using Density Functional Theory calculations at the Generalized Gradient Approximation level. A large discrepancy between experimental values and calculated ones suggests that strong correlations are likely to be dynamic in nature. This study also provides a side-by-side comparison of measurements in single crystal and polycrystalline samples of LaNiO 3 to elucidate intrinsic materials properties. A broad hump at high temperatures in the temperature dependence of magnetization found in the single crystal sample of LaNiO 3 has been rationalized by a model that includes the influence of electron correlations on the Landau diamagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π$^{*}_{⊥}$ excitations are heavily gauge-dependent with average changes of –0.17 and –0.28 eV, respectively, while π→π$^{*}_{∥}$ excitations are marginally affected (–0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. Here, the results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Advancing Molecular Weight Determination of Lignin by Multi-Angle Light Scattering

Due to the complexity and recalcitrance of lignin, its chemical characterization is a key factor preventing the valorization of this abundant material. Multi-angle light scattering (MALS) is becoming a sought-after technique for absolute molecular weight (MW) determination of polymers and proteins. Lignin is a suitable candidate for MW determination via MALS, yet further investigation is required to confirm its absolute MW values and molecular size. Studies aiming to break down lignin into a variety of renewable products will benefit greatly from a simple and reliable determination method like MALS. Recent pioneering studies, discussed in this review, addressed several key challenges in lignin’s MW characterization. Nevertheless, some lignin-specific issues still need to be considered for in-depth characterization. This study explores how MALS instrumentation manages the complexities of determining lignin’s MW, e.g., with simultaneous fractionation and fluorescence interference mitigation. Additionally, we rationalize the importance of a more detailed light scattering analysis for lignin characterization, including aspects like the second virial coefficient and radius of gyration.

differential refractive index increment↗
DOE OSTI2023

Solid‐Adsorbed Polymer‐Electrolyte Interphases for Stabilizing Metal Anodes in Aqueous Zn and Non‐Aqueous Li Batteries

Abstract Polymers are known to adsorb spontaneously from liquid solutions in contact with high‐energy substrates to form configurationally complex, but robust phases that often exhibit higher durability than might be expected from the individual physical bonds formed with the substrate. Rational control of the physical, chemical, and transport properties of such interphases has emerged as a fundamental opportunity for scientific and technological advances in energy storage technology but requires in‐depth understanding of the conformation states and electrochemical effect of the adsorbed polymers. Here, we analyze the interfacial adsorption of oligomeric polyethylene glycol (PEG) chains of moderate sizes dissolved in protic and aprotic liquid electrolytes and find that there is an optimum polymer molecular weight of approximately 400 Da at which the highest columbic efficiency is achieved for both Zn and Li deposition. These findings point to a simple, versatile approach for extending the lifetime of batteries.

Jin, Shuo↗
DOE OSTI2023

Solid–Adsorbed Polymer–Electrolyte Interphases for Stabilizing Metal Anodes in Aqueous Zn and Non–Aqueous Li Batteries

Polymers are known to adsorb spontaneously from liquid solutions in contact with high-energy substrates to form configurationally complex, but robust phases that often exhibit higher durability than might be expected from the individual physical bonds formed with the substrate. Rational control of the physical, chemical, and transport properties of such interphases has emerged as a fundamental opportunity for scientific and technological advances in energy storage technology but requires in-depth understanding of the conformation states and electrochemical effect of the adsorbed polymers. Here, we analyze the interfacial adsorption of oligomeric polyethylene glycol (PEG) chains of moderate sizes dissolved in protic and aprotic liquid electrolytes and find that there is an optimum polymer molecular weight of approximately 400 Da at which the highest columbic efficiency is achieved for both Zn and Li deposition. Furthermore, these findings point to a simple, versatile approach for extending the lifetime of batteries.

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

Ensemble Simulations and Experimental Free Energy Distributions: Evaluation and Characterization of Isoxazole Amides as SMYD3 Inhibitors

Optimization of binding affinities for ligands to their target protein is a primary objective in rational drug discovery. Herein, we report on a collaborative study that evaluates various compounds designed to bind to the SET and MYND domain-containing protein 3 (SMYD3). SMYD3 is a histone methyltransferase and plays an important role in transcriptional regulation in cell proliferation, cell cycle, and human carcinogenesis. Experimental measurements using the scintillation proximity assay show that the distributions of binding free energies from a large number of independent measurements exhibit non-normal properties. We use ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and TIES (thermodynamic integration with enhanced sampling) protocols to predict the binding free energies and to provide a detailed chemical insight into the nature of ligand-protein binding. Our results show that the 1-trajectory ESMACS protocol works well for the set of ligands studied here. Although one unexplained outlier exists, we obtain excellent statistical ranking across the set of compounds from the ESMACS protocol and good agreement between calculations and experiments for the relative binding free energies from the TIES protocol. ESMACS and TIES are again found to be powerful protocols for the accurate comparison of the binding free energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Computational remodeling of an enzyme conformational landscape for altered substrate selectivity

Structural plasticity of enzymes dictates their function. Yet, our ability to rationally remodel enzyme conformational landscapes to tailor catalytic properties remains limited. Here, we report a computational procedure for tuning conformational landscapes that is based on multistate design of hinge-mediated domain motions. Using this method, we redesign the conformational landscape of a natural aminotransferase to preferentially stabilize a less populated but reactive conformation and thereby increase catalytic efficiency with a non-native substrate, resulting in altered substrate selectivity. Steady-state kinetics of designed variants reveals activity increases with the non-native substrate of approximately 100-fold and selectivity switches of up to 1900-fold. Structural analyses by room-temperature X-ray crystallography and multitemperature nuclear magnetic resonance spectroscopy confirm that conformational equilibria favor the target conformation. Our computational approach opens the door to targeted alterations of conformational states and equilibria, which should facilitate the design of biocatalysts with customized activity and selectivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Toughening Sm–Co sintered magnets via microstructure modification with additives

We report the mechanical properties of the brittle Smsingle bondCo permanent magnets are of great practical significance. However, studies on the magnets have mostly focused on their magnetic properties. This paper reports the modified microstructure and refined unimodal grain size, enhanced flexural strength, and magnetic properties of Sm 2 (Co,Fe,Cu,Zr) 17 sintered magnets doped with La 2 O 3 , MgO, and CaF 2 fine particulates. The correlations between microstructure, phase composition, and mechanical and magnetic properties were studied. Doping of a small amount (e.g., 0.5–3 wt%) of La 2 O 3 , MgO, or CaF 2 fine particulates could significantly refine the unimodal grain sizes of the Smsingle bondCo magnets via the Zener pinning effect. Moreover, doping significantly improved the flexural strengths σ of the magnets. For example, the σ values of the magnets with 0.5 wt% MgO, 1 wt% La 2 O 3 , and 1 wt% CaF 2 were approximately 65%, 63%, and 42% higher than that of the reference magnet, respectively. Micromechanical simulations revealed that the fine particles of La 2 O 3 could deflect crack growth, while the CaF 2 particles could attract or arrest cracks during the fracture process. The mechanical strengthening effect was mainly due to grain size refinement. The Smsingle bondCo magnets with 0.5–1.5 wt% CaF2 and 0.5 wt% La 2 O 3 exhibited excellent magnetic properties while doping 1–3 wt% La2O3 and 0.5–3 wt% MgO deteriorated magnetic performance. The rational design of CaF 2 - or La 2 O 3 -doped microstructure can be an economical and effective method for producing toughened Sm–Co sintered magnets with high magnetic performance.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Analysis of spin frustration in an Fe III 7 cluster using a combination of computational, experimental, and magnetostructural correlation methods

The synthesis, structure, and magnetic properties are reported for [Fe 7 O 3 (O 2 C t Bu) 9 (mda) 3 (H 2 O) 3 ] ( 1 ), where mdaH 2 is N -methyldiethanolamine. 1 was prepared from the reaction of [Fe 3 O(O 2 C t Bu) 6 (H 2 O) 3 ](NO 3 ) with mdaH 2 in a 1:~3 ratio in MeCN. The core of 1 consists of a central octahedral Fe III ion held within a non-planar Fe 6 loop by three μ 3 -O 2- and three μ 2 -RO - arms from the three mda 2- chelates. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling, leading to a ground state spin of S = 5 / 2 . The ground state was confirmed by a fit of magnetization data collected in the 0.1–7.0 T and 1.8–10.0 K ranges. The four Fe 2 pairwise exchange parameters ( J 1 - J 4 ) were estimated by independent methods: theoretical calculations using either broken symmetry energy differences (-46.3, -16.2, -3.9, and - 28.1 cm -1 , respectively) or Green’s function approximation methods (-41.4, -14.8, -13.2, and - 24.7 cm -1 ), and a magnetostructural correlation (MSC) previously developed for high nuclearity Fe III /O complexes (-39.5, -13.8, -6.7, and - 23.5 cm -1 ). Additionally, the J 1 - J 4 obtained from the MSC and theoretical methods were used with the program PHI to both simulate χ M T vs T as well as to serve as reasonable input values to fit the experimental data (-41.0, -11.4, -5.0, and - 27.3 cm -1 ). Analysis of the J ij led to identification of the spin frustration effects operative and the resultant spin vector alignments at each Fe III ion, thus allowing for the rationalization of the experimental ground state.

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

Skyrmions and hopfions in three-dimensional frustrated magnets

Here, a model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic skyrmions. In the continuum approximation, this model reduces to a nonlinear sigma model on a squashed sphere that has a natural interpolating parameter. At one limit of the parameter, the model reduces to a frustrated magnetic system earlier considered by Sutcliffe as a host to hopfions, and in the other limit, it becomes very similar to the 3D Skyrme model. To better understand the relation between hopfions and 3D skyrmions, a model interpolating between the Faddeev-Niemi and the Skyrme models is reconsidered and it is shown that energies of the solitons obey a linear Bogomol'nyi-Prasad-Sommerfeld bound. The 3D skyrmions in the frustrated magnetic model are found and compared to the rational map ansatz.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Investigation of the iodate sorption mechanism by CoAl LDH through experiments and ab initio molecular dynamics simulations

Radioiodine released during the nuclear-fuel cycle constitutes a persistent radiological hazard. In this study, the IO 3 – uptake mechanism of CoAl LDH was resolved by combining pH-controlled sorption experiments, synchrotron XAFS, and DFT-based AIMD simulations. At pH close to 6, approximately 90% of IO 3 – was removed, and the equilibrium distribution coefficient reached about 1.7 × 10 4 mL g –1 . EXAFS analysis indicated an average iodine–oxygen bond length of 1.81 Å and a coordination number near 3, with the fit R-factor equal to 0.002. The simulations faithfully reproduced the experimental spectrum and revealed transient proton hopping events that generated metastable I–O–H species inside the interlayer, thereby confirming nitrate-to-iodate exchange as the controlling capture pathway. Atomic density profiles and radial distribution functions further showed that IO 3 – adopt an end-on orientation perpendicular to the hydroxide sheets, while water molecules mediate proton migration without disturbing the host lattice. In conclusion, the integrated experimental–computational evidence demonstrates that CoAl LDH can rapidly and selectively sequester IO 3 – under near-neutral conditions, offering atomic scale guidance for the rational engineering of layered sorbents for advanced radioactive-waste treatment.

Kang, Jaehyuk [Jeju National Univ. (Korea, Republi↗
DOE OSTI2021

Towards Realistic Models of Heterogeneous Catalysis: Simulations of Oxidation Catalysis from First Principles

Among the most significant developments in heterogeneous catalysis in the last 20 years is the emergence of microkinetic models, often parameterized from density functional theory (DFT) calculations, used to quantify observed catalyst performance and to guide the discovery of new catalytic materials. While DFT directly reports binding energies and elementary step activation energies, the free energies that enter into microkinetic models must be computed from additional approximations. Frequently these free energy approximations assume ideal behavior—that adsorbates do not interact with one another, or that adsorbates are immobile or vibrate harmonically about a binding site. These assumptions can and do have an impact on predicted catalyst performance and potentially even on predicted trends. Our work relates to three categories of non-idealities, explored in the context of nitrogen oxidation and reduction catalysis on metal surfaces. One component relates to adsorbate translational free energy, the contribution least well described by conventional models, in which we develop modeling approaches that improve accuracy with limited increase in computational expense. A second component relates adsorbate-adsorbate interactions, in which we develop benchmark on-lattice interaction models and compare kinetic predictions with conventional mean-field models, in an effort to develop more robust coverage-dependent mean field modeling approaches. The last relates the most fundamental assumption of all—that of energy equipartition—in an effort to rationalize and guide plasma-enhanced catalysis.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

Atomistic Simulations of Polydisperse Lignin Melts Using Simple Polydisperse Residue Input Generator

Understanding the physics of lignin will help rationalize its function in plant cell walls as well as aiding practical applications such as deriving biofuels and bioproducts. Here, in this work, we present SPRIG (Simple Polydisperse Residue Input Generator), a program for generating atomic-detail models of random polydisperse lignin copolymer melts i.e., the state most commonly found in nature. Using these models, we use all-atom molecular dynamics (MD) simulations to investigate the conformational and dynamic properties of polydisperse melts representative of switchgrass (Panicum virgatum L.) lignin. Polydispersity, branching and monolignol sequence are found to not affect the calculated glass transition temperature, T g . The Flory–Huggins scaling parameter for the segmental radius of gyration is 0.42 ± 0.02, indicating that the chains exhibit statistics that lie between a globular chain and an ideal Gaussian chain. Below T g the atomic mean squared displacements are independent of molecular weight. In contrast, above T g , they decrease with increasing molecular weight. Therefore, a monodisperse lignin melt is a good approximation to this polydisperse lignin when only static properties are probed, whereas the molecular weight distribution needs to be considered while analyzing lignin dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Effects of edge-localized electron cyclotron current drive on edge-localized mode suppression by resonant magnetic perturbations in DIII-D

Abstract According to recent DIII-D experiments (Logan et al 2024 Nucl. Fusion 64 014003), injecting edge localized electron cyclotron current drive (ECCD) in the counter-plasma-current (counter- I p ) direction reduces the n = 3 resonant magnetic perturbation (RMP) current threshold for edge-localized mode (ELM) suppression, while co- I p ECCD during the suppressed ELM phase causes a back transition to ELMing. This paper presents nonlinear two-fluid simulations on the ECCD manipulation of edge magnetic islands induced by RMP using the TM1 code. In the presence of a magnetic island chain at the pedestal-top, co- I p ECCD is found to decrease the island width and restore the initially degraded pedestal pressure when its radial deposition location is close to the rational surface of the island. With a sufficiently strong co- I p ECCD current, the RMP-driven magnetic island can be healed, and the pedestal pressure fully recovers to its initial ELMing state. On the contrary, counter- I p ECCD is found to increase the island width and further reduce the pedestal pressure to levels significantly below the peeling-ballooning-mode limited height, leading to even stationary ELM suppression. These simulations align with the results from DIII-D experiments. However, when multiple magnetic island chains are present at the pedestal-top, the ECCD current experiences substantial broadening, and its effects on the island width and pedestal pressure become negligible. Further simulations reveal that counter- I p ECCD enhances RMP penetration by lowering the penetration threshold, with the degree of reduction proportional to the amplitude of ECCD current. For the ∼1 MW ECCD in DIII-D, the predicted decrease in the RMP penetration threshold for ELM suppression is approximately 20%, consistent with experimental observations. These simulations indicate that edge-localized ECCD can be used to either facilitate RMP-driven ELM suppression or optimize the confinement degradation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Initial study on cross section generation requirements for a PBR equilibrium core

A Serpent model of the HTR-PM equilibrium core was developed for use in cross section prepa-ration studies in order to guide methods development for the Griffin reactor multiphysics applica-tion. The model includes detailed isotopics for 10 distinct pebble burnup groups in 126 core zoneswith unique fuel and moderator temperatures obtained from a coupled neutronics-thermal-fluidsequilibrium core calculation using Griffin-Pronghorn. A sensitivity study of the fuel and mod-erator temperatures for various core regions was performed with the MOOSE stochastic tools.The results show that the uncertainties are, not unexpectedly, dominated by the value of the fluidtemperature and that the power level, heat transfer coefficient and effective conduction to neigh-boring pebbles and fluid constitute, at best, second order effects. The temperature uncertaintyrange varies from 28 K to 57 K at the core entry and exit planes, respectively, but these val-ues are probably higher. We still have to quantify the significance of these uncertainties in thepreparation of cross sections, which will be postponed for future work. In addition, we verifythat the single effective pebble approach works well for the preparation of region averaged crosssections in the infinite domain approximation. Nevertheless, there are significant discrepanciesin the cross sections when compared to the multi-pebble model. This could affect the predictionof peak values and in the depletion calculation. We conclude that is highly desirable for futurestudies with Griffin to be able to handle both the ?effective? pebble approximation and the multi-pebble approach for the various pebble burnup groups. This enables Griffin users the flexibilityto perform higher-fidelity studies. Finally, we initiate the preparation of cross sections for variouscore regions from the full core Serpent reference model. We quantify the differences in 26 groupcross sections from infinite domain models. These reference cross sections will serve to validatethe double heterogeneity, self-shielding, and spectrum-correction methods in Griffin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Identification of and Structural Insights into Hit Compounds Targeting N -Myristoyltransferase for Cryptosporidium Drug Development

Each year, approximately 50,000 children under 5 die as a result of diarrhea caused by Cryptosporidium parvum, a protozoan parasite. There are currently no effective drugs or vaccines available to cure or prevent Cryptosporidium infection, and there are limited tools for identifying and validating targets for drug or vaccine development. We previously reported a high throughput screening (HTS) of a large compound library against Plasmodium N-myristoyltransferase (NMT), a validated drug target in multiple protozoan parasite species. To identify molecules that could be effective against Cryptosporidium, we counter-screened hits from the Plasmodium NMT HTS against Cryptosporidium NMT. We identified two potential hit compounds and validated them against CpNMT to determine if NMT might be an attractive drug target also for Cryptosporidium. We tested the compounds against Cryptosporidium using both cell-based and NMT enzymatic assays. We then determined the crystal structure of CpNMT bound to Myristoyl-Coenzyme A (MyrCoA) and structures of ternary complexes with MyrCoA and the hit compounds to identify the ligand binding modes. The binding site architectures display different conformational states in the presence of the two inhibitors and provide a basis for rational design of selective inhibitors.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗