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At least 307 records · Page 17

3D spherical functional expansion tallies in Serpent 2 Monte Carlo code

This work extends the application of functional expansion tallies to 3D spherical geometries. The 3D Zernike polynomials are set as an orthonormal polynomials basis for the functional reconstruction. The study describes the construction of the complete set of polynomials, a natural expansion of the spherical harmonics polynomials where 3D Zernike moments can be evaluated as a linear combination of the geometrical moments. The 3D Zernike polynomials formulation and the computational approach implemented in Serpent 2 are presented and tested through the Godiva model from the ICSBEP criticality benchmark test cases. The implementation results are in agreement with a reference solution described in a fine-resolution mesh, enhancing also the performance and memory demand. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Transmission Interface Limits for High-Spatial Resolution Capacity Expansion Modeling

Large-scale capacity expansion models typically rely on estimates of the power transfer limits between modeled zones. Accurate estimation of these interface transfer limits (ITLs) requires modeling the underlying transmission network. Here we expand on a maximum flow optimization method that uses linearized power flow to estimate transfer limits. We apply this method to a data set of the U.S. transmission network to estimate ITLs between U.S. counties. By calculating ITLs using different subsets of the network, we evaluate how the size of the network used in the estimation affects the results. The results show diminishing returns to ITL accuracy after six hops, suggesting that a network subset can reasonably be used to approximate ITLs. The county-level estimates produced in this study will support more spatially resolved capacity expansion modeling and will help inform policy making at local and national levels.

capacity planning↗

Pion Nucleon Scattering in BCHPT Combined with 1/Nc Expansion

Pion nucleon scattering has played a crucial role in advancing our understanding of the low-energy regime of strong interactions. This dissertation presents the development of a new theoretical framework that combines Baryon Chiral Perturbation Theory (BChPT) with the 1/Nc Expansion to analyze pion nucleon scattering. The resulting effective Lagrangian incorporates both chiral and spin-flavor symmetries. Scattering amplitudes are calculated up to the one-loop level (NNLO), which includes four tree-level Feynman diagrams and 45 non-zero loop diagrams. The effective Lagrangian is renormalized at the one-loop level. With spin-3/2 baryons naturally included, the framework demonstrates strong convergence at higher energies. The NNLO pion nucleon scattering amplitude shows good agreement with experimental data from the SAID database. This novel approach, BChPT combined with 1/Nc Expansion, demonstrates substantial predictive power at higher energies where other low-energy theories fall short, achieving the goals of this combined framework. The contribution from loop diagrams is essential for achieving good agreement with the data, highlighting the importance of conducting the calculation up to NNLO. Extracted values for physically measurable quantities agree reasonably well with independently extracted values, underscoring the robustness of the theory.

Jayakodige, Dulitha [Hampton Univ., Hampton, VA (U↗

From zonal to nodal capacity expansion planning: Spatial aggregation impacts on a realistic test-case

Solving power system capacity expansion planning (CEP) problems at realistic spatial resolutions is computationally challenging. Thus, a common practice is to solve CEP over zonal models with low spatial resolution rather than over full-scale nodal power networks. Due to improvements in solving large-scale stochastic mixed integer programs, these computational limitations are becoming less relevant, and the assumption that zonal models are realistic and useful approximations of nodal CEP is worth revisiting. Here, this work is the first to conduct a systematic computational study on the assumption that spatial aggregation can reasonably be used for ISO-scale CEP. By considering a realistic, large-scale test network based on the state of California with over 8000 buses, we find that well-designed small spatial aggregations can yield good approximations but that coarser zonal models may result in large distortions of investment decisions, e.g., capacity under-investment of up to 41% for the lowest resolution model considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Phase transformations and thermal expansion coefficients of unirradiated U-X wt.% Zr (X = 6, 10, 20, 30) measured via neutron diffraction

This work characterizes the crystallographic evolution of unirradiated U-X wt.% Zr (X = 6, 10, 20, 30) while cooling from equilibration, single phase γ-U-Zr, at 900 °C to ambient temperature using time-of-flight neutron diffraction. The β-U phase was unobserved during cooling at 1 °C/min in all alloys. All alloys followed the phase transformation pathway of γ-U-Zr→γ-U-Zr+α-U→α-U +δ-UZr2 with an observed miscibility gap in γ-U-Zr. The α-U and δ-UZr2 transformation took place simultaneously in the U-30 wt.% Zr sample. These findings strengthen the need to re-approach the U-Zr phase diagram in entirety. Bulk volumetric CTEs agree well with published data, strengthening the quantification of lattice-specific CTEs reported in this study. A compositionally dependent discontinuity in thermal expansion, increasing in magnitude with decreasing U content, occurs during the γ-U-Zr→α-U+δ-UZr2 transformation. The γ-U-Zr lattice parameter was measured to have a compositional dependency.

36 MATERIALS SCIENCE↗

Supramolecular Metal‐Organic Framework Electrocatalysts With Hydration‐Adaptive Gallery Expansion and Linker‐Mediated Distal Ni‐Co Cooperation Enable Framework‐Retentive Oxygen Evolution

Atomic‑level tailoring of electronic communication between spatially separated metal sites offers a route to accelerate multielectron electrocatalysis. We report Ni-TPTC, Co-TPTC, and heterobimetallic Ni-Co-TPTC supramolecular metal-organic frameworks (SMOFs) for the oxygen evolution reaction (OER) built from a terphenyl‑tetracarboxylate (TPTC) linker. Single-crystal X-ray diffraction of heterobimetallic Ni–Co–TPTC reveals trans-bis-aqua octahedral chains assembled into a π-stacked, hydrogen-bonded lattice and confirms retention of the parent architecture, while powder X-ray diffraction supports an isostructural Co analog. In 1.0 M KOH, Ni-Co-TPTC reaches 20 mA cm −2 at 350 mV and maintains operation at ∼60 mA cm −2 for 45 h with modest decay of the initial current. Time‑dependent ex situ diffraction shows dominant framework reflections with low‑angle shifts consistent with gallery dilation (d‑spacing ∼7.7 → ∼9.2 Å) during early operation, while Co K‑edge X‑ray absorption and microscopy reveal Co‑rich oxide/oxyhydroxide‑like domains at longer times that correlate with decay. X‑ray photoelectron spectroscopy, quantified by the Remote Binding‑Energy Differential, tracks composition‑dependent Ni-Co polarization, and DFT free‑energy analysis suggests that a model Ni-Co environment lowers the Co‑centered potential‑limiting step by ∼0.24 eV relative to the Co‑only framework. Furthermore, these results suggest that framework‑retentive expansion and distal Ni-Co coupling can drive OER activity before gradual deligation and oxide formation mark longer‑time degradation.

Supramolecular metal-organic frameworks (SMOFs)↗

Phase diagram of magnetic shape memory alloy Ni 50 Mn $50–x$ In $x$ , 0 < $x$ , 25 from first principles, via spin cluster expansion and phonon vibrational entropies

The metamagnetic shape memory Heusler alloy Ni 50 Mn $50–x$ In $x$ exhibits a rich phase diagram featuring competing magnetic states, coupled magnetic–structural phase transitions, and strong compositional sensitivity. Existing first-principles approaches struggletocapturetheintertwinedchemical, magnetic, andvibrationaleffectsinthesealloys, necessitating a more integrated modeling framework. We develop a spin cluster expansion (spin-CE) framework augmented by a quasi-harmonic phonon model to capture both configurational (chemical and magnetic) and vibrational contributions to the free energy of Ni 50 Mn $50–x$ In $x$ over the full compositional range 0 ≤ x ≤25. The spin-CE includes both chemical clusters and composition-dependent Ising spin interactions, with parameters fit to a first-principles density functional theory (DFT) dataset. Using this approach, we predict the complete magnetostructural phase diagram and transformation temperatures of Ni 50 Mn $50–x$ In $x$ across the composition space. We find that vibrational entropy alone is insufficient to reproduce the martensitic transformation in the magnetic shape memory alloy regime, highlighting the essential role of magnetism. Incorporating both magnetic and vibrational contributions allows us to reproduce all experimentally known phases, including the disappearance of the stable martensite phase at a critical In concentration and the Curie temperature of the austenite phase. The method also captures the transition with increasing In in martensite from antiferromagnetic to ferromagnetic order and predicts re-entrant ferromagnetism, though the latter occurs at higher In content than reported experimentally. We discuss possible sources of this discrepancy and highlight the broader applicability of the method to other magnetostructurally complex materials, where it may offer mechanistic insight and predictive design capabilities.

Cluster expansion↗

Investigating the effects of cooperative transmission expansion planning on grid performance during heat waves with varying spatial scales

There is growing recognition of the advantages of interregional transmission capacity to decarbonize electricity grids. A less explored benefit is potential performance improvements during extreme weather events. This study examines the impacts of cooperative transmission expansion planning using an advanced modeling chain to simulate power grid operations of the United States Western Interconnection in 2019 and 2059 under different levels of collaboration between transmission planning regions. Two historical heat waves in 2019 with varying geographical coverage are replayed under future climate change in 2059 to assess the transmission cooperation benefits during grid stress. The results show that cooperative transmission planning yields the best outcomes in terms of reducing wholesale electricity prices and minimizing energy outages both for the whole interconnection and individual transmission planning regions. Compared to individual planning, cooperative planning reduces wholesale electricity prices by 64.3 % and interconnection-wide total costs (transmission investments + grid operations) by 34.6 % in 2059. It also helps decrease greenhouse gas emissions by increasing renewable energy utilization. However, the benefits of cooperation diminish during the widespread heat wave when all regions face extreme electricity demand due to higher space cooling needs. Despite this, cooperative transmission planning remains advantageous, particularly for California Independent System Operator with significant diurnal solar generation capacity. This study suggests that cooperation in transmission planning is crucial for reducing costs and increasing reliability both during normal periods and extreme weather events. It highlights the importance of optimizing the strategic investments to mitigate challenges posed by wider-scale extreme weather events of the future.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Large negative thermal expansion in GdFe(CN) 6 driven by unusual low-frequency modes

Understanding the negative thermal expansion (NTE) mechanism is of great importance. In this work, we consider the new NTE compound GdFe(CN) 6 (αv = -34.2×10 -6 K -1 ) as a case study to investigate the NTE mechanism from the perspective of the lattice vibrational dynamics. The atomic mean-square displacements suggest that the NTE of GdFe(CN) 6 comes from the strong tension effect induced by the transverse vibrations of the atomic –Fe–Ctriple bondN–Gd– linkages, with the largest contribution given by N atoms. Lattice dynamics calculations show that three low-frequency optical modes at about 50 cm -1 show the largest negative Grüneisen parameters thus providing the largest contribution to the NTE. In conclusion, the existence of these unusual low-frequency vibrational modes can be ascribed to the presence of GdN 6 trigonal prisms in the framework structure of GdFe(CN) 6 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest

The development of next-generation molten salt reactors relies on accurate knowledge of the thermophysical properties of the candidate coolant and fueled molten salts. These thermophysical properties include density, viscosity, thermal conductivity, and heat capacity. Because of difficulties in measuring thermophysical properties of molten salts, there are many gaps in the current state of thermophysical property knowledge of these salts, particularly those that contain actinides or beryllium. Therefore, leveraging modeling techniques to estimate unknown molten salt thermophysical properties and guide future experimental measurements has high value for the nuclear industry. Here, the densities of molten fluoride pseudo-ternary salt systems, which are of interest to the nuclear industry, were estimated using Redlich-Kister expansion and Muggianu interpolation techniques. The pseudo-ternary systems considered for estimation in this study were NaF-LiF-ZrF 4 , LiF-BeF 2 -ZrF 4 , LiF-BeF 2 -ThF 4 , NaF-LiF-BeF 2 , NaF-KF-BeF 2 , NaF-ZrF 4 -UF 4 , and NaF-BeF 2 -UF 4 . This Redlich-Kister estimation approach accounts for nonideal mixing behavior based on pseudo-binary subsystem interaction parameters determined from experimentally measured pseudo-binary system density data sets. The Redlich-Kister estimation was compared with the method of additive molar volumes, which assumes ideal mixing. Additionally, the Redlich-Kister approach was used to determine previously unknown binary and ternary interaction parameters based on experimentally measured density data sets for select pseudo-ternary salt systems. The results of this study show improvement in density estimation using the Redlich-Kister approach for all systems considered compared with estimation by additive molar volumes. Furthermore, this analysis allowed for the estimation of nonideal density behavior in experimentally unstudied ZrF 4 -UF 4 and BeF 2 -UF 4 , as well as the quantification of ternary interaction in NaF-LiF-ZrF 4 , NaF-BeF 2 -UF 4 , and NaF-ZrF 4 -UF 4 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties

This paper presents an extended polynomial chaos formalism for epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions (PDF) to uncertainty in probabilistic models of input variables. An ”extended” polynomial chaos expansion (PCE) approach is developed that accounts for both aleatory and epistemic uncertainties, modeled as random variables, thus allowing a unified treatment of both types of uncertainty. We explore in particular epistemic uncertainty associated with the choice of prior probabilistic models for input parameters. A PCE-based Kernel Density (KDE) construction provides a composite map from the PCE coefficients and germ to the PDF of quantities of interest (QoI). Here, the sensitivities of these PDF with respect to the input parameters are then evaluated. Input parameters of the probabilistic models are considered. By sampling over the epistemic random variable, a family of PDFs is generated and the failure probability is itself estimated as a random variable with its own PCE. Integrating epistemic uncertainties within the PCE framework results in a computationally efficient paradigm for propagation and sensitivity evaluation. Two typical illustrative examples are used to demonstrate the proposed approach.

Aleatory uncertainty↗

Projection pursuit adaptation on polynomial chaos expansions

Here, the present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities of interest (QoI). The present paper addresses one difficulty with these adaptations, namely their reliance on quadrature point sampling, which limits the reusability of potentially expensive samples. Projection pursuit (PP) is a statistical tool to find the “interesting” projections in high-dimensional data and thus bypass the curse-of-dimensionality. In the present work, we combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data. While this projection pursuit adaptation (PPA) can be entirely data-driven, the constructed approximation exhibits mean-square convergence to the solution of an underlying governing equation and thus captures the supports and probability distributions associated with the physics constraints. The proposed approach is demonstrated on a borehole problem and a structural dynamics problem, demonstrating the versatility of the method and its ability to discover low-dimensional manifolds with high accuracy with limited data. In addition, the method can learn surrogate models for different quantities of interest while reusing the same data set.

97 MATHEMATICS AND COMPUTING↗

Multisublattice cluster expansion study of short-range ordering in iron-substituted strontium titanate

Owing to the challenges in obtaining realistic atomic configurations in large chemical phase spaces, it is not straightforward to describe structure–property relations in materials exhibiting configurational disorder. One example is iron-substituted strontium titanate (SrTi 1–x Fe x O 3–d , STF), a promising perovskite-derivative cathode material in solid oxide fuel cells that exhibits full solid solubility 0 ≤ x ≤ 1 and a tendency to exhibit short-range order. Here we demonstrate a multisublattice cluster expansion (CE) framework and apply it to STF across the full composition range. The CE approach is distinct from more traditional CE formulations in that clusters are defined explicitly by the chemical species distributed among multiple sublattices, rather than via cluster functions of occupation variables with decoration. The modified CE approach makes it easy to distinguish meaningful chemical interactions that are harder to extract from conventional CE, since for the latter chemical identity in a cluster is expressed as a product of site occupations. The least absolute shrinkage and selection operator (LASSO) is implemented as a regression analysis tool to select key clusters and avoid overfitting. We demonstrate this formulation on STF, and show that it can accurately predict configurational energies in comparison to conventional CE. From the key clusters, we identify that short-range ordering between substitutional Fe and oxygen vacancies (V O ) results in the formation of Fe–VO strings. In addition, we consider the stability of STF through CE-based Monte Carlo (MC) simulations and confirm the presence of superstructures that were previously observed in transmission electron microscopy. In this work, analysis of atomic configurations from MC samples reveals variations in the oxidation state of Fe atoms, which can be explained by the ordering tendency of Fe and V O . The cluster description and selection formalism described here may be applied to other disordered multisublattice systems for accurate and efficient material modeling.

36 MATERIALS SCIENCE↗

Assessing Mg–Sc–(rare earth) ternary phase stability via constituent binary cluster expansions

The disordered Mg–Sc body-centered cubic (bcc) phase is both lightweight and strong; however, the system is impractical for general industrial use due to the high cost of scandium. Here we propose a computationally efficient metric that assesses ternary rare earth element additions that may stabilize the bcc phase at lower Sc concentrations. We find that the bcc phase is stabilized by the ternary addition of Y or Er, but not by La, Ce, or Nd, and we validate these predictions by experimental production and characterization of Mg–Sc–(Y,Er,Nd) alloys. The results suggest a computationally efficient method to anticipate integration of ternary elements into binary systems using cluster expansions of constituent binaries.

36 MATERIALS SCIENCE↗

Radionuclide incorporation in negative thermal expansion α-Zr(WO 4 ) 2 : A density functional theory study

The incorporation of uranium, plutonium and technetium in the negative thermal expansion (NTE) α-Zr (WO 4 ) 2 has been investigated within the framework of density functional theory (DFT). It is found that the vacancy formation energies of the charged vacancies are overall larger than that of its counterpart neutral Frenkel defects and Schottky defects. DFT calculations suggest that U and Pu substitutions for the Zr site are preferred in α-Zr (WO 4 ) 2 . In case of Tc substitution, both Tc(IV) for the Zr site and Tc(VII) for the W site are considered under oxygen-poor and oxygen-rich conditions, while Tc(VII) substitution can be improved significantly by including Y 2 O 3 (charge compensation).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A hierarchical gray-box dynamic modeling methodology for direct-expansion cooling systems to support control stability analysis; Méthodologie de modélisation dynamique hiérarchique de type boîte grise pour les systèmes de refroidissement à détente directe afin de soutenir l'analyse de stabilité de la commande

In this paper, a gray-box dynamic modeling approach for direct-expansion cooling systems is presented. The overall approach incorporates a multi-stage training procedure that consists of 1) identification of component sub-models from quasi-steady-state performance data, 2) system model integration with estimation of refrigerant charge and 3) fine tuning of thermal capacitances of the evaporator and condenser to capture the system dynamic responses. Compared to traditional physics-based models, the proposed modeling approach has advantages including reduced engineering efforts in the model development phase, improved computational efficiency and enhanced prediction accuracy. The modeling method was validated using a 3-ton variable-speed heat pump and proved to be capable of accurately predicting the system transient behaviors over a wide range of operating conditions. The established dynamic model was then applied for control stability analysis, with a specific goal of determining a proper control execution time step. The case study results showed that the stable control execution time step could change significantly, from 3 sec to 19 sec, as the operating conditions and control settings vary, and a proper selection of the execution time step is critical to ensure stable and reliable operations.

42 ENGINEERING↗

Thin film combinatorial sputtering of Al-Ce alloys: Investigating the phase separation of as-deposited solid solutions and determining the coefficient of thermal expansion

Al x Ce 100–x thin films with a composition range of ~75.0 < x < 99.5 at% (36.5 < x < 97.5 wt%) were synthesized via combinatorial co-sputtering from an Al and an Al 50 Ce 50 target. The crystal structure, phase fraction, film morphology, electrical resistivity, and temperature-dependent coefficients of thermal expansion (CTE) are all correlated to the Al x Ce 100–x composition. The as-deposited films form a metastable solid-solution, and annealing leads to the formation of the thermodynamically stable two-phase system of Al and the α-Al 11 Ce 3 intermetallic. Temperature dependent x-ray diffraction (XRD) reveals that the two phases expand independently of one another, and the thin film Al temperature-dependent CTE is similar to bulk Al. The thin film Al 11 Ce 3 intermetallic phase has a nearly constant CTE of ~1.5 × 10 –5 /°C within the temperature range studied (25–550 °C). To confirm the thin film Al 11 Ce 3 results, bulk stoichiometric Al 11 Ce 3 and +/- 1 wt% Ce samples were prepared and the CTE of each was measured with the same conditions. A Rietveld analysis of the bulk data enabled an estimation of the CTE in each of the 3 orthorhombic lattice parameters, which displayed anisotropic behavior. The thin film and bulk CTE measurements were in very good agreement. Estimations of the temperature dependent CTE of the two-phase alloys are made via the Reuss and Voigt models. Finally, by demonstrating the efficacy of the approach, more complex multi-component rapid materials discovery of low CTE Al-alloys can be pursued via the combinatorial thin film synthesis and XRD measurement.

36 MATERIALS SCIENCE↗

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

Angular momentum↗