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DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗

DOE OSTI2025

A novel transformation of the ice sheet Stokes equations and some of its properties and applications

We introduce a novel transformation of the Stokes equations into a form closely resembling the shallow Blatter–Pattyn equations. The two forms differ by only a few additional terms, while their variational formulations differ only by a single term in each horizontal direction. Specifically, the variational formulation of the Blatter–Pattyn model drops the vertical velocity in the second invariant of the strain rate tensor. Here we make use of the new transformation in two ways. First, we consider incorporating the transformed equations into a code that can be very easily converted from a Stokes to a Blatter–Pattyn model, and vice versa, by switching these terms on or off. This may be generalized so that the Stokes model is switched on adaptively only where the Blatter–Pattyn model loses accuracy. Second, the key role played by the vertical velocity in the Blatter–Pattyn approximation motivates new approximations. Two examples are presented. These require a mesh that enables the discrete continuity equation to be invertible for the vertical velocity in terms of the horizontal velocity components. Examples of such meshes, such as the first-order P1–E0 mesh and the second-order P2–E1 mesh, are given in both 2D and 3D. However, the transformed Stokes model has the same type of gravity forcing as the Blatter–Pattyn model, determined by the ice surface slope, thereby forgoing some of the mesh generality of the traditional formulation of the Stokes model.

58 GEOSCIENCES↗

DOE OSTI2025

Optimizing Insulation Design for Transformers in Medium Voltage Power Conversion Systems

Medium-frequency transformers (MFTs) play a crucial role in medium-voltage (MV) solidstate transformer (SST) systems, particularly in extreme fast charging applications. Achieving partial discharge (PD)-free operation while maintaining high power density is a significant challenge due to the high electric field (E-field) stresses inherent in MV applications. This dissertation focuses on the insulation design and optimization of MFTs used in both the main power electronics circuits and auxiliary power supplies. The study begins with an overview of insulation testing methodologies, including high potential tests, basic insulation level tests, and PD tests, which are critical for evaluating MFT insulation reliability. Given the importance of PD-free operation for long-term reliability, particular emphasis is placed on understanding PD mechanisms, including void, corona, and surface discharge, and their mitigation strategies. A high voltage isolated auxiliary power supply is then introduced, utilizing a gapped transformer encapsulated in silicone gel. This design achieves PD-free insulation up to 18 kV RMS while maintaining low coupling capacitance to minimize common-mode current. The proposed solution ensures reliable operation in MV environments and offers a scalable approach for auxiliary power in cascaded SST architectures. To improve MFT insulation in main power conversion circuits, a novel structure is developed using polypropylene sheets and potting compounds to create a void-free air gap, effectively mitigating E-field intensity. A prototype transformer with this insulation structure is built and achieves PD-free operation up to 30 kV RMS. This design is experimentally validated in a resonant converter operating at 46 kW, demonstrating its feasibility for MV SST applications. Further optimization is implemented to enhance MFT performance for dual-active-bridge(DAB) converters by integrating a semiconductive shielding layer within the insulation structure. This shielding layer improves the magnetic coupling coefficient while effectively confining the E-field within high insulation materials, thereby reducing eddy current losses. The optimized MFT achieves PD-free operation at 12.6 kV RMS and is successfully tested in a DAB converter operating at 43 kW, which meets the insulation requirements for a 13.2 kV SST system. This dissertation advances MFT insulation design by introducing and experimentally validating novel approaches that improve high voltage insulation while optimizing magnetic coupling and manufacturability. The proposed insulation structures enable PD-free operation while minimizing insulation material usage and simplifying assembly, making them ideal for high power, high voltage applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Temporal sequence transformer to advance long-term streamflow prediction

Accurate streamflow prediction is crucial for understanding climate change impacts on water resources and for effective management of extreme hydrological events. While Long Short-Term Memory (LSTM) networks have been the dominant data-driven approach for streamflow forecasting, recent advancements in transformer architectures for time series tasks have shown promise in outperforming traditional LSTM models. This study introduces a transformer-based model that integrates historical streamflow data with climatic variables to enhance streamflow prediction accuracy. We evaluated our transformer model against a benchmark LSTM across five diverse basins in the United States. Results demonstrate that the transformer architecture consistently outperforms the LSTM model across all evaluation metrics, highlighting its potential as a more effective tool for hydrological forecasting. This research contributes to the ongoing development of advanced AI techniques for improved water resource management and climate change adaptation strategies.

Singh, Ruhaan [Farragut High School]↗

DOE OSTI2025

Spatially Aware Linear Transformer (SAL-T) for Particle Jet Tagging

Transformers are very effective in capturing both global and local correlations within high-energy particle collisions, but they present deployment challenges in high-data-throughput environments, such as the CERN LHC. The quadratic complexity of transformer models demands substantial resources and increases latency during inference. In order to address these issues, we introduce the Spatially Aware Linear Transformer (SAL-T), a physics-inspired enhancement of the linformer architecture that maintains linear attention. Our method incorporates spatially aware partitioning of particles based on kinematic features, thereby computing attention between regions of physical significance. Additionally, we employ convolutional layers to capture local correlations, informed by insights from jet physics. In addition to outperforming the standard linformer in jet classification tasks, SAL-T also achieves classification results comparable to full-attention transformers, while using considerably fewer resources with lower latency during inference. Experiments on a generic point cloud classification dataset (ModelNet10) further confirm this trend. Our code is available at https://github.com/aaronw5/SAL-T4HEP.

Wang, Aaron [Illinois U., Chicago] (ORCID:00000003↗

DOE OSTI2026

Hybrid Quantum–Classical Graph Transformers for Efficient Sentiment Analysis

Quantum Machine Learning (QML) offers a promising paradigm that leverages quantum computing principles to develop efficient and expressive models for learning from complex and structured data. Recent advances in natural language processing (NLP) and artificial intelligence (AI) have demonstrated capabilities in understanding, generating, and reasoning over linguistic and multimodal information. In this work, we present the Quantum Graph Transformer (QGT), a hybrid quantum–classical architecture that extends graph transformer capabilities through quantum self-attention. The QGT models variable-length sentences as token graphs, where both the embedding encoding and the self-attention mechanisms are implemented using parameterized quantum circuits (PQCs), enabling efficient contextual learning with significantly fewer trainable parameters. We train QGT using both fully connected and 𝑘 -nearest-neighbor graph structures and evaluate it on five benchmark sentiment-classification datasets. Experimental results show that QGT consistently achieves higher or comparable accuracy to existing quantum NLP models and outperforms a Classical Graph Transformer (CGT) baseline with identical architecture, achieving 29.4 × fewer parameters while requiring 3–5 × fewer samples to reach comparable performance. These findings highlight the potential of graph-based quantum models as scalable and data-efficient architectures for natural language understanding.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Mechanistic Transformation of CuI Nanoparticles Into Oxidation‐Resistant 2D Copper Nanoplates

Unconventional phase transformations reveal new crystallization mechanisms, yet direct observation of such pathways during nanoscale solution-phase synthesis remains challenging. This study uncovers an atypical growth process in which thermodynamically stable CuI nanoparticles (NPs) transform into high-energy 2D Cu plates. Using a combination of in situ transmission electron microscopy, ex situ structural analysis, and density functional theory calculations shows that the formation of structural defects induced by hexadecylamine and chloride ions facilitates the transformation by promoting surface iodine vacancies. The resulting Cu{111} nanoplates, with ultrathin thicknesses (≈4 nm) and exceptionally high aspect ratios (≈450), display enhanced oxidation resistance and long-term stability under ambient conditions. This resistance is attributed to the close-packed {111} facets, which suppress chemical oxidation even after extended exposure to air over 100 days. These findings provide new insights into non-classical crystallization pathways in metal nanomaterials and suggest a versatile approach for preparing oxidation-resistant, structurally defined Cu nanostructures.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Atomistic evidence of nucleation mechanism for the direct graphite-to-diamond transformation

The direct graphite-to-diamond transformation mechanism has been a subject of intense study and remains debated concerning the initial stages of the conversion, the intermediate phases, and their transformation pathways. Here, we successfully recover samples at the early conversion stage by tuning high-pressure/high-temperature conditions and reveal direct evidence supporting the nucleation-growth mechanism. Atomistic observations show that intermediate orthorhombic graphite phase mediates the growth of diamond nuclei. Furthermore, we observe that quenchable orthorhombic and rhombohedra graphite are stabilized in buckled graphite at lower temperatures. These intermediate phases are further converted into hexagonal and cubic diamond at higher temperatures following energetically favorable pathways in the order: graphite → orthorhombic graphite → hexagonal diamond, graphite → orthorhombic graphite → cubic diamond, graphite → rhombohedra graphite → cubic diamond. Furthermore, these results significantly improve our understanding of the transformation mechanism, enabling the synthesis of different high-quality forms of diamond from graphite.

Graphite-diamond phase transformation↗

DOE OSTI2026

Solid-state transformations during laser directed energy deposition of Ti-6Al-4V powder hydride-dehydrided from scrap metals

During laser directed energy deposition (DED-LB), thermal cycling and powder chemical composition produce distinct thermal histories, which vary mechanical properties. Using real-time X-ray diffraction, this study investigates solid-state transformations during DED-LB to understand process-structure-property relationships for angular Ti-6Al-4V powder hydride–dehydrided from scrap metals. Results showed that regions near the molten pool experienced high cooling rates, leading to martensitic transformation from the β phase and increased hardness. Regions farther from the molten pool underwent tempering without solid-state transformation and decreased hardness. These findings support alternative feedstocks for metal additive manufacturing for a circular economy and resilient supply chains.

Additive manufacturing (AM)↗

DOE OSTI2026

Effects of interstitial oxygen on ω transformations and twin formation in bcc NbTaTiHf multi-principal element alloy from first-principles

Transformation- and twinning-induced plasticity (TRIP and TWIP) have been reported to contribute to the low-temperature deformation of some body-centered cubic (bcc) multi-principal element alloys (MPEAs) containing large fractions of group IV transition metals. The influence of interstitial solutes on the mechanisms underlying these forms of plasticity, however, remains unclear. Using first-principles calculations, we study the effects of interstitial O atoms on the relative stability of bcc and ω phases and on unstable and twin boundary stacking fault energy profiles in a representative bcc MPEA with high group-IV elemental fraction: NbTaTiHf. We find that O additions generally promote the relaxation of ω configurations back to their parent bcc structure, therefore inhibiting ω transformation. Calculations of the Rice parameter for bulk bcc and phases, as well as bcc-ω interfaces, further show that ω formation is a potent embrittlement factor, an effect that is enhanced by O additions, suggesting that the formation of bcc-ω interfaces is energetically preferred over the formation of the bulk ω phase. By contrast, the Rice parameter for twin boundaries indicates that these interfaces do not embrittle the material, even with O atoms at twin boundaries, providing a more favorable pathway for plastic deformation compared to ω transformation.

Density functional theory↗

DOE OSTI2026

AGFormer: Adaptive Spatiotemporal graph informed transformer for multi-reservoir inflow forecasting

Accurate reservoir inflow forecasting is crucial for effective water resource management, yet most machine learning models focus on single-reservoir prediction and overlook spatial dependencies among hydrologically connected reservoirs. Here, we propose AGFormer (Adaptive Graph-Informed Transformer), an end-to-end framework that integrates adaptive graph learning with temporal sequence modeling for multi-reservoir inflow forecasting. A shared encoder and graph attention mechanism generate reservoir-specific embeddings, which are then processed by the Transformer-based encoder–decoder for multi-step inflow forecasting. We also introduce a pretraining paradigm to learn robust temporal embeddings from misaligned historical records. Evaluated on 30 reservoirs in the Upper Colorado River Basin, AGFormer achieves superior seven-day-ahead forecasts, with NSE > 0.75 for 20 reservoirs—outperforming Encoder–Decoder LSTM, GCN+LSTM, and Transformer baselines. Adaptive graph learning captures dynamic inter-reservoir dependencies, and feature attribution aligns with snowmelt-driven hydrology. Incorporating forecasted meteorological inputs further enhances accuracy, demonstrating AGFormer’s potential to support reservoir management under dynamic hydrological conditions.

Adaptive graph learning↗

DOE OSTI2025

Phase transformation kinetics model for metals

We develop a new model for phase transformation kinetics in metals by generalizing the Levitas–Preston (LP) phase field model of martensite phase transformations (see Levitas and Preston (2002a,b) and Levitas et al. (2003)) to arbitrary pressure. Furthermore, we account for and track: the interface speed of the pressure-driven phase transformation, properties of critical nuclei, as well as nucleation at grain sites and on dislocations and homogeneous nucleation. The volume fraction evolution of each phase is described by employing KJMA (Kolmogorov, 1937; Johnson and Mehl, 1939; Avrami, 1939, 1940, 1941) kinetic theory. We then test our new model for iron under ramp loading conditions and compare our predictions for the α → ϵ iron phase transition to experimental data of Smith et al. (2013). In conclusion, more than one combination of material and model parameters (such as dislocation density and interface speed) led to good agreement of our simulations to the experimental data, thus highlighting the importance of having accurate microstructure data for the sample under consideration.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Martensitic transformation induced strength-ductility synergy in additively manufactured maraging 250 steel by thermal history engineering

Maraging steels are known for their exceptional strength but suffer from limited work hardening and ductility. Here, in this study, we report an intermittent printing strategy to tailor the microstructure and mechanical properties of maraging 250 steel via tuning the thermal history during wire-arc directed energy deposition. By introducing a dwell time between adjacent layers, the maraging 250 steel is cooled below the martensite start temperature, triggering thermally-driven martensitic transformation during the printing process. Thermal cycling during subsequent layer deposition results in the formation of reverted austenite which shows a refined microstructure and induces elemental segregation between martensite and reverted austenite. The Ni enrichment in the austenite promotes stabilization of the reverted austenite upon cooling to room temperature. The reverted austenite is metastable during deformation, leading to strain-induced martensitic transformation under loading. Specifically, a 3 min interlayer dwell time produces a maraging 250 steel with approximately 8% reverted austenite, resulting in improved work hardening via martensitic transformation induced plasticity during deformation. Meanwhile, the higher cooling rate and refined prior austenite grains lead to substantially refined martensitic grains (by approximately fivefold) together with an increased dislocation density. With 3 min interlayer dwell time, the yield strength of the printed maraging 250 steel increases from 836 MPa to 990 MPa, and the uniform elongation is doubled from 3.2% to 6.5%. This intermittent deposition strategy demonstrates the potential to tune the microstructure of maraging steels for achieving strength-ductility synergy by engineering the thermal history during additive manufacturing.

Additive manufacturing↗

DOE OSTI2026

Spatially resolved phase transformation mapping in 410 stainless steel during additive manufacturing visualized via real-time infrared data

Here, in this study, we demonstrate that spatially resolved cooling curves derived from real-time infrared (IR) thermography during additive manufacturing (AM) can capture spatial variations in phase transformation temperatures through cooling curve analysis (CCA). Using this approach, we show that during laser hot-wire deposition of 410 stainless steel (410SS), the martensite start temperature (M s ) evolves dynamically throughout the build. The M s temperature is spatially nonuniform, ranging from 185 °C to 348 °C, with the lowest values toward the build center and higher values toward the upper region of the deposit. In the lower portion of the build, no M s inflection is detected via CCA, consistent with transformation occurring earlier during thermal cycling followed by tempering during subsequent thermal cycles. These trends in M s are corroborated by characterizing the microstructure by electron backscatter diffraction (EBSD). Traditionally, M s is assumed to be constant, and a single interpass temperature is applied during both deposition and residual stress modeling. Our results demonstrate that IR-derived cooling curves provide a route to spatially and temporally resolved transformation temperature tracking for dynamic interpass control and improved residual-stress modeling.

Additive manufacturing↗

DOE OSTI2025

Dynamics and structure of the B2→B19’ phase transformation in NiTi revealed through in situ 4D-STEM

The structural evolution of NiTi during the B2→B19’ martensitic phase transformation via thermal cycling is investigated using in situ four dimensional scanning transmission electron microscopy (4D-STEM). With 4D-STEM, we can directly visualize and quantify the nanoscale evolution of the martensitic structure on thermal cycling and also investigate the origin of diffuse scattering of NiTi in the pre-transitional state. Mapping of the martensite orientation and strain visualizes the progression of the transformation front and self-accommodation of the B19’ structure. Diffuse streaking and strain are measured in the pre-transitional austenite (B2) phase and demonstrate no localization or preferential directionality hinting that long-range homogeneous instability rather than nanoscale heterogeneities may be the origin of the pre-transitional anomalies in NiTi. Finally, it is revealed that NiTi does not reform the same martensite nanostructure on thermal cycling but does express similar features. This small variation is likely owing to transformation-induced dislocations.

36 MATERIALS SCIENCE↗

DOE OSTI2024

The Mobility of Mo during Microbially Mediated Ferrihydrite Phase Transformation

Molybdenum (Mo) is an essential nutrient for almost all organisms. However, at high concentrations, it can be toxic to animals and plants. This study investigated the interactions of Mo(VI) with iron oxyhydroxides during ferrihydrite bioreduction in the presence of the Fe(III)- reducing Geobacter sulfurreducens. Here, in this study, we showed that Mo concentration controlled ferrihydrite phase transformation, leading to Mo release. With the biotic reduction of ferrihydrite and Fe(II) production, Mo(VI) reduction and Mo(IV)O 2 formation were observed for the first time, which further immobilised Mo after surface adsorption of Mo(VI). At low Mo levels (Mo/Fe molar ratios of 1-2 %), sufficient Fe(II) adsorption onto ferrihydrite resulted in its transformation into magnetite nanoparticles (>80%, ~25 nm) which catalysed the reduction of Mo(VI) to form Mo(IV)O 2 and immobilised Mo. Contrastingly, at high Mo concentrations (Mo/Fe molar ratios of 5-10%), Mo(VI)O 4 2- adsorption onto ferrihydrite limited Fe(II) adsorption, subsequently less magnetite (<8-12%) formed while more goethite (~30- 50%, width & length > 15 & 100 nm, respectively) and siderite (~20-30%, width & length > 100 & 200 nm, respectively) with larger particle sizes formed instead, causing Mo(VI) release due to lower Mo adsorption. This study provides a comprehensive understanding of the interaction mechanisms among Geobacter sulfurreducens, Mo(VI), and iron oxyhydroxides, enabling predictions and controls of long-term Mo mobility and Fe mineral transformation under a variety of biogeochemical scenarios.

Geobacter sulfurreducens↗

DOE OSTI2025

Chemical Vapor Transformation of Lithium Metal: Mechanism and Enhanced Stability

Constructing a stable solid electrolyte interface (SEI) with high productivity and scalability is essential for the practical application of thin Li metal anodes. Here, in this work, we report a chemical vapor transformation (CVT) strategy in which Li metal is exposed to trimethylaluminum (TMA), inducing a rapid and spontaneous surface reaction that forms a robust, multilayered SEI. In situ quartz crystal microbalance (QCM) and quadrupole mass spectrometry (QMS), combined with ex situ X-ray photoelectron spectroscopy (XPS), UV Raman spectroscopy, and density functional theory (DFT) calculations, reveal that TMA removes the native passivation layer, reacts with Li metal, and drives a coupled bulk-surface transformation involving Li–Al interdiffusion. The resulting SEI exhibits a chemically graded structure consisting of an inner Li–Al alloy and an outer amorphous carbon layer formed via demethylation and ligand-exchange pathways. This modified surface exhibits significantly enhanced stability compared to that of bare Li in electrochemical cycling using liquid and solid-state electrolytes. This work unveils a unique surface-mediated bulk transformation mechanism for lithium metal and establishes CVT as a scalable and fundamentally distinct approach for the interfacial engineering of reactive metals.

Li metal↗