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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Comparative study of He 6 β -decay based on different similarity-renormalization-group evolved chiral interactions

We report on a study of the Gamow-Teller matrix element contributing to ${}^6$He $\beta$-decay with similarity renormalization group (SRG) versions of momentum- and configuration-space two-nucleon interactions. These interactions are derived from two different formulations of chiral effective field theory ($\chi$EFT) -- without and with the explicit inclusion of $\Delta$-isobars. We consider evolution parameters $\Lambda_{\rm SRG}$ in the range between 1.2 and 2.0 fm$^{-1}$ and, for the $\Delta$-less case, also the unevolved (bare) interaction. The axial current contains one- and two-body terms, consistently derived at tree level (no loops) in the two distinct $\chi$EFT formulations we have adopted here. The ${}^6$He and ${}^6$Li ground-state wave functions are obtained from hyperspherical-harmonics (HH) solutions of the nuclear many-body problem. In $A\,$=$\,6$ systems, the HH method is limited at present to treat only two-body interactions and non-SRG evolved currents. Our results exhibit a significant dependence on $\Lambda_{\text{SRG}}$ of the contributions associated with two-body currents, suggesting that a consistent SRG-evolution of these is needed in order to obtain reliable estimates. We also show that the contributions from one-pion-exchange currents depend strongly on the model (chiral) interactions and on the momentum- or configuration-space cutoffs used to regularize them. These results might prove helpful in clarifying the origin of the sign difference recently found in No-Core-Shell-Model and Quantum Monte Carlo calculations of the ${}^6$He Gamow-Teller matrix element.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

High-Fidelity Simulations of Gravity Currents Using a High-Order Finite-Difference Spectral Vanishing Viscosity Approach

This numerical work investigates the potential of a high-order finite-difference spectral vanishing viscosity approach to simulate gravity currents at high Reynolds numbers. The method introduces targeted numerical dissipation at small scales through altering the discretisation of the second derivatives of the viscous terms in the incompressible Navier-Stokes equations to mimic the spectral vanishing viscosity (SVV) operator, originally designed for the regularisation of spectral element method (SEM) solutions of pure advection problems. Using a sixth-order accurate finite-difference scheme, the adoption of the SVV method is straightforward and comes with a negligible additional computational cost. In order to assess the ability of this high-order finite-difference spectral vanishing viscosity approach, we performed large-eddy simulations (LES) of a gravity current in a channelised lock-exchange set-up with our SVV model and with the well-known explicit static and dynamic Smagorinsky sub-grid scale (SGS) models. The obtained data are compared with a direct numerical simulation (DNS) based on more than 800 million mesh nodes, and with experimental measurements. A framework for the energy budget is introduced to investigate the behaviour of the gravity current. First, it is found that the DNS is in good agreement with the experimental data for the evolution of the front location and velocity field as well as for the stirring and mixing inside the gravity current. Secondly, the LES performed with less than 0.4% of the total number of mesh nodes compared to the DNS, can reproduce the main features of the gravity currents, with the SVV model yielding slightly more accurate results. It is also found that the dynamic Smagorinsky model performs better than its static version. For the present study, the static and dynamic Smagorinsky models are 1.8 and 2.5 times more expensive than the SVV model, because the latter does not require the calculation of explicit SGS terms in the Navier-Stokes equations nor spatial filtering operations.

direct numerical simulation↗
DOE OSTI2024

Causally‐Informed Deep Learning to Improve Climate Models and Projections

Abstract Climate models are essential to understand and project climate change, yet long‐standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid‐scale processes, particularly clouds and convection. Deep learning can learn these subgrid‐scale processes from computationally expensive storm‐resolving models while retaining many features at a fraction of computational cost. Yet, climate simulations with embedded neural network parameterizations are still challenging and highly depend on the deep learning solution. This is likely associated with spurious non‐physical correlations learned by the neural networks due to the complexity of the physical dynamical system. Here, we show that the combination of causality with deep learning helps removing spurious correlations and optimizing the neural network algorithm. To resolve this, we apply a causal discovery method to unveil causal drivers in the set of input predictors of atmospheric subgrid‐scale processes of a superparameterized climate model in which deep convection is explicitly resolved. The resulting causally‐informed neural networks are coupled to the climate model, hence, replacing the superparameterization and radiation scheme. We show that the climate simulations with causally‐informed neural network parameterizations retain many convection‐related properties and accurately generate the climate of the original high‐resolution climate model, while retaining similar generalization capabilities to unseen climates compared to the non‐causal approach. The combination of causal discovery and deep learning is a new and promising approach that leads to stable and more trustworthy climate simulations and paves the way toward more physically‐based causal deep learning approaches also in other scientific disciplines.

Meteorology & Atmospheric Sciences↗
DOE OSTI2022

Multiscale plasticity of geomaterials predicted via constrained optimization‐based granular micromechanics

Abstract A general framework to derive nonlinear elastic and elastoplastic material models from granular micromechanics is proposed, where a constraint‐based variational structure is introduced to classical grain contact‐based homogenization methods of hyperelasticity. Like the classical hyperelastic methods, reference solutions for closed‐form hyperelastic material models are analytically derived from the grain‐scale contact mechanics. However, unlike prior methods, the proposed homogenization framework defines closed‐form hyperelastoplastic material models that extend multiscale variational methods to granular plasticity. The proposed framework is used to develop novel granular micromechanics‐based macroscopic models for a Mises type solid, Drucker–Prager type plasticity, and grain‐contact cohesive‐debonding with a deviatorically and volumetrically coupled nonlinearly elastic response. Macroscopic plastic parameters and yield criteria are explicitly related to their microscale counterparts, for example, the friction coefficient governing intergranular slip. Numerical examples and comparison to measurements from the literature, including triaxial compaction of concrete, are provided to investigate model predictions and demonstrate calibration to experimental data.

Bryant, E. C.↗
DOE OSTI2024

BioRT‐HBV 1.0: A Biogeochemical Reactive Transport Model at the Watershed Scale

Abstract Reactive Transport Models (RTMs) are essential tools for understanding and predicting intertwined ecohydrological and biogeochemical processes on land and in rivers. While traditional RTMs have focused primarily on subsurface processes, recent watershed‐scale RTMs have integrated ecohydrological and biogeochemical interactions between surface and subsurface. These emergent, watershed‐scale RTMs are often spatially explicit and require extensive data, computational power, and computational expertise. There is however a pressing need to create parsimonious models that require minimal data and are accessible to scientists with limited computational background. To that end, we have developed BioRT‐HBV 1.0, a watershed‐scale, hydro‐biogeochemical RTM that builds upon the widely used, bucket‐type HBV model known for its simplicity and minimal data requirements. BioRT‐HBV uses the conceptual structure and hydrology output of HBV to simulate processes including advective solute transport and biogeochemical reactions that depend on reaction thermodynamics and kinetics. These reactions include, for example, chemical weathering, soil respiration, and nutrient transformation. The model uses time series of weather (air temperature, precipitation, and potential evapotranspiration) and initial biogeochemical conditions of subsurface water, soils, and rocks as input, and output times series of reaction rates and solute concentrations in subsurface waters and rivers. This paper presents the model structure and governing equations and demonstrates its utility with examples simulating carbon and nitrogen processes in a headwater catchment. As shown in the examples, BioRT‐HBV can be used to illuminate the dynamics of biogeochemical reactions in the invisible, arduous‐to‐measure subsurface, and their influence on the observed stream or river chemistry and solute export. With its parsimonious structure and easy‐to‐use graphical user interface, BioRT‐HBV can be a useful research tool for users without in‐depth computational training. It can additionally serve as an educational tool that promotes pollination of ideas across disciplines and foster a diverse, equal, and inclusive user community.

Sadayappan, Kayalvizhi↗
DOE OSTI2024

Asymptotic consistency of the WSINDy algorithm in the limit of continuum data

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy estimator is unconditionally asymptotically consistent for a wide class of models that includes the Navier–Stokes, Kuramoto–Sivashinsky and Sine–Gordon equations. We thus provide a mathematically rigorous explanation for the observed robustness to noise of weak-form equation learning. Conversely, we also show that, in general, the WSINDy estimator is only conditionally asymptotically consistent, yielding discovery of spurious terms with probability one if the noise level exceeds a critical threshold σ c . We provide explicit bounds on σ c in the case of Gaussian white noise and we explicitly characterize the spurious terms that arise in the case of trigonometric and/or polynomial libraries. Furthermore, we show that, if the data is suitably denoised (a simple moving average filter is sufficient), then asymptotic consistency is recovered for models with locally-Lipschitz, polynomial-growth nonlinearities. Our results reveal important aspects of weak-form equation learning, which may be used to improve future algorithms. We demonstrate our findings numerically using the Lorenz system, the cubic oscillator, a viscous Burgers-growth model and a Kuramoto–Sivashinsky-type high-order PDE.

asymptotic consistency↗
DOE OSTI2025

Remote Sensing and Fluxes Upscaling for Real-world Impact (Workshop Report)

The "Remote Sensing and Fluxes Upscaling for Real-world Impact" workshop, held on July 9-10, 2024, at Lawrence Berkeley National Lab, was a collaborative effort led by the AmeriFlux Management Project, NEON, and the Carbon Dew Community of Practice. The event brought together over 200 registrants and approximately 100 attendees each day, including leading experts, researchers, and practitioners. The primary focus was on bridging the gap between cutting-edge research and practical applications in environmental monitoring by integrating remote sensing and flux data. Key themes included the importance of site-level measurements for validating remote sensing products, providing nature-based climate solutions, and addressing challenges such as instrument costs and the need for standardized methods. At the regional scale, discussions centered on addressing spatial heterogeneity and using high-resolution remote sensing and machine learning methods to enhance data interpretation. Global scale challenges included data consistency, gap filling, and accurate emission source identification, with opportunities for international collaboration and standardized practices to improve global carbon budget assessments. The workshop emphasized the critical need for integrating data across local, regional, and global scales through explicit scale-matching and developed a workflow for scaling flux data using "straight shot" and "explicit nesting" approaches. The event highlighted the importance of connecting scientific research with real-world applications in carbon, energy, and water management, ensuring that advancements translate into tangible societal benefits. These insights will guide future research, technology transfer, and collaboration, maximizing the potential of environmental fluxes to address real-world challenges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Hybrid learning techniques for scientific data reduction with performance guarantees

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Final report- UFL - RAPIDS2: A SciDAC Institute for Computer Science, Data, and Artificial Intelligence

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Influence of physical and chemical hydrology on bioremediation of a U-contaminated aquifer informed by reactive transport modeling incorporating 238 U/ 235 U ratios

Microbially-catalyzed reductive immobilization of aqueous uranium (U) as a solid phase has been proposed as a U remediation technique. Both laboratory and field experiments have demonstrated that this reduction reaction alters the 238 U/ 235 U ratio, producing a 238 U-enriched U(IV) solid. In contrast, other major U reactive transport processes fractionate these isotopes much less. This suggests the potential to quantify the extent of bioreduction occurring in groundwater containing U using the 238 U/ 235 U ratio, which would substantially improve upon current practices largely relying on U concentration measurements alone. Current reactive transport models for uranium dynamics include only concentration measurements, which are strongly influenced by highly coupled reactive transformation and aqueous transport processes. The complex physical and chemical behavior of U potentially compromises such quantitative analysis of U storage and release. Here we report the first numerical reactive transport model which explicitly incorporates variations in the 238 U/ 235 U ratio of U and demonstrates improved interpretation of the principal chemical reactions and groundwater transport processes affecting the subsurface mobility and distribution of this widespread contaminant. Recent U bioreduction studies performed in a contaminated aquifer in Rifle, Colorado, USA applied Rayleigh distillation models to interpret U stable isotope fractionation observed as a result of acetate amendment. These simplified models were unable to resolve the spatiotemporal pattern of U isotope fractionation recorded in the aqueous solutes. Here, we employ the multi-component, isotope-enabled CrunchTope reactive transport software to interpret these measured U isotope ratios, and demonstrate accurate reproduction of observed trends in both geochemistry and 238 U/ 235 U ratios for two consecutive years of field experiments. Overall, our results indicate that accurately modeling both the U concentration and isotope ratio distributions greatly constrains the parameter space of the model. We find that the transport properties of U in the Rifle aquifer are governed by the presence of low-permeability regions, which the isotopes are uniquely sensitive to. When U reduction is spatially constrained by these low-permeability regions, the shift in the 238 U/ 235 U ratio becomes more muted. Accurate modeling of observed U isotope ratios thus provides a powerful means to better understand bioremediation, and the current study serves to advance the application of this novel method.

238U/235U↗
DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗
DOE OSTI2021

Rapid 3D nanoscale coherent imaging via physics-aware deep learning

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of phase recovery is iterative in nature. As a result, the image formation is time consuming and computationally expensive, precluding real-time imaging. Here, we use 3D nanoscale X-ray imaging as a representative example to develop a deep learning model to address this phase retrieval problem. We introduce 3D-CDI-NN, a deep convolutional neural network and differential programing framework trained to predict 3D structure and strain, solely from input 3D X-ray coherent scattering data. Our networks are designed to be “physics-aware” in multiple aspects; in that the physics of the X-ray scattering process is explicitly enforced in the training of the network, and the training data are drawn from atomistic simulations that are representative of the physics of the material. We further refine the neural network prediction through a physics-based optimization procedure to enable maximum accuracy at lowest computational cost. 3D-CDI-NN can invert a 3D coherent diffraction pattern to real-space structure and strain hundreds of times faster than traditional iterative phase retrieval methods. Our integrated machine learning and differential programing solution to the phase retrieval problem is broadly applicable across inverse problems in other application areas.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

A radioisotope - enabled reactive transport model for deep vadose zone carbon

In mountainous regions, which constitute the principle source of recharge to major rivers and regional aquifers, infiltration occurs through fractured, partially saturated, weathered bedrock that acts as a boundary layer between saturated aquifers and surface soil. Commonly this deep vadose zone (DVZ) is many meters thick, and yet its role in regulating the generation, retention and mobility of reactive solutes, including nutrients, contaminants and weathering products, is largely unknown. In particular, many of the key reactions that drive the formation of the weathered DVZ and the quality of water moving through it are redox processes, regulated by the availability of organic carbon and oxygen below the soil layer. The role of the DVZ is thus also poorly constrained in the context of carbon stocks and mobility, particularly in lithologies that are naturally high in organic carbon, such as shales. The overarching hypothesis of this study is that upland regions developed in geologic settings with abundant petrogenic carbon store and actively cycle carbon in the weathered DVZ below the soil and above the water table at rates that are significant and currently unconstrained. In order to quantify this cycling, the current study combines novel instrumentation techniques allowing new direct sampling of DVZ systems with advanced numerical reactive transport simulations of carbon transport and transformation. Critically, these simulations will explicitly treat the three isotopes of carbon (the abundant 12C, the stable rare 13C and the radioactive 14C) in a unified framework, thus clearly parsing between the contributions of modern surface derived carbon and lithologic carbon sources in integrated measurements of fluid and gas phase fluxes. This novel model capability will be applied to test the role of DVZ carbon cycling as a regulator of water quality and geological weathering in two complementary field sites both located in organic carbon rich shale lithologies. The first is the Eel River Critical Zone Observatory (ERCZO) in Mendocino County, California, and the second is the Lawrence Berkeley National Laboratory Watershed Function Scientific Focus Area (SFA) in the East River watershed, near Crested Butte, Colorado. At the ERCZO, a novel vadose zone monitoring system has been installed in a 20 m thick, partially saturated, weathered shale hillslope, and preliminary data already indicate substantial CO2 flux generated many meters below the soil surface. At the SFA field site, an instrumented hillslope transect indicates a more complex multi-dimensional fluid and solute transport regime, which will serve as a key test of the calibrated models. Collectively, this project will advance understanding of the cycling of carbon belowground and in relation to transport pathways across the poorly constrained DVZ characteristic of primary water recharge areas. The key product of this work will be enhanced isotope simulation capabilities that are robust and publicly available for application across a broad diversity of systems.

58 GEOSCIENCES↗
DOE OSTI2021

Modeling and Optimization Methods for Controlling and Sizing Grid-connected Energy Storage: A Review

Purpose of Review Energy storage is capable of providing a variety of services and solving a multitude of issues in today's rapidly evolving electric power grid. This paper reviews recent research on modeling and optimization methods for optimally controlling and sizing grid-connected battery energy storage systems (BESSs). Open issues and promising research directions are discussed. Recent Findings Recent studies on BESS dispatch, evaluation, and sizing focus on advanced modeling and optimization methods to maximize stacked value streams from multiple services. BESS models have been improved to better represent operational characteristics or capture degradation effects. Different solution methods and optimization techniques have been proposed to improve the benefits and cost-effectiveness of BESSs, using deterministic approaches prevalently but with impressive progress in capturing and addressing uncertainties. Summary Recent progress in BESS scheduling and sizing better supports planning and operational decision-making in different use cases, which is highly important to advance the deployment of BESSs. Additional research is required to properly model the trade-off between short-term benefits and service life with multiple degradation effects explicitly considered in the decision-making process. Advanced methods are to be developed for effectively determining optimal BESS sizes that maximize overall benefits within a varying lifetime considering diversified system, conditions as well as uncertainties at planning and operational stages.

Wu, Di↗
DOE OSTI2023

Downward quantum learning from element 118: Automated generation of Fermi–Löwdin orbitals for all atoms

A new algorithm based on a rigorous theorem and quantum data computationally mined from element 118 guarantees automated construction of initial Fermi–Löwdin-Orbital (FLO) starting points for all elements in the Periodic Table. It defines a means for constructing a small library of scalable FLOs for universal use in molecular and solid-state calculations. The method can be systematically improved for greater efficiency and for applications to excited states such as x-ray excitations and optically silent excitations. FLOs were introduced to recast the Perdew–Zunger self-interaction correction (PZSIC) into an explicit unitarily invariant form. The FLOs are generated from a set of N quasi-classical electron positions, referred to as Fermi-Orbital descriptors (FODs), and a set of N-orthonormal single-electron orbitals. FOD positions, when optimized, minimize the PZSIC total energy. However, creating sets of starting FODs that lead to a positive definite Fermi orbital overlap matrix has proven to be challenging for systems composed of open-shell atoms and ions. The proof herein guarantees the existence of a FLOSIC solution and further guarantees that if a solution for N electrons is found, it can be used to generate a minimum of N – 1 and a maximum of 2 N – 2 initial starting points for systems composed of a smaller number of electrons. As a result, applications to heavy and super-heavy atoms are presented. All starting solutions reported here were obtained from a solution for element 118, Oganesson.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods

In this paper, we present a Fourier analysis of wave propagation problems subject to a class of continuous and discontinuous discretizations using high-degree Lagrange polynomials. This allows us to obtain explicit analytical formulas for the dispersion relation and group velocity and, for the first time to our knowledge, characterize analytically the emergence of gaps in the dispersion relation at specific wavenumbers, when they exist, and compute their specific locations. Wave packets with energy at these wavenumbers will fail to propagate correctly, leading to significant numerical dispersion. We also show that the Fourier analysis generates mathematical artifacts, and we explain how to remove them through a branch selection procedure conducted by analysis of eigenvectors and associated reconstructed solutions. The higher frequency eigenmodes, named erratic in this study, are also investigated analytically and numerically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum Many-Body Theory from a Solution of the N -Representability Problem

Here, in this study, we present a many-body theory based on a solution of the N-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an N-particle density matrix, known as N-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H 8 ring.

74 ATOMIC AND MOLECULAR PHYSICS↗