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Results for “Green's function methods”

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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Multiscale Approach to Fast ModSim for Laser Processing of Metals for Future Nuclear Deterrence Environments

Predicting performance of parts produced using laser-metal processing remains an out- standing challenge. While many computational models exist, they are generally too computationally expensive to simulate the build of an engineering-scale part. This work develops a reduced order thermal model of a laser-metal system using analytical Green's function solutions to the linear heat equation, representing a step towards achieving a full part performance prediction in an "overnight" time frame. The developed model is able to calculate a thermal history for an example problem 72 times faster than a traditional FEM method. The model parameters are calibrated using a non-linear solution and microstructures and residual stresses calculated and compared to a non-linear case. The calibrated model shows promising agreement with a non-linear solution.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Versatile recognition of graphene layers from optical images under controlled illumination through green channel correlation method

In this study, a simple yet versatile method is proposed for identifying the number of exfoliated graphene layers transferred on an oxide substrate from optical images, utilizing a limited number of input images for training, paired with a more traditional number of a few thousand well-published Github images for testing and predicting. Two thresholding approaches, namely the standard deviation-based approach and the linear regression-based approach, were employed in this study. The method specifically leverages the red, green, and blue color channels of image pixels and creates a correlation between the green channel of the background and the green channel of the various layers of graphene. This method proves to be a feasible alternative to deep learning-based graphene recognition and traditional microscopic analysis. The proposed methodology performs well under conditions where the effect of surrounding light on the graphene-on-oxide sample is minimum and allows rapid identification of the various graphene layers. Here, the study additionally addresses the functionality of the proposed methodology with nonhomogeneous lighting conditions, showcasing successful prediction of graphene layers from images that are lower in quality compared to typically published in literature. In all, the proposed methodology opens up the possibility for the non-destructive identification of graphene layers from optical images by utilizing a new and versatile method that is quick, inexpensive, and works well with fewer images that are not necessarily of high quality.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Code verification for practically singular equations

We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Notes on the complex Sachdev-Ye-Kitaev model

We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions with N $\gg$ 1 flavors and a global U(1) charge. We provide a general definition of the charge in the ( G, Σ) formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the many-body density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Lattice Green’s Functions for High-Order Finite Difference Stencils

Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that are unbounded in one or more directions. The majority of existing numerical solvers that make use of LGFs rely on a second-order discretization and operate on domains with free-space boundary conditions in all directions. Under these conditions, fast expansion methods are available that enable precomputation of 2D or 3D LGFs in linear time, avoiding the need for brute-force multi-dimensional quadrature of numerically unstable integrals. Here we focus on higher-order discretizations of the Laplace operator on domains with more general boundary conditions, by (1) providing an algorithm for fast and accurate evaluation of the LGFs associated with high-order dimension-split centered finite differences on unbounded domains, and (2) deriving closed-form expressions for the LGFs associated with both dimension-split and Mehrstellen discretizations on domains with one unbounded dimension. Through numerical experiments we demonstrate that these techniques provide LGF evaluations with near machine-precision accuracy, and that the resulting LGFs allow for numerically consistent solutions to high-order discretizations of the Poisson's equation on fully or partially unbounded 3D domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Analytical solution for partial heating on the exterior of the pipe with application to measuring fluid flow rate

An analytical model using Green’s functions for partial external heating of a pipe is developed, which results in an exact mathematical solution for the radial and axial temperature distribution in the pipe wall. Partial heating consists of a constant heat flux function imposed over a small section of the exterior of a pipe and for a limited time duration. The solution comprises steady-state and transient parts, and an algebraic identity is used to decrease the number of summation terms in the slowly-converging steady- state part. Intrinsic verification principles are used to verify the solution. As an example application, this transient solution is applied toward the development of a simple, noninvasive method for in-field measurement of the flow rate in pipes. Furthermore, to simulate this application, a pulse of energy is imposed to the wall of the pipe, and the developed mathematical solution is used to find the flow rate of the fluid inside the pipe. An optimal experiment is designed to find the best measurement location and time.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Importance of charge self-consistency in first-principles description of strongly correlated systems

First-principles approaches have been successful in solving many-body Hamiltonians for real materials to an extent when correlations are weak or moderate. As the electronic correlations become stronger often embedding methods based on first-principles approaches are used to better treat the correlations by solving a suitably chosen many-body Hamiltonian with a higher level theory. The success of such embedding theories, often referred to as second-principles, is commonly measured by the quality of self-energy Σ which is either a function of energy or momentum or both. However, Σ should, in principle, also modify the electronic eigenfunctions and thus change the real space charge distribution. While such practices are not prevalent, some works that use embedding techniques do take into account these effects. In such cases, choice of partitioning, of the parameters defining the correlated Hamiltonian, of double-counting corrections, and the adequacy of low-level Hamiltonian hosting the correlated subspace hinder a systematic and unambiguous understanding of such effects. Further, for a large variety of correlated systems, strong correlations are largely confined to the charge sector. Then an adequate nonlocal low-order theory is important, and the high-order local correlations embedding contributes become redundant. Here we study the impact of charge self-consistency within two example cases, TiSe 2 and CrBr 3 , and show how real space charge re-distribution due to correlation effects taken into account within a first-principles Green’s function-based many-body perturbative approach is key in driving qualitative changes to the final electronic structure of these materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Delayed leaf greening involves a major shift in the expression of cytosolic and mitochondrial ribosomes to plastid ribosomes in the highly phosphorus-use-efficient Hakea prostrata (Proteaceae)

Abstract Background and aims Hakea prostrata (Proteaceae) is a highly phosphorus-use-efficient plant native to southwest Australia. It maintains a high photosynthetic rate at low leaf phosphorus (P) and exhibits delayed leaf greening, a convergent adaptation that increases nutrient-use efficiency. This study aimed to provide broad physiological and gene expression profiles across leaf development, uncovering pathways leading from young leaves as nutrient sinks to mature leaves as low-nutrient, energy-transducing sources. Methods To explore gene expression underlying delayed greening, we analysed a de novo transcriptome for H. prostrata across five stages of leaf development. Photosynthesis and respiration rates, and foliar pigment, P and nitrogen (N) concentrations were determined, including the division of P into five biochemical fractions. Key results Transcripts encoding functions associated with leaf structure generally decreased in abundance across leaf development, concomitant with decreases in foliar concentrations of 85% for anthocyanins, 90% for P and 70% for N. The expression of genes associated with photosynthetic function increased during or after leaf expansion, in parallel with increases in photosynthetic pigments and activity, much later in leaf development than in species that do not have delayed greening. As leaves developed, transcript abundance for cytosolic and mitochondrial ribosomal proteins generally declined, whilst transcripts for chloroplast ribosomal proteins increased. Conclusions There was a much longer temporal separation of leaf cell growth from chloroplast development in H. prostrata than is found in species that lack delayed greening. Transcriptome-guided analysis of leaf development in H. prostrata provided insight into delayed greening as a nutrient-saving strategy in severely phosphorus-impoverished landscapes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

An Overview of Gemma FY2021 Verification Activities

Though the method-of-moments implementation of the electric-field integral equation plays an important role in computational electromagnetics, it provides many code-verification challenges due to the different sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. In this report, we document our research to address these issues, as well as its implementation and testing in Gemma.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Covalent integration of polymers and porous organic frameworks

Covalent integration of polymers and porous organic frameworks (POFs), including metal-organic frameworks (MOFs), covalent organic frameworks (COFs) and hydrogen-bonded organic frameworks (HOFs), represent a promising strategy for overcoming the existing limitations of traditional porous materials. This integration allows for the combination of the advantages of polymers, i.e., flexibility, processability and chemical versatility etc., and the superiority of POFs, like the structural integrity, tunable porosity and the high surface area, creating a type of hybrid materials. These resulting polymer-POF hybrid materials exhibit enhanced mechanical strength, chemical stability and functional diversity, thus opening up new opportunities for applications across a large variety of fields, such as gas separation, catalysis, biomedical applications, environmental remediation and energy storage. In this review, an overview of synthetic routes and strategies on how to covalently integrate different polymers with various POFs is discussed, especially with a particular focus on methods like polymerization within, on and among POF structures. To investigate the unique properties and functions of these resultant hybrid materials, the characterization techniques, including nuclear magnetic resonance spectroscopy (NMR), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), thermogravimetric analysis (TGA), transmission electron microscopy (TEM) and scanning electron microscopy (SEM), gas adsorption analysis (BET) and computational modeling and machine learning, are also presented. The ability of polymer-POFs to manipulate the pore environments at the molecular level affords these materials a wide range of applications, providing a versatile platform for future advancements in material science. Looking forward, to fully realize the potential of these hybrid materials, the authors highlight the scalability, green synthesis methods, and potential for stimuli-responsive polymer-POF materials as critical areas for future research.

Hossain, Md Amjad↗
DOE OSTI2021

Shape- and Orientation-Dependent Scattering of Isolated Gold Nanostructures Using Polarized Dark-Field Microscopy

In this work, we demonstrate a simple and robust method for measuring the shape- and orientation-dependent optical scattering of various plasmonic nanostructures adsorbed onto a solid surface using polarized dark-field microscopy. By analyzing the dark-field scattering images of gold nanostructures using grazing incidence polarized light with a bench-top microscope, we are able to correlate optical scattering from the individual nanostructures with their shape and orientation. Depending on the size, shape, and orientation of the plasmonic nanostructures, they exhibit characteristic angle- and polarization-dependent scattering signals. Extracting the red, green, and blue channels of the scattering signals from a color-imaging detector as a function of azimuthal angle provides a polar plot of color intensity values that is characteristic of the underlying nanostructure. Examples are presented for various nanostructures, including spherical nanoparticles, nanotriangles, and nanorods. Experimental results are complemented by numerical calculations of the scattering spectra of representative model nanostructures. We demonstrate that the polarization- and orientation-dependent scattering behavior is a consequence of various localized surface plasmon modes existing in the nanostructures and can be used to verify the shape of individual objects as well as quickly identify the orientation of numerous objects on a densely populated substrate. We anticipate that this method will provide a rapid and efficient complement to the typical structural analysis of nanoparticles that is achieved by electron microscopy as well as providing a simple method for generating detailed information of the optical scattering of various types of individual plasmonic nanostructures.

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

Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green’s function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green’s function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green’s function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green’s function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green’s function approach and other Green’s function approaches in the numerical exact limit.

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

3D-Printed Porous Supramolecular Sorbents for Cobalt Recycling

Electronic waste recycling is a recognized global challenge that requires new strategies to bind and release critical materials selectively, such as cobalt present in lithium-ion batteries. To address this challenge, hierarchical 3D-printed porous polymer scaffolds bearing supramolecular receptors were prepared using vat photopolymerization and their cobalt binding profiles were examined as a function of matrix polarity. By combining high-resolution digital light processing (DLP) with polymerization-induced phase separation (PIPS), functional acrylic copolymer networks with micrometer-level precision of geometry and nanometer-level pores were generated. Covalent integration of a methacrylate-functionalized bisdicyclohexyl acetamide (BDCA-MA) receptor enabled binding and release of cobalt(II) chloride (CoCl 2 ) via a solvent polarity switch mechanism involving a change in solvent from ethanol to water. The present structures proved reusable as shown by sustained high binding efficiency over five bind and release cycles. Finally, this platform represents a “green” and energy conscious method for future electronic waste recycling.

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

Deep Learning Prediction of Protein Complex Structures

Proteins interact to form protein complex to carry out biological functions such as catalytic chemical reaction. Therefore, it is important to develop computational methods to predict protein-protein interaction and the structures of protein complexes to study and enhance protein function. In this project, we successfully developed several deep learning methods to predict inter-protein contacts and the reinforcement learning and optimization methods to reconstruct protein complex structures from predicted inter-chain contacts. The methods were integrated with the MULTICOM protein complex structure prediction system and applied to predict the complex structures of biomass production-related proteins of green algae. During the two and a half years of research and development, all the specific milestones of the project were achieved successfully. 16 publications/manuscripts were produced. 10 software tools were developed. A patent application was submitted. Our MULTICOM predictors leveraging some tools developed in this project were ranked among the top predictors in the 15th Critical Assessment of Techniques for Protein Structure Prediction (CASP15) in 2022.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Strategies for designing biocatalysts with new functions

Enzymes can be optimized to accelerate chemical transformations via a range of methods. In this review, we showcase how protein engineering and computational design techniques can be interfaced to develop highly efficient and selective biocatalysts.

09 BIOMASS FUELS↗
DOE OSTI2020

Equation of motion coupled-cluster cumulant approach for intrinsic losses in x-ray spectra

We present an equation of motion coupled cluster approach for calculating and understanding intrinsic inelastic losses in core level x-ray absorption spectra (XAS). The method is based on a factorization of the transition amplitude in the time-domain, which leads to a convolution of an effective one-body spectrum and the core-hole spectral function. The spectral function characterizes these losses in terms of shake-up excitations and satellites, and is calculated using a cumulant representation of the core-hole Green’s function that includes non-linear corrections. The one-body spectrum also includes orthogonality corrections that enhance the XAS at the edge.

Rehr, John J.↗
DOE OSTI2026

Transformer-based operator learning framework for self-energy in strongly correlated systems

We introduce Σ-Attention, a transformer-based operator-learning framework for approximating the self-energy operator of strongly correlated electronic systems. By creating a batched dataset that combines results from three complementary approaches, i.e., many-body perturbation theory, strong-coupling expansion, and exact diagonalization, each effective in specific parameter regimes, Σ-Attention is applied to learn an accurate approximation for the self-energy operator that is valid across a wide range of parameter regimes. This hybrid strategy leverages the strengths of existing methods while relying on the transformer's ability to generalize beyond individual limitations. More importantly, the scalability of the transformer architecture allows the learned self-energy to be extended to systems with larger sizes, leading to much improved computational scaling. Using the one-dimensional Hubbard model, we demonstrate that Σ-Attention can accurately predict the Matsubara Green's function of large systems with a wide range of coupling strength. Our framework offers a promising and scalable pathway for studying strongly correlated systems with many possible generalizations.

Zhu, Yuanran↗
DOE OSTI2020

Reduced Artifact Approach for Determining Diffusion Coefficients in Time-Resolved Microscopy

Ultrafast microscopy methods traditionally assume a Gaussian profile to extract excited state diffusivities from transport measurements. Although this fitting method recovers accurate diffusion coefficients when the point spread function is well-represented by a Gaussian, even minor spatial aberrations introduced by the imaging system cause significant errors in the determined value. To provide a more accurate measure of excited state transport in nano- and microscale materials systems, in this work an alternative analysis protocol is proposed that numerically convolves the Green’s function solution to the diffusion equation with the experimentally measured point spread function. In contrast to the Gaussian fitting approach, the numerical convolution is shown to be robust against artifacts caused by nonideal point spread functions. Furthermore, the numerical convolution approach is highly effective at resolving anisotropic diffusion in modeled data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗