Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “EXACT SOLUTIONS”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Real-time dispatch optimization for concentrating solar power with thermal energy storage

Concentrating solar power (CSP) plants present a promising path towards utility-scale renewable energy. The power tower, or central receiver, configuration can achieve higher operating temperatures than other forms of CSP, and, like all forms of CSP, naturally pairs with comparatively inexpensive thermal energy storage, which allows CSP plants to dispatch electricity according to market price incentives and outside the hours of solar resource availability. Currently, CSP plants commonly include a steam Rankine power cycle and several heat exchange components to generate high-pressure steam using stored thermal energy. The efficiency of the steam Rankine cycle depends on the temperature of the plant's operating fluid, and so is a main concern of plant operators. However, the variable nature of the solar resource and the conservatism with which the receiver is operated prevent perfect control over the receiver outlet temperature. Therefore, during periods of solar variability, collection occurs at lower-than-design temperature. To support operator decisions in a real-time setting, we develop a revenue-maximizing non-convex mixed-integer, quadradically-constrained program which determines a dispatch schedule with sub-hourly time fidelity and considers temperature-dependent power cycle efficiency. The exact nonlinear formulation proves intractable for real-time decision support. Here we present exact and inexact techniques to improve problem tractability that include a hybrid nonlinear and linear formulation. Our approach admits solutions within approximately 3% of optimality, on average, within a five-minute time limit, demonstrating its usability for decision support in a real-time setting.

14 SOLAR ENERGY↗
DOE OSTI2023

Restoring permutational invariance in the Jordan–Wigner transformation

The Jordan–Wigner transformation is a powerful tool for converting systems of spins into systems of fermions, or vice versa. While this mapping is exact, the transformation itself depends on the labelling of the spins. One consequence of this dependence is that approximate solutions of a Jordan–Wigner-transformed Hamiltonian may depend on the (physically inconsequential) labelling of the spins. In this work, we turn to an extended Jordan–Wigner transformation which remedies this problem and which may also introduce some correlation atop the Hartree–Fock solution of a transformed spin Hamiltonian. We demonstrate that this extended Jordan–Wigner transformation can be thought of as arising from a unitary version of the Lie algebraic similarity transformation (LAST) theory. Here, we show how these ideas, particularly in combination with the standard (non-unitary) version of LAST, can provide a potentially powerful tool for the treatment of the XXZ and J 1 –J 2 Heisenberg Hamiltonians.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Fate of false vacuum in non-perturbative regimes

Abstract We use some exact results in scalar field theory to revise the analysis by Coleman and Callan about false vacuum decay and propose a simple non-perturbative formalism. We introduce an exact Green’s function which incorporates non-perturbative corrections in the strong coupling regimes of the theory. The solution of the scalar field theory involves the Jacobi elliptical function and has been used to calculate the effective potential for any arbitrary coupling values. We demonstrate the use of this formalism in a simpleλϕ 4 theory, and show that the effective potential exhibits a false minimum at the origin. We then calculate the false vacuum decay rate in the thin wall approximation, and suggest simple analytic formulae that may be useful for the analysis for the first-order phase transition beyond the perturbative regime. In our methodology, we show that the standard results obtained in perturbation theory are reproduced by making the coupling values very small.

Physics↗
DOE OSTI2021

Opening the reheating box in multifield inflation

The robustness of multi-field inflation to the physics of reheating is investigated. In order to carry out this study, reheating is described in detail by means of a formalism which tracks the evolution of scalar fields and perfect fluids in interaction (the inflatons and their decay products). This framework is then used to establish the general equations of motion of the background and perturbative quantities controlling the evolution of the system during reheating. Next, these equations are solved exactly by means of a new numerical code. Moreover, new analytical techniques, allowing us to interpret and approximate these solutions, are developed. As an illustration of a physical prediction that could be affected by the micro-physics of reheating, the amplitude of non-adiabatic perturbations in double inflation is considered. It is found that ignoring the fine-structure of reheating, as usually done in the standard approach, can lead to differences as big as ~ 50%, while our semi-analytic estimates can reduce this error to ~ 10%. Finally, we conclude that, in multi-field inflation, tracking the perturbations through the details of the reheating process is important and, to achieve good precision, requires the use of numerical calculations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

IIA Incremental Interval Assignment

IIA is a solver for optimizing integer matrix problems Ax=b. It was developed to decide the number of mesh edges on model curves (intervals) for quad and hex meshing. Meshing schemes impose constraints ranging from the mild requirement (i.e. that any quad mesh must have an even number of edges on its boundary) to structured mapped patches where opposite sides of a rectangle must have exactly equal numbers of edges. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2020-13618 M

MItchell, Scott↗
DOE OSTI2020

Spent Crystalline Silicotitanate Storage Study

Washington River Protection Solutions is working to support initial production of immobilized low-activity waste (LAW) by feeding Hanford tank supernate from tank farms to the Hanford Waste Treatment and Immobilization Plant (WTP) LAW Facility. This goal incorporates the design of a Tank-Side Cesium Removal (TSCR) system, which filters tank waste supernate to remove suspended solids and then removes Cs by processing it through crystalline silicotitanate (CST) ion exchange media manufactured by Honeywell UOP, LLC. The 137 Cs-depleted product is intended to be sent to the WTP for vitrification. The Cs-loaded CST columns will be stored indefinitely, with a goal of eventual CST removal and treatment. Thus, the spent CST needs to be recoverable. The testing described herein looks to potential upset process conditions where CST storage may be required before various rinse steps are completed. This study evaluated upset conditions at three sequential processing steps envisioned for TSCR (feed, 0.1 M NaOH rinse, water rinse), and in-column drying with compressed air (normal end step) to assess impacts on the nature of the CST bed. Testing was conducted at the small scale (12-mL bed volume); simulated AP-105 tank waste was used as the feed. Following process disruption, the CST bed was dried in place at 70 °C. Post-dried CST bed physical properties (angle of repose, penetration depth, particle morphological changes) were measured to evaluate how CST moved and flowed. The testing is intended to provide a preliminary assessment of issues that may arise from desiccation of CST with the indicated salt solutions in place. Since these were small-scale tests, the processing conditions will not match full scale conditions exactly; however, the tests do provide insight into the impact of stopping processing at an earlier step than normal. Except for the feed that was dried in-place, all other process stop-conditions showed the CST bed flowed well after drying. At this small scale, CST beds would not present an issue for retrievability. The feed that was dried in place had solidified into a rock-hard monolith with no movement possible. Samples had to be chipped from the surface.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Probing the exact form and doping preference of magnesium in ordinary Portland cement clinker phases: A study from experiments and DFT simulations

Highlights: • The doping behaviors of Mg in OPC clinker phases were systematically studied. • About 1.3 wt% MgO enter OPC clinker phases by forming substitutional solid solutions. • In the 4 composed minerals, C{sub 3}S, C{sub 3}A and C{sub 4}AF can host more Mg ions than C{sub 2}S. • Mg ions prefer to replace Ca in C{sub 3}S, C{sub 2}S and C{sub 3}A while replace Fe and Ca in C{sub 4}AF. • Both the large structure distortions and formation energies governs the low solubility. A systematic study was performed to learn the exact existence form and doping behaviors of magnesium in ordinary Portland cement (OPC) clinker. Our results show that about 1.3 wt% MgO incorporates into OPC clinker phases by forming substitutional solid solutions while excess Mg accumulate and exist as periclase. Results from Rietveld refinement present a substitution preference in C{sub 3}S and C{sub 3}A over C{sub 2}S. More in-depth analyses from density function theoretical simulations show that in C{sub 3}S, C{sub 2}S and C{sub 3}A, the substitution occurs by replacing Ca while in C{sub 4}AF, it probably occurs by substituting Fe and Ca ions. The large structure distortions and sharp increase in formation energies with increasing MgO determines its low solubility. This work provides a clear understanding of the existence states and the intrinsic mechanism governing doping behaviors of Mg, thus should be very important in guiding the synthesis of OPC clinker by utilizing high-Mg limestone.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Preserving Superconvergence of Spectral Elements for Curved Domains

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using geometric refinement, which both refines the mesh near high-curvature regions and increases the degree of geometric basis functions. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce ApSEM, a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and 3D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries. We also show the efficiency of ApSEM as it can recover superconvergence in nodal solutions without drastically increasing the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Impact of solvation on the electronic resonances in uracil

Interactions of low-energy electrons with the DNA and RNA nucleobases are known to form metastable states, known as electronic resonances. In this work, we study electron attachment to solvated uracil, an RNA nucleobase, using the orbital stabilization method at the Equation of Motion-Coupled Cluster for Electron Affinities with Singles and Doubles (EOM-EA-CCSD) level of theory with the Effective Fragment Potential (EFP) solvation method. We benchmarked the approach using multireference methods, as well as by comparing EFP and full quantum calculations. The impact of solvation on the first one particle (1p) shape resonance, formed by electron attachment to the π* LUMO orbital, as well as the first two particle one hole (2p1h) resonance, formed by electron attachment to neutral uracil's π–π* excited state, was investigated. We used molecular dynamics simulations for solvent configurations and applied charge stabilization technique-based biased sampling to procure configurations adequate to cover the entire range of the electron attachment energy distribution. The electron attachment energy in solution is found to be distributed over a wide range of energies, between 4.6 eV to 6.8 eV for the 2p1h resonance, and between −0.1 eV to 2 eV for the 1p resonance. The solvent effects were similar for the two resonances, indicating that the exact electron density of the state is not as important as the solvent configurations. Multireference calculations extended the findings showing that solvation effects are similar for the lowest four resonances, further indicating that the specific solute electron density is not as important, but rather the water configurations play the most important role in solvation effects. Lastly, by comparing bulk solvation to clusters of uracil with a few water molecules around it, we find that the impact of microsolvation is very different from that of bulk solvation.

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

Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values

We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent root-bracketing techniques or Chebyshev interpolation to locate bifurcation points. Only positive singular values have to be computed, though the method relies on the existence of an analytic or smooth singular value decomposition (SVD). The sign of the determinant of the Jacobian, computed as part of the bidiagonal reduction in the SVD algorithm, eliminates slope discontinuities at the zeros of the smallest singular value. We use the method to search for spatially quasi-periodic traveling water waves that bifurcate from large-amplitude periodic waves. The water wave equations are formulated in a conformal mapping framework to facilitate the computation of the quasi-periodic Dirichlet-Neumann operator. We find examples of pure gravity waves with zero surface tension and overhanging gravity-capillary waves. In both cases, the waves have two spatial quasi-periods whose ratio is irrational. We follow the secondary branches via numerical continuation beyond the realm of linearization about solutions on the primary branch to obtain traveling water waves that extend over the real line with no two crests or troughs of exactly the same shape. The pure gravity wave problem is of relevance to ocean waves, where capillary effects can be neglected. Such waves can only exist through secondary bifurcation as they do not persist to zero amplitude. The gravity-capillary wave problem demonstrates the effectiveness of using the signed smallest singular value as a test function for multi-parameter bifurcation problems. This test function becomes mesh independent once the mesh is fine enough.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A high order Cartesian grid, finite volume method for elliptic interface problems

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Fermionic mean-field theory as a tool for studying spin Hamiltonians

The Jordan–Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Furthermore, Jordan–Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J 1 –J 2 Heisenberg models, as well as to the pairing or reduced Bardeen–Cooper–Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Spent Crystalline Silicotitanate Storage Study—Post AP-105DF Processing

A Tank-Side Cesium Removal (TSCR) system is under development by Washington River Protection Solutions to support initial production of immobilized low-activity waste (LAW) by feeding Hanford tank supernate from tank farms to the Hanford Waste Treatment and Immobilization Plant (WTP) LAW Facility. Tank waste supernate will be filtered to remove suspended solids and then Cs will be removed by processing it through crystalline silicotitanate (CST) ion exchange media manufactured by Honeywell UOP, LLC. The Cs-loaded CST columns will be stored indefinitely, with a goal of eventual CST removal and treatment. Thus, the spent CST needs to be recoverable after undetermined storage time. Previous testing with AP-105 simulant showed that rinsing the CST bed with 3 bed volumes (1.4 apparatus volumes [AVs]) of 0.1 M NaOH resulted in a dried bed that maintained flow characteristics indicative of ease of recovery. This study explored the intermediate conditions (between feed dried in place and the 1.4 AVs of 0.1 M NaOH rinse) to evaluate CST bed properties after: 1) stoppage with feed in place; 2) stoppage after draining feed; 3) stoppage after 0.7 AV of 0.1 M NaOH rinse through column; 4) stoppage after 1.5 AVs of 0.1 M NaOH rinse through column. Post processing, each column was heated at 50 °C for 19 days under pseudo-storage conditions to simulate the expected dried and stored CST bed conditions. Testing was conducted at the small scale (12-mL bed volume); actual, Cs-depleted, AP-105 tank waste was used as the feed. Post-dried CST bed physical properties (angle of repose and penetration depth) were measured to evaluate how CST moved and flowed. All process stop-conditions resulted in a solidified CST bed except for the final condition, 1.5 AVs of 0.1 M NaOH rinse. At this small scale, the three CST beds presented an issue for retrievability after the short storage period (19 days at 50 °C). The latter case confirmed the results from simulant testing. The testing was intended to provide a preliminary assessment of issues that may arise from desiccation of CST during storage with the indicated salt solutions in place. Since these were small-scale tests, the processing system did not scale to full scale conditions exactly; however, the tests did provide insight into the impact on the dried and stored CST bed after stopping processing at an earlier step (upset condition) than normal. These results indicate that if an upset condition occurs at TSCR, a dilute hydroxide rinse should be considered before the CST dries from internal heating.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

High-temperature fractional quantum Hall state in the Floquet kagome flat band

A fractional quantum Hall effect (FQHE) has been predicted in a topological flat band (FB) by a single-particle band structure combined with phenomenological theory or solution of a many-body lattice Hamiltonian with fuzzy parameters. A long-standing roadblock toward the realization of a FB-FQHE is lacking the many-body solution of specific materials under realistic conditions. Here, we demonstrate a combined study of single-particle Floquet band theory with exact diagonalization (ED) of a many-body Hamiltonian. We show that a time-periodic circularly polarized laser inverts the sign of second-nearest-neighbor hopping in a kagome lattice and enhances spin-orbit coupling in one spin channel to produce a Floquet FB with a high flatness ratio of bandwidth over band gap, as exemplified in monolayer Pt 3 C 36 S 12 H 12 . The ED of the resultant Floquet-kagome lattice Hamiltonian gives a one-third-filling ground state with a laser-dependent excitation gap of a FQH state, up to an estimated temperature above 70 K. Our findings pave the way for exploring the alluding high-temperature FB-FQHE.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions

Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges–local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. Furthermore, the simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent–solvent and solute–solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.

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

Dirac-Harper Theory for One-Dimensional Moiré Superlattices

In this work, we study a Dirac-Harper model for moiré bilayer superlattices where layer antisymmetric strain periodically modulates the interlayer coupling between two honeycomb lattices in one spatial dimension. Discrete and continuum formulations of this model are analyzed. For a sufficiently long moiré period we find low-energy spectra that host a manifold of weakly dispersive bands arising from a hierarchy of momentum and position-dependent mass inversions. We analyze their charge distributions, mode count, and valley coherence using exact symmetries of the lattice model and approximate symmetries of a four-flavor version of the Jackiw-Rebbi one-dimensional solution.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Health Hazards of Exposures to Radioiodine

Iodine is a chemical element with atomic number 53. Iodine-127 is stable (non-radioactive) and commonly found in nature. Elemental iodine is a purple-colored solid at room temperature and pressure, but spontaneously sublimates (turns into vapor). Iodine is an essential element for life, and is required for proper functioning of the thyroid. Iodine is present in many foods, and is readily absorbed by the body and concentrated in the thyroid gland. A fraction of iodine ingested or inhaled is rapidly removed by the kidneys. The rest of the inhaled or ingested iodine is absorbed the by thyroid and retained for many months. Iodine has a biological half-life of approximately 120 days in health individuals. The biological half-life can be shorter in individuals with hyperthyroidism, and longer in individuals with hypothyroidism. Iodine has a number of radioactive isotopes, most of which have relatively short half-lives (days or weeks). Short half-life iodine isotopes are useful for a variety of medical applications, including imaging and cancer therapy. For example, Iodine-123 (half-life 13 hours) is commonly used for medical imaging of the thyroid, while iodine-131 (half-life 8 days) is used for suppressing thyroid function in individuals with hyperthyroidism or ablating (killing) thyroid cells to treat thyroid cancer. Iodine-125 (half-life 59 days) is produced in nuclear reactors, and has medical uses. Although iodine-125 can be used for thyroid imaging, Iodine-123 is more commonly used for that purpose because of its shorter half-life and higher-energy emissions. Iodine-125 is more commonly used for cancer treatment, and can be processed into small metal pellets (seeds) inserted directly into a tumor. Iodine-125 emits low-energy x-rays which can kill tumor cells and generally cannot escape the tumor, sparing other tissues. Medical iodine for imaging or treatment is typically administered orally in the form a pill or liquid solution. A typical adult thyroid scan using iodine-123 involves having the patient swallow between one and four 0.1 millicuries pills, with the exact dose dependent on the patient’s weight. This results in a whole-body committed effective dose of 80 – 320 mrem, and a thyroid equivalent dose of 1443 – 5772 mrem. Note that the whole-body effective dose relates to the overall cancer risk, while the larger equivalent dose to the thyroid only indicates that most of this risk is the result of exposure to the thyroid. These doses are considered safe, although the procedure is not recommended for pregnant or breastfeeding women. In contrast, the quantities of iodine-131 used for treatment of hyperthyroidism and thyroid cancers are much higher. For treatment of hyperthyroidism, 4 – 10 millicuries are administered, while for thyroid cancer the administration can range from 50 – 150 millicuries of I-131. In addition to medical exposures, large populations were exposed to radioiodine as result of the atomic bombings of Hiroshima and Nagasaki in Japan, and the Chernobyl nuclear accident. These populations have been carefully followed for many years to assess the effect of their radiation exposures on cancer risk. As a result, a great deal is known about the cancer risks associated with radioiodine exposure. Because iodine is concentrated in the thyroid, the principal risk of exposure to radioiodine is thyroid cancer. Children have the highest risk of thyroid cancer after exposure to radioactive iodine. According to a large study of Japanese atomic bomb survivors, an effective dose of one Sievert (100,000 mrem) has been observed to increase the risk of thyroid cancer by a factor of 9.5 in children aged zero to nine years old, by a factor of 3 in children aged 10 to 19 years old, and by barely detectable amounts in adults. Another way of quantifying the risk from radioiodine exposure is from risk coefficients, which provide the risk per unit intake of radionuclides in terms of both morbidity (any cancer) and mortality (death). Both morbidity (risk of cancer) and mortality (death) risks are shown in the table below. Note that because thyroid cancer is almost never fatal, the morbidity coefficients are much larger than the mortality coefficients.

61 RADIATION PROTECTION AND DOSIMETRY↗