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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 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Photodepositing CdS on the Active Cyano Groups Decorated g‐C 3 N 4 in Z‐Scheme Manner Promotes Visible‐Light‐Driven Hydrogen Evolution

Abstract g‐C 3 N 4 /CdS heterojunctions are potential photocatalysts for hydrogen production but their traditional type‐II configuration generally leads to weak oxidative and reductive activity. How to construct the novel Z‐scheme g‐C 3 N 4 /CdS counterparts to address this issue remains a great challenge in this field. In this work, a new direct Z‐scheme heterojunction of defective g‐C 3 N 4 /CdS is designed by introducing cyano groups (NC‐) as the active bridge sites. Experimental observations in combination with density functional theory (DFT) calculations reveal that the unique electron‐withdrawing feature of cyano groups in the defective g‐C 3 N 4 /CdS heterostructure can endow this photocatalyst with numerous advantageous properties including high light absorption ability, strong redox performance, satisfactory charge separation efficiency, and long lifetime of charge carriers. Consequently, the resultant photocatalytic system exhibits more active performance than CdS and g‐C 3 N 4 under visible light and reaches an excellent hydrogen evolution rate of 1809.07 µmol h −1 g −1 , which is 6.09 times higher than pristine g‐C 3 N 4 . Moreover, the defective g‐C 3 N 4 /CdS photocatalyst maintains good stability after 40 h continuous test. This work provides new insights into design and construction of Z‐scheme heterojunctions for regulating the visible‐light‐induced photocatalytic activity for H 2 evolution.

Wang, Zhipeng↗
DOE OSTI2021

Post-Fukushima Research and Development Strategy for MELCOR

Numerous MELCOR modeling improvements and analyses have been performed in the time since the severe accidents at Fukushima Daiichi Nuclear Power Station that occurred in March 2011. This report briefly summarizes the related accident reconstruction and uncertainty analysis efforts. It further discusses a number of potential pursuits to further advance MELCOR modeling and analysis of the severe accidents at Fukushima Daiichi and severe accident modeling in general. Proposed paths forward include further enhancements to identified MELCOR models primarily impacting core degradation calculations, and continued application of uncertainty analysis methods to improve model performance and a develop deeper understanding of severe accident progression.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Use of Stable Mercury Isotopes to Assess Mercury and Methylmercury Transformation and Transport across Critical Interfaces from the Molecular to the Watershed Scale (Final Report)

This project titled “Use of Stable Mercury Isotopes to Assess Mercury and Methylmercury Transformation and Transport across Critical Interfaces from the Molecular to the Watershed Scale” represents a collaborative effort between the University of Michigan (Jason Demers, PI) and Oak Ridge National Laboratory (Scott Brooks, co-I). Much has been learned about mercury (Hg) cycling in stream ecosystems, and East Fork Poplar Creek (EFPC) in particular, through decades of previous research. Nevertheless, some of the most fundamental questions regarding the sources of bioavailable Hg and its transformation to toxic methylmercury (MeHg) have remained unanswered. These fundamental questions include: (1) what are the sources and biogeochemical processes that lead to the input of dissolved Hg to stream water across critical subsurface interfaces within stream ecosystems, and EFPC in particular? and (2) what are the sources and biogeochemical processes that control the production and fate of bioaccumulative MeHg within stream ecosystems, and in EFPC in particular? To address these fundamental questions, our project aimed to couple laboratory experiments and field observations, both utilizing natural abundance Hg stable isotope techniques, to identify the processes responsible for generating mobile, bioavailable dissolved Hg from recalcitrant legacy sources within critical subsurface zones (e.g., streambed hyporheic zone, riparian floodplain subsurface). We used the isotopic signature of this bioavailable dissolved Hg to track its mobilization across these critical interfaces in order to link diffuse subsurface sources of dissolved Hg with increases in surface water dissolved Hg flux measured at the watershed scale. Additionally, our research aimed to determine the isotopic composition of MeHg within these same critical subsurface zones. We directly assessed the isotopic composition of MeHg within biota in order to gain insight into which subsurface sources of inorganic Hg and toxic MeHg are available for bioaccumulation within the EFPC ecosystem. Net fluxes of dissolved Hg along the flow path of EFPC were shown to vary spatially and temporally. In the Upper EFPC, within the Y12 boundary, stream water flux of dissolved Hg consistently decreased between the outfall and the downstream boundary of Y12 (57% ± 29%, 1SD). Within the Upper EFPC, an assessment of Hg isotopic composition suggested that losses were strongly reaction-driven, although isotopic diagnostics did not conform to any known processes. Downstream of Y12, in the upper reach of the Lower EFPC, dissolved Hg fluxes tended to increase during the dormant season (net gain of 11-120%), and decrease during the growing season (net loss of 23% +/- 18%, 1SD). In the downstream-most reach of Lower EFPC, dissolved Hg fluxes increased by 12-108% in 9 out of 10 monthly assessments. Overall, diffuse fluxes from the non-Y12 watershed accounted for 34% (+/- 17%, 1SD) of all dissolved Hg exported during base flow. Within Lower EFPC, an assessment of Hg isotopic composition was consistent with the contribution of diffuse Hg inputs from high-concentration hotspots within riparian floodplains and streambed hyporheic pore water. To investigate remobilization of recalcitrant Hg from legacy sediment sources, we developed procedures that coupled isotopic analysis with sequential extractions of streambed sediment. We found that the proportion of weakly-bound Hg within EFPC streambed sediment was relatively small, but could still account for a large proportion of the annual flux of dissolved Hg from EFPC. These sequential extractions also showed that this weakly-bound Hg fraction could be replenished from the much larger fraction of recalcitrant Hg in sediment. The isotopic composition of these weakly-bound and remobilized recalcitrant Hg fractions within the sediment was consistent with high-concentration dissolved Hg hotspots within hyporheic pore water. Thus, this research provided novel evidence that legacy mercury sources within streambed sediment could provide an ongoing contribution of dissolved Hg to surface waters. Finally, we developed new methods for the direct determination of the MeHg isotopic composition of organisms, which allowed a more direct evaluation of inorganic Hg and MeHg sources accumulating in the food web. We found that fish and aquatic invertebrates in both EFPC and a regional background site obtained inorganic Hg and MeHg from multiple isotopically distinct sources, including sediment, suspended particulates, and periphyton. Photodemethylation was found to be an important reaction influencing MeHg dynamics at both sites. However, the balance of microbial methylation and demethylation processes differed between the two streams, with fractionation resulting from methylation and demethylation processes being relatively in balance within the regional background site, whereas microbial methylation appeared to be dominant over microbial demethylation within the EFPC ecosystem. Broadly, the application of Hg isotopic analysis in this study led to numerous novel insights regarding the biogeochemical cycling of Hg in stream ecosystems. This research project promoted the development of two new approaches, including the coupling of sequential extractions with Hg isotopic analysis to assess remobilization of recalcitrant Hg within sediments, and a new method for the isotopic analysis of MeHg isolated from environmental samples. Both of these efforts represent advances in capacity for the field of mercury isotopic analysis and environmental assessment. Overall, this study demonstrates that the application of Hg stable isotope techniques continues to provide new insights into the biogeochemical cycling of Hg in complex aquatic environments, both within the EFPC and beyond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Ab initio molecular dynamics on quantum computers

Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann-Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H-2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.

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

Using optimal estimation to retrieve winds from velocity-azimuth display (VAD) scans by a Doppler lidar

Abstract. Low-powered commercially available coherent Doppler lidar (CDL) wind profilers provide continuous measurement of vertical profiles of wind in the lower troposphere, usually close to or up to the top of the planetary boundary layer. The vertical extent of these wind profiles is limited by the availability of scatterers and thus varies substantially throughout the day and from one day to the next. This makes it challenging to develop continuous products that rely on CDL-observed wind profiles. In order to overcome this problem, we have developed a new method for wind profile retrievals from CDL that combines the traditional velocity-azimuth display (VAD) technique with optimal estimation (OE) to provide continuous wind profiles up to 3 km. The new method exploits the level-to-level covariance present in the wind profile to fill in the gaps where the signal-to-noise ratio of the CDL return is too low to provide reliable results using the traditional VAD method. Another advantage of the new method is that it provides the full error covariance matrix of the solution and profiles of information content, which more easily facilitates the assimilation of the observed wind profiles into numerical weather prediction models. This method was tested using yearlong CDL measurements at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) Central Facility in 2019. Comparison with the ARM operational CDL wind profile product and collocated radiosonde wind measurements shows excellent agreement (R2>0.99) with no degradation in results where the traditional VAD provided a valid solution. In the region where traditional VAD does not provide results, the OE wind speed and wind vector have uncertainties of 3.44 and 4.33 m s−1, respectively. As a result, the new method provides additional information over the standard technique and increases the effective range of existing CDL systems without the need for additional hardware.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A digital twin solution for floating offshore wind turbines validated using a full-scale prototype

Abstract. In this work, we implement, verify, and validate a physics-based digital twin solution applied to a floating offshore wind turbine. The digital twin is validated using measurement data from the full-scale TetraSpar prototype. We focus on the estimation of the aerodynamic loads, wind speed, and section loads along the tower, with the aim of estimating the fatigue lifetime of the tower. Our digital twin solution integrates (1) a Kalman filter to estimate the structural states based on a linear model of the structure and measurements from the turbine, (2) an aerodynamic estimator, and (3) a physics-based virtual sensing procedure to obtain the loads along the tower. The digital twin relies on a set of measurements that are expected to be available on any existing wind turbine (power, pitch, rotor speed, and tower acceleration) and motion sensors that are likely to be standard measurements for a floating platform (inclinometers and GPS sensors). We explore two different pathways to obtain physics-based models: a suite of dedicated Python tools implemented as part of this work and the OpenFAST linearization feature. In our final version of the digital twin, we use components from both approaches. We perform different numerical experiments to verify the individual models of the digital twin. In this simulation realm, we obtain estimated damage equivalent loads of the tower fore–aft bending moment with an accuracy of approximately 5 % to 10 %. When comparing the digital twin estimations with the measurements from the TetraSpar prototype, the errors increased to 10 %–15 % on average. Overall, the accuracy of the results is promising and demonstrates the possibility of using digital twin solutions to estimate fatigue loads on floating offshore wind turbines. A natural continuation of this work would be to implement the monitoring and diagnostics aspect of the digital twin to inform operation and maintenance decisions. The digital twin solution is provided with examples as part of an open-source repository.

17 WIND ENERGY↗
DOE OSTI2024

SGD-OD: investigating the potential oxygen demand of submarine groundwater discharge in coastal systems

Submarine groundwater discharge (SGD) supplies nutrients, carbon, metals, and radionuclide tracers to estuarine and coastal waters. One aspect of SGD that is poorly recognized is its direct effect on dissolved oxygen (DO) demand in receiving waters, denoted here as SGD-OD. Sulfate-mediated oxidation of organic matter in salty coastal aquifers produces numerous reduced byproducts including sulfide, ammonia, dissolved organic carbon and nitrogen, methane, and reduced metals. When these byproducts are introduced to estuarine and coastal systems by SGD and are oxidized, they may substantially reduce the DO concentration in receiving waters and impact organisms living there. We consider six estuarine and coastal sites where SGD derived fluxes of reduced byproducts are well documented. Using data from these sites we present a semiquantitative model to estimate the effect of these byproducts on DO in the receiving waters. Without continued aeration with atmospheric oxygen, the study sites would have experienced periodic hypoxic conditions due to SGD-OD. The presence of H2S supplied by SGD could also impact organisms. This process is likely prevalent in other systems worldwide.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Effects of Landau quantization on neutrino emission and absorption

Some neutron stars known as magnetars possess very strong magnetic fields, with surface fields as large as 10 15 G and internal fields that are possibly stronger. Recent observations of the radio pulsar GLEAM-X J1627 suggest it may have a surface field as strong as 10 16 G. In the presence of a strong magnetic field, Leinson and Perez showed and Baiko and Yakovlev confirmed that the energy levels of electrons and protons are quantized and the direct Urca process allows neutron stars to cool rapidly, even at low density. For the case of magnetic fields 𝐵 ≳ 10 16 G, we find features in the emissivity due to energy quantization that are not captured by the frequently employed quasiclassical approximation where energy levels are treated as nearly continuous. Resonances can result in amplification of the neutrino emissivity at specific densities compared to a calculation that neglects quantization, particularly at low temperature. These effects are not important for the thermal evolution of an entire neutron star, but may be relevant for phenomena that depend on behavior at specific densities. Here, we present a fully relativistic calculation of the direct Urca rate in a strong magnetic field using the standard V-A weak Lagrangian incorporating mean field nuclear effects and discuss approaches to the numerical challenge the modified wave functions present and a new semianalytic approximation. These tools are also applicable to calculating neutrino opacities in strong magnetic fields in the ejecta of binary neutron star mergers. We calculate the opacities for neutrinos capturing on free nucleons at subsaturation densities and temperatures exceeding an MeV. We find an enhancement to capture processes of the lowest energy neutrinos by an order of magnitude or more due to suppression of electron Pauli blocking in the case of capture on neutrons, and from the effect of the nucleon magnetic moments in the case of capture on protons.

astrophysical electromagnetic fields↗
DOE OSTI2024

Modeling information flow in a computer processor with a multi-stage queuing model

In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another. The model is formulated as a spatially-extended, continuous-time Markov chain where space represents different stages. This model is equivalent to a spatially-extended version of the M/M/s queue. The main modeling feature is the throttling function which describes the processor slowdown when the amount of information falls below a certain threshold. We derive the stationary distribution for this stochastic model and develop a closure for a deterministic ODE system that approximates the evolution of the mean and variance of the stochastic model. In conclusion, we demonstrate the validity of the closure with numerical simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Machine learning changes the rules for flux limiters

Learning to integrate non-linear equations from highly resolved direct numerical simulations has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock capturing methods. Focusing on flux limiters provides a specific plug-and-play component for existing numerical methods. Since their introduction, an array of flux limiters has been designed. Using the coarse-grained Burgers' equation, we show that flux-limiters may be rank-ordered in terms of their log-error relative to high-resolution data. We then develop a theory to find an optimal flux-limiter and present flux-limiters that outperform others tested for integrating Burgers' equation on lattices with [Formula: see text], and 2x, 3x, 4x, and 8x coarse-grainings. We train a continuous piecewise linear limiter by minimizing the mean-squared misfit to six-grid point segments of high-resolution data, averaged over all segments. While flux limiters are generally designed to have an output of φ(r) = 1 at a flux ratio of r = 1, our limiters are not bound by this rule and yet produce a smaller error than standard limiters. Here we find that our machine learned limiters have distinctive features that may provide new rules-of-thumb for the development of improved limiters. Additionally, we use our theory to learn flux-limiters that outperform standard limiters across a range of values (as opposed to at a specific fixed value) of coarse-graining, number of discretized bins, and diffusion parameter. This demonstrates the ability to produce flux limiters that should be more broadly useful than standard limiters for general applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum spin helices more stable than the ground state: Onset of helical protection

Topological magnetic structures are promising candidates for resilient information storage. An elementary example is spin helices in one-dimensional easy-plane quantum magnets. To quantify their stability, we numerically implement the stochastic Schrödinger equation and time-dependent perturbation theory for spin chains with fluctuating local magnetic fields. Here, we find two classes of quantum spin helices that can reach and even exceed ground-state stability: spin-current-maximizing helices and, for fine-tuned boundary conditions, the recently discovered “phantom helices.” Beyond that, we show that the helicity itself (left or right rotating) is even more stable. We explain these findings by separated helical sectors and connect them to topological sectors in continuous spin systems. The resulting helical protection mechanism is a promising phenomenon for stabilizing helical quantum structures, e.g., in ultracold atoms and solid-state systems. We also identify a third type of phantom helix in the system.

1-dimensional spin chains↗
DOE OSTI2021

Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions

Here we propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We additionally assume that the composition $h\circ F$ defines a continuous selection. Manifold sampling algorithms can be classified as model-based derivative-free methods, in that models of $F$ are combined with particularly sampled information about $h$ to yield local models for use within a trust-region framework. We demonstrate that cluster points of the sequence of iterates generated by the manifold sampling algorithm are Clarke stationary. We consider the tractability of three particular subproblems generated by the manifold sampling algorithm and the extent to which inexact solutions to these subproblems may be tolerated. Numerical results demonstrate that manifold sampling as a derivative-free algorithm is competitive with state-of-the-art algorithms for nonsmooth optimization that utilize first-order information about $f$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

FaceBase 3: analytical tools and FAIR resources for craniofacial and dental research

ABSTRACT The FaceBase Consortium was established by the National Institute of Dental and Craniofacial Research in 2009 as a ‘big data’ resource for the craniofacial research community. Over the past decade, researchers have deposited hundreds of annotated and curated datasets on both normal and disordered craniofacial development in FaceBase, all freely available to the research community on the FaceBase Hub website. The Hub has developed numerous visualization and analysis tools designed to promote integration of multidisciplinary data while remaining dedicated to the FAIR principles of data management (findability, accessibility, interoperability and reusability) and providing a faceted search infrastructure for locating desired data efficiently. Summaries of the datasets generated by the FaceBase projects from 2014 to 2019 are provided here. FaceBase 3 now welcomes contributions of data on craniofacial and dental development in humans, model organisms and cell lines. Collectively, the FaceBase Consortium, along with other NIH-supported data resources, provide a continuously growing, dynamic and current resource for the scientific community while improving data reproducibility and fulfilling data sharing requirements.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Model Development for Multi-Component Fuel Vaporization and Flash Boiling

The objectives of this project are to improve the multi-component fuel droplet and film vaporization models used in internal combustion engine simulation, and to develop a comprehensive model to predict the characteristics of multi-component flash boiling spray. This work explores two approaches to fuel composition treatment for modeling multi-component fuel vaporization: one based on discretization and surrogates, and the other based on continuous thermodynamic distribution of fuel properties. The experimental data collected for model validation are done under three fuel form factors: droplet, spray, and thin film. The study on sprays also include experimentation under non-flash and flash boiling conditions, a phenomenon that enhances fuel vaporization. The main goals of this work are: Design and develop a multi-component fuel droplet and wall film vaporization model using both discrete and continuous thermodynamics methods. Design and develop an analytical model for multi-component flash boiling. Integrate the multi-component droplet and film model into multi-dimensional engine calculations to predict the fuel vaporization process under engine operation condition. Conduct multi-component droplet and fuel film vaporization experiments in a non-combusting chamber to verify the proposed vaporization models. Characterize flash boiling phenomena of multi-component fuel sprays by optical and laser diagnostic techniques. This report will detail the experimental setup and the numerical basis for developing a model to achieve the main goals listed above. Key features of observed multi-component fuel vaporization will be summarized at the end of each experimental sections, and corresponding model performance evaluation will be presented at the end of each model development section.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Observations and Modeling of the Onset of Fast Reconnection in the Solar Transition Region

Magnetic reconnection is a fundamental plasma process that plays a critical role not only in energy release in the solar atmosphere, but also in fusion, astrophysics, and other space plasma environments. One of the challenges in explaining solar observations in which reconnection is thought to play a critical role is to account for the transition of the dynamics from a slow quasi-continuous phase to a fast and impulsive energetic burst of much shorter duration. Despite the theoretical progress in identifying mechanisms that might lead to rapid onset, a lack of observations of this transition has left models poorly constrained. High-resolution spectroscopic observations from NASA's Interface Region Imaging Spectrograph now reveal tell-tale signatures of the abrupt transition of reconnection from a slow phase to a fast, impulsive phase during UV bursts or explosive events in the Sun's atmosphere. Our observations are consistent with numerical simulations of the plasmoid instability, and provide evidence for the onset of fast reconnection mediated by plasmoids and new opportunities for remote-sensing diagnostics of reconnection mechanisms on the Sun.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Identification of Climatological Representative Days in the Mid-Atlantic for High-Fidelity Offshore Wind Energy Modeling

The goal of reaching 30 GW of offshore wind energy by 2030 becomes more realistic with the continued approval of offshore wind energy areas by the Biden Administration. In the Mid-Atlantic, where wind energy projects are in the most advanced stages of development, there is increased research focus on the eventual interaction of these wind farms. These interactions, in the form of wakes and cluster wakes, or wakes from multiple wind farms, could have detrimental effects on power production and forecastability for downwind wind farms (Pryor et al. 2022, Golbazi et al. 2022, Rosencrans et al. 2023). To help alleviate these issues, numerical simulations in the form of numerical weather prediction (NWP) and large eddy simulations (LES) can provide insight into when cluster wake situations may occur, but running such simulations can be expensive and difficult to run for multiple years. In this study, we leverage and build upon existing techniques in the literature (Fischereit et al. 2022) to identify climatologically representative days for wind energy areas in the Mid-Atlantic where conditions would promote cluster wake situations. We select meteorological variables (wind speed, wind direction, atmospheric stability, boundary-layer height, TKE) critical to understanding wind energy production and wake propagation. We then consider two different NWP datasets of varying spatial and temporal resolution: ERA5 provides data at hourly intervals from 1940 to present at 0.25 deg (31 km) spatial resolution (Hersbach et al. 2020), and the NOW-23 dataset provides data at 5-minute resolution for 21 years at 2-km spatial resolution (Bodini et al. 2020). Our first step is to compare these two datasets for an overlapping 21-year time period. Initial results show that the required number of days to represent the long-term climate increases with each additional variable considered. In their study of the German Bight, Fischereit et al. (2022) found that they could represent the long-term wind and wave climate in a "near-perfect" way with -180 days, by reaching a Perkins Skill Score (PSS) of 0.9; our investigation of the mid-Atlantic wind resource region with ERA5 and NOW-23 data suggests that we will need -100 days to reach a PSS of 0.9. As we expand our parameter space to include multiple variables, the number of required days will likely grow. These results will ultimately be used to select case studies to best represent cluster wake conditions that apply to this region for the lifetime of likely wind farms in this mid-Atlantic region.

clusterwakes↗
DOE OSTI2023

Probability of Initiation in Neutron Transport

We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed-point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.

42 ENGINEERING↗
DOE OSTI2021

Accretion of Gas Giants Constrained by the Tidal Barrier

After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues to diffuse onto horseshoe streamlines under the effect of viscous dissipation, and to meander in and out of the planets' Hill sphere. Within the Hill sphere, the horseshoe streamlines intercept gas flow in circumplanetary disks. The host star's tidal perturbation induces a barrier across the converging streamlines' interface. Viscous transfer of angular momentum across this tidal barrier determines the rate of mass diffusion from the horseshoe streamlines onto the circumplanetary disks, and eventually the accretion rate onto the protoplanets. Here, we carry out a series of numerical simulations to test the influence of this tidal barrier on superthermal planets. In weakly viscous disks, the protoplanets' accretion rate steeply decreases with their masses above the thermal limit. As their growth timescale exceeds the gas depletion timescale, their masses reach asymptotic values comparable to that of Jupiter. In relatively thick and strongly viscous disks, protoplanets' asymptotic masses exceed several times that of Jupiter. Two-dimensional numerical simulations show that such massive protoplanets strongly excite the eccentricity of nearby horseshoe streamlines, destabilize orderly flow, substantially enhance the diffusion rate across the tidal barrier, and elevate their growth rate until their natal disk is severely depleted. In contrast, eccentric streamlines remain stable in three-dimensional simulations. Based on the upper falloff in the observed mass distribution of known exoplanets, we suggest that their natal disks had relatively low viscosity (α ~ 10 –3 ) and modest thickness (H/R ~ 0.03–0.05).

79 ASTRONOMY AND ASTROPHYSICS↗