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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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An analytic model approach is applied to several simple atmospheric inversion problems. This method gives a sharp determination of aerosol size distribution parameters. It is shown that this analytic approach, together with ground level point sampling data measurements, can be used to infer information on the tropospheric ozone profile.
Next-generation neutrino oscillation experiments such as the Deep Underground Neutrino Experiment require percent-level knowledge of neutrino-nucleon interaction cross sections. The nucleon axial form factor 𝐹 𝐴 (𝑄 2 ), parametrized by the axial mass 𝑀 𝐴 , is the dominant source of uncertainty in the quasielastic channel, and the parity-violating structure function 𝑥𝐹 3 is poorly constrained on free nucleons. We propose using charged-current (CC) electron-proton scattering at the Electron-Ion Collider (EIC) to address both problems simultaneously. The measurement exploits three key features of the EIC: (1) helicity-selective electron bunches provide in situ electromagnetic background rejection; (2) a longitudinally polarized proton target enables extraction of 𝐹 𝐴 (𝑄 2 ) through the target-spin asymmetry 𝐴 𝑈𝐿 ; and (3) the 𝑦-distribution leverage in CC deep inelastic scattering (DIS) separates 𝐹 2 and 𝑥𝐹 3 on a free proton, without nuclear corrections. Using a Fisher information analysis at $\sqrt{𝑠}$ =141 GeV with 500 fb −1 of integrated luminosity, we project the Cramér-Rao statistical floor of 𝛿𝑀 𝐴 ≈0.03 GeV (3%). Incorporating first-order realistic detector effects, such as zero-degree calorimeter acceptance, 𝑄 2 smearing (5%), and background noise from helicity subtraction, the projected sensitivity is severely background-limited due to the small signal-to-background ratio (𝑆/𝐵 ≈ 3 ×10 −4 ) in the elastic channel. Achieving competitive sensitivity (𝛿𝑀 𝐴 ≈ 0.14 GeV) would require ∼10 −7 background suppression, 3 orders of magnitude beyond current projections. The CC DIS 𝑦 distribution provides subpercent extraction of 𝑥𝐹$^{𝑊^{−}}_{3}$ over 0.05 < 𝑥 < 0.5, representing the most robust electroweak measurement in the near term.
To represent the final results in terms of matrices, one expands all appropriate physical quantities in terms of partial wave basis states. This includes expansions for the incident and scattered fields and the surface quantities. The method then utilizes the Huygen-Poincare integral representation for both the exterior and interior solutions, leading to the required matrix equations. One thus deals with matrix equations, the complexity of which depends on the nature of the problem. It is shown that in general a transition matrix T can be obtained relating the incident field A with the scattered field f having the form T = PQ(-1), where f = TA. The structure of Q can be quite complicated and can itself be composed of other matrix inversions such as arise from layered objects. Recent improvements in this method appropriate for a variety of physical problems are focused on, and on their implementation. Results are outlined from scattering simulations for very elongated submerged objects and resonance scattering from elastic solids and shells. The final improvement concerns eigenfunction expansions of surface terms, arising from solution of the interior problem, obtained via a preconditioning technique. This effectively reduces the problem to that of obtaining eigenvalues of a Hermitian operator. This formalism is reviewed for scattering from targets that are rigid, sound-soft, acoustic, elastic solids, elastic shells, and elastic layered objects. Two sets of the more interesting results are presented. The first concerns scattering from elongated objects, and the second to thin elastic spheroids.
Calculation of the stopping power of a plasma for fast electrons and positrons. First the classical limit is considered where beta = v/c is much less than alpha is the fine structure constant. Then the nonrelativistic Born-approximation formulas are derived; this domain corresponds to alpha much less than beta much less than 1. Finally, the general case of relativistic electrons and positrons is treated; in the relativistic case the scattering cross sections of Moller (electron-electron) and Bhabha (positron-electron) are used in the calculation. In all three energy domains the problem is broken up into cases of small and large momentum transfers. For large q, scattering off individual plasma electrons is considered, while in the limit of very small q for the quantum-mechanical domain, excitation of quantized plasma oscillations contributes to dE/dx; in the classical limit for small q the polarizability of the plasma provides the effective cutoff. The formulas for the stopping power differ slightly from those for a heavy ion going through a plasma because there are exchange effects and the fast electrons and positrons can lose a large fraction of their energy in one scattering off a plasma electron.
The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown.
The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi
In aerospace design, where minimizing weight is always a priority, achieving the full capacity from fasteners is essential. To do so, the initial bolt preload must be maximized. The benefits of high preload are well documented and include improved fatigue resistance, a stiffer joint, and resistance to loosening. But many factors like elastic interactions and embedment tend to lower the initial preload placed on the bolt. These factors provide additional motivation to maximize the initial preload. But, to maximize bolt preload, you must determine what torque to apply. Determining this torque is greatly complicated by the large preload scatter generally seen with torque control. This paper presents a detailed methodology for generating limit torques for threaded fasteners. This methodology accounts for the large scatter in preload found with torque control, and therefore, addresses the statistical nature of the problem. It also addresses prevailing torque, a feature common in aerospace fasteners. Although prevailing torque provides a desired locking feature, it can also increase preload scatter. In addition, it can limit the amount of preload that can be generated due to the torsion it creates in the bolt. This paper discusses the complications of prevailing torque and how best to handle it. A wide range of torque-tension bolt testing was conducted in support of this research. The results from this research will benefit the design engineer as well as analyst involved in the design of bolted joints, leading to better, more optimized structural designs.
Here, this work introduces a new benchmark problem for calculating shutdown dose rates (SDDRs) aimed at fusion reactor applications. The model is designed to represent a simplified version of a typical ITER port plug. The responses of interest include neutron flux, gamma flux, and gamma SDDR at 12 different locations scattered throughout the port. This article outlines the geometry specifications of the problem, provides material definitions for the components, specifies the required responses to be calculated, and presents the source definition information. The need for this benchmark arises from the limited availability of publicly accessible references, with only one benchmark representing the typical dimensions and materials found in fusion systems. This existing benchmark has been cited extensively, reflecting the demand within the scientific community to test both established and novel workflows for SDDR calculations. However, since its presentation at a conference in 2011, the results have become increasingly well known. Moreover, the absence of formal publication and peer review has led to the details of this benchmark being extracted from secondary sources, such as subsequent studies that reference it. As a result, analysts are left with significant flexibility in interpreting the key parameters, which can be adjusted to account for unknown systematic errors, ultimately reproducing the already well-known responses. This new benchmark serves as an updated version of that earlier work, with the aim of providing a more reliable description of the materials and their impurities, which is crucial for assessing activation and subsequent gamma emission. Additionally, it seeks to provide a geometry that more closely represents an ITER port plug. The improvements in the problem definition will lead to a more reproducible benchmark problem, while also presenting the radiation transport community with a completely new challenge. The results will be published in a future article to allow analysts adequate time to analyze this problem independently.
In this work, we expand the weighted delta-tracking routine to include a treatment for scattering. The weighted delta-tracking routine adds survival biasing to normal delta-tracking, improving problem figure of merit. In the original formulation of this method, only absorption events were considered. We have expanded the method to include scattering and investigated the method’s effectiveness with two test cases: a pressurized water reactor pin cell and a fast reactor pin cell. We compare the figure of merit for calculating infinite flux and total cross-section while incrementally changing the amount of weighted delta-tracking used. Thus, we find that this new weighted delta-tracking (WDT) routine has strong potential to improve the efficiency of fast reactor calculations, and may be useful for light water reactor calculations.
In this work, we consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. Here, we find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties.
The key to understanding the cycling mechanism of lithium-ion battery electrodes is to develop methods to monitor the dynamic cell chemistry, but the complexity of the problem has continued to pose an obstacle. Here we describe the use of operando small-angle neutron scattering (SANS) to show directly how the use of concentrated LiTFSI electrolyte in Li/ordered mesoporous carbon (OMC) half-cells influences the mechanism of solid electrolyte interphase (SEI) formation, lithium intercalation, and carbon framework expansion. We find that a complex interplay between the viscosity, lithium solvation shell and electrode microstructure in the concentrated 4 M electrolyte changes the dynamics of SEI formation and pore filling at a given applied potential. Both the filling of micropores and co-intercalation are found to drive the expansion of the carbon framework. Lithium-rich reduction products form at much higher potentials in the micropores of the 4 M electrolyte system, while on mesopore surfaces the lithium-rich salts form quickly before giving way to carbonaceous products. As a result, this study reveals operando SANS as a unique method for providing microstructure dependent information on the dynamics of electrochemical processes.
The Monte Carlo method is used for two types of problems. First, there are interpretation problems of optical observations from meteorological satellites in the short wave part of the spectrum. The sphericity of the atmosphere, the propagation function, and light polarization are considered. Second, problems dealt with the theory of spreading narrow light beams. Direct simulation of light scattering and the mathematical form of medium radiation model representation are discussed, and general integral transfer equations are calculated. The dependent tests method, derivative estimates, and solution to the inverse problem are also considered.
The small fatigue crack problem is critically reviewed from the perspective of airframe applications. Different types of small cracks-microstructural, mechanical, and chemical-are carefully defined and relevant mechanisms identified. Appropriate analysis techniques, including both rigorous scientific and practical engineering treatments, are briefly described. Important materials data issues are addressed, including increased scatter in small crack data and recommended small crack test methods. Key problems requiring further study are highlighted.
Here, we demonstrate, on a scramjet combustion problem, a constrained probabilistic learning approach that augments physics-based datasets with realizations that adhere to underlying constraints and scatter. The constraints are captured and delineated through diffusion maps, while the scatter is captured and sampled through a projected stochastic differential equation. The objective function and constraints of the optimization problem are then efficiently framed as non-parametric conditional expectations. Different spatial resolutions of a large-eddy simulation filter are used to explore the robustness of the model to the training dataset and to gain insight into the significance of spatial resolution on optimal design.
In an attempt to gain some insight into the problem of how close particles have to be on the average before phase effects become important, the cross section and phase matrices for two identical particles as a function of the distance between their centers for both broadside and end-on illumination have been calculated. The point dipole approximation is employed to build two pseudospherical particles each consisting of 32 dipoles with an effective size parameter of 0.9283 and refractive index of 1.54-0.0i. In regard to cross sections, it is found that in certain cases several percent deviation from the converged value, which is twice the single particle cross section, could be found up to distances of separation of 25 single particle diameters. The maxima and minima in the cross section curves can be explained in terms of simple interference effects. Also the element P11 of the phase matrix showed a great deal of structure, and the position of maxima and minima could be explained by phase shift analysis.
Physics-informed neural networks (PINNs), introduced, are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly encoded into the NN using automatic differentiation, while the sum of the mean-squared PDE residuals and the mean-squared error in initial-boundary conditions is minimized with respect to the NN parameters. Here we extend PINNs to fractional PINNs (fPINNs) to solve space-time fractional advection-diffusion equations (fractional ADEs), and we study systematically their convergence, hence explaining both fPINNs and PINNs for the first time. Specifically, we demonstrate their accuracy and effectiveness in solving multidimensional forward and inverse problems with forcing terms whose values are only known at randomly scattered spatio-temporal coordinates (black-box (BB) forcing terms). A novel element of the fPINNs is the hybrid approach that we introduce for constructing the residual in the loss function using both automatic differentiation for the integer-order operators and numerical discretization for the fractional operators. This approach bypasses the difficulties stemming from the fact that automatic differentiation is not applicable to fractional operators because the standard chain rule in integer calculus is not valid in fractional calculus. To discretize the fractional operators, we employ the Grünwald--Letnikov (GL) formula in one-dimensional fractional ADEs and the vector GL formula in conjunction with the directional fractional Laplacian in two- and three-dimensional fractional ADEs. We first consider the one-dimensional fractional Poisson equation and compare the convergence of the fPINNs against the finite difference method (FDM). We present the solution convergence using both the mean L 2 error as well as the standard deviation due to sensitivity to NN parameter initializations. Using different GL formulas we observe first-, second-, and third-order convergence rates for small size training sets but the error saturates for larger training sets. We explain these results by analyzing the four sources of numerical errors due to discretization, sampling, NN approximation, and optimization. The total error decays monotonically (below 10 –5 for a third-order GL formula) but it saturates beyond that point due to the optimization error. We also analyze the relative balance between discretization and sampling errors and observe that the sampling size and the number of discretization points (auxiliary points) should be comparable to achieve the highest accuracy. As we increase the depth of the NN up to certain value, the mean error decreases and the standard deviation increases, whereas the width has essentially no effect unless its value is either too small or too large. We next consider time-dependent fractional ADEs and compare white-box (WB) and BB forcing. We observe that for the WB forcing, our results are similar to the aforementioned cases; however, for the BB forcing fPINNs outperform FDM. Subsequently, we consider multidimensional time-, space-, and space-time-fractional ADEs using the directional fractional Laplacian and we observe relative errors of 10 –3 ~ 10 –4 . Lastly, we solve several inverse problems in one, two, and three dimensions to identify the fractional orders, diffusion coefficients, and transport velocities and obtain accurate results given proper initializations even in the presence of significant noise.
Validated and accurate edge profiles (temperature, density, etc.) are vitally important to the Mega Ampere Spherical Tokamak Upgrade (MAST-U) divertor and confinement effort. Density profile reflectometry has the potential to significantly add to the measurement capabilities currently available on MAST-U (e.g., Thomson scattering and Langmuir probes). This work presents the diagnostic requirements, problems, and solutions facing profile reflectometry in spherical tokamaks and MAST-U in particular. Requirements include density measurements near zero electron density in the scrape off layer region, coverage for a broad range of MAST-U plasma parameters, high time (≤10 microseconds) and spatial resolutions (≤1 cm), reliability, and identification of the plasma start frequency.
Cauchy problem for relativistic Boltzmann equation, discussing initial distribution function and scattering cross section