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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quasi-linear theory of forced magnetic reconnection for the transition from the linear to the Rutherford regime

Abstract Using the in-viscid two-field reduced magneto-hydrodynamic (MHD) model, a new analytical theory is developed to unify the Hahm–Kulsrud–Taylor (HKT) linear solution and the Rutherford quasi-linear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in the Taylor problem. An integral form of an analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford quasi-linear solution. In particular, the quasi-linear effect can be described by a single coefficient K s ∝ S 8 / 5 ψ c 2 , where S = τ R τ A and ψ c are the Lundquist number and amplitude of external magnetic perturbation, respectively. The HKT linear solution for the response can be recovered when the index K s → 0. On the other hand, the quasi-linear effect plays a key role in the island growth when K s ~ 1. Our new analytical solution has also been compared with reduced MHD simulations with agreement.

Physics↗
DOE OSTI2021

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I: Flux and Eigenvalue Solutions

Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Furthermore, original analytic expressions are established to quantify the discrepancy between the ψ k (E) and ψ α (E) flux amplitudes, respective solutions of the multiplication factor k, or the exponential time-evolution frequency α eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition α=0. Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239 Pu, the 6.67-eV resonance of 238 U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions

In this paper, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

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

Open giant magnons suspended between dual giant gravitons in $$ \mathcal{N} $$ = 4 SYM

We study classical solutions to the Nambu-Goto string onAdS 2 × S 1 and AdS 3 × S 1 corresponding to strings stretched between wrapped branes extending in AdS. The solutions are obtained by analytic continuation of giant magnon solutions, cut at the position of the branes. These solutions carry one or two SO(2 , 4) charges and a single SO(6) charge. We compute their energies and show their relation to $$ \frac{1}{2} $$ 1 2 -BPS geometries. Their relevance to the SL(2) sector of $$ \mathcal{N} $$ N = 4 SYM is also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

1-D coupled surface flow and transport equations revisited via the physics-informed neural network approach

The de Saint-Venant equation (SVE) and advection–diffusion equation (ADE) are commonly employed to solve solute transport problems in surface water. In this work, we propose a mesh-free method based on the physics-informed neural network (PINN) to solve the one dimensional (1-D) SVE, ADE, and the coupled SVE and ADE (SVE-ADE) under various initial and boundary conditions. The PINN model extends the architecture of deep neural networks (DNNs) with implementation of loss function, which are additionally subject to constraints imposed by the physical laws of SVE and ADE, along with their initial and boundary conditions. In such a manner, PINNs can be quickly steered to the true solution while obeying the physical laws. The results of PINN model are compared with the analytical and/or numerical solutions under various conditions to investigate its accuracy and efficiency in solving the SVE, ADE, and SVE-ADE. Our results indicate PINN can accurately simulate the shock wave morphology and avoid numerical dissipation in unsteady flow condition. The PINN method outweighed traditional numerical methods in several aspects, including its ability to function with small amounts of data, no grid discretization, and random selection of sampling points, etc. Additionally, the PINN method is also suitable for solving inverse problems with sparse and noisy data. With 1% noise and 2000 initial and boundary condition points (N u ), the errors of the estimated flow rate (v) and diffusion coefficient (D) are 0.003% and 0.105%, respectively, which indicate the accuracy and robustness of the proposed method. Finally, our results indicate the capability and robustness of the proposed PINN methodology for solving multi-physics problems, irrespective of the presence of sparse and noisy data in the training dataset.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Fabrication and Preliminary Demonstration of Microwave Resonant Cavity Transducer Performance

We are investigating a microwave cavity-based transducer for in-core high-temperature fluid flow sensing in molten salt cooled reactors (MSCR) and sodium fast reactors (SFR). This sensor is a hollow metallic cylindrical cavity, which can be fabricated from stainless steel, and as such is expected to be resilient to radiation, high temperature and corrosive environment of MSCR and SFR. The principle of sensing consists of making one wall of the cylindrical cavity flexible enough so that dynamic pressure, which is proportional to fluid velocity, will cause membrane deflection. Membrane deflection causes cavity volume change, which leads to a shift in the resonant frequency. We have developed an initial design for proof-of-principle testing of the flow sensor performance in microwave K-band. A cylindrical resonator prototype was fabricated from brass for initial tests in water. The cavity size is matched to the flange of a standard WR-42 waveguide. Microwave field is coupled into the resonant cavity through a subwavelength-size aperture. A test article was developed, consisting of a piping Tee with bulkhead WR-42 microwave waveguide installed in leak-proof design. In the test article, the cylindrical cavity is positioned in the center of the pipe. A microwave waveguide circulator was installed in the setup to suppress microwave reflections at the cavity entrance. Preliminary spectral characterization of cavity spectral response was performed with microwave VNA. Applying mechanical pressure to cavity membrane showed a measurable shift in the microwave resonant frequency. We also investigate mechanical integrity of the flowmeter’s membrane through computer simulations. By calculating the stress on the plate due to deflection and, comparing the stress to the material ultimate tensile strength and yield strength, it can be estimated if the plate will fail. The stress on the plate was calculated with an analytic closed form solution model, and with COMSOL Structural Mechanics Module which does not involve any approximations. Both the analytic model and COMSOL model showed that maximum stresses on the plate, which are at the radial boundary of the plate, are three orders of magnitude smaller than the yield strength and ultimate tensile strength. This indicates that the sensor is at a low risk of mechanical failure.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Analyzing Mechanical integrity of Microwave resonant Cavity flowmeter

The microwave resonant cavity flow sensor has been proposed to address the difficulties of measuring high-temperature molten salt flow in reactor vessels. The flow sensor consists of a metallic cylindrical cavity coupled to a microwave waveguide. The cylindrical cavity has one of the flat surfaces thin enough to undergo microscopic deflection due to dynamic pressure of the exerted by the flowing fluid. Deflection of the membrane causes a shift in the microwave resonant frequency. Fluid velocity can be estimated from the calibration curve. The objective of this report is to investigate mechanical integrity of the flowmeter’s membrane. The membrane is a thin stainless-steel circular plate with a clamped edge, subjected to uniform load. By calculating the stress on the plate due to deflection and, comparing the stress to the material ultimate tensile strength and yield strength, it can be estimated if the plate will fail. If the maximum stress is greater than the yield strength, the plate will undergo plastic deformation, and the sensor will be disabled. A stress greater than the ultimate tensile strength will cause the plate to fracture. The stress on the plate was calculated with an analytic closed form solution model, and with COMSOL Structural Mechanics Module which does not involve any approximations. Stresses in both the analytic model and COMSOL numerical model were calculated for stainless steel 316 thin circular plates under room temperature conditions, where the fluid is water. The diameter of the circular plate is approximately one inch, and thickness is 10mil. Fluid flow velocity is in the range from 0.5m/s to 1m/s. The results from the two models are similar. Both the analytic model and COMSOL model showed that maximum stresses on the plate, which are at the radial boundary of the plate, are three orders of magnitude smaller than the yield strength and ultimate tensile strength. This indicates that the sensor is at a low risk of mechanical failure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

(U) A Theoretical Study of Asay Foil Trajectories (V.02)

We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.

42 ENGINEERING↗
DOE OSTI2022

Comparison of vapour pressure osmometry, freezing point osmometry and direct membrane osmometry for determining the osmotic pressure of concentrated solutions

Osmometry is the analytical method of measuring osmotic pressure ($π$) and related colligative properties. Accurately measuring $π$ is essential for applications that use osmosis, including drug delivery systems and water filtration methods such as forward osmosis. The three most common forms of directly or indirectly measuring $π$ are vapour pressure osmometry (VPO), freezing point osmometry (FPO), and direct membrane osmometry (DMO). In this report, the performance of VPO, FPO, and DMO are compared for various aqueous solutions, including small molecule and polymer solutes, and potentially more difficult samples such as concentrated, carbonated, or viscous solutions. Furthermore, potential problems with each of the three methods are examined. Good practices can avoid inaccuracies in DMO due to external concentration polarization and solute diffusion through the membrane. Similarly, it is important to be aware of and avoid weaknesses in VPO and FPO in order to obtain reliable results. Even with care, however, the three methods still give different values of $π$ for concentrated aqueous solutions.

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

Total metals & anion concentration data; Slate River floodplain, Crested Butte, CO; May 2020-September 2020

This data package includes processed and undiluted measurements for metal and anion concentrations from pore water (groundwater) samples from the Slate River floodplain of Crested Butte, CO, a focus field site for the SLAC Floodplain Hydro-Biogeochemistry SFA. The data was generated as part of the work targeting the overarching research question for the SLAC SFA: How do ubiquitous subsurface interfaces mediate molecular-scale biogeochemical processes and groundwater quality in floodplains and watersheds? Samples were collected between May and September of 2020. These measurements were all recorded at the Arizona Laboratory for Emerging Contaminants (ALEC) at the University of Arizona located in Tucson, AZ. Groundwater samples were extracted from a network of installed rhizon (Rhizosphere Research Products, part no. 19.60.21F, 0.6 micrometer mesh size) and piezometer wells within the river floodplain. All water samples were shaded from sun exposure during extraction from the subsurface and preserved at 4C until measured at ALEC.Analysis by ICP-MS:Measurements for total metals were made on the Agilent 7700x ICP-MS (for total metals) – Agilent Technologies, Santa Clara, CA.The analytical QA/QC protocol was adapted from US EPA Method 200.8 for analysis by ICP-MS. Calibration standards were prepared from multi-element stock solution (Sigma-Aldrich Multielement standard solution for ICP, St. Louis, MO) using matrix matched to sample solutions (either 2% HCl or HNO3 from AriStar Plus,grade acids from VWR Scientific). Calibration curves include at least 7 points with correlation coefficients > 0.995. The QC protocol includes a continuing calibration blank (CCB), a continuing calibration verification (CCV) solution and at least one quality control sample (QCS) to be analyzed just after calibration and again after every 12 samples and at the completion of the run. The QCS solutions are from an independent source, such as NIST SRM 1643e - Trace Elements in Water, or QCS solutions from High Purity Standards (Charleston, SC). Acceptable QC responses must be between 90 and 110% of the certified value. An internal standard (Rh) is added via on-line addition into the sample line using a mixing tee.Analysis by Ion Chromatography (Anions):The protocol follows Method 4110 in Standard Methods for Examination of Water and Wastewater.The instrument used is the Thermo Scientific Dionex ICS-6000 using AS+AG22 column set for anion analysis with isocratic method using sodium carbonate eluent. Detection is by chemical suppression of eluent conductivity. Quality control solutions and mixed analyte standards purchased from Inorganic Ventures, Christiansburg, VA.All files are in csv format.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Analytical expressions of the surface shape of ‘diaboloid’ mirrors

Modern deterministic polishing processes allow fabrication of x-ray optics with almost any arbitrary aspherical surface shape. Among these optics, the so called "diaboloid"mirror is of special interest. The diaboloid mirror that converts a cylindrical wave to a spherical wave would improve focusing in x-ray beamlines implementing a diffraction element between a parabolic cylinder and a toroidal mirror. The replacement of the toroidal mirror in existing beamlines by the diaboloid mirror would mitigate aberrations. The shape of the diaboloid mirror is usually calculated numerically based on a truncated polynomial solution of the optical path problem. Here, we present an exact analytical solution for the shape of a diaboloid mirror as a function of the conjugate parameters of the mirror placed in a beamline. The derived analytical expressions for the diaboloid mirror in both the canonical and mirror-based coordinate systems are implemented in ray-tracing simulations to verify the beamline performances.

Yashchuk, Valeriy V.↗
DOE OSTI2022

New superstrata from three-dimensional supergravity

We find a two-parameter family of generalized superstrata that emerge as smooth, supersymmetric solutions in three-dimensional gauged supergravity coupled to additional scalar fields. This new family of generalized superstrata are smooth microstate geometries and may be thought of as supersymmetric Coulomb-branch extensions of the original superstrata in which the underlying supertube undergoes an elliptical deformation. These solutions had already been obtained numerically, and as series solutions, to the equations of motion, and some of them were conjectured to be supersymmetric. Here we prove the supersymmetry of an entire two-parameter family and we obtain a highly non-trivial analytic and smooth solution for a one-parameter limit in which the global symmetry of the metric is enhanced to SO(3). We also confirm that the other known families of microstrata are not supersymmetric. We conclude with a cursory analysis of some of the singular brane distributions that can be accessed from three-dimensional gauged supergravity while preserving the same supersymmetries as the superstratum, and therefore of the three-charge black hole.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Fluoride Analysis by Ion Chromatography in Support of Fast Critical Assembly (FCA) Spent Nuclear Fuel Processing

INTRODUCTION The Savannah River Site (SRS) is currently processing Fast Critical Assembly (FCA) fuel received from the Japan Atomic Energy Agency (JAEA) for disposition. Stainless steel-clad plate and rods in stainless steel containers are dissolved using electrolysis with a solution mixture of nitric acid (HNO3), potassium fluoride (KF), and gadolinium (Gd). An ion chromatography (IC) was developed and vetted to monitor fluoride at various sampling points of the process. To finalize the method, FCA test solution was analyzed to qualify the analytical method followed by real FCA process solution analysis using two different analytical columns. This presentation summarizes the development and vetting of the IC method.

White, Thomas L. [Savannah River National Laborato↗
DOE OSTI2023

Evolution of coupled weakly driven waves in a dissipative plasma

The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved and time delays become unimportant. The system is then shown to be governed by two first-order coupled autonomous differential equations of cubic order for the wave amplitudes and two complementary first-order equations for the evolution of their phases. That system of equations can be decoupled and further simplified to a single second-order differential equation of Liénard's type for each amplitude. Numerical solutions for this equation are obtained in the general case, while analytic solutions are obtained for special cases in terms of parameters related to the spacing of the resonances of the two waves in frequency space, e.g., wave lengths and oscillation frequencies. These parameters are further analyzed to find classes of quasi-steady saturation and pulsating scenarios. To classify equilibrium points, local stability analysis is applied, and bifurcation conditions are determined. When the two waves saturate at similar amplitude levels, their combined signal is shown to invariably exhibit amplitude beating and phase jumps of nearly π. In conclusion, the obtained analytical results can be used to benchmark simulations and to interpret eigenmode amplitude measurements in fusion experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The Building Adapter: Automatic Mapping of Commercial Buildings for Scalable Building Analytics

This project creates new solutions for the manual metadata mapping problem: the costly process of creating a match between a building’s sensor data streams and the inputs of a building analytics engine. This goal is achieved by creating and improving techniques for metadata inference: automatically constructing new contextual information for sensing and control points based on the sensor point names and the raw time series values. The objective is to enable vendors to apply building analytics to 90% of buildings with no manual mapping, and to 10% of buildings with a 90% reduction in manual mapping. These targets are set for all types of metadata required by current analytics engines, including type, location, equipment type, and other relationships. The outcome of this project is a suite of solutions to the manual mapping problem collectively called the Building Adapter that allows vendors to apply analytics engines to new buildings at a significantly reduced cost.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2024

Bootstrap Principle for the Spectrum and Scattering of Strings

We show that the Veneziano amplitude of string theory is the unique solution to an analytically solvable bootstrap problem. Uniqueness follows from two assumptions: faster than power-law falloff in high-energy scattering and the existence of some infinite sequence in momentum transfer at which higher-spin exchanges cancel. The string amplitude—including the mass spectrum—is an output of this bootstrap. If the amplitude merely vanishes at high energies, the solution is a three-parameter family containing the Veneziano, Coon, and hypergeometric amplitudes, and more.

Field & string theory models & techniques↗
DOE OSTI2025

Quantum sensing of paramagnetic analytes by nanodiamonds in levitated microdroplets and aqueous solutions

Nanodiamonds (ND) hosting negatively charged nitrogen-vacancy (NV-) color centers have received attention for applications in magnetic field, electric field, chemical, and bio-sensing. The versatility of these probes is their excellent room-temperature optical and spin properties, along with their small size, functionalized surfaces and resistance to bleaching, making them ideal as nanoscopic sensors in picoliter volumes (e.g. single cells, but also microcompartments and aerosols). For quantitative ND-NV- sensing of paramagnetic analytes in such contexts, however, there remains an incomplete understanding of how factors related to the aqueous phase environment control detection efficiency. To address this, optically detected magnetic resonance (ODMR) is measured in bulk macroscale solutions and single levitated microdroplets as a function of Gd+3 concentration (340 nM to 1.5 mM), nanodiamond size, pH, competitor ions, and ligands. The ODMR response to [Gd+3] is found to be nonlinear, and pH, ND and sample volume dependent; indicating the detection of Gd+3 requires efficient adsorption of the analyte to the diamond surface. Langmuir adsorption isotherms embedded in a quantitative photophysical model links the ODMR response to adsorption thermodynamics of Gd+3. The equilibrium constant for Gd+3 adsorption to a carboxylated ND surface is determined to be (1 ± 0.5) x 105 M-1 corresponding to a free energy of adsorption of (-28 ± 1) kJ mol-1. These results provide general insight into how complex aqueous and microscale environments impact nanodiamond based quantum sensing modalities, and portend their application as quantitative chemical sensors in microenvironments.

Brown, Emily K↗
DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗