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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Modeling magnetic fields with helical solutions to Laplace’s equation

The series solution to Laplace's equation in a helical coordinate system is derived and refined using symmetry and chirality arguments. These functions and their more commonplace counterparts are used to model solenoidal magnetic fields via linear, multidimensional curve-fitting. A judicious choice of functional forms, a small number of free parameters and sparse input data can lead to highly accurate, fine-grained modeling of solenoidal magnetic fields, including helical features arising from the winding of the solenoid, with overall field accuracy at better than one part per million.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Validating corrosion models: A comparison of governing equations

Experimental validation of Finite Element Method (FEM) models varying electrochemical governing equations, inclusion of chemical reactions, and time on the resultant damage profile for two galvanic couples is explored. Two anode materials (Magnesium AZ31 and Carbon Steel) in contact with a cathode (Stainless Steel 304 L) were modeled in/exposed to NaCl (1 and 0.1 M respectively for the anode materials) for up to one week. The physics approach, inclusion of chemical reactions, and the boundary conditions required to accurately represent the damage profile in FEM models depended on the galvanic couple materials and, ultimately, the corrosion rate. For high rates of corrosion (i.e., magnesium anode), the Nernst-Planck equation with Electroneutrality was sufficient to describe the damage, while, for low rates of corrosion (i.e., carbon steel anode), the Laplace equation was sufficient. In all cases, the most complete governing equation (Nernst-Planck-Poisson Equation) was not necessary to accurately describe the damage. Precipitation reactions in solution also played a critical role in the predicted damage profile, especially for high corrosion rate systems. Finally, for short time periods (< 6 h), the choice of governing equations does not significantly influence damage profile results. Overall, the choice of physics to reduce error in simulations relies on the boundary conditions, geometry, conductivity of the solution, electrochemical potential differences, and time of exposure. The above results are discussed with regard to accuracy and computational savings.

Carbon steel↗
DOE OSTI2026

Validating corrosion models: Influence of physical properties

In chloride containing environments, two metals in physical contact can undergo galvanic corrosion limiting the lifetime of components. Being able to accurately predict galvanic corrosion damage distributions over time has not been widely presented in literature. Therefore, Finite Element Method (FEM) corrosion models were experimentally validated for two galvanic couples as a function of governing equations, environment, anode material, anode:cathode ratio, and time. Carbon steel/stainless steel (CS/SS) and zinc/stainless steel (Zn/SS) galvanic couples were exposed to NaCl solutions at room temperatures for up to 14 days. For the galvanic couples and environments, the Laplace equation with variable conductivity and reactions was sufficient to model the experimental corrosion damage. Increasing the chloride concentration for the CS/SS galvanic couple, regardless of the anode:cathode ratio, decreased the observed and modeled corrosion damage. Decreasing the anode:cathode ratio (i.e., increasing the cathode length), increased the experimentally observed and modeled corrosion damage. For small anode:cathode ratios, the governing equations deviate over long time periods with the Nernst-Plank equation being conservative. For the Zn/SS galvanic couple, the cathode length controls the dominant cathodic reduction reaction. For small cathode lengths, the hydrogen evolution reaction is dominant. For larger cathode lengths, the oxygen reduction reaction is dominant. The results are discussed with regard to the influence of solution chemistry, ohmic drop, and governing reactions. Overall, validated FEM models were presented, and the resultant models, physics, and mechanisms can be applied to other corrosion scenarios with confidence.

Carbon steel↗
DOE OSTI2021

An extended numerical manifold method for unsaturated soil-water interaction analysis at micro-scale

To investigate unsaturated soil-water interaction at micro-scale, this work extends the numerical manifold method (NMM) by incorporating a soil-water coupling model considering specific capillary water distribution and capillary force calculation. The soil skeleton is constructed by a soil skeleton generation algorithm with random polygons. To more realistically capture the interaction between soil grains and capillary water, a capillary mechanics-based geometric algorithm is proposed to iteratively calculate the capillary water distribution. The capillary forces corresponding to the capillary water distribution are calculated based on the Young-Laplace equation. The proposed capillary water solving framework is first verified by reproducing the soil-water characteristic curve and the capillary water distribution of an ideal contact-disk model against analytical solutions. To further validate the ability of the capillary water solving framework to predict hydraulic behavior of the real soil, a laboratory test on the Toyoura sand is reproduced numerically. Then an ideal direct shear test is performed to further validate the two-way soil-water coupling procedure, in which a comparison between the numerical and analytical results regarding the shear strength and matric suction is presented. Finally, microscopic hydraulic and compression tests are conducted on two soil specimens with the same porosity and mean grain diameter but different uniformity coefficients. The results elucidate that the extended method is a potential tool to explore unsaturated soil behaviors at micro-scale.

58 GEOSCIENCES↗
DOE OSTI2020

A class of solutions of the two-dimensional Toda lattice equation

In this study, a method is proposed to systematically generate solutions of the two-dimensional Toda lattice equation in terms of previously known solutions &straightphi;(x,y) of the two-dimensional Laplace's equation. The solitonic solution of Nakamura's [J. Phys. Soc. Jpn. 52 (1983) 380] is shown to correspond to one particular choice of &straightphi;(x,y).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Beam impedance and heating analysis of the diagnostic stripline

In this work the heat transfer analysis has been performed for the stripline kicker, design of which is used at many accelerator facilities as a part of the transverse bunch-by-bunch feed-back system, including NSLS-II. The experimental data of the electrode temperature have been collected from a special diagnostic stripline designed with six infrared view ports. The temperature analysis is based on the power loss calculations and the loss factor computed by the 3-D electromagnetic simulation code GdfidL. To estimate the power loss, we analyze the real part of the longitudinal impedance and the loss factor for two different regimes. We use the ANSYS finite element code to correlate the temperature with the power loss. Lambertson and Shafer formalisms of the longitudinal and transverse beam impedances are discussed for the simplified stripline geometries. The required characteristic impedances and the geometric factors are determined analytically for the simplified geometries and compared with the results for the designed stripline geometry using the 2-D POISSON code by solving the Laplace’s equation in two dimensions. Lambertson’s equations are compared with numerical results. We introduce the frequency range, within which we can apply the analytical approach.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Graph interpolating activation improves both natural and robust accuracies in data-efficient deep learning

Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning (DL) research. In this paper, we replace the output activation function of DNNs, typically the data-agnostic softmax function, with a graph Laplacian-based high-dimensional interpolating function which, in the continuum limit, converges to the solution of a Laplace–Beltrami equation on a high-dimensional manifold. Furthermore, we propose end-to-end training and testing algorithms for this new architecture. The proposed DNN with graph interpolating activation integrates the advantages of both deep learning and manifold learning. Compared to the conventional DNNs with the softmax function as output activation, the new framework demonstrates the following major advantages: First, it is better applicable to data-efficient learning in which we train high capacity DNNs without using a large number of training data. Second, it remarkably improves both natural accuracy on the clean images and robust accuracy on the adversarial images crafted by both white-box and black-box adversarial attacks. Third, it is a natural choice for semi-supervised learning. This paper is a significant extension of our earlier work published in NeurIPS, 2018. For reproducibility, the code is available at https://github.com/BaoWangMath/DNN-DataDependentActivation .

Mathematics↗
DOE OSTI2022

Design optimization of gap distance for the capillary limitation of a heat pipe with annular-type wick structure

In this study, an experimental investigation was conducted on the rising height and contact angle of fluid in an annular wick-type heat pipe. The annular wick-type heat pipe was characterized by a small gap between the wick structure and tube wall, which compensated for the pressure drop along the porous media and created additional capillary force. To describe and model the advantage of this gap, the rising of a wetting liquid in the gap between a vertical solid plate and a mesh (with a small angle between them) was experimentally measured and analyzed. An additional experiment was performed to investigate the effect of curvature on the capillary rise using tubes and meshes of varying radii. Resultantly, we confirmed that the linear combination of the contact angles of the solid plate and mesh could be applied to calculate the rising height from the Laplace–Young equation. Furthermore, the effect of curvature on the rising height of the liquid was negligible. These results were extended to the investigation of finding the optimal gap distance for the annular wick-type heat pipe by referring to previous studies. We observed that a gap distance of 1.27 mm provided the largest permeability (K) over the effective pore radius (r eff ) value for a heat pipe with ethanol, which in turn resulted in the highest capillary limitation. For a sodium heat pipe, a gap distance of 0.84 mm resulted in the highest capillary limitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Measured Potential Profile in a Quantum Anomalous Hall System Suggests Bulk-Dominated Current Flow

Ideally, quantum anomalous Hall systems should display zero longitudinal resistance. Yet in experimental quantum anomalous Hall systems elevated temperature can make the longitudinal resistance finite, indicating dissipative flow of electrons. Here, we show that the measured potentials at multiple locations within a device at elevated temperature are well-described by solution of Laplace's equation, assuming spatially-uniform conductivity, suggesting non-equilibrium current flows through the two-dimensional bulk. Extrapolation suggests that at even lower temperatures current may still flow primarily through the bulk rather than, as had been assumed, through edge modes. In conclusion, an argument for bulk current flow previously applied to quantum Hall systems supports this picture.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Feynman diagrams for matter wave interferometry

We introduce a new theoretical framework based on Feynman diagrams to compute phase shifts in matter wave interferometry. The method allows for analytic computation of higher order quantum corrections, beyond the traditional semi-classical approximation. These additional terms depend on the finite size of the initial matter wavefunction and/or have higher order dependence on ℏ. We apply the method to compute the response of matter wave interferometers to power law potentials and potentials with an arbitrary spatial dependence. The analytic expressions are validated by comparing to numerical simulations, and estimates are provided for the scale of the quantum corrections to the phase shift response to the gravitational field of the earth, anharmonic trapping potentials, and gravitational fields from local proof masses. We also find that for certain experimentally feasible parameters, these corrections are large enough to be measured and could lead to systematic errors if they are not mitigated. We find that to first order in a spatially dependent potential, quantum corrections vanish when the initial matter wavepacket has spherical symmetry and the potential satisfies Laplace's equation. We anticipate these quantum corrections will be especially important for trapped matter wave interferometers and for free-space matter wave interferometers in the presence of proof masses. These interferometers are becoming increasingly sensitive tools for mobile inertial sensing, gravity surveying, tests of gravity and its interplay with quantum mechanics, and searches for dark energy.

Glick, Jonah [Northwestern U.; Fermilab] (ORCID:00↗
DOE OSTI2026

Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Kampa, Cole [Caltech] (ORCID:0000000192972920)↗
DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Renormalization and scale evolution of the soft-quark soft function

Soft functions defined in terms of matrix elements of soft fields dressed by Wilson lines are central components of factorization theorems for cross sections and decay rates in collider and heavy-quark physics. While in many cases the relevant soft functions are defined in terms of gluon operators, at subleading order in power counting soft functions containing quark fields appear. We present a detailed discussion of the properties of the soft-quark soft function consisting of a quark propagator dressed by two finite-length Wilson lines connecting at one point. This function enters in the factorization theorem for the Higgs-boson decay amplitude of the h → γγ process mediated by light-quark loops. We perform the renormalization of this soft function at one-loop order, present a conjecture for its two-loop anomalous dimension and discuss solutions to its renormalization-group evolution equation in momentum space, in Laplace space and in the “diagonal space”, where the evolution is strictly local in the momentum variable.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Evaluating dynamic thermal performance of building envelope components using small-scale calibrated hot box tests

The hot box test method has been applied to evaluate both the steady-state (U-value) and dynamic thermal properties of building envelopes. However, the high construction cost of full-scale hot box apparatus and the testing time required (usually several days) may prevent its wider adoption. To overcome the limitations of full-scale hot box tests, here we propose a novel method to evaluate the dynamic thermal performance of building envelope components using a small-scale calibrated hot box and scaled-down specimen. In this paper, the scaling relationships of thermal properties evaluated using a full-size specimen and a scaled-down specimen are established based on the Laplace transform of the heat transfer equations. In addition, dynamic thermal properties obtained from scaled-down experimental tests are compared to the values calculated by the EN ISO13768 (ISO) method. A small-scale hot box with a 355 mm × 355 mm metering area was constructed and calibrated to validate the correlations. Three scaled-down concrete sandwich wall panels were then tested and the scaling relationship was cross-validated using the experimental results, finite difference (FD) simulations, and the ISO method. The results indicate that the dynamic thermal properties obtained from a scaled-down hot box test can be correlated to its full-size counterpart when certain conditions are met. The scaled-down hot box test is demonstrated to be an effective yet economical alternative to a full-scale test with significantly reduced experimentation cost and turn-around time.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Pressure falloff testing to characterize CO 2 plume and dry-out zone during CO 2 injection in saline aquifers

The fluid mobilities and the lateral extent of the CO 2 plume and the dry-out zone are among important unknowns required to effectively manage CO 2 storage in saline aquifers projects. These unknowns can be derived from pressure falloff testing which has been widely used to characterize the subsurface. This paper provides a three-region analytical solution for falloff pressure during the infinite-acting period of CO 2 injection in saline aquifers. The solution is derived using Laplace transformation technique of the governing diffusivity equations and the accompanying initial and boundary conditions. The exact solution is validated against numerical results obtained from a black-oil reservoir simulator for two cases. The solution is approximated into simple forms in real-time domain considering different time periods. Then, a graphical semi-log analysis technique based on the approximate solutions is provided as an interpretation tool of falloff tests where the fluid mobilities and the extents of dry-out zone and CO 2 plume can be inferred. The interpretation technique is applied to synthetic falloff test data to investigate its potential and reliability.

02 PETROLEUM↗
DOE OSTI2021

A Spatiotemporal Prediction Model for Regional Scheduling of Shared Bicycles Based on the INLA Method

Dock-less bicycle-sharing programs have been widely accepted as an efficient mode to benefit health and reduce congestions. And modeling and prediction has always been a core proposition in the field of transportation. Most of the existing demand prediction models for shared bikes take regions as research objects; therefore, a POI-based method can be a beneficial complement to existing research, including zone-level, OD-level, and station-level techniques. Point of interest (POI) is the location description of spatial entities, which can reflect the cycling route characteristics for both commuting and noncommuting trips to a certain extent, and is also the main generating point and attraction point of shared-bike travel flow. In this study, we make an effort to model a POI-level cycling demand with a Bayesian hierarchical method. The proposed model combines the integrated nested Laplace approximation (INLA) and random partial differential equation (SPDE) to cope with the huge computation in the modeling process. In particular, we have adopted the dock-less bicycle-sharing rental records of Mobike as a case study to validate our method; the study area was one of the fastest growing urban districts in Shanghai in August 2016. The operation results show that the method can help better understand, measure, and characterize spatiotemporal patterns of bike-share ridership at the POI level and quantify the impact of the spatiotemporal effect on bicycle-sharing use.

Yu, Zhuoran↗
DOE OSTI2022

A 6th Order Mehrstellen Finite Volume Discretization of Poisson's Equation in Three Dimensions

We discuss the derivation of a new, sixth-order finite volume scheme for Poisson’s equation on 3D Cartesian equispaced grids. The scheme is based on a discretization of the Laplace operator with a compact (Mehrstellen) 27-point stencil. To achieve sixth order convergence the right hand side of the equation is replaced with a discrete operator that involves the discrete Laplace and Biharmonic operators and the sum of discrete fourth-order cross derivatives applied to the charge function. Numerical tests demonstrate the superiority of the proposed method compared to the well known schemes associated with the 7-point and 19-point discretizations of the Laplacian.

97 MATHEMATICS AND COMPUTING↗