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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Correspondence of NNGP Kernel and the Matérn Kernel

Kernels representing limiting cases of neural network architectures have recently gained popularity. However, the application and performance of these new kernels compared to existing options, such as the Matérn kernel, is not well studied. We take a practical approach to explore the neural network Gaussian process (NNGP) kernel and its application to data in Gaussian process regression. We first demonstrate the necessity of normalization to produce valid NNGP kernels and explore related numerical challenges. We further demonstrate that the predictions from this model are quite inflexible, and therefore do not vary much over the valid hyperparameter sets. We then demonstrate a surprising result that the predictions given from the NNGP kernel correspond closely to those given by the Matérn kernel under specific circumstances, which suggests a deep similarity between overparameterized deep neural networks and the Matérn kernel. Finally, we demonstrate the performance of the NNGP kernel as compared to the Matérn kernel on three benchmark data cases, and we conclude that for its flexibility and practical performance, the Matérn kernel is preferred to the novel NNGP in practical applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗
DOE OSTI2023

New machine learning techniques for simulation-based inference: InferoStatic nets, kernel score estimation, and kernel likelihood ratio estimation

We propose an intuitive, machine-learning approach to multiparameter inference, dubbed the InferoStatic Networks (ISN) method, to model the score and likelihood ratio estimators in cases when the probability density can be sampled but not computed directly. The ISN uses a backend neural network that models a scalar function called the inferostatic potential \varphi φ . In addition, we introduce new strategies, respectively called Kernel Score Estimation (KSE) and Kernel Likelihood Ratio Estimation (KLRE), to learn the score and the likelihood ratio functions from simulated data. We illustrate the new techniques with some toy examples and compare to existing approaches in the literature. We mention en passant some new loss functions that optimally incorporate latent information from simulations into the training procedure.

Kong, Kyoungchul↗
DOE OSTI2022

New Machine Learning Techniques for Simulation-Based Inference: InferoStatic Nets, Kernel Score Estimation, and Kernel Likelihood Ratio Estimation

We propose an intuitive, machine-learning approach to multiparameter inference, dubbed the InferoStatic Networks (ISN) method, to model the score and likelihood ratio estimators in cases when the probability density can be sampled but not computed directly. The ISN uses a backend neural network that models a scalar function called the inferostatic potential $\varphi$. In addition, we introduce new strategies, respectively called Kernel Score Estimation (KSE) and Kernel Likelihood Ratio Estimation (KLRE), to learn the score and the likelihood ratio functions from simulated data. We illustrate the new techniques with some toy examples and compare to existing approaches in the literature. We mention en passant some new loss functions that optimally incorporate latent information from simulations into the training procedure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Porting the Kitten Lightweight Kernel Operating System to RISC-V

Hardware design in high-performance computing (HPC) is often highly experimental. Exploring new designs is difficult and time-consuming, requiring lengthy vendor cooperation. RISC-V is an open-source processor ISA that improves the accessibility of chip design, including the ability to do hardware/software co-design using open-source hardware and tools. Co-design allows design decisions to easily flow across the hardware/software boundary and influence future design ideas. However, new hardware designs require corresponding software to drive and test them. Conventional operating systems like Linux are massively complex and modification is time-prohibitive. In this paper, we describe our port of the Kitten lightweight kernel operating system to RISC-V in order to provide an alternative to Linux for conducting co-design research. Kitten's small code base and simple resource management policies are well matched for quickly exploring new hardware ideas that may require radical operating system modifications and restructuring. Our evaluation shows that Kitten on RISC-V is functional and provides similar performance to Linux for single-core benchmarks. This provides a solid foundation for using Kitten in future co-design research involving RISC-V.

Gordon, Nick↗
DOE OSTI2024

Effects of spatiotemporal plasma power distribution on the modeling of ignition kernel evolution in quiescent and turbulent methane/air mixtures

Abstract The present work improves a phenomenological plasma-assisted combustion model by integrating the spatiotemporal distribution of plasma power density, thereby considering the evolution of plasma streamers in the modeling, and subsequently, better predicting the ignition kernel evolution. The improved phenomenological model is validated against experiments representing the plasma discharge and post-discharge ignition kernel evolution. Specifically, the new model demonstrates a more accurate prediction of ultrafast gas heating and O 2 dissociation during the plasma discharge, compared to the original model. In addition, the new model is found to closely match the experimental pressure wave and heated channel profiles post-discharge without the need for tuning the energy deposition (unlike the original model), highlighting its accuracy of post-discharge ignition kernel dynamics. The improved phenomenological model is then employed to investigate ignition kernel evolution for a stoichiometric methane-air discharge across various discharge gap configurations. Simulations reveal a non-uniform temperature and streamer distribution progressing from the electrode tips toward the center, contrasting uniform cylindrical discharges previously described in the original model. Streamer propagation is observed to be faster for larger gaps when maintained at the same average electric field for different discharge gaps. The tendency of smaller gaps to produce detached toroidal ignition kernels is observed, while larger gaps promote cylindrical and attached ignition kernels. Interactions between successive ignition kernels from consecutive discharges varied significantly, with the smallest gap (1 mm) promoting the quenching of the preceding ignition kernel due to the initial kernel–kernel separation. The intermediate gap (2 mm) promotes detached kernel growth. In contrast, in the largest gap (4 mm), kernels consistently combine and expand attached to electrodes. The impact of homogeneous isotropic turbulence is also explored, showing the persistence of ignition kernels early on but eventually quenching due to enhanced radical and heat losses with pronounced turbulence intensity.

Johnson, Praise Noah↗
DOE OSTI2021

Microstructural and Micro-Chemical Evolutions in the Irradiated UCO Fuel Kernels of AGR-1 and AGR-2 TRISO Fuel Particles

AGR-1 and AGR-2 TRISO fuel particles were fabricated with slightly different fuel kernel chemical compositions, modified fabrication processes, different fuel kernel diameters, and changed 235U enrichments. To correlate those differences with the fuel kernel responses to neutron irradiations in terms of irradiated fuel microstructure, fission products chemical and physical states, and fission gas bubble evolutions, extensive microstructural and analytical characterizations were conducted. The studies used a state of art transmission electron microscopy (TEM) equipped with Energy-dispersive X-ray spectroscopy (EDS) of four silicon solid-state detectors which have super sensitivity and fast speed. The TEM specimens were prepared from selected AGR-1 and AGR-2 irradiated fuel kernels exposed to safety testing after irradiation. The particles were chosen to represent a representative irradiation conditions with a fuel burnup within the range from 10.8 to 18.6% FIMA, and the time-average volume-average temperatures vary from 1070 to 1287°C. The 235U enrichment was 19.74 wt.% for the AGR1 fuel kernels and 14.03 wt.% for the AGR-2 fuel kernels. The TEM results show that there were significant microstructural reconstructions in the irradiated fuel kernels for both the AGR-1 and AGR-2 fuels. There are four major phases including fuel matrix of UO2 and UC, U2RuC2, and UMoC2 in the irradiated AGR2 fuel kernel. Zr and Nb form solid solution in the UC phase. UMoC2 phase often shows a detectable concentration of Tc. Pd was found to mainly locate in the buffer layer or to be associated with fission gas bubble within the UMoC2 phase. The EDS maps qualitatively show that the rare-earth fission products (Nb, et al.) preferentially reside in the UO2 phase. In contrast, in the irradiated AGR1 fuel kernel, no U2RuC2 or UMoC2 precipitates were positively identified. Instead, there is a high number of rod-shape precipitates enriched with Ru, Tc, Rh, and Pd observed in the fuel kernel center and edge zone. The difference of microstructural and micro-chemical evolutions in irradiated fuel kernels between the AGR-1 and AGR-2 TRISO fuel particle may result from a combined factor of irradiation temperature, fuel geometry and chemical composition. However, the irradiation temperature probably play a more deterministic role. Limited electron energy loss spectroscopy (EELS) characterizations on the AGR2 fuel kernel show that there is nearly no carbon in the UO2 phase while a small fraction of oxygen was detected in the UC/UMoC2 phase.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Numerical and experimental investigation of the flame kernel growth in a methane/air mixture near the lean flammability limit

Lean combustion has the potential to improve the thermal efficiency of spark-ignition engines, but it faces the significant challenge of increased cycle-to-cycle variation due to low mixture reactivity and unstable flame dynamics. Computational fluid dynamics (CFD) employing predictive models can guide engine design and optimize operating strategies for lean combustion. However, ignition and combustion models have rarely been validated at fuel-lean conditions, and a fundamental understanding of the early flame kernel growth process is also lacking for a successful sub-model development. Here, the present study develops a numerical simulation framework used to investigate early flame kernel growth in methane/air mixtures. A nanosecond-pulsed discharge (NPD) approach is employed to effectively decouple the flame kernel growth from the electrical discharge due to their difference in timescales, and equivalence ratios near the experimentally measured lean flammability limit (LFL) are selected to focus on challenging mixture conditions. Three numerical investigations, such as the choice of turbulence modeling, grid size, and grid control strategies, are examined to match both LFL and flame kernel structure measured from experiments. It is demonstrated that a quasi-direct numerical simulation (QDNS) with a fixed grid embedding of 10 μm can predict the LFL as φ CFD =0.61 and match the displacement speed of the kernel’s boundary marked in schlieren images. To predict the LFL and flame kernel shape, a fine grid (Δ≤12.5 μm) is needed to capture the consumption of formaldehyde (CH 2 O) in kernel’s reaction branches attached to the anode, and adaptive mesh refinement is replaced with the fixed embedding due to loss of simulation accuracy. Also, it is found that a large-eddy simulation (LES) using the Dynamic Structure model is not suitable for the NPD-induced flame kernel simulation because artificial sub-grid turbulent kinetic energy induced by shock dynamics alters the flow velocity calculation, resulting in divergence of LES from QDNS. Lastly, the simulation well matches the experimental data for the flame kernel evolution in three mixture conditions (φ = 0.7, 0.61, 0.55), showing toroidal flame kernel expansion and flame kernel growth/extinction.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Physical Properties of Moist, Fermented Corn Kernels

A novel approach to producing corn stover biomass feedstock has been investigated. In this approach, corn grain and stover are co-harvested at moisture contents much less than typical corn silage. The grain and stover are conserved together by anaerobic storage and fermentation and then separated before end use. When separated from the stover, the moist, fermented grain had physical characteristics that differ from typical low-moisture, unfermented grain. A comprehensive study was conducted to quantify the physical properties of this moist, fermented grain. Six corn kernel treatments, either fermented or unfermented, having different moisture contents, were used. Moist, fermented kernels (26 and 36% w.b. moisture content) increased in size during storage. The fermented kernels’ widths and thicknesses were 10% and 15% greater, respectively, and their volume was 28% greater than the dry kernels (15% w.b.). Dry basis particle density was 9% less for moist, fermented kernels. Additionally, the dry basis bulk density was 29% less, and the dry basis hopper-discharged mass flow rate was 36% less. Moist, fermented grain had significantly greater kernel-to-kernel coefficients of friction and angles of repose compared to relatively dry grain. The friction coefficient on four different surfaces was also significantly greater for fermented kernels. Fermented corn kernels had lower individual kernel rupture strengths than unfermented kernels. These physical differences must be considered when designing material handling and processing systems for moist, fermented corn grain.

09 BIOMASS FUELS↗
DOE OSTI2024

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE↗
DOE OSTI2026

Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

MONTE CARLO CROSS SECTION LOOKUP KERNEL FOR THE CEREBRAS WSE-2 IN CSL

This is a small kernel that was used to collect data for an upcoming paper. We would like to have the code be open source so that the reviewers (and then readers) of the paper can see the whole code, and can reproduce/verify our results. This is not a fully featured application, it cannot produce any useful simulation results, it just executes a small abstracted kernel using synthetic data. The purpose of the kernel is to understand the basic performance characteristics of an HPC kernel on novel AI accelerator architectures. The main kernel is written in the CSL coding language for use with the Cerebras WSE-2 AI accelerator. The kernel represented is the Monte Carlo cross section lookup kernel, which is a small kernel used by the Monte Carlo neutral particle transport algorithm. There is also a baseline kernel written in CUDA that we will include in the repository to form a basis for comparing the WSE-2 to GPU.

Tramm, John↗
NASA NTRS2020

The HadGEM3-GA7.1 radiative kernel: the importance of a well-resolved stratosphere

We present top-of-atmosphere and surface radiative kernels based on the atmospheric component (GA7.1) of the HadGEM3 general circulation model developed by the UK Met Office. We show that the utility of radiative kernels for forcing adjustments in idealised CO2 perturbation experiments is greatest where there is sufficiently high resolution in the stratosphere in both the target climate model and the radiative kernel. This is because stratospheric cooling to a CO2 perturbation continues to increase with height, and low-resolution or low-top kernels or climate model output are unable to fully resolve the full stratospheric temperature adjustment. In the sixth phase of the Coupled Model Intercomparison Project (CMIP6), standard atmospheric model data are available up to 1 hPa on 19 pressure levels, which is a substantial advantage compared to CMIP5. We show in the IPSL-CM6A-LR model where a full set of climate diagnostics are available that the HadGEM3-GA7.1 kernel exhibits linear behaviour and the residual error term is small, as well as from a survey of kernels available in the literature that in general low-top radiative kernels underestimate the stratospheric temperature response. The HadGEM3-GA7.1 radiative kernels are available at https://doi.org/10.5281/zenodo.3594673 (Smith, 2019).

radiative kernels↗
DOE OSTI2026

Irradiation of UC1+x kernels using the MiniFuel vehicle: Microstructure, phase analysis, and initial post-irradiation examination

Uranium carbide is a candidate fuel form for a wide range of advanced reactors, including larger Generation IV reactors as well as small modular reactors and microreactors. However, its commercial deployment timeline faces challenges via traditional qualification approaches. To address this issue, an accelerated fission rate irradiation test was performed to collect basic fuel performance data to inform fuel performance models and potential future integral tests. Hyperstoichiometric UC (UC1+x) kernels were irradiated in the High Flux Isotope Reactor using the MiniFuel irradiation vehicle. The test matrix spanned two temperature regimes (700 °C and 800 °C) and burnup levels (1.8 % FIMA and 2.8 % FIMA). Between 21 and 63 kernels were tested at each unique temperature and burnup condition. As-fabricated microstructural analysis revealed a multiphase composition with UC, UC2, UC2−y, and U-C-O bearing phases for the irradiated kernels. Following irradiation, fission gas release, swelling, and microstructures were analyzed. Measured fission gas release was below 5 % for all irradiation conditions, reaching a maximum at the highest temperature and burnup condition. A binary swelling response was observed; the lower burnup and temperature conditions resulted in negligible swelling, but the higher burnup and temperature conditions produced significant anisotropic swelling and densification in a subset of kernels. The basic microstructural exams of kernels following irradiation were not capable of showing a correlation between kernels that exhibited excessive swelling and those that did not. Characterization of a subset of samples using the Advanced Photon Source and more detailed microstructural examination of unirradiated kernels revealed that a subset of kernels contained very high UC2 phase fractions. The anomalous swelling response is hypothesized to have been driven by this chemical variation. The results of this irradiation highlight the potential of accelerated fission rate irradiation testing to explore such behaviors and inform the development of fuel specifications.

Adorno Lopes, Denise [ORNL] (ORCID:000900023705987↗
NASA NTRS1955

On the Kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow

This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady case) are given. The derivation of the integral equation which involves this Kernel function is reproduced as an appendix. Another appendix gives the reduction of the form of the Kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the Kernel function, and a fourth appendix presents an alternate form of expression for the Kernel function.

Watkins, Charles E↗
NASA NTRS2008

Integrating the Gradient of the Thin Wire Kernel

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

Champagne, Nathan J.↗