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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Identification of crystal plasticity model parameters by multi-objective optimization integrating microstructural evolution and mechanical data

Crystal plasticity models evolve a polycrystalline yield surface using meso-scale descriptions of deformation mechanisms. The activation of deformation mechanisms is governed by crystallography and a set of model parameters, which are typically calibrated through the fitting of mechanical data such as stress–strain curves and elastic lattice strains. Microstructural data such as phase fractions and texture evolution are used for verifying crystal plasticity parameters. In this study, we use a multi-objective genetic algorithm to identify hardening parameters from flow stress curves with an option to incorporate texture into the optimization approach. Robust, generalized objective functions are developed and used to identify sets of parameters pertaining to dislocation density-based hardening laws in visco-plastic and elasto-plastic self-consistent (VPSC and EPSC) homogenization models. First, the parameters are identified for pure Nb directly from texture using an objective function based on generalized spherical harmonics. Since texture evolution is driven by the relative contribution of active slip systems, the parameters governing the evolution of slip resistance ratios can be recovered from fitting discrete textures at a series of strains. Next, a comprehensive set of load reversal data for dual phase (DP) 780 steel is used to fit a hardening law and a back-stress law in EPSC. Finally, parameters pertaining to a complex hardening law for the evolution of slip and twinning in pure α-Ti are identified. Remarkably, using texture as an objective in combination with stress–strain objectives constrains the model of Ti to fully reproduce not only stress–strain and texture evolution but also hierarchical twinning measurements as a function of initial grain size and texture. Furthermore, given an appropriate model fit to representative experimental texture evolution, underlying twin volume fractions contributing to texture evolution can be predicted.

42 ENGINEERING↗
DOE OSTI2023

Many-Body Potential for Simulating Self-Assembly of Polymer-Grafted Nanoparticles in a Polymer Matrix

Many-body interactions between polymer-grafted nanoparticles (NPs) play a key role in promoting their assembly into low-dimensional structures within polymer melts, even when the particles are spherical and isotropically grafted. However, capturing such interactions in simulations of NP assembly is very challenging because explicit modeling of the polymer grafts and melt chains is highly computationally expensive, even using coarse-grained models. Here, we develop a many-body potential for describing the effective interactions between spherical polymer-grafted NPs in a polymer matrix through a machine-learning approach. The approach involves using permutationally invariant polynomials to fit two- and three-body interactions derived from the potential of mean force calculations. The potential developed here reduces the computational cost by several orders of magnitude, thereby, allowing us to explore assembly behavior over large length and time scales. We show that the potential not only reproduces previously known assembled phases such as 1D strings and 2D hexagonal sheets, which generally cannot be achieved using isotropic two-body potentials, but can also help discover interesting phases such as networks, clusters, and gels. We demonstrate how each of these assembly morphologies intrinsically arises from a competition between two- and three-body interactions. Our approach for deriving many-body effective potentials can be readily extended to other colloidal systems, enabling researchers to make accurate predictions of their behavior and dissect the role of individual interaction energy terms of the overall potential in the observed behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2021

AT2017gfo: Bayesian inference and model selection of multicomponent kilonovae and constraints on the neutron star equation of state

The joint detection of the gravitational wave GW170817, of the short γ-ray burst GRB170817A and of the kilonova AT2017gfo, generated by the the binary neutron star (NS) merger observed on 2017 August 17, is a milestone in multimessenger astronomy and provides new constraints on the NS equation of state. We perform Bayesian inference and model selection on AT2017gfo using semi-analytical, multicomponents models that also account for non-spherical ejecta. Observational data favour anisotropic geometries to spherically symmetric profiles, with a log-Bayes’ factor of ~104, and favour multicomponent models against single-component ones. The best-fitting model is an anisotropic three-component composed of dynamical ejecta plus neutrino and viscous winds. Using the dynamical ejecta parameters inferred from the best-fitting model and numerical–relativity relations connecting the ejecta properties to the binary properties, we constrain the binary mass ratio to q < 1.54 and the reduced tidal parameter to $120\lt \tilde{\Lambda }\lt 1110$. Finally, we combine the predictions from AT2017gfo with those from GW170817, constraining the radius of a NS of 1.4 M ⊙ to 12.2 ± 0.5 km (1σ level). This prediction could be further strengthened by improving kilonova models with numerical-relativity information.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Characterization of thermal transport and evolution of Au plasma in ICF experiments by Thomson scattering

Here, this paper demonstrates the capability of optical Thomson scattering (OTS) to measure thermal transport, and provides support to radiation hydrodynamic and kinetic simulations of electron thermal transport and plasma evolution. OTS theory and plasma simulations are applied to the interpretation of experimental measurements of laser-produced plasma from spherical gold targets on the OMEGA laser facility. The dynamical form factor, S($\vec{k}$, ω), of electron density fluctuations that is used in the fitting of Thomson scattering spectra includes ion–ion collisions and effects of non-Maxwellian distribution functions. OTS measurements and their interpretation are consistent with the nonlocal transport model in radiation hydrodynamic simulations as well as with kinetic simulations in the second half of the probe pulse duration. In particular, the reversal of heat transport during cooling is observed to be consistent with simulations, while some discrepancies are noted during the initial heating of the Au targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Symplectic effective field theory for nuclear structure studies

Here, a Symplectic Effective Field Theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory applied against symplectic basis states is shown to yield a Hamiltonian system with one fitted parameter. The scale of the system can be determined self consistently as the ratio of the average volume of a nucleus assumed to be spherical to its volume as determined by the average number of oscillator quanta, which is stretched by the fact that the plane-wave solution satisfies the equations of motion at every order without the need for perturbative corrections. As an application of the theory, results for 20 Ne, 22 Ne and 22 Mg are presented that yield energy spectra, B(E2) values, and matter radii in good agreement with experimentally measured results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Assessment of DFT methods for the prediction of detachment energies and electronic structures of complex and multiply charged anions

Here, in this work, we assess the ability of different density functional theory methods to reproduce the vertical/adiabatic detachment energies (VDEs/ADEs) of a series of 40 anions, including monoanion versus multiply charged anions (MCAs) and covalent versus noncovalent interaction. The statistical analysis of errors is firstly performed by comparing the theoretical values with the experimental benchmark data obtained from the negative ion photoelectron spectroscopy (NIPES). The proposed optimally tuned range-separated (OTRS) functionals are proved to not only well reproduce the experimental VDEs/ADEs, but also simulate experimental NIPES. The result implies a more serious issue of delocalization error for MCAs and a balanced description of electron-rich/- deficient region of anions is necessary. The radius of the spherically symmetric average electron localization function (ELF) region is demonstrated as a useful descriptor for the characterization of electronic structure of anionic systems and a quasilinear fitting model is proposed to efficiently obtain their OTRS parameters.

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

Burning velocities of R-32/O 2 /N 2 mixtures: Experimental measurements and development of a validated detailed chemical kinetic model

This work entails characterizing the flammability of the refrigerant R-32 (CH 2 F 2 ) by both experimental measurements and modeling. Burning velocities S u were measured using a constant-volume spherical-flame method for R-32/O2/N 2 mixtures with O 2 /N 2 ratios ranging from 21% (synthetic air) to 40%, pressures of (1 to 3) bar, and equivalence ratios $\phi$ of (0.8 to 1.3). Based on a critical assessment of available data, and extended by our own calculations, a detailed chemical kinetic model was developed and key reactions determined using reaction path and sensitivity analyses. Initiation and combustion were identified as distinct kinetic regimes and burning velocities were found to be controlled by two primary reactions: unimolecular decomposition of CH 2 F 2 → CHF + HF and the subsequent reaction, CHF + O 2 → CHFO + O, the latter reaction initiating the radical chain propagating and branching by producing O atoms. Sensitive rate constants in the kinetic model were critically adjusted within their uncertainties and current knowledge bounds to best fit the experimental burning velocities. We found that rate constants in the model could be adjusted to match a given experimental S u for specific conditions (O 2 loading, P, T, $\phi$). This, however, then fixes predicted burning velocities for other all conditions within (3 to 4)% if physically realistic rate parameters are maintained. Thus, the entire set of experimental data is fit, not just to particular conditions. Relative random uncertainties in the experimental Su measurements were (4 to 6)%, but assumptions made for thermal radiation lost by the burned gas in the spherical-flame experiments add an additional systematic uncertainty. Systematic differences between the limiting cases of adiabatic (no thermal radiation lost) and optically-thin (all thermal radiation lost) varied significantly with conditions and ranged from (4 to 30)% at high to low velocities, respectively, translating into uncertainties of (2 to 15)% considering the average of two limiting cases. Comparison of experimental and kinetically modeled Su values suggests that the burned gas tends towards the optically-thin limit at the lowest pressures and fuel loadings and toward the adiabatic limit at the highest pressures and loadings. We tested and found support for this conclusion with a detailed analysis as a function of all the conditions (T, P, % O 2 , $\phi$). This behavior appears to transition from optically-thin to adiabatic as the density of the initial fuel increases, which results in increased CO 2 in the burned gas and thus increased absorption of the thermal radiation (consistent with the Beer-Lambert Law). The validated detailed model based on evaluated kinetics is shown to accurately predict burning velocities for R-32 O 2 /N 2 mixtures over a wide range of conditions and provides a reliable basis for extrapolation to other conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Industrial scale mesofluidic particle separation

Here we explore the potential of a mesofluidic separator that fits within industrial piping and is designed to remove large aspherical particles out of an abrasive slurry at fast flow rates. Mesofluidic separators have recently demonstrated separation of spherical particles at flow rates of ~1 gallon/min (gpm) (6.3.10 -5 m 3 /s). Yet, the performance of these separators at flow rates achievable within industrial piping have not been explored. Here we evaluate the permeate flowrate fraction, large particle mass fraction, and pressure drop from approximately 35-100 gpm (2.2.10-3-6.3.10-3 m 3 /s) in a three inch tube using an abrasive and modestly non-spherical slurry. Faster flow rates may be achieved with larger pumps and larger diameters. We find the permeate fraction and pressure drop both increase with flow rate, though the pressure drop remains modest. Only two feet of inserts removed 97.6±2.1% of large particles for conditions tested. Separation was demonstrated in both vertical and horizontal orientations with the horizontal orientation benefiting marginally from gravitational settling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Long-Range Fit: A Software Package for the Representation and Study of Long-Range Molecular Interactions

Describing intermolecular forces is fundamental to modeling and predicting the behavior of molecular systems. In particular, long-range molecular interactions─with electrostatic, induction, and dispersion as the main components─play a critical role, especially for low-temperature and low-density regimes. Long-range interactions are often described through perturbation theory, representing the electronic charge distribution via a multipolar series of the moments and polarizability tensors corresponding to each molecule. However, while the theory is well established, obtaining the resulting analytical expressions (and their practical implementation) constitutes a highly complex and system-dependent task. To address this challenge, we developed long-range-fit (LRF), an interactive and user-friendly software package designed to automate the generation and fitting of long-range interaction terms for arbitrary molecules in nondegenerate (ground or excited) electronic states. We have derived and implemented all terms up to 15th order, without approximations, via a spherical tensor representation, with symmetry adaptation to all molecular point-group symmetries. The resulting potential energy surface is compatible with most representations of the close interaction region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Phase space distribution functions and energy distributions of dark matter particles in haloes

ABSTRACT For a spherical dark matter halo with isotropic velocity distribution, the phase space distribution function (DF), the energy distribution, and the density profile form a set of self-consistent description of its equilibrium state, and knowing one is sufficient to determine the other two. The Navarro–Frenk–White density profile (NFW profile) is known to be a good approximation to the spherically averaged density distribution in simulated haloes. The DARKexp energy distribution is also known to compare well with the simulated energy distribution. We present a quantitative assessment of the NFW and DARKexp fits to the simulated DF and energy distribution for a wide range of haloes in a dark-matter-only simulation from the IllustrisTNG Project. As expected, we find that the NFW fits work well except at low energy when the density at small radii deviates from the NFW profile. Further, the NFW and DARKexp fits have comparable accuracy in the region where both fit well, but the DARKexp fits are better at low energy because they require matching of the central gravitational potential. We also find an approximate relation between the energy scale parametrizing the DARKexp energy distribution and that defined by the characteristic density and radius of the NFW profile. This relation may be linked to the relaxation process during halo formation.

Astronomy & Astrophysics↗
DOE OSTI2025

Optical evolution of AT 2024wpp: the high-velocity outflows in Cow-like transients are consistent with high spherical symmetry

ABSTRACT We present the analysis of optical/near-infrared (NIR) data and host galaxy properties of a bright, extremely rapidly evolving transient, AT 2024wpp, which resembles the enigmatic AT 2018cow. AT 2024wpp rose to a peak brightness of $c=-21.9$ mag in 4.3 d and remained above the half-maximum brightness for only 6.7 d. The blackbody fits to the photometry show that the event remained persistently hot ($T\gtrsim 20\, 000$ K) with a rapidly receding photosphere ($v\sim 11\, 500$ km s$^{-1}$), similarly to AT 2018cow albeit with a several times larger photosphere. $JH$ photometry reveals an NIR excess over the thermal emission at $\sim +20$ d, indicating a presence of an additional component. The spectra are consistent with blackbody emission throughout our spectral sequence ending at $+21.9$ d, showing a tentative, very broad emission feature at $\sim 5500$ Å – implying that the optical photosphere is likely within a near-relativistic outflow. Furthermore, reports of strong X-ray and radio emission cement the nature of AT 2024wpp as a likely Cow-like transient. AT 2024wpp is the second event of the class with optical polarimetry. Our $BVRI$ observations obtained from $+6.1$ to $+14.4$ d show a low polarization of $P\lesssim 0.5$ per cent across all bands, similar to AT 2018cow that was consistent with $P\sim 0$ per cent during the same outflow-driven phase. In the absence of evidence for a preferential viewing angle, it is unlikely that both events would have shown low polarization in the case that their photospheres were aspherical. As such, we conclude that the near-relativistic outflows launched in these events are likely highly spherical, but polarimetric observations of further events are crucial to constrain their ejecta geometry and stratification in detail.

Pursiainen, M.↗
DOE OSTI2022

Estimate of the Mass and Radial Profile of the Orphan–Chenab Stream's Dwarf-galaxy Progenitor Using MilkyWay@home

We fit the mass and radial profile of the Orphan–Chenab Stream's (OCS) dwarf-galaxy progenitor by using turnoff stars in the Sloan Digital Sky Survey and the Dark Energy Camera to constrain N-body simulations of the OCS progenitor falling into the Milky Way on the 1.5 PetaFLOPS MilkyWay@home distributed supercomputer. We infer the internal structure of the OCS's progenitor under the assumption that it was a spherically symmetric dwarf galaxy composed of a stellar system embedded in an extended dark matter halo. We optimize the evolution time, the baryonic and dark matter scale radii, and the baryonic and dark matter masses of the progenitor using a differential evolution algorithm. The likelihood score for each set of parameters is determined by comparing the simulated tidal stream to the angular distribution of OCS stars observed in the sky. We fit the total mass of the OCS's progenitor to (2.0 ± 0.3) × 10 7 M ⊙ with a mass-to-light ratio of γ = 73.5 ± 10.6 and (1.1 ± 0.2) × 10 6 M ⊙ within 300 pc of its center. Within the progenitor's half-light radius, we estimate a total mass of (4.0 ± 1.0) × 10 5 M ⊙ . We also fit the current sky position of the progenitor's remnant to be (α, δ) = ((166.0 ± 0.9)°, (–11.1 ± 2.5)°) and show that it is gravitationally unbound at the present time. The measured progenitor mass is on the low end of previous measurements and, if confirmed, lowers the mass range of ultrafaint dwarf galaxies. Our optimization assumes a fixed Milky Way potential, OCS orbit, and radial profile for the progenitor, ignoring the impact of the Large Magellanic Cloud.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Efficient analysis of small-angle scattering curves for large biomolecular assemblies using Monte Carlo methods

Structure elucidation from small-angle scattering curves of large biomolecular assemblies is notoriously challenging. This is because the simulation of high-resolution features in the structure of large macromolecular assemblies, such as de novo protein assemblies, is computationally demanding when it needs to cover a broad range of length scales. Conventional methods, such as the numerical approximation to the Debye equation or the use of spherical harmonics, do not scale well as the size of the assembly increases, which limits their application to small structures (e.g. individual proteins). This work explores the effectiveness of a Monte Carlo method to simulate and fit scattering curves for large biomolecular assemblies spanning over ranges covering atomic and molecular detail (e.g. spacing and orientation of proteins in an assembly) as well as large-scale (hundreds of nanometres) features. Owing to its speed and scalability, it can be combined with a fitting algorithm to extract structural features from experimental small-angle scattering curves in biomolecular assemblies that are otherwise intractable for interpretation. This work first demonstrates the effectiveness of the tool using experimental small-angle X-ray scattering (SAXS) data from tile-like proteins that assemble into 1D tube-like macromolecular structures. Here, the diameter distribution of tubes is extracted from SAXS fits, and this is quantitatively compared with distributions from electron microscopy. SAXS data are also obtained from 2D sheet-like protein assemblies, and the proposed method is used to quantify structural features such as the separation distance between protein building blocks and the flexing of the sheet. An open-source implementation of the methodology is provided for use in a broad range of biological systems involving multi-scale scattering analysis.

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

Real-time nuclear activation detectors for measuring neutron angular distributions at the National Ignition Facility (invited)

The Real Time Nuclear Activation Detector (RTNAD) array at NIF measures the distribution of 14 MeV neutrons emitted by deuterium-tritium (DT) fueled inertial confinement fusion implosions. The uniformity of the neutron distribution is an important indication of implosion symmetry and DT shell integrity. The array consists of 48 LaBr 3 (Ce) crystal gamma-ray spectrometers mounted outside the NIF target chamber, which continuously monitor the slow decay of the 909 keV gamma-ray line from activated 89 Zr located in Zr cups surrounding each crystal. The measured decay rate dramatically increases during a DT implosion in proportion to the number of 14 MeV neutrons striking each Zr cup. The neutrons produce activated 89 Zr through an (n, 2n) reaction on 90 Zr, which is insensitive to low energy neutrons. The neutron flux along the detector line-of-sight at shot time is determined by extrapolating the fitted 909 keV decay curve back to shot time. Automatic analysis algorithms were developed to handle the non-stop data stream. The large number of detectors and the high statistical accuracy of the array enable the spherical harmonic modes of the neutron angular distribution to be measured up to L ≤ 4 to provide a better understanding of implosion dynamics. In addition, these data combined with measurements of the down-scattered neutrons can be used to derive fuel areal density distributions. This paper will describe the RTNAD hardware and analysis procedures.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

X-ray morphology of cluster-mass haloes in self-interacting dark matter

ABSTRACT We perform cosmological zoom-in simulations of 19 relaxed cluster-mass haloes with the inclusion of adiabatic gas in the cold dark matter (CDM) and self-interacting dark matter (SIDM) models. These clusters are selected as dynamically relaxed clusters from a parent simulation with $M_{\rm 200} \simeq (1\!-\!3)\times 10^{15}{\, \rm M_\odot }$. Both the dark matter and the intracluster gas distributions in SIDM appear more spherical than their CDM counterparts. Mock X-ray images are generated based on the simulations and are compared to the real X-ray images of 84 relaxed clusters selected from the Chandra and ROSAT archives. We perform ellipse fitting for the isophotes of mock and real X-ray images and obtain the ellipticities at cluster-centric radii of $r\simeq 0.1\!-\!0.2R_{\rm 200}$. The X-ray isophotes in SIDM models with increasing cross-sections are rounder than their CDM counterparts, which manifests as a systematic shift in the distribution function of ellipticities. Unexpectedly, the X-ray morphology of the observed non-cool-core clusters agrees better with SIDM models with cross-section $(\sigma /m)= 0.5\!-\!1\, {\rm cm}^2\, {\rm g}^{-1}$ than CDM and SIDM with $(\sigma /m)=0.1\, {\rm cm}^2\, {\rm g}^{-1}$. Our statistical analysis indicates that the latter two models are disfavoured at the $68{{\ \rm per\ cent}}$ confidence level (as conservative estimates). This conclusion is not altered by shifting the radial range of measurements or applying a temperature selection criterion. However, the primary uncertainty originates from the lack of baryonic physics in the adiabatic model, such as cooling, star formation and feedback effects, which still have the potential to reconcile CDM simulations with observations.

Shen, Xuejian (ORCID:000000026196823X)↗
DOE OSTI2021

Unseeded, spontaneous nucleation of spherulitic magnesium calcite

Most of the sedimentary carbonates deposited in the marine environments are composed of calcium carbonate minerals with varying amounts of incorporated Mg 2+ . However, understanding how interactions of impurities with carbonate and their incorporation affect sediments behavior remains a challenge. Here, a new insight is obtained by monitoring solution composition, morphology, and electrokinetic potential of carbonate particles formed in a spontaneous unseeded batch precipitation experiment using electrochemical and scanning electron microscopy methods. The solid composition and growth rate are extracted from changes in the bulk composition and fitted to chemical affinity rate law, revealing that the precipitation pathway consists of second-order dissolution and first-order precipitation. The molecular dynamics simulations show that the lattice strain induced by randomly substituting Ca 2+ by Mg 2+ stabilizes spherical nanoparticles and reduces their surface area and volume. Combining kinetics and thermodynamics insight, we conclude that variation in the carbonate bulk and interfacial energies, along with the solution supersaturation, lead to the dissolution-precipitation transformation pathway from Mg-rich to Mg-poor carbonate phase that preserves spherulitic morphology. Furthermore, our findings are relevant for long-standing questions of how impurities influence diagenesis of carbonate sediments and spherulitic carbonate particles' origin.

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

Local models for scatter estimation and descattering in polyenergetic X-ray tomography

We propose a new modeling approach for scatter estimation and descattering in polyenergetic X-ray computed tomography (CT) based on fitting models to local neighborhoods of a training set. X-ray CT is widely used in medical and industrial applications. X-ray scatter, if not accounted for during reconstruction, creates a loss of contrast in CT reconstructions and introduces severe artifacts including cupping, shading, and streaks. Even when these qualitative artifacts are not apparent, scatter can pose a major obstacle in obtaining quantitatively accurate reconstructions. Our approach to estimating scatter is, first, to generate a training set of 2D radiographs with and without scatter using particle transport simulation software. To estimate scatter for a new radiograph, we adaptively fit a scatter model to a small subset of the training data containing the radiographs most similar to it. We compared local and global (fit on full data sets) versions of several X-ray scatter models, including two from the recent literature, as well as a recent deep learning-based scatter model, in the context of descattering and quantitative density reconstruction of simulated, spherically symmetrical, single-material objects comprising shells of various densities. Our results show that, when applied locally, even simple models provide state-of-the-art descattering, reducing the error in density reconstruction due to scatter by more than half.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Resistive heating in an electrified domain with a spherical inclusion: an ALEGRA verification study

A verification study is conducted for the ALEGRA software, using the problem of an electrified medium with a spherical inclusion, paying special attention to resistive heating. We do so by extending an existing analytic solution for this problem to include both conducting and insulating inclusions, and we examine the effects of mesh resolution and mesh topology, considering both body-fitted and rectangular meshes containing mixed cells. We present observed rates of convergence with respect to mesh refinement for four electromagnetic quantities: electric potential, electric field, current density and Joule power.

97 MATHEMATICS AND COMPUTING↗