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At least 181 records · Page 10

Close-in characteristics of LH2/LOX reactions

In deriving shock overpressures from space vehicles employing LH2 and LOX, separate methods of analyses and prediction are recommended, as a function of the distance. Three methods of treatment are recommended. For the Far Field - where the expected shock overpressure is less than 40 psi (lambda = 5) - use the classical PYRO approach to determine TNT yield, and employ classical ordnance (Kingery) curve to obtain the overall value. For the Close-In Range, a suggested limit is 3D, or a zone from a distance of three times the tank diameter to the tank wall. Rather than estimate a specific distance from the center of explosion to the target, it is only necessary to estimate whether this could be within one, two, or three diameters away from the wall; i.e., in the 1, 2, or 3D zone. Then assess whether mixing mode is by the PYRO CBGS (spill) mode or CBM (internal mixing) mode. From the zone and mixing mode, the probability of attaining various shock overpressures is determined from the plots provided herein. For the transition zone, between 40 psi and the 3D distance, it is tentatively recommended that both of the preceding methods be used, and to be conservative, the higher resulting value be used.

Riehl, W. A.↗

Recent Progress on RANS-Based Transition Model Verification

The current efforts to assess and improve the Reynolds-averaged Navier-Stokes (RANS)-coupled transition models in the NASA FUN3D and OVERFLOW codes are summarized in this study. The first AIAA Transition Modeling Workshop and the NATO AVT-313 Transition Workshop both emphasized the need for code verification for transport equations based transition models as a top priority. We discuss the methods used for the model verification, the resulting grid families, the flow solutions, and other supporting information collected with at least two established NASA flow solvers, namely, FUN3D and OVERFLOW. These results, which will be uploaded onto the NASA Turbulence Modeling Resource, should assist other members of the computational fluid dynamics (CFD) community in verifying their own implementations of various transition models, such as the Langtry-Menter (LM2009) model, the one-equation γ model, and Coder’s amplification factor transport (AFT) model. Grid convergence is assessed using both global and local flow metrics of interest such as lift and drag as well as local skin-friction coefficients. We also explore the anisotropic unstructured metric-based adaptive mesh refinement library known as refine with the NASA FUN3D solver to determine if this capability can achieve the same accuracy as handcrafted structured grids with a significantly smaller node count and to learn the characteristics of the resulting grid distribution, especially in the vicinity of the transition zone.

RANS↗

Direct Numerical Simulation of Transition Due to Traveling Crossflow Vortices

Previous simulations of laminar breakdown mechanisms associated with stationary crossflow instability over a realistic swept-wing configuration are extended to investigate the alternate scenario of transition due to secondary instability of traveling crossflow modes. Earlier analyses based on secondary instability theory and parabolized stability equations have shown that this alternate scenario is viable when the initial amplitude of the most amplified mode of the traveling crossflow instability is greater than approximately 0.03 times the initial amplitude of the most amplified stationary mode. The linear growth predictions based on the secondary instability theory and parabolized stability equations agree well with the direct numerical simulation. Nonlinear effects are initially stabilizing but subsequently lead to a rapid growth followed by the onset of transition when the amplitude of the secondary disturbance exceeds a threshold value. Similar to the breakdown of stationary vortices, the transition zone is rather short and the boundary layer becomes completely turbulent across a distance of less than 15 times the boundary layer thickness at the completion of transition.

Li, Fei↗

Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, mu(sub t), with the intermittency factor, gamma. Turbulent quantities are predicted by using Menter's two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

Suzen, Y. Bora↗

Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, t , with the intermittency factor, y. Turbulent quantities are predicted by using Menter s two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

Suzen, Y. B.↗

Resolving complex intralayer transition motifs in high-Ni-content layered cathode materials for lithium-ion batteries

High-Ni-content layered materials are promising cathodes for next-generation lithium-ion batteries. However, investigating the atomic configurations of the delithiation-induced complex phase boundaries and their transitions remains challenging. Here, in this study, by using deep-learning-aided super-resolution electron microscopy, we resolve the intralayer transition motifs at complex phase boundaries in high-Ni cathodes. We reveal that an O3 → O1 transformation driven by delithiation leads to the formation of two types of O1–O3 interface, the continuous- and abrupt-transition interfaces. The interfacial misfit is accommodated by a continuous shear-transition zone and an abrupt structural unit, respectively. Atomic-scale simulations show that uneven in-plane Li+ distribution contributes to the formation of both types of interface, and the abrupt transition is energetically more favourable in a delithiated state where O1 is dominant, or when there is an uneven in-plane Li + distribution in a delithiated O3 lattice. Moreover, a twin-like motif that introduces structural units analogous to the abrupt-type O1–O3 interface is also uncovered. The structural transition motifs resolved in this study provide further understanding of shear-induced phase transformations and phase boundaries in high-Ni layered cathodes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

PSE-Based Aerodynamic Flow Transition Prediction Using Automated Unstructured CFD Integration

Accurate, robust, and efficient prediction of transition in viscous flows is a significant challenge in computational fluid dynamics. We present a coupled, high-fidelity, iterative approach that leverages the FUN3D flow solver and the LASTRAC stability code to predict transition in low-disturbance environments, initiated by the linear growth of boundary-layer instability modes. Our method integrates the ability of FUN3D to compute mixed laminar-transitional-turbulent mean flows via transition-sensitized Reynolds-Averaged Navier-Stokes equations with the ability of LASTRAC to perform linear stability analysis, all within an automated framework that requires no intermediate user involvement. Unlike conventional frameworks that rely on classical stability theory or reduced-order metamodels, our approach employs the parabolized stability equations to provide more accurate and reliable estimates of disturbance growth for multiple instability mechanisms, including Tollmien-Schlichting, Kelvin-Helmholtz, and crossflow modes. By accounting for the effects of mean-flow nonparallelism as well as the surface curvature, this approach lays the foundation for improved N-factor correlations for transition onset prediction in a broad class of flows. We apply this method to three distinct flow configurations: 1) flow over a zero-pressure-gradient flat plate, 2) the NLF-0416 airfoil with both natural and separation-induced transitions, and 3) a 6:1 prolate spheroid, where transition is primarily driven by crossflow instability. For the two-dimensional cases, a formulated intermittency distribution is used to model the transition zone in between the laminar and fully turbulent flows. The results include comparisons with experimental measurements, similar numerical approaches, and transport-equations-based models, demonstrating good agreement in surface pressure coefficients, transition onset locations, and skin-friction coefficients for all three configurations. Besides contributing a couple of new insights into boundary-layer transition in these canonical cases, this study provides a powerful tool for transition modeling in both research and design applications in aerodynamics.

Transition Prediction↗

Spherical disharmonics in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations

There is increasing use of statistical correlations between geophysical fields and between geochemical and geophysical fields in attempts to understand how the Earth works. Typically, such correlations have been based on spherical harmonic expansions. The expression of functions on the sphere as spherical harmonic series has many pitfalls, especially if the data are nonuniformly and/or sparsely sampled. Many of the difficulties involved in the use of spherical harmonic expansion techniques can be avoided through the use of spatial domain correlations, but this introduces other complications, such as the choice of a sampling lattice. Additionally, many geophysical and geochemical fields fail to satisfy the assumptions of standard statistical significance tests. This is especially problematic when the data values to be correlated with a geophysical field were collected at sample locations which themselves correlate with that field. This paper examines many correlations which have been claimed in the past between geochemistry and mantle tomography and between hotspot, ridge, and slab locations and tomography using both spherical harmonic coefficient correlations and spatial domain correlations. No conclusively significant correlations are found between isotopic geochemistry and mantle tomography. The Crough and Jurdy (short) hotspot location list shows statistically significant correlation with lowermost mantle tomography for degree 2 of the spherical harmonic expansion, but there are no statistically significant correlations in the spatial case. The Vogt (long) hotspot location list does not correlate with tomography anywhere in the mantle using either technique. Both hotspot lists show a strong correlation between hotspot locations and geoid highs when spatially correlated, but no correlations are revealed by spherical harmonic techniques. Ridge locations do not show any statistically significant correlations with tomography, slab locations, or the geoid; the strongest correlation is with lowermost mantle tomography, which is probably spurious. The most striking correlations are between mantle tomography and post-Pangean subducted slabs. The integrated locations of slabs correlate strongly with fast areas near the transition zone and the core-mantle boundary and with slow regions from 1022-1248 km depth. This seems to be consistent with the 'avalanching' downwellings which have been indicated by models of the mantle which include an endothermic phase transition at the 670-km discontinuity, although this is not a unique interpretation. Taken as a whole, these results suggest that slabs and associated cold downwellings are the dominant feature of mantle convection. Hotspot locations are no better correlated with lower mantle tomography than are ridge locations.

Ray, Terrill W.↗

Global Assessment of the SMAP Level-4 Soil Moisture Product Using Assimilation Diagnostics

The Soil Moisture Active Passive (SMAP) mission Level-4 Soil Moisture (L4_SM) product provides 3-hourly, 9-km resolution, global estimates of surface (0-5 cm) and root-zone (0-100 cm) soil moisture and related land surface variables from 31 March 2015 to present with approx. 2.5-day latency. The ensemble-based L4_SM algorithm assimilates SMAP brightness temperature (Tb) observations into the Catchment land surface model. This study describes the spatially distributed L4_SM analysis and assesses the observation-minus-forecast (O-F) Tb residuals and the soil moisture and temperature analysis increments. Owing to the climatological rescaling of the Tb observations prior to assimilation, the analysis is essentially unbiased, with global mean values of approx. 0.37 K for the O-F Tb residuals and practically zero for the soil moisture and temperature increments. There are, however, modest regional (absolute) biases in the O-F residuals (under approx. 3 K), the soil moisture increments (under approx. 0.01 cu m/cu m), and the surface soil temperature increments (under approx. 1 K). Typical instantaneous values are approx. 6 K for O-F residuals, approx. 0.01 (approx. 0.003) cu m/cu m for surface (root-zone) soil moisture increments, and approx. 0.6 K for surface soil temperature increments. The O-F diagnostics indicate that the actual errors in the system are overestimated in deserts and densely vegetated regions and underestimated in agricultural regions and transition zones between dry and wet climates. The O-F auto-correlations suggest that the SMAP observations are used efficiently in western North America, the Sahel, and Australia, but not in many forested regions and the high northern latitudes. A case study in Australia demonstrates that assimilating SMAP observations successfully corrects short-term errors in the L4_SM rainfall forcing.

Reichle, Rolf↗

Using Data Assimilation Diagnostics to Assess the SMAP Level-4 Soil Moisture Product

The Soil Moisture Active Passive (SMAP) mission Level-4 Soil Moisture (L4_SM) product provides 3-hourly, 9-km resolution, global estimates of surface (0-5 cm) and root-zone (0-100 cm) soil moisture and related land surface variables from 31 March 2015 to present with approx.2.5-day latency. The ensemble-based L4_SM algorithm assimilates SMAP brightness temperature (Tb) observations into the Catchment land surface model. This study describes the spatially distributed L4_SM analysis and assesses the observation-minus-forecast (O-F) Tb residuals and the soil moisture and temperature analysis increments. Owing to the climatological rescaling of the Tb observations prior to assimilation, the analysis is essentially unbiased, with global mean values of approx. 0.37 K for the O-F Tb residuals and practically zero for the soil moisture and temperature increments. There are, however, modest regional (absolute) biases in the O-F residuals (under approx. 3 K), the soil moisture increments (under approx. 0.01 cu m/cu m), and the surface soil temperature increments (under approx. 1 K). Typical instantaneous values are approx. 6 K for O-F residuals, approx. 0.01 (approx. 0.003) cu m/cu m for surface (root-zone) soil moisture increments, and approx. 0.6 K for surface soil temperature increments. The O-F diagnostics indicate that the actual errors in the system are overestimated in deserts and densely vegetated regions and underestimated in agricultural regions and transition zones between dry and wet climates. The O-F auto-correlations suggest that the SMAP observations are used efficiently in western North America, the Sahel, and Australia, but not in many forested regions and the high northern latitudes. A case study in Australia demonstrates that assimilating SMAP observations successfully corrects short-term errors in the L4_SM rainfall forcing.

SMAP↗

CORC $^{\circledR}$ cable terminations with integrated Hall arrays for quench detection

ReBCO superconducting cables have the potential to enable compact thermonuclear fusion reactors that operate at magnetic fields exceeding 20 T and allow operation at temperatures far exceeding the boiling point of liquid helium, potentially allowing for demountable magnets. Normal zone detection remains a challenge, and while novel quench detection techniques are an active area of research, few are non-invasive, provide real-time quench detection, and have been demonstrated with current ramp rates relevant for fusion reactors. To address this problem, a CORC$^{\circledR}$ cable termination is developed with integrated Hall sensors to monitor current redistribution as a proxy for quench detection. The methodology exploits the current sharing and layered topology in CORC$^{\circledR}$ cables, and allows quench detection using a localized sensor instead of co-wound voltage wires or optical fibers. Furthermore, experiments are presented where current redistribution is measured from induced quenches, and in a 0.2 meter CORC$^{\circledR}$ sample it is found that the Hall sensors detect normal zone transitions with a similar magnitude and temporal resolution as voltage measurements. To emulate the conditions of dynamic poloidal and central solenoidal fields, experiments are repeated with ramp rates up to 10 kA s -1 that demonstrate the potential to detect normal zone development over a range of experimental parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A New Formulation for Hybrid LES-RANS Computations

Ideally, a hybrid LES-RANS computation would employ LES only where necessary to make up for the failure of the RANS model to provide sufficient accuracy or to provide time-dependent information. Current approaches are fairly restrictive in the placement of LES and RANS regions; an LES-RANS transition in a boundary layer, for example, yields an unphysical log-layer shift. A hybrid computation is formulated here to allow greater control over the placement of LES and RANS regions and the transitions between them. The concept of model invariance is introduced, which provides a basis for interpreting hybrid results within an LES-RANS transition zone. Consequences of imposing model invariance include the addition of terms to the governing equations that compensate for unphysical gradients created as the model changes between RANS and LES. Computational results illustrate the increased accuracy of the approach and its insensitivity to the location of the transition and to the blending function employed.

Woodruff, Stephen L.↗

TPSAS-NF1676L-31185-DND

Accurate predictive modeling of EPA-defined criteria pollutants in transition zones such as the land/water interface has proven challenging due to differing emission sources, meteorology, and environmental conditions (e.g. temperature, humidity). Chemical species that are “trapped" over water may contribute to exceedence events over land due to land/sea breeze events. The Ozone Water-Land Environmental Transition Study (OWLETS) during the 2017 summer was initiated to study how ozone and ozone precursor concentrations differ over two proximate sites (separated by 20 km). One site (NASA's Langley Research Center) is a land-based site, with the second site being located on the third island of the Chesapeake Bay Bridge Tunnel, approximately 14 km offshore. Both sites had ozone lidars from the Tropospheric Ozone Lidar NETwork(TOLNET) for continuous profiling of the boundary layer and lower-tropospheric ozone and sounding capabilities for profiling the atmosphere up to 35 km. Coincident sonde launches were conducted from both sites to allow intercomparison of ozone mixing ratios and temperature/humidity. Preliminary results regarding ozone gradients are presented herein.

E Gargulinski↗

Flare parameters for the 7 September, 1973 two-ribbon flare

A study is made of the relative importance of the various energy loss mechanisms for the long-decay event of September 7, 1973, using spectral scans in the 400 A-1335 A range. This spectral range contains many of the important electron density and temperature diagnostic line ratios for the solar transition zone. Earlier analyses of the flare energy budget are refined, using more detailed emission measure curves and density diagnostics. The constant pressure assumptions used in both coronal loop models and in the interpretation of observations in terms of flare energetics are examined. It is found that much of the upper transition region emission originates in cooling loops. Radiative losses are found to dominate.

Doyle, J. G.↗

Production of hydrogen peroxide in an intra-meander hyporheic zone at East River, Colorado.

The traditionally held assumption that photo-dependent processes are the predominant source of H 2 O 2 in natural waters has been recently questioned by an increasing body of evidence showing the ubiquitiousness of H 2 O 2 in dark water bodies and in groundwater. In this study, we conducted field measurement of H 2 O 2 in an intra-meander hyporheic zone and in surface water at East River, CO. On-site detection using a sensitive chemiluminescence method suggests H 2 O 2 concentrations in groundwater ranging from 6 nM (at the most reduced region) to ~ 80 nM (in a locally oxygen-rich area) along the intra-meander transect with a maxima of 186 nM detected in the surface water in an early afternoon, lagging the maximum solar irradiance by ~1.5 h. Our results suggest that the dark profile of H 2 O 2 in the hyporheic zone is closely correlated to local redox gradients, indicating that interactions between various redox sensitive elements could play an essential role. Due to its transient nature, the widespread presence of H 2 O 2 in the hyporheic zone indicates the existence of a sustained balance between H 2 O 2 production and consumption, which potentially involves a relatively rapid succession of various biogeochemically important processes (such as organic matter turnover, metal cycling and contaminant mobilization). More importantly, this study confirmed the occurrence of reactive oxygen species at a subsurface redox transition zone and further support our understanding of redox boundaries on reactive oxygen species generation and as key locations of biogeochemical activity.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

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↗

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↗

Heating the sun's lower transition region with fine-scale electric currents

Analytical and observational data are presented to show that the lower transition zone, a 100 km thick region at 10,000-200,000 K between the solar chromosphere and corona, is heated by local electric currents. The study was spurred by correlations between the enhanced atmospheric heating and magnetospheric flux in the chromospheric network and active regions. Field aligned current heated flux loops are asserted to mainly reside in and make up most of the transition region. It is shown that thermal conduction from the sides of hot gas columns generated by the current dissipation is the source of the observed temperature distribution in the transition regions.

Rabin, D.↗