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DOE OSTI2024

ToF-SIMS spectral analysis of Shewanella oneidensis MR-1 biofilms

Analysis of bacterial biofilms is particularly challenging and important with diverse applications from systems biology to biotechnology. Among the variety of techniques that have been applied, time-of-flight secondary ion mass spectrometry (ToF-SIMS) has many powerful features in studying the surface characteristics of biofilms. ToF-SIMS offers high spatial resolution, mass resolution, and mass accuracy, which permit surface sensitive analysis of biofilm components. Thus, ToF-SIMS provides a powerful solution to addressing the challenge of bacterial biofilm analysis. This dataset covers ToF-SIMS analysis of Shewanella oneidensis MR-1 isolated from freshwater lake sediment in New York state. The MR-1 strain is known to have metal and sulfur reducing properties and it can be used for bioremediation and wastewater treatment. There is a current need to identify small molecules and fragments produced from bacterial biofilms, especially those from extracellular polymeric substance (EPS). Static ToF-SIMS spectra of MR-1 were obtained using an IONTOF TOF.SIMS V instrument equipped with a 25 keV Bi$^+_3$ metal ion gun. Identified molecules and molecular fragments are compared against known biological databases and the reported peaks have at least 65 ppm mass accuracy. These molecules range from lipids, fatty acids, flavonoids, and quinolones to other naturally occurring organic compounds. It is anticipated that the mass spectral identification of key peaks will assist detection of metabolites, EPS molecules like polysaccharides, and biologically relevant small organic molecules using ToF-SIMS in future surface and interface research.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

The use of a digital micromirror array as a temporal gate and spatial-filtering device for laser-induced breakdown spectroscopy and laser ablation molecular isotopic spectrometry

A digital micromirror array (DMMA) is used in a simple and inexpensive approach for spatially resolved temporal gating of atomic emission detection in laser-induced breakdown spectroscopy (LIBS). Selected mirrors in the array are actuated at a time delayed from the primary laser pulse, permitting optical gating with a response time of 160 ns while using a conventional CCD detector. Detector gating is shown to decrease noise from short-lived spectroscopic background (both continuum and N II from air), improving signal-to-background ratios by 22-times for selected samples and emission lines. The utility of rapid temporal gating is also demonstrated for the optical detection of isotopes using the laser-ablation molecular isotope spectrometry (LAMIS) experiment. Additionally, optical temporal gating and spatial filtering are used to isolate regions of the laser-induced plasma, enhancing signal from molecular emission. The potential of the simple technique for use in field-portable LIBS and LAMIS experiments is explored.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Removal, distribution and retention of metals in a constructed wetland over 20 years

The A-01 wetland treatment system (WTS) was designed to remove metals (primarily copper) from the effluent at the A-01 National Pollution Discharge Elimination System (NPDES) outfall at the Savannah River Site, Aiken, SC. This research investigated metal removal, distribution and retention in the A-01 WTS over a period of 20 years. The findings are important for ensuring continued metal sequestration in the A-01 WTSs over time, providing management guidance for constructed wetlands, and investigating changes in metal remediation effectiveness as a wetland ages. During 20 years of operation, systematic water and sediment sampling validated the wetlands' performance. After passage through the treatment cells, Cu concentrations were well below permit limits during all years of operation, often falling below 10 μg L -1 . Cu removal has been consistent over time, averaging about 80% despite large changes in influent Cu concentrations. Most divalent metals were rapidly removed from the water and held in the sediments shortly after the water entered the treatment wetland. Average removal of Pb from water by the wetland system was 67 and 74% in 2004 and 2020, respectively. Comparable values for Zn were 52 and 65%, respectively. Generally, the highest concentrations of Cu, Pb, and Zn were found in the sediment from the first cell in each pair of cells suggesting that most of the Cu, Pb, and Zn in the A-01 effluent was bound to the sediment quickly. Diffusive gradients in thin films (DGT) measurements of Cu and Zn in the sediments were much lower than bulk sediment concentrations. These results suggest that most of the Cu and Zn in the A-01 WTS sediments was not bioavailable, hence not toxic to aquatic organisms, as a likely consequence of adsorption to sediment particles and complexation with organic and inorganic substances.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Fragmentation of the edge of a terminated Cu nanolayer within a Nb matrix upon annealing

Here, we investigate the evolution of the tip of a terminated Cu nano-layer embedded within a Nb matrix upon annealing at 800°C. The tip of the terminated Cu layer fragments progressively into a series of single-crystal Cu particles upon continued annealing. This finding shows that layer fragmentation is the second step, after layer pinchoff, in the thermal coarsening of nanolayered metal composites. Comparison to prior phase-field modeling permits us to infer that the mobility at 800°C of Cu-Nb, as modeled by the Cahn-Hillard equation, is M(c)=(M 0 = 7.3 ± 3.6 nm 5 / s • eV) |1 – c 2 |, where the order parameter, c, is 1 for Cu and -1 for Nb.

36 MATERIALS SCIENCE↗

DOE OSTI2020

An approach for broad molecular imaging of the root-soil interface via indirect matrix-assisted laser desorption/ionization mass spectrometry

Understanding of rhizospheric processes is limited by the need for imaging complex molecular transformations at relevant spatial scales within the root soil continuum. In this work, we demonstrate a method to enable this analysis by first extracting organic compounds from the rhizosphere onto a PVDF membrane while maintaining their 2D distribution. We then image the distribution of chemical compounds using matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS). This approach permitted us to visualize and identify compounds on the root surface and presumed root exudates in the rhizosphere. Within a 1.8 cm x 0.6 cm sampling area of a switchgrass rhizosphere, we could observe at least four chemically distinct zones. Using high performance Fourier transform ion cyclotron MS, we were able to accurately annotate numerous molecules co-localized to each of these zones.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Sputter-deposited CdMgTe for rear contact to CdSeTe/CdTe solar cells

CdTe-based photovoltaic device performance improvement is predominantly limited by open-circuit voltage. This work approaches the voltage deficit challenge through the incorporation of a cadmium magnesium telluride (CdMgTe) electron reflector layer at the back of 1.5- μm CdSeTe/CdTe absorbers to reduce back-surface recombination through a conduction band offset. A sputtered CdMgTe electron reflector layer permitted low fabrication temperatures and circumvented the intolerance of CdMgTe to thermal processing present in traditional close-space sublimation (CSS)-deposited CdMgTe devices. Here, we demonstrate that sputtered CdMgTe simultaneously promotes the retention of chlorine passivation and magnesium which is not feasible with CSS fabrication. We also show the importance of the Cu and Te back contact order in CdMgTe devices. Through the optimization of the sputtered CdMgTe substrate temperature, doping, and back structure configuration, 1.5 μm CdSeTe/CdTe devices with a sputtered CdMgTe layer achieved an efficiency of 16.0%, significantly higher than with CSS CdMgTe, and demonstrated partial enactment of electron-reflector behavior.

14 SOLAR ENERGY↗

DOE OSTI2026

Cryo-electron microscopy structure of a zinc uptake ABC transporter

Zn2+ is an essential micronutrient required for many biological processes. Microorganisms employ high-affinity Zn2+ ABC transporters to take up zinc from the environment when it is scarce, yet the mechanism of zinc uptake and its regulation remain poorly understood. Here, we report the cryo-electron microscopy structure of the Zn2+ ABC transporter complex ZnuB-ZnuC from Escherichia coli. It contains two ZnuB transport and two ZnuC regulatory subunits. The ZnuB homodimer is in an outward-facing, closed conformation with a large hydrophilic cavity at the dimer interface. Each ZnuC subunit contains an N-terminal nucleotide-binding domain and a C-terminal zinc-sensing domain (ZSD). Zn2+ binding to the ZSD locks the transporter in a closed state, whereas under low-Zn2+ conditions, the disorder of ZSD permits ATP-driven zinc uptake. Zn2+ ABC transporters are ubiquitously utilized by pathogenic bacteria to compete with hosts for Zn2+. These findings reveal potential therapeutic targets for disrupting Zn2+ homeostasis in antibiotic-resistant pathogens.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

A Markov framework for generalized post-event systems recovery modeling: From single to multihazards

State-dependent models can be used to represent the system recovery process as a series of stochastic transitions from lower to higher functional states. However, the applications of these models have been limited in scope and there is a lack of a generalized recovery modeling framework. A generalized framework would permit a robust forecasting of systems and system-of-systems recovery under multiple hazards, and more broadly, would contribute to community disaster preparedness. This paper develops a generalized post hazard-event recovery modeling framework based on state-dependent Markov-type processes. We then apply the proposed framework to solve a spectrum of problems that range from hind-casting single-system recovery following a single hazard event to forecasting post-event trajectories under multiple hazards and modeling the recovery of a system-of-systems. First, Markov chains are used to hind-cast the observed recovery for a portfolio of buildings affected by the 2014 South Napa, California, earthquake. Next, Markov processes are used to formulate a parametric post hazard-event recovery model, which can be updated using Bayesian statistics when relevant datasets become available. Semi-Markov processes are then used to develop a more general model of single hazard recovery, which accounts for the intensity of the loading and level of damage caused by the event. Semi-Markov processes with non-renewal features are then used to account for multihazard interactions in a post-event recovery model, and applied to a case study that involves a community in Charleston, South Carolina. Lastly, Markov-type processes are combined with Bayesian networks to model the recovery of residential, commercial, educational, and industrial buildings (system-of-systems) following a hazard event. Overall, these applications demonstrate the versatility of the Markov framework towards handling recovery problems with varying levels of complexity.

42 ENGINEERING↗

DOE OSTI2025

Tomographic assessment of peening for metallurgical bonding in cold spray

It is widely asserted that peening densifies cold spray coatings and improves particle–particle and particle–substrate bonding, yet systematic studies analyzing the evolution of bonding due to peening particle strikes are scarce. We explore peening at the level of individual particle impacts, by creating two-particle Cu-on-Cu stacks using laser-induced particle impact testing. Exploring impact velocities that range from the onset of bonding at the “critical velocity”, V cr , to its peak near 1.4⋅V cr , we perform full 3D tomography of the particle stacks to characterize the bonding state at the particle-substrate interface. Direct labeling of non-bonded patches and the total particle-substrate interface permits quantification and comparison of bonding in single impacts with bonding after subsequent impacts to reveal the origins of the peening effect. The data reveal a surprising finding: although a second impact directly atop the first particle increases the area of the particle-substrate interface (~40% area increase), there is no improvement in metallurgical bonding. Analysis of these data suggest that not only area expansion (and associated oxide rarefication), but also stress-induced extrusion of metal at that interface needs to occur to achieve metal-on-metal contact to see an enhancement in bonding. Furthermore, our analysis suggests that the subsequent impacting particle needs to have ~70% more kinetic energy to produce additional bonding; this implies that particle and velocity distributions within a spray may be helpful, and that peening may rely on unaligned impacts.

Bonding↗

DOE OSTI2020

Challenges in the post-licensing stage of U.S. hydropower development: Current status and some potential solutions

The issuance of a Federal Energy Regulatory Commission (FERC) license is an important milestone in the development process of new U.S. hydropower projects. The complexity and uncertain timeline of the licensing process have been often cited as a key deterrent to new hydropower installations in the United States. However, very little attention has been paid to post-licensing timelines and attrition rates. This article explores the challenges faced by developers in bringing their FERC-licensed hydropower projects to the construction stage. Post-licensing activities to be completed before starting construction include obtaining additional permitting from other federal or state agencies, completing the technical design, securing financing, and in most cases, negotiating a power purchase agreement. For the set of projects that obtained a FERC license between 2007 and 2018, we assembled a dataset—combining information from FERC dockets and responses from a questionnaire to developers—to calculate attrition rates and development timelines and to examine the reasons for delays and cancellations.

13 HYDRO ENERGY↗

DOE OSTI2022

Future changes in extreme precipitation over the San Francisco Bay Area: Dependence on atmospheric river and extratropical cyclone events

Extreme precipitation poses a major challenge for local governments, including the City and County of San Francisco, California, as flooding can damage and destroy infrastructure and property. As the climate continues to warm, reliable future precipitation projections are needed to provide the best possible information to decision makers. However, future changes in the magnitude of extreme precipitation are uncertain, as current state-of-the-art global climate models are typically run at relatively coarse horizontal resolutions that require the use of convective parameterization and have difficulty simulating observed extreme rainfall rates. Here, we performed ensembles of convection-permitting regional climate model simulations to investigate how five historically impactful extreme precipitation events over the San Francisco Bay Area could change if similar events occurred in future climates. We found that changes in storm-total precipitation depend strongly on storm type. Precipitation associated with an atmospheric river (AR) accompanied by an extratropical cyclone (ETC) is projected to increase at a rate exceeding (by up to 1.5 times) the theoretical Clausius Clapeyron scaling of 6–7% per °C warming. On the other hand, future precipitation changes are weak or negative for events characterized by an AR only, despite increases in precipitable water and integrated vapor transport that are similar to those of the co-occurring AR and ETC events. The differences in the sign of future precipitation change between AR-only events and co-occurring AR and ETC events is instead linked with changes in mid-tropospheric vertical velocity. Given that the majority of observed ARs are associated with an ETC, this research has important implications for future precipitation impacts over the Bay Area, as it indicates that storm-total precipitation associated with the most common type of storm event may increase by up to 26–37% in 2100 relative to historical.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Community structure and function during periods of high performance and system upset in a full-scale mixed microalgal wastewater resource recovery facility

Microalgae have the potential to exceed current nutrient recovery limits from wastewater, enabling water resource recovery facilities (WRRFs) to achieve increasingly stringent effluent permits. The use of photobioreactors (PBRs) and the separation of hydraulic retention and solids residence time (HRT/SRT) further enables increased biomass in a reduced physical footprint while allowing operational parameters (e.g., SRT) to select for desired functional communities. However, as algal technology transitions to full-scale, there is a need to understand the effect of operational and environmental parameters on complex microbial dynamics among mixotrophic microalgae, bacterial groups, and pests (i.e., grazers and pathogens) and to implement robust process controls for stable long-term performance. Here, we examine a full-scale, intensive WRRF utilizing mixed microalgae for tertiary treatment in the US (EcoRecover, Clearas Water Recovery Inc.) during a nine-month monitoring campaign. We investigated the temporal variations in microbial community structure (18S and 16S rRNA genes), which revealed that stable system performance of the EcoRecover system was marked by a low-diversity microalgal community (D INVSIMPSON = 2.01) dominated by Scenedesmus sp. (MRA = 55 %-80 %) that achieved strict nutrient removal (effluent TP < 0.04 mg·L -1 ) and steady biomass concentration (TSS monthly avg . = 400–700 mg·L −1 ). Operational variables including pH, alkalinity, and influent ammonium (NH 4 + ), correlated positively (p < 0.05, method = Spearman) with algal community during stable performance. Further, the use of these parameters as operational controls along with N/P loading and SRT allowed for system recovery following upset events. Importantly, the presence or absence of bacterial nitrification did not directly impact algal system performance and overall nutrient recovery, but partial nitrification (potentially resulting from NO 2 − accumulation) inhibited algal growth and should be considered during long-term operation. The microalgal communities were also adversely affected by zooplankton grazers (ciliates, rotifers) and fungal parasites (Aphelidium), particularly during periods of upset when algal cultures were experiencing culture turnover or stress conditions (e.g., nitrogen limitation, elevated temperature). Altogether, the active management of system operation in order to maintain healthy algal cultures and high biomass productivity can result in significant periods (>4 months) of stable system performance that achieve robust nutrient recovery, even in winter months in northern latitudes (WI, USA).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Techno-economic assessment of distributed wellhead RO water treatment for nitrate removal and salinity reduction: A field study in small disadvantaged communities

Techno-economic analysis of distributed wellhead water treatment and desalination (DWTD) systems was carried out based on a three-year field study in three small, disadvantaged communities (DACs) to evaluate the reliability and affordability of upgrading their impaired well water. The local water supplies of the three study DACs, located in Salinas Valley, California, were contaminated with nitrate at levels (~ 12–87 mg/L NO$^{-}_{3}$ - N) ) above the California maximum contaminant level (MCL) of 10 mg/L NO$^{-}_{3}$ - N , and had elevated water salinity (~600–1,600 mg/L total dissolved solids(TDS)) above its secondary MCL (SMCL) of 500 mg/L TDS. Well water nitrate removal and salinity reduction were accomplished via reverse osmosis (RO) based DWTD systems that operated autonomously, supported by remote monitoring and supervisory cyberinfrastructure. Reliable DWTD operation provided treated water quality, with respect to nitrate and salinity, in the range of 0.5–6.3 mg/L NO$^{-}_{3}$ - N and 57–161 mg/L TDS, respectively, which were well below the respective MCL and SMCL. The levelized cost of water treatment was in the range of ~$$2/m 3 - $$2.9/m 3 which aligns with typical residential water costs in California and in the study region, and monthly residential water costs (39 dollars-74 dollars/residential unit/month) were also within the range in California. The study showcased the DWTD approach as a viable and potentially scalable solution for upgrading impaired local potable water supply of communities lacking centralized water delivery infrastructure. However, streamlined permitting processes and standardized regulatory frameworks are critical to promoting wider adoption and maximizing the socio-economic benefits of the DWT approach. Moreover, DACs are likely to require government subsidies in order to cover the CapEx of DWTD systems in addition to upgrade of site infrastructure.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Carrier gradients and the role of charge selective contacts in lateral heterojunction all back contact perovskite solar cells

Realizing photovoltaic devices that achieve the full potential of the metal halide perovskite material will require improved insight regarding the role of selective contacts and how key interfaces operate when mobile defects are present. However, measuring interface properties in typical device stacks where the perovskite layer is thin and sandwiched between two contacts has been a challenge. Here, we fabricate p-i-n and p-n lateral heterojunctions with nickel oxide/titanium oxide all back contacts, permitting us to employ a comprehensive analysis approach, including ultraviolet and X-ray photoemission spectroscopy (UPS/XPS), angle-resolved X-ray absorption spectroscopy (XAS), Kelvin probe force microscopy (KPFM), surface photovoltage (SPV), hyperspectral imaging (HSI), and time-resolved fluorescence lifetime imaging microscopy (TR-FLIM) to discern the role of selective contacts. Specifically, we tune the selectivity of the contacts, changing the gradient in the carrier concentration across the surface of the active layer, which is connected to carrier extraction at the buried interface, and thus the device functionality.

25 ENERGY STORAGE↗

DOE OSTI2023

Phase imaging of irradiated foils at the OMEGA EP facility using phase-stepping X-ray Talbot–Lau deflectometry

Abstract Diagnosing the evolution of laser-generated high energy density (HED) systems is fundamental to develop a correct understanding of the behavior of matter under extreme conditions. Talbot–Lau interferometry constitutes a promising tool, since it permits simultaneous single-shot X-ray radiography and phase-contrast imaging of dense plasmas. We present the results of an experiment at OMEGA EP that aims to probe the ablation front of a laser-irradiated foil using a Talbot–Lau X-ray interferometer. A polystyrene (CH) foil was irradiated by a laser of 133 J, 1 ns and probed with 8 keV laser-produced backlighter radiation from Cu foils driven by a short-pulse laser (153 J, 11 ps). The ablation front interferograms were processed in combination with a set of reference images obtained ex situ using phase-stepping. We managed to obtain attenuation and phase-shift images of a laser-irradiated foil for electron densities above ${10}^{22}\;{\mathrm{cm}}^{-3}$ . These results showcase the capabilities of Talbot–Lau X-ray diagnostic methods to diagnose HED laser-generated plasmas through high-resolution imaging.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Implications of inertial subrange scaling for stably stratified mixing

In this work, we investigate the effects of the turbulent dynamic range on active scalar mixing in stably stratified turbulence by adapting the theoretical passive scalar modelling and demonstrating their usefulness through consideration of the results of direct numerical simulations of statistically stationary homogeneous stratified and sheared turbulence. By analysis of inertial and inertial–convective subrange scalings, we show that the relationship between the active scalar and turbulence time scales is predicted by the ratio of the Kolmogorov and Obukhov–Corrsin constants, provided mean flow parameters permit the two subrange scalings to be appropriate approximations. We use the resulting relationship between time scales to parameterise an appropriate turbulent mixing coefficient $\varGamma \equiv \chi /\epsilon$, defined here as the ratio of available potential energy ($E_p$) and turbulent kinetic energy ($E_k$) dissipation rates. With the analysis presented here, we show that $\varGamma$ can be estimated by $E_p,E_k$ and a universal constant provided an appropriate Reynolds number is sufficiently high. This large Reynolds number regime appears here to occur at $ {{Re_b}} \equiv \epsilon / \nu N^{2} \gtrapprox 300$ where $\nu$ is the kinematic viscosity and $N$ is the characteristic buoyancy frequency. We propose a model framework for irreversible diapycnal mixing with robust theoretical parametrisation and asymptotic behaviour in this high-$ {{Re_b}}$ limit.

42 ENGINEERING↗

DOE OSTI2024

Discussion: Presentation of Atmospheric 14 C O2 data

ABSTRACT Observations of radiocarbon ( 14 C) in Earth’s atmosphere and other carbon reservoirs are important to quantify exchanges of CO 2 between reservoirs. The amount of 14 C is commonly reported in the so-called Delta notation, i.e., Δ 14 C, the decay- and fractionation-corrected departure of the ratio of 14 C to total C from that ratio in an absolute international standard; this Delta notation permits direct comparison of 14 C/C ratios in the several reservoirs. However, as Δ 14 C of atmospheric CO 2 , Δ 14 CO 2 is based on the ratio of 14 CO 2 to total atmospheric CO 2 , its value can and does change not just because of change in the amount of atmospheric 14 CO 2 but also because of change in the amount of total atmospheric CO 2 , complicating ascription of change in Δ 14 CO 2 to change in one or the other quantity. Here we suggest that presentation of atmospheric 14 CO 2 amount as mole fraction relative to dry air (moles of 14 CO 2 per moles of dry air in Earth’s atmosphere), or as moles or molecules of 14 CO 2 in Earth’s atmosphere, all readily calculated from Δ 14 CO 2 and the amount of atmospheric CO 2 (with slight dependence on δ 13 CO 2 ), complements presentation only as Δ 14 CO 2 , and can provide valuable insight into the evolving budget and distribution of atmospheric 14 CO 2 .

Geochemistry & Geophysics↗

DOE OSTI2020

Collisional effects on resonant particles in quasilinear theory

A careful examination of the effects of collisions on resonant wave–particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel & Engelmann ( Phys. Fluids , vol. 9, 1966, pp. 2377–2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that scatter them out of and into resonance, as for Landau damping as shown by Johnston ( Phys. Fluids , vol. 14, 1971, pp. 2719–2726) and Auerbach ( Phys. Fluids , vol. 20, 1977, pp. 1836–1844). As a result, the resonant particle–wave interactions occur in the centre of a narrow collisional boundary when the collision frequency $\unicode[STIX]{x1D708}$ is very small compared to the wave frequency $\unicode[STIX]{x1D714}$ . The diffusive nature of the pitch angle scattering combined with the wave–particle resonance condition enhances the collision frequency by $(\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708})^{2/3}\gg 1$ , resulting in an effective resonant particle collisional interaction time of $\unicode[STIX]{x1D70F}_{\text{int}}\sim (\unicode[STIX]{x1D708}/\unicode[STIX]{x1D714})^{2/3}/\unicode[STIX]{x1D708}\ll 1/\unicode[STIX]{x1D708}$ . A collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel–Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.

Physics↗