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Compositional analysis of projectile residues on LDEF instrument AO187-1

Impact craters greater than 30 microns and associated projectile residues were analyzed by Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Analysis (EDXA). Objectives were to analyze a statistically significant number of projectiles to evaluate their chemical variability and possible clustering into discrete particle types. Bay A11 exposed six collector surfaces of anodized 1100-T4 (greater than 99 percent pure) aluminum sheets, 0.32 cm thick, yielding an exposed surface area of 1.1 sq. m. Four of the six panels have been retained at JSC, and were optically scanned, one (A11E00E) was prepared for SEM/EDX analysis. Bay A03 was occupied by high purity (99.99 percent) gold sheets, 0.5 mm thick, yielding an exposed surface area of 0.85 sq. m. Sample processing included the optical scanning (6X), labeling, and dislodging (by a punch-die device) of each individual impact greater than 75 microns for the aluminum and 30 microns for the gold. The 209 craters were dislodged form A11E00E, having crater diameters up to 3500 microns. Optical examination of the gold surfaces detected 238 craters, 198 of which were retained at JSC and analyzed via SEM/EDX. The analytical procedures included maximizing the geometric efficiency (take-off angles), using relatively long count times (500-1000 sec) and sufficiently high accelerating currents (25-30Kev). Despite diligent examination, a large number of craters did not exhibit measurable signals above background. Detectable resides were classified as either micrometeoritic or as man-made debris.

Bernhard, Ronald P.↗

Erosion rate diagnostics in ion thrusters using laser-induced fluorescence

We have used laser-induced fluorescence (LIF) to monitor the charge-exchange ion erosion of the molybdenum accelerator electrode in ion thrusters. This real-time, nonintrusive method was implemented by operating a 30cm-diam ring-cusp thruster using xenon propellant. With the thruster operating at a total power of 5 kW, laser radiation at a wavelength of 390 nm (corresponding to a ground state atomic transition of molybdenum) was directed through the extracted ion beam adjacent to the downstream surface of the molybdenum accelerator electrode. Molybdenum atoms, sputtered from this surface as a result of charge-exchange ion erosion, were excited by the laser radiation. The intensity of the laser-induced fluorescence radiation, which is proportional to the sputter rate of the molybdenum atoms, was measured and correlated with variations in thruster operating conditions such as accelerator electrode voltage, accelerator electrode current, and test facility background pressure. We also demonstrated that the LIF technique has sufficient sensitivity and spatial resolution to evaluate accelerator electrode lifetime in ground-based test facilities.

Gaeta, C. J.↗

Rapid Ice Mass Loss: Does It Have an Influence on Earthquake Occurrence in Southern Alaska?

The glaciers of southern Alaska are extensive, and many of them have undergone gigatons of ice wastage on time scales on the order of the seismic cycle. Since the ice loss occurs directly above a shallow main thrust zone associated with subduction of the Pacific-Yakutat plate beneath continental Alaska, the region between the Malaspina and Bering Glaciers is an excellent test site for evaluating the importance of recent ice wastage on earthquake faulting potential. We demonstrate the influence of cumulative glacial mass loss following the 1899 Yakataga earthquake (M=8.1) by using a two dimensional finite element model with a simple representation of ice fluctuations to calculate the incremental stresses and change in the fault stability margin (FSM) along the main thrust zone (MTZ) and on the surface. Along the MTZ, our results indicate a decrease in FSM between 1899 and the 1979 St. Elias earthquake (M=7.4) of 0.2 - 1.2 MPa over an 80 km region between the coast and the 1979 aftershock zone; at the surface, the estimated FSM was larger but more localized to the lower reaches of glacial ablation zones. The ice-induced stresses were large enough, in theory, to promote the occurrence of shallow thrust earthquakes. To empirically test the influence of short-term ice fluctuations on fault stability, we compared the seismic rate from a reference background time period (1988-1992) against other time periods (1993-2006) with variable ice or tectonic change characteristics. We found that the frequency of small tectonic events in the Icy Bay region increased in 2002-2006 relative to the background seismic rate. We hypothesize that this was due to a significant increase in the rate of ice wastage in 2002-2006 instead of the M=7.9, 2002 Denali earthquake, located more than 100km away.

Sauber, Jeanne M.↗

Effects of Forcing Differences and Initial Conditions on Inter-Model Agreement in the VolMIP Volc-Pinatubo-Full Experiment

This paper provides initial results from a multi-model ensemble analysis based on the volc-pinatubo-full experiment performed within the Model Intercomparison Project on the climatic response to Volcanic forcing (VolMIP) as part of the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The volc-pinatubo-full experiment is based on an ensemble of volcanic forcing-only climate simulations with the same volcanic aerosol dataset across the participating models (the 1991–1993 Pinatubo period from the CMIP6-GloSSAC dataset). The simulations are conducted within an idealized experimental design where initial states are sampled consistently across models from the CMIP6-piControl simulation providing unperturbed preindustrial background conditions. The multi-model ensemble includes output from an initial set of six participating Earth system models (CanESM5, GISS-E2.1-G, IPSL-CM6A-LR, MIROC-E2SL, MPI-ESM1.2-LR and UKESM1). The results show overall good agreement between the different models on the global and hemispheric scales concerning the surface climate responses, thus demonstrating the overall effectiveness of VolMIP's experimental design. However, small yet significant inter-model discrepancies are found in radiative fluxes, especially in the tropics, that preliminary analyses link with minor differences in forcing implementation; model physics, notably aerosol–radiation interactions; the simulation and sampling of El Niño–Southern Oscillation (ENSO); and, possibly, the simulation of climate feedbacks operating in the tropics. We discuss the volc-pinatubo-full protocol and highlight the advantages of volcanic forcing experiments defined within a carefully designed protocol with respect to emerging modelling approaches based on large ensemble transient simulations. We identify how the VolMIP strategy could be improved in future phases of the initiative to ensure a cleaner sampling protocol with greater focus on the evolving state of ENSO in the pre-eruption period.

metadata↗

Comparison of chemical lateral boundary conditions for air quality predictions over the contiguous United States during pollutant intrusion events

The National Air Quality Forecast Capability (NAQFC) operated in U.S.’s National Oceanic and Atmospheric Administration (NOAA) provides the operational forecast guidance for ozone and fine particulate matters with aerodynamic diameters less than 2.5μm (PM2.5) over the contiguous 48 U.S. states (CONUS) using the Community Multi-scale Air Quality (CMAQ) model. The existing NAQFC uses climatological chemical lateral boundary conditions ( CLBCs), which cannot capture pollutant intrusion events originating outside of the model domain. In this study, we developed a model framework to use dynamic CLBCs from the Goddard Earth Observing System Model, version 5 (GEOS) to drive NAQFC. A mapping of the GEOS chemical species to the CMAQ’s Carbon Bond 5 (CB05)-Aero6 species was developed. The utilization of the GEOS dynamic CLBCs in NAQFC showed the best overall performance in simulating the surface observations during the Saharan dust intrusion and Canadian wildfire events in summer 2015.The simulated PM2.5 was improved from 0.18 to 0.37 and the mean bias was reduced from -6.74 μg/m3 to -2.96 μg/m3 over CONUS. Although the effect of CLBCs on the PM2.5 correlation was mainly near the inflow boundary, its impact on the background concentrations reached further inside the domain. The CLBCs could affect background ozone concentrations through the inflows of ozone itself and its precursors, such as CO. It was further found that the aerosol optical thickness (AOT) from satellite retrievals correlated well with the column CO and elemental carbon from GEOS. The satellite-derived AOT CLBCs generally improved the model performance for the wildfire intrusion events during a summer 2018 case study, and demonstrated how satellite observations of atmospheric composition could be used as an alternative method to capture the air quality effects of intrusions when the global model CLBCs, such as GEOS CLBCs, are not available.

Community Multi-scale Air Quality (CMAQ) model↗

Asteroid (142) Polana at 3 µM and Its Linkage to the Primitive Asteroid (101955) Bennu

The Polana family is a low-albedo family located at a low inclination and a semimajor axis of ~2.42 au in the inner main asteroid belt. This family is likely the source of primitive near-Earth asteroids, including the OSIRIS-REx mission target (101955) Bennu. The B-type asteroid 142 Polana is the largest remnant of the "New Polana" family, and it has been spectrally (~0.5-2.5 µm) and dynamically linked to Bennu. Here, we investigate the compositional linkage of asteroids Polana and Bennu using spectra measured at longer wavelengths (~1.6-4.0 µm), which cover the 3- µm band. Polana’s spectra were measured at NASA IRTF using the LXD mode of SpeX. Bennu’s spectra were measured by OSIRIS-REx’s OVIRS spectrometer and revealed that this primitive asteroid is hydrated consistent with CM, CI, or CR carbonaceous chondrites. Polana’s LXD spectra, on the hand, show that the parent body of the Polana family is not hydrated (i.e., no absorption band at ~ 3.0 µm). Additionally, Polana’s LXD spectra do not indicate the presence of organics and/or carbonates. Polana's lack of significant water, organic, and carbonate spectral features on its surface could be related to the degree of heating in the Polana family-forming event and the reaccretion of ejecta that contributed to additional heating. The Polana family-forming event could also expose the parent body's dehydrated, organic/carbonate-poor interior. These results will be placed in the context of other low-albedo families and background objects in the inner main belt. An approved JWST program to observe Polana (with both NIRSpec and MIRI) will be able to assess if there is a Ryugu-like band and should allow a comparison of the MIR spectrum to Bennu.

Driss Takir↗

Reducing uncertainty of polar to midlatitude linkages using DOE’s E3SM in a coordinated model-experiment setting

This project brought DOE’s climate modeling effort with the Energy Exascale Earth System Model into the Polar Amplification Model Intercomparison Project (PAMIP), which is part of the sixth and latest Coupled Model Intercomparison Project, CMIP6. PAMIP examines the causes and consequences of polar amplification, when external forcing results in a larger temperature increase in high latitudes than the global average, in a coordinated set of model experiments with a common modeling protocol. Our teams from UC Irvine and the University of Toronto have designed, carried out, analyzed, and disseminated PAMIP output from the Energy Exascale Earth System Model (E3SM) and the Community Earth System Model (CESM). PAMIP’s ongoing stream of significant new results have advanced progress in the community’s understanding and led to new outstanding research questions that have motivated further work. PAMIP has led to improved consensus on the atmospheric response to sea ice loss. The important finding is that for a similar sea ice anomaly forcing, the simulated atmospheric response in the troposphere is remarkably consistent among the 16 models’ runs analyzed. The zonal-mean tropospheric response consists of a very robust equatorward shift of the westerly flow in mid-latitudes. However, while the multi-model mean response is robust, it has a weak amplitude relative to internal variability. We identified a weakness in the models (including E3SM) in terms of their response to sea-ice forcing that is related to eddy forcing (or nonlinear dynamical effects) at mid- to high latitudes. In fact, E3SM is an outlier in terms of the models participating, and in that sense, it turned out to be a vital participant model. We found that reductions in energy transport due sea-ice loss and involving dry air only are compensated by increases in moist energy transport from warmer sea surface temperature in midlatitudes. This leads to a large spread in energy transport into the Arctic and is a potential source of spread in Arctic amplification. We identified an important role that climate modes, including tropical modes of variability (El Nino and the Southern Oscillation (ENSO); the Quasi-biennial Oscillation (QBO)) play in the response to sea-ice anomalies, including in ocean coupled experiments. Similarly, we identified and quantified the contribution of sea-ice thickness to the atmospheric response compared to the response to sea-ice extent only. We found that it is important to run large ensembles and even with an ensemble size of 100 simulations the response is largely influenced by internal variability. We demonstrated convincingly that Ural blocking, not sea-ice loss, provides the weakening of the stratospheric polar vortex in fall/early winter and a negative phase of the North Atlantic Oscillation that can last for up to two months. However, sea-ice anomalies can influence the background flow so that the response to Ural blocking is more persistent under low sea-ice conditions in the Barents/Kara Sea than high sea ice Atmospheric model hierarchies that progressively add individual processes have a long history in providing dynamical insight for modeling the atmosphere. Similarly, coupled model hierarchies that progressively add individual ocean processes can provide insights into the workings of the coupled climate system, however such hierarchies have not been available except for a non-dynamical slab ocean model. Because of the missing processes, surface flux corrections must be added to produce a target climate. In this project, we managed to overcome this problem and develop a globally coupled ocean model hierarchy in CESM that can turn on and off the processes of mixed-layer entrainment and Ekman flow. We used the hierarchy to study the impact of Arctic sea-ice loss on the climate system. We find that the effect of mixed-layer entrainment on ocean heat uptake influences the atmospheric circulation by shifting the latitudinal positions of the mid-latitude westerly jet and the Intertropical Convergence Zone (ITCZ). In quadrupled CO 2 experiments, we studied how air-sea coupling affects the response of tropical rainfall under global warming. In order to identify the importance of individual ocean processes, we used the hierarchy of ocean models to separate the effects of seasonal mixed-layer entrainment, wind-driven Ekman flows, and frictional flows. We showed that including Ekman and frictional flows allows our simulation to produce the Pacific Ocean's enhanced equatorial warming pattern and equatorward ITCZ contraction noted in previous climate simulations. We also showed that the frictional flow, which has yet to receive much attention, is as important as the Ekman flow in generating equatorial heat convergence.

54 ENVIRONMENTAL SCIENCES↗

Research on Superconducting Magnet in a Superconducting Synchronous Generator

Design and test of superconducting magnet (SM) for a superconducting synchronous generator (SSG) are studied in this paper. First, a suitable superconducting material is selected to make SM by analyzing the characteristics and application background of the five practical superconducting materials, and the applicability and feasibility of the selected superconducting materials are demonstrated. Second, the initial structural parameters of the SM are obtained by finite element method (FEM). In addition, the influence of structural parameters of SM on the performance of SSG is analyzed by simulation. Then, an optimal algorithm combining response surface methodology (RSM) and particle swarm optimization (PSO) is proposed to optimize the structure of SM in order to give full play to the advantages of SM. The simulated results verify that the proposed optimal algorithm is feasible and effective. Finally, the prototype of SM is made by the optimized size, and the SM is tested at a low temperature to obtain the critical temperature and critical current of the SM; the experimental results verify that the designed SM can meet the requirements of SSG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Discovery of 1-(3,3-Dimethylbutyl)-3-(2-fluoro-4-methyl-5-(7-methyl-2-(methylamino)pyrido[2,3- d ]pyrimidin-6-yl)phenyl)urea (LY3009120) as a Pan-RAF Inhibitor with Minimal Paradoxical Activation and Activity against BRAF or RAS Mutant Tumor Cells

The RAS-RAF-MEK-MAPK cascade is an essential signaling pathway, with activation typically mediated through cell surface receptors. The kinase inhibitors vemurafenib and dabrafenib, which target oncogenic BRAF V600E, have demonstrated significant clinical efficacy in melanoma patients harboring this mutation. Because of paradoxical pathway activation, both agents were demonstrated to promote growth and metastasis of tumor cells with RAS mutations in preclinical models and are contraindicated for treatment of cancer patients with BRAF WT background, including patients with KRAS or NRAS mutations. In order to eliminate the issues associated with paradoxical MAPK pathway activation and to provide therapeutic benefit to patients with RAS mutant cancers, we sought to identify a compound not only active against BRAF V600E but also wild type BRAF and CRAF. On the basis of its superior in vitro and in vivo profile, compound 13 was selected for further development and is currently being evaluated in phase I clinical studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Probing unintentional Fe impurity incorporation in MOCVD homoepitaxy GaN: Toward GaN vertical power devices

Unintentional impurity incorporation in GaN drift layers represents a challenging issue that can limit their potential performance in vertical power devices. In this paper, we focus on studying the origins of Fe impurity incorporation in metal-organic chemical vapor deposition (MOCVD) grown GaN materials. Acting as a compensator in n-type GaN drift layers, Fe impurities can reduce the electron mobility in GaN and limit the lowest controllable doping level. Two sources, the sample cleaning process and growth susceptor, were identified as the main mechanisms of Fe incorporation in the MOCVD GaN growth process. It was found that solvent cleaning of the wafer can introduce significant Fe contamination at the growth interface, which would slowly be incorporated into the GaN epilayer, thus causing background Fe impurity as high as 10 17 cm -3 level. Moreover, the Fe impurity in the coating material on the susceptor can introduce additional Fe impurity during the growth process. Our studies revealed that the Fe impurity level could be significantly suppressed by more than two orders when an alternative cleaning process was used and the susceptor surface was fully covered by substrates. Characterization of the Fe impurity concentrations was performed via secondary ion mass spectrometry. The trap level (E C - 0.57) eV from deep-level transient spectroscopy that had previously been attributed to Fe confirmed the carrier compensation effect from Fe. Room temperature Hall mobility as high as 1007 cm 2 /V s was achieved on the MOCVD grown low-Fe GaN. Results from this work will provide guidance for achieving high purity GaN toward high performance GaN vertical power devices.

42 ENGINEERING↗

Metallic wire grid behavior and testing in a low pressure gaseous noble elements detector

High voltage performance has been a challenge for noble element detectors. One piece of this challenge is the emission of electrons from metal electrodes when applying high voltage. This has become a major concern for low-background detectors such as LUX-ZEPLIN (LZ). LZ is a liquid xenon Time Projection Chamber (TPC) searching for Weakly Interactive Massive Particles (WIMPs). In this work, we demonstrate a method to measure electron emission from metallic electrode grids via detection of proportional scintillation light. As a result, we find consistency with Fowler-Nordheim emission with a surface parameter β = 1988 after electro-polishing treatment of a stainless steel grid.

47 OTHER INSTRUMENTATION↗

The effect of finite field size on classification and atmospheric correction

The atmospheric effect on the upward radiance of sunlight scattered from the Earth-atmosphere system is strongly influenced by the contrasts between fields and their sizes. For a given atmospheric turbidity, the atmospheric effect on classification of surface features is much stronger for nonuniform surfaces than for uniform surfaces. Therefore, the classification accuracy of agricultural fields and urban areas is dependent not only on the optical characteristics of the atmosphere, but also on the size of the surface do not account for the nonuniformity of the surface have only a slight effect on the classification accuracy; in other cases the classification accuracy descreases. The radiances above finite fields were computed to simulate radiances measured by a satellite. A simulation case including 11 agricultural fields and four natural fields (water, soil, savanah, and forest) was used to test the effect of the size of the background reflectance and the optical thickness of the atmosphere on classification accuracy. It is concluded that new atmospheric correction methods, which take into account the finite size of the fields, have to be developed to improve significantly the classification accuracy.

Kaufman, Y. J.↗

Simultaneous Retrieval of Multiple Aerosol Parameters Using a Multi-Angular Approach

Atmospheric aerosol particles, both natural and anthropogenic, are important to the earth's radiative balance through their direct and indirect effects. They scatter the incoming solar radiation (direct effect) and modify the shortwave reflective properties of clouds by acting as cloud condensation nuclei (indirect effect). Although it has been suggested that aerosols exert a net cooling influence on climate, this effect has received less attention than the radiative forcing due to clouds and greenhouse gases. In order to understand the role that aerosols play in a changing climate, detailed and accurate observations are a prerequisite. The retrieval of aerosol optical properties by satellite remote sensing has proven to be a difficult task. The difficulty results mainly from the tenuous nature and variable composition of aerosols. To date, with single-angle satellite observations, we can only retrieve reliably against dark backgrounds, such as over oceans and dense vegetation. Even then, assumptions must be made concerning the chemical composition of aerosols. The best hope we have for aerosol retrievals over bright backgrounds are observations from multiple angles, such as those provided by the MISR and POLDER instruments. In this investigation we examine the feasibility of simultaneous retrieval of multiple aerosol optical parameters using reflectances from a typical set of twelve angles observed by the French POLDER instrument. The retrieved aerosol optical parameters consist of asymmetry factor, single scattering albedo, surface albedo, and optical thickness.

Kuo, K. S.↗

Mineral Mapping Using AVIRIS Data at Ray Mine, AZ

Imaging Spectroscopy enables the identification and mapping of surface mineralogy over large areas. This study focused on assessing the utility of Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data for environmental impact analysis over the Environmental Protection Agency's (EPA) high priority Superfund site Ray Mine, AZ. Using the Spectral Angle Mapper (SAM) algorithm to analyze AVIRIS data makes it possible to map surface materials that are indicative of acid generating minerals. The improved performance of the AVIRIS sensor since 1996 provides data with sufficient signal to noise ratio to characterize up to 8 image endmembers. Specifically we employed SAM to map minerals associated with mine generated acid waste, namely jarositc, goethite, and hematite, in the presence of a complex mineralogical background.

McCubbin, Ian↗

Electron Field Emission Properties of Textured Platinum Surfaces

During ground tests of electric microthrusters and space tests of electrodynamic tethers the electron emitters must successfully operate at environmental pressures possibly as high as 1x10(exp -4) Pa. High partial pressures of oxygen, nitrogen, and water vapor are expected in such environments. A textured platinum surface was used in this work for field emission cathode assessments because platinum does not form oxide films at low temperatures. Although a reproducible cathode conditioning process did not evolve from this work, some short term tests for periods of 1 to 4 hours showed no degradation of emission current at an electric field of 8 V/mm and background pressures of about 1x10(exp -6) Pa. Increases of background pressure by air flow to about 3x10(exp -4) Pa yield a hostile environment for the textured platinum field emission cathode.

Sovey, James S.↗

Mineralogy of Asteroids from Observations with the Spitzer Space Telescope

Visible and near-infrared (approx.0.3 to 4.0 microns) spectroscopy has been successfully employed since the early 1970 s to infer the surface compositions of asteroids. Spectroscopic observations in the thermal infrared (approx.5 to 40 microns) are similarly promising. Silicate spectra in this range are dominated by Si-O stretch and bend fundamentals, and other minerals have similarly diagnostic bands [e.g., 1,2]. Observations in this spectral range are difficult from the ground due to strong telluric absorptions and background emission. Nevertheless, spectral structure has been detected on a few asteroids in the 8 to 14-m range from the ground [3,4], as well as from orbit with the ISO satellite [e.g., 5]. The Spitzer Space Telescope can observe asteroids with much higher sensitivity over a broader wavelength range than is possible from the ground or was possible with ISO. We present results of measurements of asteroids with the Infrared Spectrograph (IRS) on the Spitzer Space Telescope.

Emery, J. P.↗

Airborne Ku-Band Polarimetric Radar Remote Sensing of Terrestrial Snow Cover

Preliminary analyses of the POLSCAT data acquired from the CLPX-II in winter 2006-2007 are described in this paper. The data showed the response of the Ku-band radarechoes to snowpack changes for various types of background vegetation. We observed about 0.2 to 0.4 dB increases in backscatter for every 1 cm SWE accumulation for sage brush and agricultural fields. The co-polarized VV and HH radar resposnes are similar, while the corss-polarized (VH or HV) echoes showedgreater resposne to the change of SWE. The data also showed the impact of surface hoar growth and freeze/thaw cycles, whichcreated large snow grain sizes and ice lenses, respectively, and consequently increased the radar signals by a few dBs.

microwave remote sensing↗

Self-similarity of scalar isosurface area density in a temporal mixing layer

Understanding the behaviour of scalar isosurfaces in a turbulent flow is of particular interest for many problems in turbulent mixing that contain sharp interfaces between regions of the flow. Common examples include combustion, where the chemical reactions occur in thin regions within the flow, and the turbulent/non-turbulent interface in shear flows, where a thin region separates the rotational, turbulent motions from the irrotational, non-turbulent background. Recent advances in computing technology allow for in-depth analysis of these interface problems that are difficult to quantify in a laboratory setting. In this paper, the results of a direct numerical simulation of a passive scalar $\varPhi$ evolving on a turbulent, temporally developing mixing layer are described. A novel approach has been taken to calculate the surface area of individual scalar isosurfaces, $A_{iso}$ , throughout the simulation, as well as the mean isosurface area density, $\varSigma$ , as a function of the cross-stream direction and time. A notable finding is that the profiles of $\varSigma$ develop in a self-similar manner when scaled by the Taylor scale of the scalar field, $\lambda _\phi$ . Remarkably, the scaling appears to hold for a wide range of isovalues. A rough scaling argument based on the formal definition of $\varSigma$ and properties of a temporal mixing layer is presented which also exposes a dependence on $\lambda _\phi$ . Based on these results, a possible scaling for the isosurface area is presented as $A_{iso}/A_0 \sim (Re \, Sc)^{1/2}$ , where $Re$ and $Sc$ are local Reynolds and Schmidt numbers, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗