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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Diffusion of chromium and aluminum in Ni-20Cr and TDNiCr /Ni-20Cr-2ThO2/.

Diffusion coefficients have been measured for Cr51 in fine- and coarse-grained TDNiCr (Ni-20Cr-2ThO2) and in fine-grained Ni-20Cr in the temperature range from 1038 to 1200 C. Selective diffusivities have also been determined for specimens of these alloys which were aluminized to give an initial surface concentration of 5.8 wt % Al. Finally, diffusion coefficients for interdiffusion of aluminum in TDNiCr and Ni-20Cr have been obtained from electron probe microanalysis of the aluminized specimens. For a given grain size and temperature there is no difference in diffusivities for chromium diffusion in TDNiCr or Ni-20Cr. Diffusion coefficients increase with decreasing grain size for both alloys. Comparison of aluminum diffusion data obtained from electron microprobe profiles with radiotracer chromium diffusivities suggests that aluminum diffuses approximately three times faster than chromium in TDNiCr and Ni-20Cr.

Seltzer, M. S.↗
NASA NTRS1979

Interfacial geometry and D-variation effects in two-phase systems

Numerical solutions of the governing diffusion equation for two-phase concentration dependent diffusion coefficients are examined. Solutions were also calculated for planar, cylindrical, and spherical geometries to compare the effect of interface geometries with those caused by concentration-dependent diffusion coefficients, and two methods of averaging D were considered to determine the best averaging method for different types of D-variations. The effects of interface-location criteria on mass conservation and convergence of interface location, diffusion coefficient variation in the alpha and beta-phases of a two-phase binary alloy system, effect of D(alpha) variation in a cylindrical couple on beta-phase thickness, and geometry and D-variation effects on the degree of homogenization were determined. It is concluded that typical D(alpha)-variations can have a greater influence on the kinetics of interdiffusion than the geometry.

Tenney, D. R.↗
NASA NTRS1973

Diffusion across the modified polyethylene separator GX in the heat-sterilizable AgO-Zn battery

Models of diffusion across an inert membrane have been studied using the computer program CINDA. The models were constructed to simulate various conditions obtained in the consideration of the diffusion of Ag (OH)2 ions in the AgO-Zn battery. The effects on concentrations across the membrane at the steady state and on the fluxout as a function of time were used to examine the consequences of stepwise reducing the number of sources of ions, of stepwise blocking the source and sink surfaces, of varying the magnitude of the diffusion coefficient for a uniform membrane, of varying the diffusion coefficient across the membrane, and of excluding volumes to diffusion.

Lutwack, R.↗
DOE OSTI2020

A comprehensive diffusion mobility database comprising 23 elements for magnesium alloys

We report that reliable experimental diffusion coefficients of 10 key alloying elements in Mg obtained by the present authors together with experimental data in the literature enabled us to perform a systematic test of the reliability of diffusion coefficients obtained from DFT calculations. The computed activation energy values were found to be quite accurate (mostly within 0.2 eV) but the computed pre-factors were less reliable. Such insights allowed us to develop a practical and yet robust strategy to perform diffusion mobility assessments by adopting the computed activation energy while fitting only the pre-factor when available experimental data are limited to a narrow temperature range. The overall good agreement between the DFT data and experimental data also gave us the confidence to employ the computed data for those that were still missing or inaccessible from experimental measurements. A systematic assessment of both the measured and computed diffusion data in hcp Mg was performed using the above holistic approach to yield the most comprehensive open Mg mobility database to date, comprising 23 elements (Mg, Ag, Al, Be, Ca, Cd, Ce, Cu, Fe, Ga, Gd, In, La, Li, Mn, Nd, Ni, Pu, Sb, Sn, U, Y, Zn). This more reliable mobility database will contribute to future development of advanced Mg alloys. The holistic approach developed in this study will be very beneficial to the future establishment of reliable mobility databases for other alloy systems as well.

36 MATERIALS SCIENCE↗
NASA NTRS1979

The dynamical halo and the variation of cosmic-ray path length with energy

It is shown that the dynamical halo model offers a natural explanation for the form of the variation of the cosmic-ray path length with energy. The variation above about 1 GeV per nucleon can be understood as due to the variation of the diffusion coefficient, and hence the resident time, with energy. The flattening of the curve below 1 GeV per nucleon is seen to mark a transition to a convection-dominated regime where the diffusion coefficient is no longer the determining parameter. A fit to the observations yields a halo outflow velocity of 8 km/s. An attempt is made to determine the overall scale of the halo and the diffusion coefficient using recent Be-10 flux measurements, but the data do not agree well enough to pin down these variables to within less than four or five orders of magnitude.

Jones, F. C.↗
NASA NTRS1981

Solute partitioning under continuous cooling conditions as a cooling rate indicator

A model of solute partitioning in a finite body under conditions of continuous cooling is developed for the determination of cooling rates from concentration profile data, and applied to the partitioning of zirconium between ilmenite and ulvospinel in the Apollo 15 Elbow Crater rocks. Partitioning in a layered composite solid is described numerically in terms of concentration profiles and diffusion coefficients which are functions of time and temperature, respectively; a program based on the model can be used to calculate concentration profiles for various assumed cooling rates given the diffusion coefficients in the two phases and the equilibrium partitioning ratio over a range of temperatures. In the case of the Elbow Rock gabbros, the cooling rates are calculated from measured concentration ratios 10 microns from the interphase boundaries under the assumptions of uniform and equilibrium initial conditions at various starting temperatures. It is shown that the specimens could not have had uniform concentrations profiles at the previously suggested initial temperature of 1350 K. It is concluded that even under conditions where the initial temperature, grain sizes and solute diffusion coefficients are not well characterized, the model can be used to estimate the cooling rate of a grain assemblage to within an order of magnitude.

Onorato, P. I. K.↗
NASA NTRS1974

M558 radioactive tracer diffusion

This experiment was performed in Skylab 3 with two objectives in mind. First, the experimental self-diffusion coefficients for liquid zinc were to be determined in a convection-free environment. Secondly the reduction in convective mixing in earth gravity by going into the zero-gravity environment of space was to be estimated. The experiment was designed to utilize high temperatures and linear thermal gradients provided by the M518 Multipurpose Electric Furnace, and the radioactivity of zinc-65 of 245-day half-life to investigate self-diffusion in liquid zinc. The distribution of zinc-65 tracer, after melting, maintaining at soak temperature for 1 hour of soak time and then resolidifying, was obtained by sample sectioning. The concentration of activity of each section (microcurie-gram) was plotted against positions along the sample axial and radial position. Experimental data and theoretical results from solution of Fick's law of diffusion in one dimensional were compared. Samples tested on earth showed very rapid diffusion. Diffusion coefficient in unit gravity was 50 times the zero-gravity diffusion coefficient of Skylab.

Ukanwa, A. O.↗
NASA NTRS1976

Absorption of radiation belt particles by the inner satellites of Jupiter

The study of trapped particle absorption by the inner Jovian satellites is reviewed from the viewpoint of radiation belt physics. Both pre- and post-Pioneer work is discussed but the emphasis is on methods used to deduce radial diffusion coefficients of particle transport from particle data. The phenomenon of particle absorption as observed by experiments on Pioneers 10 and 11 is considered; absorption effects are found to depend on the satellite, and on particle energy and species. Approximate diffusion coefficients derived from the data are found to follow a steeper spatial dependence than previously expected. The assumptions and limitations of absorption analysis and diffusion coefficient estimation are pointed out.

Mogro-Campero, A.↗
NASA NTRS2014

Improved Algorithms for Accurate Retrieval of UV - Visible Diffuse Attenuation Coefficients in Optically Complex, Inshore Waters

Photochemical processes driven by high-energy ultraviolet radiation (UVR) in inshore, estuarine, and coastal waters play an important role in global bio geochemical cycles and biological systems. A key to modeling photochemical processes in these optically complex waters is an accurate description of the vertical distribution of UVR in the water column which can be obtained using the diffuse attenuation coefficients of down welling irradiance (Kd()). The Sea UV Sea UVc algorithms (Fichot et al., 2008) can accurately retrieve Kd ( 320, 340, 380,412, 443 and 490 nm) in oceanic and coastal waters using multispectral remote sensing reflectances (Rrs(), Sea WiFS bands). However, SeaUVSeaUVc algorithms are currently not optimized for use in optically complex, inshore waters, where they tend to severely underestimate Kd(). Here, a new training data set of optical properties collected in optically complex, inshore waters was used to re-parameterize the published SeaUVSeaUVc algorithms, resulting in improved Kd() retrievals for turbid, estuarine waters. Although the updated SeaUVSeaUVc algorithms perform best in optically complex waters, the published SeaUVSeaUVc models still perform well in most coastal and oceanic waters. Therefore, we propose a composite set of SeaUVSeaUVc algorithms, optimized for Kd() retrieval in almost all marine systems, ranging from oceanic to inshore waters. The composite algorithm set can retrieve Kd from ocean color with good accuracy across this wide range of water types (e.g., within 13 mean relative error for Kd(340)). A validation step using three independent, in situ data sets indicates that the composite SeaUVSeaUVc can generate accurate Kd values from 320 490 nm using satellite imagery on a global scale. Taking advantage of the inherent benefits of our statistical methods, we pooled the validation data with the training set, obtaining an optimized composite model for estimating Kd() in UV wavelengths for almost all marine waters. This optimized composite set of SeaUVSeaUVc algorithms will provide the optical community with improved ability to quantify the role of solar UV radiation in photochemical and photobiological processes in the ocean.

UV↗
NASA NTRS1995

Stormtime ring current and radiation belt ion transport: Simulations and interpretations

We use a dynamical guiding-center model to investigate the stormtime transport of ring current and radiation-belt ions. We trace the motion of representative ions' guiding centers in response to model substorm-associated impulses in the convection electric field for a range of ion energies. Our simple magnetospheric model allows us to compare our numerical results quantitatively with analytical descriptions of particle transport, (e.g., with the quasilinear theory of radial diffusion). We find that 10-145-keV ions gain access to L approximately 3, where they can form the stormtime ring current, mainly from outside the (trapping) region in which particles execute closed drift paths. Conversely, the transport of higher-energy ions (approximately greater than 145 keV at L approximately 3) turns out to resemble radial diffusion. The quasilinear diffusion coefficient calculated for our model storm does not vary smoothly with particle energy, since our impulses occur at specific (although randomly determined) times. Despite the spectral irregularity, quasilinear theory provides a surprisingly accurate description of the transport process for approximately greater than 145-keV ions, even for the case of an individual storm. For 4 different realizations of our model storm, the geometric mean discrepancies between diffusion coefficients D(sup sim, sub LL) obtained from the simulations and the quasilinear diffusion coefficient D(sup ql, sub LL) amount to factors of 2.3, 2.3, 1.5, and 3.0, respectively. We have found that these discrepancies between D(sup sim, sub LL) and D(sup ql, sub LL) can be reduced slightly by invoking drift-resonance broadening to smooth out the sharp minima and maxima in D(sup ql, sub LL). The mean of the remaining discrepancies between D(sup sim, sub LL) and D(sup ql, sub LL) for the 4 different storms then amount to factors of 1.9, 2.1, 1.5, and 2.7, respectively. We find even better agreement when we reduce the impulse amplitudes systematically in a given model storm (e.g., reduction of all the impulse amplitudes by half reduces the discrepancy factor by at least its square root) and also when we average our results over an ensemble of 20 model storms (agreement is within a factor of 1.2 without impulse-amplitude reduction). We use our simulation results also to map phase-space densities f in accordance with Liouville's theorem. We find that the stormtime transport of approximately greater than 145-keV ions produces little change in f-bar the drift-averaged phase-space density on any drift shell of interest. However, the stormtime transport produces a major enhancement from the pre-storm phase-space density at energies approximately 30-145 keV, which are representative of the stormtime ring current.

Lyons, Larry R.↗
DOE OSTI2023

Molecular dynamics simulation studies of 1,3-dimethyl imidazolium nitrate ionic liquid with water

The fundamental understanding of intermolecular interactions of ionic liquids (ILs) with water is essential in predicting IL–water thermodynamic properties. In this study, intermolecular or noncovalent interactions were studied for 1,3-dimethyl imidazolium [DMIM]+ cation and nitrate [NO 3 ] – anion with water, employing quantum mechanics and molecular dynamics simulations. Molecular dynamics simulations were performed using a revised multipolar polarizable force field. The effect of water on ionic liquids was evaluated in terms of thermodynamic and dynamic properties. Thermodynamic properties included liquid densities ρ, excess molar volumes ΔV E , and liquid structures g(r)⁠. Dynamic properties included self-diffusion coefficients D of mixture constituents as a function of water concentration. The density of ionic liquid–water mixtures monotonically decrease with increasing concentration of water. A negative excess volume was obtained for low and high water concentrations, demonstrating strong intermolecular interactions of water with ionic liquid components. Liquid structures of ionic liquid–water mixtures revealed a tendency for anions to interact with cations at shorter intermolecular distances when the water concentration is increased. Diffusion rates were found to increase for all mixture components with increase in the fraction of water. A significant change in the diffusion rate was found at ~0.3 weight fraction of water. However, the water self-diffusion coefficient was dominant at all concentrations. Furthermore, the ratio of water/anion and anion/cation self-diffusion coefficients was found to decrease linearly with increasing concentration of water molecules.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Dynamics of the O ( 4 ) critical point in QCD: Critical pions and diffusion in model G

We present a detailed study of the finite momentum dynamics of the O ( 4 ) critical point of QCD, which lies in the dynamic universality class of “model G.” The critical scaling of the model is analyzed in multiple dynamical channels. For instance, the finite momentum analysis allows us to precisely extract the pion dispersion curve below the critical point. The pion velocity is in striking agreement with the predictions relation and static universality. The pion damping rate and velocity are both consistent with the dynamical critical exponent ζ = 3 / 2 of model G. Similarly, although the critical amplitude for the diffusion coefficient of the conserved O ( 4 ) charges is small, it is clearly visible both in the restored phase and with finite explicit symmetry breaking, and its dynamical scaling is again consistent with ζ = 3 / 2 . We determine a new set of universal dynamical critical amplitude ratios relating the diffusion coefficient to a suitably defined order parameter relaxation time. We also show that in a finite volume simulation, the chiral condensate diffuses on the coset manifold in a manner consistent with dynamical scaling, and with a diffusion coefficient that is determined by the transport coefficients of hydrodynamic pions. Finally, the amplitude ratios (together with other nonuniversal amplitudes also reported here) compile all relevant information for further studies of model G both in and out of equilibrium. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1989

Dynamics of the middle atmosphere in winter (Dynamics). Interrelation between the different variations of turbulent diffusion and ionospheric absorption originating in the middle atmosphere

The turbulent diffusion coefficient was computed from the parameters of sporadic E layers using the wind shear theory of midlatitude sporadic E and models of the ionosphere as well as that of the neutral upper atmosphere. The turbulent diffusion coefficient obtained for the period of circulation disturbances associated with stratospheric warmings and for the intervals of the winter anomaly indicate changes similar to the ionospheric absorption of radio waves, in the former case decreased, in the latter case increased values. This may hit at the role of turbulent transport in the formation of these anomalies. On the basis of these findings, a seasonal variation of the turbulent diffusion coefficient having a minimum in summer and an increase of this parameter with increasing geomagnetic activity are anticipated.

Bencze, P.↗
DOE OSTI2020

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells (Final Report)

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co2O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly4 increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co 2 O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO 2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly 4 increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co 2 O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO 2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres

01 COAL, LIGNITE, AND PEAT↗
NASA NTRS1980

The effect of convection on the propagation of relativistic galactic electrons

The paper presents exact analytical solutions which describe steady-state transport of relativistic electrons subject to diffusion, convection, and radiation losses. The diffusion coefficient is spatially and energy dependent; the bulk convection velocity is considered to be constant and directed outward from the galactic plane. The electron spectral behavior with respect to galactic height and energy indicates that convection provides a 'break' in the steady-state energy spectrum without recourse to distribution of sources. Radio observations of NGC 891 and NGC 4631 galaxies can be used to estimate their diffusion coefficient and its energy dependence. Application of analytical solutions to our Galaxy indicates that the diffusion coefficient and outflow velocity deduced from relativistic electron measurements and radio observations of their synchrotron radiation agree with values based on the transport of the cosmic ray nucleonic component.

Lerche, I.↗