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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 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Shielding from Solar Particle Event Exposures in Deep Space

The physical composition and intensities of solar particle event exposures or sensitive astronaut tissues are examined under conditions approximating an astronaut in deep space. Response functions for conversion of particle fluence into dose and dose equivalent averaged over organ tissue, are used to establish significant fluence levels and the expected dose and dose rates of the most important events from past observations. The BRYNTRN transport code is used to evaluate the local environment experienced by sensitive tissues and used to evaluate bioresponse models developed for use in tactical nuclear warfare. The present results will help to the biophysical aspects of such exposure in the assessment of RBE and dose rate effects and their impact on design of protection systems for the astronauts. The use of polymers as shielding material in place of an equal mass of aluminum would prowide a large safety factor without increasing the vehicle mass. This safety factor is sufficient to provide adequate protection if a factor of two larger event than has ever been observed in fact occurs during the mission.

Wilson, John W.↗
NASA NTRS2003

Interfacial Reaction Studies Using ONIOM

In this report, we focus on the calculations of the energetics and chemical kinetics of heterogeneous reactions for Organometallic vapor phase epitaxy (OMVPE). The work described in this report builds upon our own previous thermochemical and chemical kinetics studies. The first of these articles refers to the prediction of thermochemical properties, and the latter one deals with the prediction of rate constants for gaseous homolytic dissociation reactions. The calculations of this investigation are at the microscopic level. The systems chosen consisted of a gallium nitride (GaN) substrate, and molecular nitrogen (N2) and ammonia (NH3) as adsorbants. The energetics for the adsorption and the adsorbant dissociation processes were estimated, and reaction rate constants for the dissociation reactions of free and adsorbed molecules were predicted. The energetics for substrate decomposition was also computed. The ONIOM method, implemented in the Gaussian98 program, was used to perform the calculations. This approach has been selected since it allows dividing the system into two layers that can be treated at different levels of accuracy. The atoms of the substrate were modeled using molecular mechanics6 with universal force fields, whereas the adsorbed molecules were approximated using quantum mechanics, based on density functional theory methods with B3LYP functionals and 6-311G(d,p) basis sets. Calculations for the substrate were performed in slabs of several unit cells in each direction. The N2 and NH3 adsorbates were attached to a central location at the Ga-lined surface.

Cardelino, Beatriz H.↗
NASA NTRS1999

Circadian and sleep-dependent regulation of hormone release in humans

Daily oscillations characterize the release of nearly every hormone. The circadian pacemaker, located in the suprachiasmatic nucleus of the hypothalamus, generates circadian, approximately 24-hour rhythms in many physiologic functions. However, the observed hormonal oscillations do not simply reflect the output of this internal clock. Instead, daily hormonal profiles are the product of a complex interaction between the output of the circadian pacemaker, periodic changes in behavior, light exposure, neuroendocrine feedback mechanisms, gender, age, and the timing of sleep and wakefulness. The interaction of these factors can affect hormonal secretory pulse frequency and amplitude, with each endocrine system differentially affected by these factors. This chapter examines recent advances in understanding the effects on endocrine rhythms of a number of these factors. Sleep exerts a profound effect on endocrine secretion. Sleep is a dynamic process that is characterized by periodic changes in electrophysiologic activity. These electrophysiologic changes, which are used to mark the state and depth of sleep, are associated with periodic, short-term variations in hormonal levels. The secretion of hormones such as renin and human growth hormone are strongly influenced by sleep or wake state, while melatonin and cortisol levels are relatively unaffected by sleep or wake state. In addition, sleep is associated with changes in posture, behavior, and light exposure, each of which is known to affect endocrine secretion. Furthermore, the tight concordance of habitual sleep and wake times with certain circadian phases has made it difficult to distinguish sleep and circadian effects on these hormones. Specific protocols, designed to extract circadian and sleep information semi-independently, have been developed and have yielded important insights into the effects of these regulatory processes. These results may help to account for changes in endocrine rhythms observed in circadian rhythm sleep disorders, including the dyssomnia of shift work and visual impairment. Yet to be fully investigated are the interactions of these factors with age and gender. Characterization of the factors governing hormone secretion is critical to understanding the temporal regulation of endocrine systems and presents many exciting areas for future research.

Non-NASA Center↗
NASA NTRS2006

Formation of Triplet Positron-helium Bound State by Stripping of Positronium Atoms in Collision with Ground State Helium

Formation of triplet positron-helium bound state by stripping of positronium atoms in collision with ground state helium JOSEPH DI RlENZI, College of Notre Dame of Maryland, RICHARD J. DRACHMAN, NASA/Goddard Space Flight Center - The system consisting of a positron and a helium atom in the triplet state e(+)He(S-3)(sup e) was conjectured long ago to be stable [1]. Its stability has recently been established rigorously [2], and the values of the energies of dissociation into the ground states of Ps and He(+) have also been reported [3] and [4]. We have evaluated the cross-section for this system formed by radiative attachment of a positron in triplet He state and found it to be small [5]. The mechanism of production suggested here should result in a larger cross-section (of atomic size) which we are determining using the Born approximation with simplified initial and final wave functions.

Drachman, Richard J.↗
NASA NTRS2007

A Simple Stochastic Model for Generating Broken Cloud Optical Depth and Top Height Fields

A simple and fast algorithm for generating two correlated stochastic twodimensional (2D) cloud fields is described. The algorithm is illustrated with two broken cumulus cloud fields: cloud optical depth and cloud top height retrieved from Moderate Resolution Imaging Spectrometer (MODIS). Only two 2D fields are required as an input. The algorithm output is statistical realizations of these two fields with approximately the same correlation and joint distribution functions as the original ones. The major assumption of the algorithm is statistical isotropy of the fields. In contrast to fractals and the Fourier filtering methods frequently used for stochastic cloud modeling, the proposed method is based on spectral models of homogeneous random fields. For keeping the same probability density function as the (first) original field, the method of inverse distribution function is used. When the spatial distribution of the first field has been generated, a realization of the correlated second field is simulated using a conditional distribution matrix. This paper is served as a theoretical justification to the publicly available software that has been recently released by the authors and can be freely downloaded from http://i3rc.gsfc.nasa.gov/Public codes clouds.htm. Though 2D rather than full 3D, stochastic realizations of two correlated cloud fields that mimic statistics of given fields have proved to be very useful to study 3D radiative transfer features of broken cumulus clouds for better understanding of shortwave radiation and interpretation of the remote sensing retrievals.

Prigarin, Sergei M.↗
NASA NTRS2013

File Specification for GEOS-5 FP (Forward Processing)

The GEOS-5 FP Atmospheric Data Assimilation System (GEOS-5 ADAS) uses an analysis developed jointly with NOAA's National Centers for Environmental Prediction (NCEP), which allows the Global Modeling and Assimilation Office (GMAO) to take advantage of the developments at NCEP and the Joint Center for Satellite Data Assimilation (JCSDA). The GEOS-5 AGCM uses the finite-volume dynamics (Lin, 2004) integrated with various physics packages (e.g, Bacmeister et al., 2006), under the Earth System Modeling Framework (ESMF) including the Catchment Land Surface Model (CLSM) (e.g., Koster et al., 2000). The GSI analysis is a three-dimensional variational (3DVar) analysis applied in grid-point space to facilitate the implementation of anisotropic, inhomogeneous covariances (e.g., Wu et al., 2002; Derber et al., 2003). The GSI implementation for GEOS-5 FP incorporates a set of recursive filters that produce approximately Gaussian smoothing kernels and isotropic correlation functions. The GEOS-5 ADAS is documented in Rienecker et al. (2008). More recent updates to the model are presented in Molod et al. (2011). The GEOS-5 system actively assimilates roughly 2 × 10(exp 6) observations for each analysis, including about 7.5 × 10(exp 5) AIRS radiance data. The input stream is roughly twice this volume, but because of the large volume, the data are thinned commensurate with the analysis grid to reduce the computational burden. Data are also rejected from the analysis through quality control procedures designed to detect, for example, the presence of cloud. To minimize the spurious periodic perturbations of the analysis, GEOS-5 FP uses the Incremental Analysis Update (IAU) technique developed by Bloom et al. (1996). More details of this procedure are given in Appendix A. The assimilation is performed at a horizontal resolution of 0.3125-degree longitude by 0.25- degree latitude and at 72 levels, extending to 0.01 hPa. All products are generated at the native resolution of the horizontal grid. The majority of data products are time-averaged, but four instantaneous products are also available. Hourly data intervals are used for two-dimensional products, while 3-hourly intervals are used for three-dimensional products. These may be on the model's native 72-layer vertical grid or at 42 pressure surfaces extending to 0.1 hPa. This document describes the gridded output files produced by the GMAO near real-time operational FP, using the most recent version of the GEOS-5 assimilation system. Additional details about variables listed in this file specification can be found in a separate document, the GEOS-5 File Specification Variable Definition Glossary. Documentation about the current access methods for products described in this document can be found on the GMAO products page: http://gmao.gsfc.nasa.gov/products/.

GSI↗
NASA NTRS2013

File Specification for GEOS-5 FP-IT (Forward Processing for Instrument Teams)

The GEOS-5 FP-IT Atmospheric Data Assimilation System (GEOS-5 ADAS) uses an analysis developed jointly with NOAA's National Centers for Environmental Prediction (NCEP), which allows the Global Modeling and Assimilation Office (GMAO) to take advantage of the developments at NCEP and the Joint Center for Satellite Data Assimilation (JCSDA). The GEOS-5 AGCM uses the finite-volume dynamics (Lin, 2004) integrated with various physics packages (e.g, Bacmeister et al., 2006), under the Earth System Modeling Framework (ESMF) including the Catchment Land Surface Model (CLSM) (e.g., Koster et al., 2000). The GSI analysis is a three-dimensional variational (3DVar) analysis applied in grid-point space to facilitate the implementation of anisotropic, inhomogeneous covariances (e.g., Wu et al., 2002; Derber et al., 2003). The GSI implementation for GEOS-5 FP-IT incorporates a set of recursive filters that produce approximately Gaussian smoothing kernels and isotropic correlation functions. The GEOS-5 ADAS is documented in Rienecker et al. (2008). More recent updates to the model are presented in Molod et al. (2011). The GEOS-5 system actively assimilates roughly 2 × 10(exp 6) observations for each analysis, including about 7.5 × 10(exp 5) AIRS radiance data. The input stream is roughly twice this volume, but because of the large volume, the data are thinned commensurate with the analysis grid to reduce the computational burden. Data are also rejected from the analysis through quality control procedures designed to detect, for example, the presence of cloud. To minimize the spurious periodic perturbations of the analysis, GEOS-5 FP-IT uses the Incremental Analysis Update (IAU) technique developed by Bloom et al. (1996). More details of this procedure are given in Appendix A. The analysis is performed at a horizontal resolution of 0.625-degree longitude by 0.5-degree latitude and at 72 levels, extending to 0.01 hPa. All products are generated at the native resolution of the horizontal grid. The majority of data products are time-averaged, but four instantaneous products are also available. Hourly data intervals are used for two-dimensional products, while 3-hourly intervals are used for three-dimensional products. These may be on the model's native 72-layer vertical grid or at 42 pressure surfaces extending to 0.1 hPa. This document describes the gridded output files produced by the GMAO near real-time operational GEOS-5 FP-IT processing in support of the EOS instrument teams. Additional details about variables listed in this file specification can be found in a separate document, the GEOS-5 File Specification Variable Definition Glossary.

3D Var↗
NASA NTRS2019

Dust Abrasion Damage on Martian Solar Arrays: Experimental Investigation and Opportunity Rover Performance Analysis

Here we investigate the effects of erosion and weathering that occur on III-V cover-glass interconnected cells (CICs) after exposure to Mars dust storm conditions. The durability of these materials in a Martian environment is not well characterized so we perform analogous experimentation. To replicate the dust impingement, test coupons were placed in an enclosure and sandblasted with Mars dust simulant. We show the J-V response dependency on both incident angle and exposure times. We find that the simulated Martian dust storm often results in damage to the anti-reflective coating and subsequent reduced short circuit current. Reduction in the open circuit voltage is observed, likely caused by structural damage to the crystal lattice after CIC fracture. We employ data-driven modeling to determine a performance degradation rate that is consistent with zero within uncertainty. We also quantify the soiling contribution and power degradation of the photovoltaic cells on Mars through analysis of 4.95 Martian years of report-out power conditions from the Opportunity rover. We find that atmospheric dust suspended due to a weather event does not result in instantaneous settled dust on the PV cells. We calculate via autocorrelation function that the dust settling rate is approximately 21 Sols from atmospheric dust suspension. The findings presented here deliver a realistic approximation for the insolation values and subsequent PV power expected over time on the Martian surface thus informing future dust abatement systems.

McMillon-Brown, Lyndsey↗
NASA NTRS2019

Dust Abrasion Damage on Martian Solar Arrays: Experimental Investigation and Opportunity Rover Performance Analysis

Here we investigate the effects of erosion and weathering that occur on III-V cover-glass interconnected cells (CICs) after exposure to Mars dust storm conditions. The durability of these materials in a Martian environment is not well characterized so we perform analogous experimentation. To replicate the dust impingement, test coupons were placed in an enclosure and sandblasted with Mars dust simulant. We show the J-V response dependency on both incident angle and exposure times. We find that the simulated Martian dust storm often results in damage to the anti-reflective coating and subsequent reduced short circuit current. Reduction in the open circuit voltage is observed, likely caused by structural damage to the crystal lattice after CIC fracture. We employ data-driven modeling to determine a performance degradation rate that is consistent with zero within uncertainty. We also quantify the soiling contribution and power degradation of the photovoltaic cells on Mars through analysis of 4.95 Martian years of report-out power conditions from the Opportunity rover. We find that atmospheric dust suspended due to a weather event does not result in instantaneous settled dust on the PV cells. We calculate via autocorrelation function that the dust settling rate is approximately 21 Sols from atmospheric dust suspension. The findings presented here deliver a realistic approximation for the insolation values and subsequent PV power expected over time on the Martian surface thus informing future dust abatement systems.

McMillon-Brown, Lyndsey↗
NASA NTRS2022

USM3D Simulations for the Third AIAA Sonic Boom Prediction Workshop

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases included a nearfield biconvex shock-plume interaction wind tunnel model and the C608 Low Boom Flight Demonstrator. Numerical simulations were conducted on the mixed-element and tetrahedral grids provided by the workshop committee, as well as a family of grids generated by an in-house approach known as BoomGrid. The nearfield pressure signatures were extracted and propagated to the ground, and the perceived loudness levels on the ground were computed. The USM3D nearfield pressure signatures, corresponding ground signatures, and loudness levels on the ground were compared with that of mean values from other workshop participants. The effect of three flux-limiters on the accuracy of nearfield pressure signature prediction was investigated and results were compared with that of mean values from other workshop participants. The effect of using wall-function models for predicting nearfield pressure signatures was also evaluated. Results showed that the overpressure signatures extracted from the wall-modeled simulations and the wall-resolved simulations are in good agreement. The use of wall functions (wall-modeled simulations) allowed for approximately 23% savings in the time to solution and yielded comparable perceived loudness levels on the ground to the wall-resolved Reynolds-averaged Navier Stokes simulations.

Supersonics↗
NASA NTRS1975

Thermal diffuse X-ray scattering in simple metals

Calculations are reported for the ionic structure factor and X-ray scattering cross section of sodium (at T=0 K and 90 K) and lithium (both isotopes at T=0 K) within the harmonic approximation. An evaluation of the appropriate displacement- displacement correlation function by the special point method circumvents the need for a multiphonon expansion. In the case of sodium, the structure in the one-phonon scattering was straightforwardly accounted for, and an approximate expansion was obtained for all multiphonon scattering. By treating core and conduction electrons on an equal footing, it is shown that information on the conduction electron system is present in the forward scattering component. In lithium the one-phonon cross section at small angles aids in the determination of the effective electron-ion interaction.

Straus, D. M.↗
NASA NTRS1979

Modal propagation angles in a cylindrical duct with flow and their relation to sound radiation

The main emphasis is upon the propagation angle with respect to the duct axis and its relation to the far-field acoustic radiation pattern. When the steady flow Mach number is accounted for in the duct, the propagation angle in the duct is shown to be coincident with the angle of the principal lobe of far-field radiation obtained using the Wiener-Hopf technique. Different Mach numbers are allowed within the duct and in the external field. For static tests with a steady flow in an inlet but with no external Mach number the far-field radiation pattern is shifted considerably toward the inlet axis when compared to zero Mach number radiation theory. As the external Mach number is increased the noise radiation pattern is shifted away from the inlet axis. The theory is developed using approximations for sound propagation in circular ducts. An exact analysis using Hankel function solutions for the zero Mach number case is given to provide a check of the simpler approximate theory.

Rice, E. J.↗
NASA NTRS2004

Modified Coulomb-Dipole Theory for 2e Photoionization

In the light of recent experiment on 2e photoionization of Li near threshold, we have considered a modification of the Coulomb-dipole theory, retaining the basic assumption that the threshold is dominated by asymmetric events in phase space [implies r(sub 1), k(sub 1)) greater than or equal to 2(r(sub 2), k(sub )]. In this region [in a collinear model, 2/r(sub 12) approached + 2/(r(sub 1)+r(sub 2)] the interaction reduces to V(rIsub 1) is greater than or equal to 2r(sub 2) is identically equal to [(-Z/r(sub 2)-(A-1)/r(sub 1)] + [(-2r(sub 2)/r(sub 1 exp 2)] is identically equal to V(sub c)+[V(sub d)]. For two electron emission Z = 2, thus both electrons see a Coulomb potential (V(sub c)) asymptotically, albeit each seeing a different charge. The residual potential (V(sub d)) is dipole in character. Writing the total psi = psi (sub c) + psi(sub d) = delta psi, and noting that. (T+V(sub c)-E)psy(sub c) = 0 and (T+V(sub c))psi(sub d) = 0 can be solved exactly, we find, substituting psi into the complete Schrod. Eq., that delta psi = -(H-E)(exp -1)(V(sub d) psi(sub 0)+V(sub c psi (sub 1). Using the fact that the absolute value of V(sub c) is much more than the absolute value of V(sub d) in almost all of configuration space, we can replace H by H(sub 0) in 9H-E)(exp -1) to obtain an improved approximation psi (improved) = psi(sub c) + psi(sub d) -(H(sub 0)-E)(exp -1) (V(sub c) psi (sub 0) + V(sub c) psi(sub 1). Here's the Green's function (H(sub 0)-E)(exp -1), can be exhibited explicitly, but the last term in psi (improved) is small, compared to the first two terms. Inserting them into the transition matrix element, which one handles in the usual way, we obtain in the limit E approaches 0, the threshold law: Q(E) alpha E + M(E)E(exp 5/4) + higher order (Eq. 1a). The modulation function, M(E), is a well-defined (but very non-trivial integral, but it is expected to be well approximated by a sinusoidal function containing a dipole phase term (M(E) = c sin[alpha log (E) + micron] (Eq. 1b). Experimental results show definite modulations, and are well fitted by Eqs (1).

Source record↗
NASA NTRS1974

Vapor ingestion in a cylindrical tank with a concave elliptical bottom

An approximate analytical technique is presented for estimating the liquid residual in a tank of arbitrary geometry due to vapor ingestion at any drain rate and acceleration level. The bulk liquid depth at incipient pull-through is defined in terms of the Weber and Bond numbers and two functions that describe the fluid velocity field and free surface shape appropriate to the tank geometry. Numerical results are obtained for the Centaur LH2 tank using limiting approximations to these functions.

Klavins, A.↗
NASA NTRS2008

NanoSail-D: The First Flight Demonstration of Solar Sails for Nanosatellites

The NanoSail-D mission is currently scheduled for launch onboard a Falcon Launch Vehicle in the late June 2008 timeframe. The NanoSail-D, a CubeSat-class satellite, will consist of a sail subsystem stowed in a Cubesat 2U volume integrated with a CubeSat 1U volume bus provided by the NASA Ames Research Center (ARC). Shortly after deployment of the NanoSail-D from a Poly Picosatellite Orbital Deployer (P-POD) ejection system, the solar sail will deploy and mission operations will commence. This demonstration flight has two primary mission objectives: 1) to successfully stow and deploy the sail and 2) to demonstrate de-orbit functionality. Given a nearterm opportunity for launch, the project was met with the challenge of delivering the flight hardware in approximately six months, which required a significant constraint on flight system functionality. As a consequence, passive attitude stabilization will be achieved using permanent magnets to de-tumble and orient the body with the magnetic field lines and then rely on atmospheric drag to passively stabilize the sailcraft in an essentially maximum drag attitude. This paper will present an introduction to solar sail propulsion systems, overview the NanoSail-D spacecraft, describe the performance analysis for the passive attitude stabilization, and present a prediction of flight data results from the mission.

Whorton, Mark↗
NASA NTRS2014

The Evolution of the Galaxy Rest-Frame Ultraviolet Luminosity Function Over the First Two Billion Years

We present a robust measurement and analysis of the rest-frame ultraviolet (UV) luminosity function at z = 4 to 8. We use deep Hubble Space Telescope imaging over the CANDELS/GOODS fields, the Hubble Ultra Deep Field and the Hubble Frontier Field deep parallel observations near the Abell 2744 and MACS J0416.1- 2403 clusters. The combination of these surveys provides an effective volume of 0.6-1.2 ×10(exp 6) Mpc(exp 3) over this epoch, allowing us to perform a robust search for bright (M(sub UV) less than −21) and faint (M(sub UV) = −18) galaxies. We select galaxies using a well-tested photometric redshift technique with careful screening of contaminants, finding a sample of 7446 galaxies at 3.5 less than z less than 8.5, with more than 1000 galaxies at z of approximately 6 - 8. We measure both a stepwise luminosity function for galaxies in our redshift samples, as well as a Schechter function, using a Markov Chain Monte Carlo analysis to measure robust uncertainties. At the faint end our UV luminosity functions agree with previous studies, yet we find a higher abundance of UV-bright galaxies at z of greater than or equal to 6. Our bestfit value of the characteristic magnitude M* is consistent with −21 at z of greater than or equal to 5, different than that inferred based on previous trends at lower redshift. At z = 8, a single power-law provides an equally good fit to the UV luminosity function, while at z = 6 and 7, an exponential cutoff at the bright-end is moderately preferred. We compare our luminosity functions to semi-analytical models, and find that the lack of evolution in M* is consistent with models where the impact of dust attenuation on the bright-end of the luminosity function decreases at higher redshift, though a decreasing impact of feedback may also be possible. We measure the evolution of the cosmic star-formation rate (SFR) density by integrating our observed luminosity functions to M(sub UV) = −17, correcting for dust attenuation, and find that the SFR density declines proportionally to (1 + z)((exp −4.3)(+/-)(0.5)) at z greater than 4, consistent with observations at z greater than or equal to 9. Our observed luminosity functions are consistent with a reionization history that starts at redshift of approximately greater than 10, completes at z greater than 6, and reaches a midpoint (x(sub HII) = 0.5) at 6.7 less than z less than 9.4. Finally, using a constant cumulative number density selection and an empirically derived rising star-formation history, our observations predict that the abundance of bright z = 9 galaxies is likely higher than previous constraints, though consistent with recent estimates of bright z similar to 10 galaxies.

Galaxy↗
NASA NTRS1980

Optimal thermionic energy conversion with established electrodes for high-temperature topping and process heating

Applied research-and-technology (ART) work reveals that optimal thermionic energy conversion (TEC) with approximately 1000 K to approximately 1100 K collectors is possible using well established tungsten electrodes. Such TEC with 1800 K emitters could approach 26.6% efficiency at 27.4 W/sq cm with approximately 1000 K collectors and 21.7% at 22.6 W/sq cm with approximately 1100 K collectors. These performances require 1.5 and 1.7 eV collector work functions (not the 1 eV ultimate) with nearly negligible interelectrode losses. Such collectors correspond to tungsten electrode systems in approximately 0.9 to approximately 6 torr cesium pressures with 1600 K to 1900 K emitters. Because higher heat-rejection temperatures for TEC allow greater collector work functions, interelectrode loss reduction becomes an increasingly important target for applications aimed at elevated temperatures. Studies of intragap modifications and new electrodes that will allow better electron emission and collection with lower cesium pressures are among the TEC-ART approaches to reduced interelectrode losses. These solutions will provide very effective TEC to serve directly in coal-combustion products for high-temperature topping and process heating. In turn this will help to use coal and to use it well.

Morris, J. F.↗
NASA NTRS1986

A minimum entropy principle in the gas dynamics equations

Let u(x bar,t) be a weak solution of the Euler equations, governing the inviscid polytropic gas dynamics; in addition, u(x bar, t) is assumed to respect the usual entropy conditions connected with the conservative Euler equations. We show that such entropy solutions of the gas dynamics equations satisfy a minimum entropy principle, namely, that the spatial minimum of their specific entropy, (Ess inf s(u(x,t)))/x, is an increasing function of time. This principle equally applies to discrete approximations of the Euler equations such as the Godunov-type and Lax-Friedrichs schemes. Our derivation of this minimum principle makes use of the fact that there is a family of generalized entrophy functions connected with the conservative Euler equations.

Tadmor, E.↗