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NASA NTRS2018

Power-Law Statistics of Driven Reconnection in the Magnetically Closed Corona

Numerous observations have revealed that power-law distributions are ubiquitous in energetic solar processes. Hard X-rays, soft X-rays, extreme ultraviolet radiation, and radio waves all display power-law frequency distributions. Since magnetic reconnection is the driving mechanism for many energetic solar phenomena, it is likely that reconnection events themselves display such power-law distributions. In this work, we perform numerical simulations of the solar corona driven by simple convective motions at the photospheric level. Using temperature changes, current distributions, and Poynting fluxes as proxies for heating, we demonstrate that energetic events occurring in our simulation display power-law frequency distributions, with slopes in good agreement with observations. We suggest that the braiding-associated reconnection in the corona can be understood in terms of a self-organized criticality model driven by convective rotational motions similar to those observed at the photosphere.

Knizhnik, K. J.↗

NASA NTRS1991

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

Presented here is a preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. The authors show that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗

NASA NTRS1991

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

A preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity is presented. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. It is shown that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗

NASA NTRS2024

Modeling Entanglement-Based Quantum Key Distribution for the NASA Quantum Communications Analysis Suite

One of the most practical, and sought after, applications of quantum mechanics in the field of information science is the use of entanglement distribution to communicate quantum information effectively. Similar to the continued improvements of functional quantum computers over the past decade, advances in demonstrations of entanglement distribution over long distances may enable new applications in aeronautics and space communications. The existing NASA Quantum Communications Analysis Suite (NQCAS) software models such applications, but limited experimental data exists to verify the model’s theoretical results. There is, however, a large body of experimental data in the relevant literature for entanglement-based quantum key distribution (QKD). This paper details a Monte Carlo based QKD model that uses NQCAS input parameters to generate an estimated QKD link budget for verification of NQCAS. The model generates link budget statistics like key rates, error rates, and S values that can then be compared to the experimental values in the literature. Preliminary comparisons show many similarities between the simulated and experimental data, supporting the model’s validity. A verified NQCAS model will inform experimental work conducted in Glenn Research Center’s (GRC) NASA Quantum Metrology Laboratory (NQML), supporting the United States Quantum Initiative and potential NASA missions.

NASA Quantum Communications Analysis Suite↗

NASA NTRS2016

Exploration Clinical Decision Support System: Medical Data Architecture

The Exploration Clinical Decision Support (ECDS) System project is intended to enhance the Exploration Medical Capability (ExMC) Element for extended duration, deep-space mission planning in HRP. A major development guideline is the Risk of "Adverse Health Outcomes & Decrements in Performance due to Limitations of In-flight Medical Conditions". ECDS attempts to mitigate that Risk by providing crew-specific health information, actionable insight, crew guidance and advice based on computational algorithmic analysis. The availability of inflight health diagnostic computational methods has been identified as an essential capability for human exploration missions. Inflight electronic health data sources are often heterogeneous, and thus may be isolated or not examined as an aggregate whole. The ECDS System objective provides both a data architecture that collects and manages disparate health data, and an active knowledge system that analyzes health evidence to deliver case-specific advice. A single, cohesive space-ready decision support capability that considers all exploration clinical measurements is not commercially available at present. Hence, this Task is a newly coordinated development effort by which ECDS and its supporting data infrastructure will demonstrate the feasibility of intelligent data mining and predictive modeling as a biomedical diagnostic support mechanism on manned exploration missions. The initial step towards ground and flight demonstrations has been the research and development of both image and clinical text-based computer-aided patient diagnosis. Human anatomical images displaying abnormal/pathological features have been annotated using controlled terminology templates, marked-up, and then stored in compliance with the AIM standard. These images have been filtered and disease characterized based on machine learning of semantic and quantitative feature vectors. The next phase will evaluate disease treatment response via quantitative linear dimension biomarkers that enable image content-based retrieval and criteria assessment. In addition, a data mining engine (DME) is applied to cross-sectional adult surveys for predicting occurrence of renal calculi, ranked by statistical significance of demographics and specific food ingestion. In addition to this precursor space flight algorithm training, the DME will utilize a feature-engineering capability for unstructured clinical text classification health discovery. The ECDS backbone is a proposed multi-tier modular architecture providing data messaging protocols, storage, management and real-time patient data access. Technology demonstrations and success metrics will be finalized in FY16.

Biomedical support↗

NASA NTRS1983

A static model of chromospheric heating in solar flares

The response of the solar chromosphere to flare processes, namely nonthermal electrons, thermal conduction, and coronal pressure, is modeled. Finite difference methods employing linearization and iteration are used in obtaining simultaneous solutions to the equations of steady-state energy balance, hydrostatic equilibrium, radiative transfer, and atomic statistical equilibrium. The atmospheric response is assumed to be confined to one dimension by a strong vertical magnetic field. A solution is obtained to the radiative transfer equation for the most important optically thick transitions of hydrogen, magnesium, and calcium. The theoretical atmospheres discussed here are seen as elucidating the role of various physical processes in establishing the structure of flare chromospheres. At low coronal pressures, conduction is found to be more important than nonthermal electrons in establishing the position of the transition region. Only thermal conduction can adequately account for the chromospheric evaporation in compact flares. Of the mechanisms considered, only nonthermal electrons bring about significant heating below the flare transition region.

Ricchiazzi, P. J.↗

NASA NTRS1994

Comparison of low-latitude ion and neutral zonal drifts using DE 2 data

We have used data from the ion drift meter and the wind and temperature spectrometer on the DE 2 spacecraft to make statistical comparisons of the zonal ion and neutral drifts at dip latitudes (DLAT) in the +/- 35 deg range over all local times. Fourier analysis indicates that the superrotation and the diurnal components of both flows are strongly peaked at the dip equator, with the superrotation term becoming negative for the absolute value DLAT greater than or equal 20 deg. One interesting feature is the presence of a period (2200-0500 solar local time) in the 300-400 km altitude region near the dip equator where the ion drift is more strongly eastward than the neutral flow. This would seem to indicate the presence of an electric field source of greater strength than the F region dynamo elsewhere along the geomagnetic field line. Model calculations indicate that a possible mechanism for this source lies in the vertical shear in the zonal neutral wind in the 100-200 km altitude region.

Coley, W. R.↗

NASA NTRSDate not supplied

Investigating the Molecular Response in Irradiated Yeast in Support of the BioSentinel CubeSat Mission

The BioSentinel CubeSat mission is NASA’s first deep space bioscience mission scheduled to fly as a secondary payload onboard Artemis I. BioSentinel seeks to understand the impacts of deep space radiation on living organisms using the model organism Saccharomyces cerevisiae, or budding yeast. In recent years, the BioSentinel team has conducted ground-based investigations into the effects of ionizing radiation (IR) on budding yeast to better understand spaceflight data. One investigation focuses on the impacts of radiation on budding yeast metabolics using the redox dye alamarBlue, an indicator that will also be used onboard BioSentinel. In this investigation, we have observed metabolic changes in both wild-type and in mutant yeast cells deficient in DNA repair. The focus of our research is to support the ongoing investigation into the molecular mechanisms that explain these observed changes. To do this, we first conducted preliminary research into the metabolic processes of S. cerevisiae to identify any potential vulnerabilities to radiation. We then conducted a statistical kinetic analysis on past experimental metabolic data, in addition to an analysis of data from a multisensor metabolic rig experiment. Ultimately, we identified numerous redox-related changes with increasing doses of radiation in both wild-type and mutant cells. These findings highlight the mitochondrial Electron Transport Chain (ETC) as a potential candidate process to account for these observed changes. Specifically, we are focused on the electron carriers of the ETC, including NADH and FADH2, given their participation in numerous redox mechanisms. We propose future experiments, including NADH assays, an investigation into the glycerol-3-phosphate shuttle, and investigations into other ETC complexes.

BioSentinel↗

NASA NTRS1972

A study of 2-20 KeV X-rays from the Cygnus region

Two rocket-borne proportional counters, each with 650 sq c, met area and 1.8 x 7.1 deg FWHM rectangular mechanical collimation, surveyed the Cygnus region in the 2 to 20 keV energy range on two occasions. X-ray spectral data gathered on 21 September 1970 from discrete sources in Cygnus are presented. The data from Cyg X-1, Cyg X-2, and Cyg X-3 have sufficient statistical significance to indicate mutually exclusive spectral forms for the three. Upper limits are presented for X-ray intensities above 2 keV for Cyg X-4 and Cyg X-5 (Cygnus loop). A search was made on 9 August 1971 for a diffuse component of X-rays 1.5 keV associated with an interarm region of the galaxy at galactic longitudes in the vicinity of 60 degrees. A statistically significant excess associated with a narrow disk component was detected. Several possible emission models are discussed, with the most likely candidate being a population of unresolvable low luminosity discrete sources.

Bleach, R. D.↗

NASA NTRS2012

High-Reynolds Number Active Blowing Semi-Span Force Measurement System Development

Recent wind-tunnel tests at the NASA Langley Research Center National Transonic Facility utilized high-pressure bellows to route air to the model for evaluating aircraft circulation control. The introduction of these bellows within the Sidewall Model Support System significantly impacted the performance of the external sidewall mounted semi-span balance. As a result of this impact on the semi-span balance measurement performance, it became apparent that a new capability needed to be built into the National Transonic Facility s infrastructure to allow for performing pressure tare calibrations on the balance in order to properly characterize its performance under the influence of static bellows pressure tare loads and bellows thermal effects. The objective of this study was to design both mechanical calibration hardware and an experimental calibration design that can be employed at the facility in order to efficiently and precisely perform the necessary loadings in order to characterize the semi-span balance under the influence of multiple calibration factors (balance forces/moments and bellows pressure/temperature). Using statistical design of experiments, an experimental design was developed allowing for strategically characterizing the behavior of the semi-span balance for use in circulation control and propulsion-type flow control testing at the National Transonic Facility.

Lynn, Keith C.↗

NASA NTRS2012

Bayesian Analysis for Risk Assessment of Selected Medical Events in Support of the Integrated Medical Model Effort

The Exploration Medical Capability project is creating a catalog of risk assessments using the Integrated Medical Model (IMM). The IMM is a software-based system intended to assist mission planners in preparing for spaceflight missions by helping them to make informed decisions about medical preparations and supplies needed for combating and treating various medical events using Probabilistic Risk Assessment. The objective is to use statistical analyses to inform the IMM decision tool with estimated probabilities of medical events occurring during an exploration mission. Because data regarding astronaut health are limited, Bayesian statistical analysis is used. Bayesian inference combines prior knowledge, such as data from the general U.S. population, the U.S. Submarine Force, or the analog astronaut population located at the NASA Johnson Space Center, with observed data for the medical condition of interest. The posterior results reflect the best evidence for specific medical events occurring in flight. Bayes theorem provides a formal mechanism for combining available observed data with data from similar studies to support the quantification process. The IMM team performed Bayesian updates on the following medical events: angina, appendicitis, atrial fibrillation, atrial flutter, dental abscess, dental caries, dental periodontal disease, gallstone disease, herpes zoster, renal stones, seizure, and stroke.

Gilkey, Kelly M.↗

NASA NTRS2005

Diagnosis and Prognosis of Weapon Systems

The Prognostics Framework is a set of software tools with an open architecture that affords a capability to integrate various prognostic software mechanisms and to provide information for operational and battlefield decision-making and logistical planning pertaining to weapon systems. The Prognostics NASA Tech Briefs, February 2005 17 Framework is also a system-level health -management software system that (1) receives data from performance- monitoring and built-in-test sensors and from other prognostic software and (2) processes the received data to derive a diagnosis and a prognosis for a weapon system. This software relates the diagnostic and prognostic information to the overall health of the system, to the ability of the system to perform specific missions, and to needed maintenance actions and maintenance resources. In the development of the Prognostics Framework, effort was focused primarily on extending previously developed model-based diagnostic-reasoning software to add prognostic reasoning capabilities, including capabilities to perform statistical analyses and to utilize information pertaining to deterioration of parts, failure modes, time sensitivity of measured values, mission criticality, historical data, and trends in measurement data. As thus extended, the software offers an overall health-monitoring capability.

Nolan, Mary↗

NASA NTRS1986

Helicopter rotor noise due to ingestion of atmospheric turbulence

A theoretical study was conducted to develop an analytical prediction method for helicopter main rotor noise due to the ingestion of atmospheric turbulence. This study incorporates an atmospheric turbulence model, a rotor mean flow contraction model and a rapid distortion turbulence model which together determine the statistics of the non-isotropic turbulence at the rotor plane. Inputs to the combined mean inflow and turbulence models are controlled by atmospheric wind characteristics and helicopter operating conditions. A generalized acoustic source model was used to predict the far field noise generated by the non-isotropic flow incident on the rotor. Absolute levels for acoustic spectra and directivity patterns were calculated for full scale helicopters, without the use of empirical or adjustable constants. Comparisons between isotropic and non-isotropic turbulence at the rotor face demonstrated pronounced differences in acoustic spectra. Turning and contraction of the flow for hover and low speed vertical ascent cases result in a 3 dB increase in the acoustic spectrum energy and a 10 dB increase in tone levels. Compared to trailing edge noise, turbulence ingestion noise is the dominant noise mechanism below approximately 30 rotor harmonics, while above 100 harmonics, trailing edge noise levels exceed turbulence ingestion noise by 25 dB.

Simonich, J. C.↗

NASA NTRS1994

Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.

Liu, Jiwen↗

NASA NTRS1996

Uncertainty and Intelligence in Computational Stochastic Mechanics

Classical structural reliability assessment techniques are based on precise and crisp (sharp) definitions of failure and non-failure (survival) of a structure in meeting a set of strength, function and serviceability criteria. These definitions are provided in the form of performance functions and limit state equations. Thus, the criteria provide a dichotomous definition of what real physical situations represent, in the form of abrupt change from structural survival to failure. However, based on observing the failure and survival of real structures according to the serviceability and strength criteria, the transition from a survival state to a failure state and from serviceability criteria to strength criteria are continuous and gradual rather than crisp and abrupt. That is, an entire spectrum of damage or failure levels (grades) is observed during the transition to total collapse. In the process, serviceability criteria are gradually violated with monotonically increasing level of violation, and progressively lead into the strength criteria violation. Classical structural reliability methods correctly and adequately include the ambiguity sources of uncertainty (physical randomness, statistical and modeling uncertainty) by varying amounts. However, they are unable to adequately incorporate the presence of a damage spectrum, and do not consider in their mathematical framework any sources of uncertainty of the vagueness type. Vagueness can be attributed to sources of fuzziness, unclearness, indistinctiveness, sharplessness and grayness; whereas ambiguity can be attributed to nonspecificity, one-to-many relations, variety, generality, diversity and divergence. Using the nomenclature of structural reliability, vagueness and ambiguity can be accounted for in the form of realistic delineation of structural damage based on subjective judgment of engineers. For situations that require decisions under uncertainty with cost/benefit objectives, the risk of failure should depend on the underlying level of damage and the uncertainties associated with its definition. A mathematical model for structural reliability assessment that includes both ambiguity and vagueness types of uncertainty was suggested to result in the likelihood of failure over a damage spectrum. The resulting structural reliability estimates properly represent the continuous transition from serviceability to strength limit states over the ultimate time exposure of the structure. In this section, a structural reliability assessment method based on a fuzzy definition of failure is suggested to meet these practical needs. A failure definition can be developed to indicate the relationship between failure level and structural response. In this fuzzy model, a subjective index is introduced to represent all levels of damage (or failure). This index can be interpreted as either a measure of failure level or a measure of a degree of belief in the occurrence of some performance condition (e.g., failure). The index allows expressing the transition state between complete survival and complete failure for some structural response based on subjective evaluation and judgment.

Ayyub, Bilal M.↗

NASA NTRS2017

Global Energetics of Solar Flares. V. Energy Closure in Flares and Coronal Mass Ejections

In this study we synthesize the results of four previous studies on the global energetics of solar flares and associated coronal mass ejections (CMEs), which include magnetic, thermal, nonthermal, and CME energies in 399 solar M and X-class flare events observed during the first 3.5 years of the Solar Dynamics Observatory (SDO) mission. Our findings are: (1) The sum of the mean nonthermal energy of flare-accelerated particles (E(sub nt)), the energy of direct heating (E(sub dir)), and the energy in coronal mass ejections (E(sub CME)), which are the primary energy dissipation processes in a flare, is found to have a ratio of (E(sub nt)+E(sub dir)+E(sub CME))/E(sub mag) = 0.87±0.18, compared with the dissipated magnetic free energy E(sub mag), which confirms energy closure within the measurement uncertainties and corroborates the magnetic origin of flares and CMEs; (2) The energy partition of the dissipated magnetic free energy is: 0.51±0.17 in nonthermal energy of ≥ 6 keV electrons, 0.17± 0.17 in nonthermal ≥ 1 MeV ions, 0.07 ± 0.14 in CMEs, and 0.07 ± 0.17 in direct heating; (3) The thermal energy is almost always less than the nonthermal energy, which is consistent with the thick-target model; (4) The bolometric luminosity in white-light flares is comparable with the thermal energy in soft X-rays (SXR); (5) Solar Energetic Particle (SEP) events carry a fraction ≈ 0.03 of the CME energy, which is consistent with CME-driven shock acceleration; and (6) The warm-target model predicts a lower limit of the low-energy cutoff at ec ≈ 6 keV, based on the mean differential emission measure (DEM) peak temperature of T(sub e) = 8.6 MK during flares. This work represents the first statistical study that establishes energy closure in solar flare/CME events.

Solar activity↗

NASA NTRS1983

Numerical modeling of turbulent flow in a channel

Two-dimensional incompressible turbulent flow in a channel with a backward-facing step was studied numerically by Chorin's Random Vortex Method (RVM), an algorithm capable of tracing the action of elementary turbulent eddies and their cumulative effects without imposing any restrictions upon their motions. The step occurs in one side of a channel with otherwise flat, parallel walls; its height equals 1/3, 1/4 or 1/5 the width of the channel downstream. The main objective was to investigate the behavior of the large-scale turbulent eddies in a flow and the flow characteristics in the separated shear layer, the reattached zone, and the rebuilding boundary layer after reattachment. The unsteady vorticity field and the distribution of time-averaged turbulent statistics were obtained. The effects of expansion step height and initial boundary layer state were also studied. Comparisons were made with the available experimental results. The agreement is satisfactory in the velocity profiles and in the reattachment length, and fairly good in the turbulence profiles. Also a mechanism of the development of the reattaching turbulent flow was suggested by the numerical results.

Dai, Y. W.↗

NASA NTRS1999

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of understanding the relative contribution to the observations of air of either distinctly tropospheric or stratospheric origin. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High [low] potential vorticity at 300 hPa suggests that the tropopause is low [high], and the identification of the two groups helps to account for dynamic variability. Conditional probability distribution functions are used to define the statistics of the mix from both observations and model simulations. Two data sources are chosen. First, several years of ozonesonde observations are used to exploit the high vertical resolution. Second, observations made by the Halogen Occultation Experiment [HALOE] on the Upper Atmosphere Research Satellite [UARS] are used to understand the impact on the results of the spatial limitations of the ozonesonde network. The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause [about 380K]. Despite the differences in spatial and temporal sampling, the probability distribution functions are similar for the two data sources. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. By using the model, possible mechanisms for the maintenance of mix of air in the lowermost stratosphere are revealed. The relevance of the results to the assessment of the environmental impact of aircraft effluence is discussed.

Cerniglia, M. C.↗