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At least 1,387 records · Page 77

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NASA NTRS1976

Wind tunnel investigation of Nacelle-Airframe interference at Mach numbers of 0.9 to 1.4-force data

Detailed interference force and pressure data were obtained on a representative wing-body-nacelle combination at Mach numbers of 0.9 to 1.4. The model consisted of a delta wing-body aerodynamic force model with four independently supported nacelles located beneath the wing-body combination. The model was mounted on a six-component force balance, and the left-hand wing was pressure-instrumented. Each of the two right-hand nacelles was mounted on a six-component force balance housed in the thickness of the nacelle, while each of the left-hand nacelles was pressure-instrumented. The primary variables examined included Mach number, angle of attack, nacelle position, and nacelle mass-flow ratio. Four different configurations were tested to identify various interference forces and pressures on each component; these included tests of the isolated nacelle, the isolated wing-body combination, the four nacelles as a unit, and the total wing-body-nacelle combination. Nacelle axial location, relative to both the wing-body combination and to each other, was the most important variable in determining the net interference among the components.

Bencze, D. P.↗

NASA NTRS1982

Energy balance of stellar coronae. I - Methods and examples. II - Effect of coronal heating

Simplified models of magnetically open coronal regions are computed, with the aim of fulfilling appropriate boundary conditions at the base of the atmosphere, at the critical point, and at infinity. The models are determined by the stellar mass and radius and by the amount and location of coronal heating, and this dependence is analyzed in terms of pressure, temperature, characteristic heights, energy losses, mass loss, and asymptotic behavior. The results are used to classify the magnetically open coronal regions according to the energy loss mechanism that dominates in the region between the base and the critical point, and it is shown that more complicated heating mechanisms may be replaced by the presented exponential heating law, provided that the damping length is suitably chosen.

Hammer, R.↗

NASA NTRS1988

Use of satellite radiometric imagery data for improvement in the analysis of divergent wind in the tropics

A scheme is proposed to incorporate satellite radiometric imagery data into the specification of initial conditions for the National Meteorological Center (NMC) operational global prediction model in order to improve the analysis of the divergent wind field in the tropics. The basic assumptions are that outgoing longwave radiation (OLR) data can provide 1) the division between convective (upward motion) and clear sky (downward motion) areas, and 2) the height of convection cells. The intensity of ascending motion in the convective areas is estimated based on OLR data. The intensity of descending motion is evaluated from the thermodynamic energy balance between radiative cooling and adiabatic warming, since the local time change of temperature is small in the tropics. Once the vertical motion field is determined, the horizontal divergence field can be calculated from the mass continuity equation. Then a divergent wind field is determined. The total wind is the sum of the new divergent wind and the rotational part, which is assumed to be unchanged. The proposed scheme is tested using the NMC analysis dataset of 21 January 1985 with satisfactory results.

Kasahara, Akira↗

NASA NTRS1995

Numerical modeling of flame-balls in fuel-air mixtures

At low gravity, when buoyancy effects are small, flame-balls can be generated. These are stationary spherical structures whose existence appears to require a near-limit mixture, a small Lewis number and heat losses from radiation. It is our goal to combine computational modeling with existing experimental and theoretical studies (NASA) of these structures so that an improved understanding of flammability limits and near-limit phenomena will occur. The question of flammability limits is of fundamental importance and has long been examined. It is of great practical importance to predict, from first principles, a limit mixture strength that agrees with experimental values for the configuration at hand. Flame-balls provide an excellent configuration in which convective losses can be eliminated and the resulting stable solutions are produced from a diffusive, reactive and radiative balance. Although analytical modeling provides convincing evidence that the key physical ingredients of flame-balls have been identified, quantitative confirmation can only come from detailed numerical simulations. Our goal is to predict theoretically the mass fractions of the species and the temperature as functions of the independent coordinate r.

Smooke, Mitchell D.↗

NASA NTRS2001

Peripheral Signals of Food Intake in Response to Low Leptin Levels Induced by Centrifugation

The focus of the study was to examine leptin and other peripheral signals of energy balance, following hypergravity. The study was conducted in two experiments. In experiment 1 rats were centrifuged at either 1.5, 2, or remained at 1 G. During days 8 to 14 of experiment 1, mean body mass of the 1.5 and 2 G groups was significantly (p<0.05) lower than controls. No differences were found in food intake (g/day/100 g body mass). Epididymal fat in the 2 G group was 21% lower than controls and 14% lower than the 1.5 G group. Plasma leptin was reduced from controls in the 1.5 and 2 G groups by 45 and 63%, respectively. A significant correlation was found between G load and urinary catecholamines. In experiment 2, rats were centrifuged at either 1.25, 1.5, or remained at 1 G. During days 8 to 14, body mass and food intake were similar between the 1, 1.25, and 1.5 G groups. Epididymal fat was reduced from controls in the 1.25 (14%) and 1.5 (19%) G groups. Leptin was reduced from controls in the 1.25 (45%) and 1.5 (46%) G groups. No differences were found in urinary epinephrine. Urinary norepinephrine levels were significantly higher than controls in each centrifuge group. During hypergravity exposure, food intake is the result of a complex relationship between multiple pathways, which abates the importance of leptin as a primary signal.

Moran, M. M.↗

NASA NTRS2010

International Space Station Crew Quarters Ventilation and Acoustic Design Implementation

The International Space Station (ISS) United States Operational Segment has four permanent rack sized ISS Crew Quarters (CQs) providing a private crew member space. The CQs use Node 2 cabin air for ventilation/thermal cooling, as opposed to conditioned ducted air-from the ISS Common Cabin Air Assembly (CCAA) or the ISS fluid cooling loop. Consequently, CQ can only increase the air flow rate to reduce the temperature delta between the cabin and the CQ interior. However, increasing airflow causes increased acoustic noise so efficient airflow distribution is an important design parameter. The CQ utilized a two fan push-pull configuration to ensure fresh air at the crew member's head position and reduce acoustic exposure. The CQ ventilation ducts are conduits to the louder Node 2 cabin aisle way which required significant acoustic mitigation controls. The CQ interior needs to be below noise criteria curve 40 (NC-40). The design implementation of the CQ ventilation system and acoustic mitigation are very inter-related and require consideration of crew comfort balanced with use of interior habitable volume, accommodation of fan failures, and possible crew uses that impact ventilation and acoustic performance. Each CQ required 13% of its total volume and approximately 6% of its total mass to reduce acoustic noise. This paper illustrates the types of model analysis, assumptions, vehicle interactions, and trade-offs required for CQ ventilation and acoustics. Additionally, on-orbit ventilation system performance and initial crew feedback is presented. This approach is applicable to any private enclosed space that the crew will occupy.

Broyan, James L., Jr.↗

DOE OSTI2023

Development of a Heavy-Duty Electric Vehicle Integration and Implementation (HEVII) Tool

As demand for consumer electric vehicles (EVs) has drastically increased in recent years, manufacturers have been working to bring heavy-duty EVs to market to compete with Class 6-8 diesel-powered trucks. Many high-profile companies have committed to begin electrifying their fleet operations, but have yet to implement EVs at scale due to their limited range, long charging times, sparse charging infrastructure, and lack of data from in-use operation. Thus far, EVs have been disproportionately implemented by larger fleets with more resources. To aid fleet operators, it is imperative to develop tools to evaluate the electrification potential of heavy-duty fleets. However, commercially available tools, designed mostly for light-duty vehicles, are inadequate for making electrification recommendations tailored to a fleet of heavy-duty vehicles. The main challenge is that light-duty tools do not estimate real-time vehicle mass, a factor that has a disproportionate impact on the energy consumption of large commercial vehicles. The Heavy-Duty Electric Vehicle Integration and Implementation (HEVII) tool advances the state of the art in evaluating electrification potential and infrastructure requirements for fleets of commercial vehicles. In this work, the HEVII tool is demonstrated with non-uniformly sampled telematics data from an existing fleet to assess the suitability for electrification of each individual vehicle, determine optimal locations for charging infrastructure to support a fleet of EVs and analyze associated costs. Payload mass is predicted using sparse ground-truth data for all input drive cycles and an initial data analysis is conducted to assess the characteristics driving behaviors and energy consumption of the fleet using an adaptable vehicle model. Battery size requirements are determined by applying a novel charger placement algorithm to maximize routes that are viable for EVs and balance time delays with infrastructure development costs. This work details and demonstrates the different aspects of the HEVII tool, presenting preliminary results from an example use case.

ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2020

Investigating Secondary Aerosol Processes in the Amazon through Molecular-level Characterization of Semi-Volatile Organics

In areas where biogenic emissions are oxidized in the presence of anthropogenic pollutants, it has become increasingly apparent that secondary organic aerosol (SOA) formation from biogenic volatile organic compounds (BVOCs) is substantially enhanced. The Amazon forest is the dominant source of BVOCs globally, and the forest is rapidly being converted to urban and agricultural uses. We participated in a collaborative field study located in the Amazon region around Manaus, Brazil, in 2014 (Green Ocean Amazon; GoAmazon). This study was designed to comprehensively examine how BVOC emissions (specifically, the most highly emitted non-methane hydrocarbon, isoprene, and lesser studied sesquiterpenes) and their interaction with anthropogenic pollution (i.e., nitrogen oxides, sulfur dioxide, and black carbon) alter the atmosphere’s oxidative capacity, influence secondary aerosol formation, atmospheric composition and, ultimately, affect the earth’s radiation balance and climate. We provide the first hourly, in-situ measurement of 30 sesquiterpenes and 4 diterpenes, roughly estimating that sesquiterpene oxidation contributes to 10-14% of ozone reactive loss by terpenes and at least 0.4–5% (median 1 %) of total submicron OA mass. However, this is likely a low-end estimate, as evidence for additional unaccounted sesquiterpenes and their oxidation products clearly exists. We also provide new perspectives on sulfate, NO x , and particle acidity influencing isoprene-derived SOA, comparing the central Amazon environment with Southeastern U.S.A. summer, representing clean to polluted conditions, respectively. We find that summed concentrations of isoprene-derived SOA tracers correlated with particulate sulfate spanning three orders of magnitude, suggesting that 1 μg m -3 reduction in sulfate corresponds with at least ~0.5 μg m -3 reduction in isoprene-derived SOA. We also find that SOA mass derived from isoprene oxidation in the presence of NO x is primarily comprised of aerosol sulfate bound with isoprene oxidation products (i.e. organosulfates), ~97% in the Amazon and ~55% in the Southeastern U.S. We infer under natural conditions in high isoprene emission regions, preindustrial aerosol sulfate was almost exclusively isoprene-derived organosulfates, which are traditionally thought as representative of anthropogenic influence. We further report the first field observations showing that particle acidity impacts the distribution of isoprene oxidation tracers in the gas and particle phases, providing physicochemical insight into isoprene SOA formation chemistry. Coupled with other co-located measurements by the DOE Atmospheric Radiation Measurement (ARM) team and collaborating PIs at our measurement site (called T3), on the G1 aircraft, and at additional field sites (T0, T1, T2) this data set has been used to understand emission, oxidation, and particle formation pathways at the molecular level, to elucidate how these pathways change when influenced by anthropogenic sources, and to evaluate their importance for the atmospheric budget of aerosols and the earth’s radiation balance on regional scales. Recommendations: Further constraint of the role of sesquiterpenes on ozone (O 3 ) reactivity and SOA formation is limited by the availability of authentic standards and synthesized compounds of sesquiterpenes and their oxidation products. Future research efforts should focus on making such standards available via custom synthesis to allow for accurate quantification and focused oxidation experiments that will fully elucidate the chemistry of these compounds in the atmosphere. Further, reductions in aerosol sulfate (via SO 2 emissions control) continues to be one of the most effective methods to reduce SOA formation from isoprene, but the concerted role of ammonia (NH 3 ) gas emissions from (agricultural) industry and other sources requires more investigation to better understand the role of aerosol acidity in SOA formation and potential controls. As GoAmazon particles can be more acidic compared to areas with greater anthropogenic NH 3 emissions, this promotes relatively greater organosulfate (OS) formation from isoprene even in the presence of NO x . Because OS and inorganic sulfate differ in water uptake properties, this implies preindustrial aerosol sulfate (albeit less abundant) may have been less reflective than current earth system models assume. Further research should investigate the radiative impacts of organic vs inorganic sulfate in aerosols to improve model representation. Finally, future work (currently underway) should include constraint of the contributions of monoterpene (C 10 H 16 ) BVOCs and biomass burning VOCs as precursors to SOA formation in the region as well as their impacts on radiative forcing in the climate system.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1988

Semi-empirical models of the wind in cool supergiant stars

A self-consistent semi-empirical model for the wind of the supergiant in zeta Aurigae type systems is proposed. The damping of the Alfven waves which are assumed to drive the wind is derived from the observed velocity profile. Solution of the ionization balance and energy equation gives the temperature structure for given stellar magnetic field and wave flux. Physically acceptable solutions of the temperature structure place limits on the stellar magnetic field. A crude formula for a critical mass loss rate is derived. For a mass loss rate below the critical value the wind cannot be cool. Comparison between the observed and the critical mass loss rate suggests that the proposed theory may provide an explanation for the coronal dividing line in the Hertzsprung-Russell diagram. The physical explanation may be that the atmosphere has a cool wind, unless it is physically impossible to have one. Stars which cannot have a cool wind release their nonthermal energy in an outer atmosphere at coronal temperatures. It is possible that in the absence of a substantial stellar wind the magnetic field has less incentive to extend radially outward, and coronal loop structures may become more dominant.

Kuin, N. P. M.↗

NASA NTRS1993

Space Shuttle Main Engine performance analysis

For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Santi, L. Michael↗

NASA NTRS1997

Flow and Crystallization in Two-Layer Liquid Systems with and without a Magnetic Field

Flow, heat and mass transfer in a two-layer liquid system is investigated when the layers are subjected to a static magnetic field. The physical system consists of two immiscible liquids in a layer configuration with a free surface and an interfacial layer simulating two crystal growth configurations, namely, floating zone and horizontal zone melting. Mass transfer effects due to crystallization of one of the layers is also considered. The resulting flows are categorized into three types depending on: (a) the dominance of the free surface effect top layer, (b) a balance between the thermocapillary effect on the free surface and the interface effect between the two layers, or (c) the dominance of interfacial effects, in determining the system thermo-fluid characteristics. The use of an additional liquid layer atop the crystallizing layer leads to a reduction of the radial dopant inhomogeneity in comparison to the one-layer case. The effect an externally imposed magnetic field on dopant distribution in this two-layer configuration is rather ambiguous and depends on its direction and intensity resulting in the necessity of optimizing the applied magnetic field for a specific situation. In case of electrically non-conducting melts, the calculations show that some measure of flow control can be achieved by using an electrically conducting encapsulant layer of the desired thickness.

Feonychev, Alexander I.↗

NASA NTRS2001

Biology of bone and how it orchestrates the form and function of the skeleton

The principal role of the skeleton is to provide structural support for the body. While the skeleton also serves as the body's mineral reservoir, the mineralized structure is the very basis of posture, opposes muscular contraction resulting in motion, withstands functional load bearing, and protects internal organs. Although the mass and morphology of the skeleton is defined, to some extent, by genetic determinants, it is the tissue's ability to remodel--the local resorption and formation of bone--which is responsible for achieving this intricate balance between competing responsibilities. The aim of this review is to address bone's form-function relationship, beginning with extensive research in the musculoskeletal disciplines, and focusing on several recent cellular and molecular discoveries which help understand the complex interdependence of bone cells, growth factors, physical stimuli, metabolic demands, and structural responsibilities. With a clinical and spine-oriented audience in mind, the principles of bone cell and molecular biology and physiology are presented, and an attempt has been made to incorporate epidemiologic data and therapeutic implications. Bone research remains interdisciplinary by nature, and a deeper understanding of bone biology will ultimately lead to advances in the treatment of diseases and injuries to bone itself.

Review↗

NASA NTRS2008

Fuel Cell Thermal Management Through Conductive Cooling Plates

An analysis was performed to evaluate the concept of utilizing conductive cooling plates to remove heat from a fuel cell stack, as opposed to a conventional internal cooling loop. The potential advantages of this type of cooling system are reduced stack complexity and weight and increased reliability through the reduction of the number of internal fluid seals. The conductive cooling plates would extract heat from the stack transferring it to an external coolant loop. The analysis was performed to determine the required thickness of these plates. The analysis was based on an energy balance between the thermal energy produced within the stack and the heat removal from the cooling plates. To accomplish the energy balance, the heat flow into and along the plates to the cooling fluid was modeled. Results were generated for various numbers of cells being cooled by a single cooling plate. The results provided cooling plate thickness, mass, and operating temperature of the plates. It was determined that utilizing high-conductivity pyrolitic graphite cooling plates can provide a specific cooling capacity (W/kg) equivalent to or potentially greater than a conventional internal cooling loop system.

Colozza, Anthony J.↗

NASA NTRS2014

Path Toward a Unifid Geometry for Radiation Transport

The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex computer-aided design (CAD) models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN [high charge and energy transport code developed by NASA Langley Research Center (LaRC)], are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their widespread use for analysis of complex CAD models, leading to the creation and maintenance of toolkit-specific simplistic geometry models. The work presented here builds on the Direct Accelerated Geometry Monte Carlo (DAGMC) toolkit developed for use with the Monte Carlo N-Particle (MCNP) transport code. The workflow for achieving radiation transport on CAD models using MCNP and FLUKA has been demonstrated and the results of analyses on realistic spacecraft/habitats will be presented. Future work is planned that will further automate this process and enable the use of multiple radiation transport codes on identical geometry models imported from CAD. This effort will enhance the modeling tools used by NASA to accurately evaluate the astronaut space radiation risk and accurately determine the protection provided by as-designed exploration mission vehicles and habitats

Lee, Kerry↗

NASA NTRS1988

Environmental effects of large impacts on the earth; relation to extinction mechanisms

Since Alvarez et al., discovered a worldwide approx. cm-thick layer of fine sediments laden with platinum group elements in approximately chondritic proportions exactly at the Cretaceous-Tertiary (C-T) boundary, and proposed bolide-impact as triggering mass extinctions, many have studied this hypothesis and the layer itself with its associated spherules and shocked quartz. At issue is whether the mass extinctions, and this horizon has an impact versus volcanic origin. A critical feature of the Alvarez hypothesis is the suggestion that the bolide or possibly a shower of objects delivered to the earth approx. 0.6 x 10 to the 18th power g of material which resulted in aerosol-sized ejecta such that global insolation was drastically reduced for significant periods. Such an event would lower temperatures on continents and halt photosynthesis in the upper 200 m of th eocean. The latter would strangle the marine food chain and thus produce the major marine faunal extinctions which mark the C-T boundary. Crucial issues examined include: What are the dynamics of atmospheric flow occurring upon impact of a large bolide with the earth; What is the size distributions of the very fine impact ejecta and how do these compare to the models of ejecta which are used to model the earth's radiative thermal balance. The flow field due to passage of a 10 km diameter bolide through an exponential atmosphere and the interaction of the gas flow and bolide with the solid ear was calculated. The CO2 released upon impact onto shallow marine carbonate sections was modeled and found that the mass of CO2 released exceeds the present 10 to the 18th power g CO2 budget of the earth's atmosphere by several times. Using the calculations of Kasting and Toon it was found that to compute the temperature rise of the earth's surface as a function of CO2 content, it was found that sudden and prolonged global increases are induced from impact of 20 to 50 km radius projectiles and propose that sudden terrestrial greenhouse-induced heating, not cooling, produced the highly variable extinctions seen at the C-T boundary.

Okeefe, John D.↗

NASA NTRS1977

Analytical study of laser supported combustion waves in hydrogen

A one-dimensional energy equation, with constant pressure and area, was used to model the LSC wave. This equation balances convection, conduction, laser energy absorption, radiation energy loss and radiation energy transport. Solutions of this energy equation were obtained to give profiles of temperature and other properties, as well as the relation between laser intensity and mass flux through the wave. The flow through the LSC wave was then conducted through a variable pressure, variable area streamtube to accelerate it to high speed, with the propulsion application in mind. A numerical method for coupling the LSC wave model to the streamtube flow was developed, and a sample calculation was performed. The result shows that 42% of the laser power has been radiated away by the time the gas reaches the throat. It was concluded that in the radially confined flows of interest for propulsion applications, transverse velocities would be less important than in the unconfined flows where air experiments have been conducted.

Kemp, N. H.↗

NASA NTRS1981

U.S. manned space flight: The first twenty years - A biomedical status report

In the last 20 years, the biomedical problems facing man in space have been brought into sharper focus. Space motion sickness is presently the most serious problem. Its etiology remains obscure, but the 'sensory conflict' theory appears most plausible. No valid predictive tests of susceptibility exist and presently medication for prevention or mitigation of symptoms must be relied on. Adaptation/biofeedback techniques may prove useful. Cardiovascular 'deconditioning' may be effectively attenuated by use of anti-g suits or plasma expanding techniques. Recent bedrest simulation studies would seem to indicate that concerns about chronically elevated central venous pressure during space flight are unfounded. The loss of red cell mass in space flight appears to be self-limited, independent of mission duration, and not of clinical concern, based on recent Soviet experiences. And finally, clodronate, a new diphosphonate effective in preventing hypercalciuria and negative calcium balance in normal human bedrested subjects, may prove effective in preventing or lessening skeletal mineral loss in space.

Dietlein, L. F.↗

NASA NTRS1988

'Flux conservation' by a Schwarzschild gravitational lens

It is demonstrated, by an explicit calculation, that a single, isolated Schwarzschild gravitational lens leads to a vanishing net total amplification on its own, without any 'help' from other lenses. It is shown that, in the limit of small M/R (where M is the mass of the lens in geometrical units and R is the distance from the source to the observers), the positive net total amplification, obtained from the classical approximation of the amplification for small impact angle lensing, is balanced by a negative net total amplification from the first-order term in M/R in an approximation of the amplification for large impact angle lensing derived here. The relation of these results to the common interpretation of average flux conservation by gravitational lenses is discussed as due to the collective action of many lenses in a cosmological framework.

Shulami, I.↗